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UNIVERSITY OF B.C. LIBRARY
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FOREST VALUATION
BY
HERMAN HAUPT CHAPMAN, M. F.
Harriman Professor of Forest Managetnent
Yale University Forest School
FIRST EDITION
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS, Inc.
London: CHAPMAN & HALL, Limited
Copyright, 19 14,
BY
HERMAN HAUPT CHAPMAN
Stanbope ipress
F. H.GILSON COMPANY
BOSTON, U.S.A.
To
HENRY SOLON GRAVES
Forester
IN RECOGNITION OF THE SERVICES WHICH HE IS RENDERING TO THE
NATION AND TO FORESTRY BY M.\INTAINING A HIGH STAND-
ARD OF EFFICIENCY AND INTEGRITY IN PUBLIC OFFICE,
AND BY UPHOLDING BOTH THE SPIRIT AND THE
LETTER OF NATIONAL FOREST POLICY
PREFACE
The term Forest Valuation, applied to this volume, covers
only a portion of the subject of Forest Finance, which is usually
separated into two parts, termed, respectively, Valuation and
Statics. Valuation deals with the determination of the value of
standing timber, both mature and immature, and of forest soil,
and the forest as a whole. Forest Statics deals with the
comparison of financial results obtained in forestry with those
yielded by other enterprises, and compares the relative merits
of different methods of treating the forest. This subject is dis-
cussed in Chapter VIII. Since Forest Valuation includes the
greater portion of the text, and this term is more familiar to
American foresters, it has been adopted as the title, in place of
the more comprehensive term, Forest Finance.
The literature of Forest Finance is largely of German origin,
and has been developed in the latter half of the nineteenth
century, by numerous German and French authorities. The
standard English text is found in "Forest Management," by
Sir William Schlich, Vol. Ill, Part II, Forest Valuation.* This
author follows the continental treatment of the subject. In
1909, a pamphlet on " Forest Finance " was published by C. A.
Schenck, Ph.D., Forester to the Biltmore estate,! which gives a
synopsis or outline of a series of lectures on the subject. Dr.
Schenck's treatment is thoroughly American and contains valu-
able suggestions for the advanced student of Forest Finance.
Unfortunately, neither of these publications treats the subject
in a sufficiently elementary manner to serve as a textbook for
students of forestry or for persons desiring information who are
not already thoroughly familiar with the economic and mathe-
* Fourth Edition, Revised. Bradbur>-, .\gnew & Co., Ld., 10 Bouverie St.,
London, 1911.
t Inland Press, Asheville, N. C, 1909.
VI PREFACE
matical principles on which the theory of Forest Finance is
based. Forest Valuation deals with periods of time far longer
than are considered in most financial calculations. The theory
and appUcation of compound interest as a mathematical means
of determining value needs a more complete exposition than is
usually given even in courses in economics, before the signifi-
cance of the methods taught in valuation can be grasped. Forest
Valuation, while disguised as a mathematical science, is in reality
the appUcation of broad economic principles, equally serviceable
in the determination of all values.
In order that the reader who is not thoroughly grounded in
economics may readily grasp these principles as applied in
actual Forest Valuation, Chapters I to IV have been devoted
to a summary of economic subjects and tenets, with especial
emphasis on interest. The ideas set forth follow the mathematical
methods used by many economists and expressed by Prof. Irving
Fisher of Yale University.* These chapters will serve the
additional purpose of stating the economic basis upon which
the discussion of disputed questions in the text is made to rest,
and will enable students who disagree with any of these funda-
mental definitions or principles to substitute those of other
authorities more to their liking.
To the general reader and even to the student, the use of
formulae as a means of expressing economic relations is apt to
convey the impression that the subject is a difficult one to grasp.
The effort to attach the proper significance to symbols must
precede that required to reach the mathematical solution. The
first difficulty is lessened by the consistent use of symbols to
which a definite meaning is attached. An entire chapter (V)
has been devoted to an explanation of the derivation of the
formulae of compound interest. A further difficulty has arisen
in the past, because the methods of treatment of the subject of
Forest Valuation bore no relation to, and were apparently wholly
at variance with, the customs and principles of business account-
ing. An effort has been made in the present volume to indicate
* " Elementary Principles of Economics." The Macmillan Company, New
York, July, 191 2.
PREFACE vii
these relations, and enable accountants and business men to
harmonize the methods used in computing cost and value for
forest property, with the forms and ideas with which they are
familiar.
Lastly, the emphasis has been shifted from the determination
of expectation value of forest soil, so conspicuous a feature of
European Forest Finance, to the consideration of stumpage
values, sale values, damages, and other subjects of greater prac-
tical interest in this country.
The volume is intended primarily for use as a textbook.
But in recognition of the frequent need for information on such
subjects as damages, stumpage values and costs of forest pro-
duction, a consistent effort has been made to treat the entire
subject in a manner that may be readily grasped by the average
reader, without previous preparation or study.
No problems have been included in the text. These should
be supplied by instructors to suit the local economic conditions.
The table of logarithms has been included for convenience, to
enable the student to familiarize himself with its use in solving
problems of valuation.
Acknowledgment is made to Prof. Fred R. Fairchild of Yale
University for review and criticism of Chapter X on Taxation,
to Mr. J. E. Glass, accountant for John Wiley & Sons, Inc.,
for suggestions regarding forms for forestry accounts shown in
Chapter VIII, and to my colleagues on the faculty of the Yale
Forest School for valuable suggestions and assistance.
HERMAN H. CHAPMAN.
New Haven, Conn.,
October 22, 1914.
CONTENTS
CHAPTER I
VALUES
Article Pack
j2 1. Wealth and Property i
2. The Standard of Value i
3. Prices 2
4. Values 2
5. Demand 2
6. Efiort or Outlay 3
7. Ownership 3
8. Prices of Finished Products 4
ii g. Prices of Raw Materials and Natural Resources S
^10. Future Costs 5
• II. The Element of Time in Values 6
*I2. Capital 6
"* 13. The Capitalist 7
r> 14. Interest 7
» 15. Discount 8
p 16. Compound Interest and Discount 8
17. Sale Value 9
18. Appraised Value 10
CHAPTER II
OUTLAY AND INCOME
19. Proprietary Accounts versus Specific or Valuation Accounts 11
20. Capital Accounts 11
21. Outlay and Income Accounts 12
22. Investments versus Expenses 13
23. The Relation in Time between Outlay and Income 14
24. The Total Investment 14
25. Cost Accounts 16
26. Income 16
27. The Economic Opportunity 16
28. The Business Venture 17
29. Exchange 17
30. Disposition of Income 17
31. Returns on Capital 18
ix
X CONTENTS
Article Page
32. Interest versus Dividends 18
33. Profits 19
34. Wages versus Profits iq
CHAPTER III
INTEREST
* 35. The Problem of Interest 21
.. 36. Interest as a Cost 21
, 37. Interest as Income 22
«s' 38. The "Rate of Interest" 22
39. The Profits of the Undertaking 23
40. Annual Profits 23
41. Deferred Profits 23
42. Income versus Profits 24
£ 43. Influences Determining the "Rate of Interest" 26
■^ 44. The Influence of Personahty on the Rate of Interest 26
•^ 45. Risk and Expense 27
46. Fluctuating Value of Money 27
47. The Rate of Interest for Business Investments 28
48. The Effect of Deferred Income upon the Rate of Interest 28
49. Comparison of Results of Simple and Compound Interest 28
« 50. Limitation of Opportunity 29
51. Effect of the Rate of Interest upon Accumulations of Compound
Interest 30
■»■ 52. The Rate of Interest in Forest Investments 32
- 53. Comparison of Interest Rates in Forestry with Other Investments ... . zi
CHAPTER IV
VALUATION OF ASSETS
54. Valuation Accounts 35
55. The Inventory 35
56. Cost as a Basis of Value 35
57. Expenses and Interest versus Value 35
58. Essential Difference between Cost and Value 37
59. Sale Value as a Basis of Value 37
60. Appraisal of Value 38
61. Future Income as the Basis of Value 38
62. Capital \'alue or Expectation Value 39
63. Future Prices and Values 41
64. Future Expenses 41
65. The Time Element in Capital Values 42
66. Effect of Rate of Interest on Capital Values 42
67. Uncertainty of Capital Value 43
68. Independence of Capital Value and Past Outlay or Cost 44
CONTENTS Xi
Article Pace
69. Effect of Capital Value on Sale Value 44
70. ElTect of Capital Value upon Appraised Value 45
71. Inflation of Capital Values 45
72. The Regulation of Capitalization 46
73. The Problem of the Balance Sheet 46
CHAPTER V
FORMULA OF COMPOUND INTEREST
" 74. The Discount Factor 53
75. Rentals 53
• • 76. Future Value or Cost of Single Sums 53
' 77. Present, Expectation, or Capital Value of Future Sums. . . '. 54
78. Use of Logarithms and Tables 55
* 79. Future \'alue of Temporary Annual Rentals 56
80. Formulae for Geometric Series 57
81. Present, Expectation, or Capital Value of Temporary Annual Rentals 58
* 82. Future \'alue of Temporary Intermittent Rentals Due First at n Years,
and / Times at Intervals of n Years Thereafter 59
83. Present, Expectation, or Capital Value of Temporary Intermittent
Rentals, Due First at 71 Years, and t Times at Intervals of n Years
Thereafter 60
* 84. Future Value of Temporary Intermittent Rentals, Due First in a Years,
and / Times at Intervals of n Years Thereafter 60
85. Present, Expectation, or Capital Value of Temporary Intermittent
Rentals, Due First in a Years, and / Times at Intervals of ;/ Years
Thereafter 61
86. Present, Expectation, or Capital Value of Perpetual Rentals 62
87. Relation between Future V^alue of Temporary Annual Rentals, and
Present, or Capital, Value of Same 65
88. Conversion of Intermittent into .\nnual Rentals 65
89. The Ratio of Income or Earnings 66
CHAPTER VI
INVESTMENTS AND COSTS IN FOREST PRODUCTION
90. The Business of Forest Production versus Lumbering 68
91. Proprietary Accounts in Forestry 69
92. Cost -Accounts in Forestry 70
93. Investments, or Permanent Outlay 71
94. Expenses, or Temporary' Outlay in Forestry 71
95. Land 71
96. Standing Timber 72
97. Permanent Improvements and Equipment 73
98. Roads and Transportation Systems 73
xii CONTENTS
Article Page
99. Silvicultural Operations 74
100. Protection Expenses 74
101. Administrative Expenses 75
102. Taxes and Insurance 76
103. Interest Charges 76
104. Classification of Costs in Forest Production 76
105. Calculation of Total or Final Costs 77
106. Total Cost of Investments in Standing Timber 79
107. Costs of Forestry Compared with Destructive Lumbering 81
108. Cost of Many-aged Forests 83
109. Cost of Producing a Normal Forest 84
CHAPTER VII
THE VALUATION OF FORESTS
no. Valuation Accounts in Forestry 85
111. Income as the Basis of Value of Forests 85
112. Value of Forest Property for Destructive Lumbering 86
113. Value of Forest Property for Continuous Forest Production 88
114. Value of a Forest of Even Age Just Previous to Cutting 89
* 115. Value of an Even-aged Forest for Any Year 90
1 16. Value of Forest Soil 92
117. Value of Many-aged Forests Producing Regular Income 96
118. Value of Many-aged Forests Producing Irregular Income 97
119. Value of Timber Separate from Land 98
CHAPTER VIII
FOREST STATICS — THE BALANCE SHEET — PROFITS
120. Determining the Profits of an Investment 100
121. The Rate of Interest in its Relation to Profits 104
122.
123.
124.
125-
Profits in Destructive Lumbering 105
Profits on a Stand of Timber 106
Anticipated Profits on Young Timber 106
Profits from Continuous Forest Production 107
126. Anticipation of Continuous Profits 107
127. Profits Expressed as Soil Values 108
128. Profits Expressed as a Ratio of Income to Capital no
129. Earning Power of Capital Invested in Forest Production in
130. The Relative Importance of Profits in Private versus Public Forestry. 115
131. Forms for Specific .Accounts in Forestry 117
132. Forms for Economic Accounts in Forestry 119
CONTENTS Xlil
CHAPTER IX
THE APPRAISAL OF DAMAGES
Article Pace
133. Principles Underlying Appraisal of Damages 120
134. Elements of Damage to Forest Property 122
135. Physical Separation of Timber from Soil 122
136. Separation of Value of Timber from Value of Soil 1 23
137. A Basis of Damages: Cost of Replacement 126
138. A Basis of Damages: Sale Value 128
139. A Basis of Damages: Expectation or Capital Value 129
140. Damage to Merchantable Timber 131
141. Damage to Immature Timber: Partial Loss 132
142. Damage to Immature Timber: Total Loss 133
143. Damage to Forest Soil 135
144. Damage to Single Trees 136
145. Damage to Many-aged Stands 137
' 146. Damage to Watersheds 137
147. i^sthetic Values 138
148. Punitive Damages 139
CHAPTER X
FOREST TAXATION
149. Sources of Revenue from which to pay Taxes 141
150. Tax on Income 141
151. Tax on Value of^Property 142
152. Taxable Value of Property 143
153. Effect of Taxes on Property Values 143
154. The General Property Tax 144
155. The Problem of Taxation for Timberlands 145
156. Distinction between Capital and Income in Timber Property 145
, 157. The Problem of Interest in Forest Taxation 146
158. Effect of Present Condition of Forest upon Choice of Methods of
Taxation 147
159. Scientific Taxation: Forest Property Tax 149
160. Scientific Taxation : Forest Land Tax 150
•* 161. Comparison of Taxes on Forest Rent versus Soil Rent 151
162. Scientific Taxation: Income or Products Tax 152
163. Scientific Taxation: Combined Capital Tax and Income Tax 154
164. Taxes under the General Property Tax 155
' 165. Effect of the General Property Tax on Forest Production 158
166. Tax Reform for Forest Property 160
xiv CONTENTS
CHAPTER XI
STUMPAGE VALUES
Article Page
167. Definition of Stumpage Value 166
168. Sale Value of Stumpage 166
169. Stumpage Prices 167
170. Factors Determining Stumpage Prices 167
171. Appraisals of Stumpage Value 169
172. The Price Basis in Appraisals 170
173. Depreciation 173
174. Milling Costs and Profits 177
175 Logging Costs and Profits 178
176 Stumpage as a Capital Investment and as a Cost of Raw Material. ... 180
177 The Determination of Legitimate Profits: Overturn Methods 181
178. The Investment Basis for Profits 184
1 79. Overrun 187
180. Stumpage Values for Different Species in Mixed Stands 188
181. Carrying Charges versus Profits on Stumpage 191
CHAPTER XII
FUTURE VALUE OF FOREST PRODUCTS
182. Factors Affecting Future Value 195
183. The Stand: Growth in Volume 195
184. The Stand: Improvement in Quality of Products 196
185. Deterioration of Standing Timber 196
186. Closeness of Utilization 197
187. Price Levels: General Price Changes 197
188. Price Levels: Changes in Prices of Forest Products 197
189. Effects of Substitutes on Wood Prices 198
190. Future Operating Costs 201
191. Local Factors: Future Transportation Facilities 202
192. Local Factors: Industries and Markets 203
193. Local Factors: Future Supply of Timber 204
194. The Rate of Increase in Stumpage Value 204
195. Increasing Future Values as a Basis of Appraisals 206
196. Revision of Stumpage Values in Long-term Contracts 207
CHAPTER XIII
RISKS
^^197. Risks versus the Rate of Interest in Forestry 208
ii98. The Nature of Risks in Forestry 208
199. The Gauging of Risks 209
200. Physical Risks: Fire 209
201. Wind 210
CONTENTS XV
Article Pace
202. Insects 211
203. Fungous Diseases « 21 r
204. Climatic Injuries 211
205. Injurious Fumes 212
^ 206. Moral Risks: Trespass 212
207. Fire 212
. 208. Financial Risks 2j2
'209. Control of Risks: Insurance 213
'210. Public Measures 213
/ 2 1 1 . Private Measures 214
, 212. Effect of Risks on the Business of Forest Production 214
CHAPTER XfV
FIELD APPRAISALS OF TIMBER STUMPAGE
213. The Scope of Field Appraisals 216
214. Timber Reconnaissance: The Map 217
215. FJstinjation of Standing Tin^ber 218
216. Log Rules 218
217. Closeness of Utilization as Afifecting Timber Estimates 219
218. Field Methods of Timber Estimating 219
219. Strip Methods 220
220. Errors in These Methods 220
221. Types 221
222. Correction Factors • 221
223. Quality of Timber 222
224. Reports 222
CHAPTER XV
COMPARISON OF FOREST VALUES WITH AGRICULTURAL
VALUES
* 225. Agricultural Soils 226
• 226. Quality of Soil 226
227. Slope 226
228. Climate 226
229. Water 227
230. Personal Factors 227
231. Economic Factors 227
232. Comparison of Agriculture \yith Forestry as a Source of Livelihood. . . 227
233. Non-agricultural Soils 228
234. Exploitation of Land Purchasers 229
235. Land Classification 229
236. Basis of Comparison of Agricultural and Forest Values of Land 229
237. Expectation Value of Agricultural Land 230
238. Sale Value of Agricultural Land 230
XVI CONTENTS
Article Page
239. Timber as an "Agricultural" Value 230
240. Stump Land versus Cleared Land 231
241. Cost of Clearing Stump Lands 232
242. Sale Value of Stump Lands 232
243. Summary of Elements of Value for Forest Land 233
244. Value of Young Timber as a Part of the Value of Forest Soil 234
245. Sale Value of Forest Property 235
246. Discrimination against Forest Values 236
247. Discrimination in Favor of Forest Values 236
248. Results, when Values of Bare Land are Compared 237
249. Results, when Full Value of Property is used in Comparison 237
250. National Forest Policy in Land Classification 238
251. Reciprocal Values in Forestry and Agriculture 239
Appendix 240
Summary of Formulae of Compound Interest 240
Definitions of Symbols 241
Summary of Formulae in Forest Valuation 243
Costs 243
Values 244
Profits 246
Interest Earned 246
Damages 247
Depreciation 247
Geometric Series 248
Stumpage Values 248
Compound Interest Tables:
Explanation 249
Table VI 250
Tables of Logarithms of Numbers 265
FOREST VALUATION
CHAPTER I
VALUES
1. Wealth and Property. — Wealth is defined as material
objects owned by human beings. Forest wealth consists of
forest land and its resources, principally trees, but including all
other materials such as forage and game.
Property is the right represented by ownership, and not the
material object itself. The benefits derived from wealth make
its ownership desirable. The right to enjoy these benefits is
indicated by the term property. The satisfactions to be derived
from ownership of forest property, aside from the pleasures of
sport and recreation, take the form of money income from the
sale of forest products.
2. The Standard of Value. — Value is an expression of the
relative desirability of dift'erent forms of wealth or property in
terms of a common standard. The form of wealth accepted
as this standard is termed money, and is exchangeable for all
other kinds of wealth or property. The present standard in
this country' is gold. The value of money itself can only be
measured by its purchasing power, which means its relative
desirability compared with other goods. Changes in the quan-
tity and rapidity of circulation of money cause its purchasing
power or value to fluctuate, and a decline in value of money
means higher prices for all other property. Prices in the im-
mediate past have risen. If continued, this tendency wnll be
a conser\-ative factor in the valuation of forests; while in con-
trast, such property as long term bonds will tend to fall in value,
because it is redeemable in money.
2 FOREST VALUATION*
3. Prices. — A price, when expressed in terms of the common
standard of value, is the amount of money accepted in exchange
for a unit of goods. Until the actual exchange is consummated
the price is not definitely estabUshed, but exists merely as an
appraisal or opinion in the mind of the prospective buyer or the
present owner. Prices resulting from exchanges are agreements
between two persons as to the value of a unit of property.
Market prices originate in centers of trade and form the basis
of numerous transactions. Prices are therefore of human and
mental origin and are established by economic causes which
influence the opinions of the majority of purchasers and sellers.
While in the main, prices move in response to supply and demand,
yet the fluctuations in price of certain forms of property, such
as real estate and stocks, demonstrate that it is possible to
create market prices either higher or lower than circumstances
justify, by influencing general or public opinion through opti-
mism, misrepresentation, or concealment of facts.
4. Values. — Value may be defined as the price of a given
unit of wealth, multiplied by the quantity or number of units.
Thus the value of a given quantity of cordwood is the price per
cord multiplied by the munber of cords on hand. This defini-
tion holds good if prices are accepted as the final standard of
value. For finished products, especially staple commodities,
actual prices established by exchanges may be taken as deter-
mining value. But for forms of goods in an unfinished state,
or for productive wealth, such as land or growing timber, prices
furnish only contributory evidence of value, which in many
instances is entirely misleading. The very fact that prices for
finished products are the basis of value indicates that the value
of productive property must be derived from that of its products.
Ignorance of the true productiveness of property, and of the
mathematical relation between this income and the value of
the property, is the principal cause of divergence between current
prices and true value for such forms of wealth as forest lands
and young timber.
5. Demand. — The influences which determine prices are
twofold, corresponding roughly to the two persons concerned
VALUES 3
in the transfer. Demand, or the need of the purchaser, is
weighed against outlay or effort on the part of the owner. The
necessities and desires of the human mind and body, such as
food, clothing and shelter, create the demand for any form of
material wealth. Civilized society differs from primitive condi-
tions by the greater extent and complexity of its needs. V^alues
are thus created which have no existence among savages. This
fact is strikingly illustrated by the history of the timberlands
belonging to Indian tribes. To the American Indians the pine
timber was of no value whatever, and their use of the forest was
confmed to its game and fish, the destruction of which they
deeply resented. Title to much of this forest land was given
to various tribes by the government. This timber soon came
to have a high value to the white population, and the Indians
were either defrauded of values which they had failed to appre-
ciate, or found themselves enriched by these same values which
they had no part in creating.
6. Effort or Outlay. — Human demand or needs would not
alone create values. Materials indispensable to Ufe remain
without value when they can be obtained without effort. Prop-
erty which is worth owning has cost the original owner some
effort either for its acquisition or improvement. This influences
his idea of its value. A prospective purchaser gauges his price
by the possibility of securing a similar article through his own
efforts. The supply of finished products is greatly influenced
by cost of production.
7. Ownership. — The whole structure of values rests on the
institution of private property, for without the right of owner-
ship there could be no measurable value. In a primitive state
of society each individual is able, after a fashion, to supply his
own needs. But with specialization and di\'ision of labor, pro-
ducers of most forms of wealth need very little of it themselves
and must sell it, while the purchasers would be unable to produce
for themselves the small quantities they need at anything like the
price at which it is sold. Purchasers therefore seek the lowest
price, while owners, in order to dispose of their surplus or to in-
crease their output, often underbid one another. With unlimited
4 FOREST VALUATION
competition among producers, prices tend frequently to fall
below the cost of production. But where the supply of an
article of wealth is limited, and no satisfactory substitutes are
available, the owner may demand and receive exorbitant prices,
profiting by the needs of the consumers. In such cases there
is no relation between prices and cost of production. Famine
prices for food are obtained in times of flood or temporary
scarcity. Elements which tend to increase the advantage of
the owner and the margin between costs and value are: first,
absence or monopoly of transportation facilities; second, the
elimination of competition, by monopoly of the sources of supply
or manufacture; and third, monopoly of markets. In some
lines of production this control, through the power incidental to
ownership, has curtailed production and has had a marked effect
upon prices. Combinations or trade agreements may bring
about this result. This condition is manifested in the lumber
trade chiefly by the maintenance of local retail prices regard-
less of the fluctuations of the general lumber market. Rail
competition will prevent the possibility of combination on
the part of manufacturers of lumber for an indefinite
period.
8. Prices of Finished Products. — Since the immediate
needs of persons and their satisfaction from material sources
create value, it follows (§ 4) that the prices established for goods
ready for immediate consumption or use are the basis or source
of value for all forms of wealth. Both needs and prices are a
matter of to-day. The element of cost, in so far as it affects
prices, is completed in the final product. Purchasers and venders
are separated into two classes with sharply divided interests,
the one obliged to buy, the other with no recourse but even-
tually to sell. Under such circumstances prices absolutely
determine value. The price of lumber, ties, cordwood and other
forest products depends to as great an extent upon the demand
and markets as upon the cost of production, and in periods of
depression, lumber frequently sells for less than this cost. But
whatever the conditions, these market prices determine the
value of forest products.
VALUES 5
9. Prices of Raw Materials and Natural Resources. — Raw
materials, such as pig iron or wool, are valuaijle to owner or
purchaser only for further manufacture. A lowering of the cost
of production makes it possible to sell these products more
cheaply, but scarcity and increased demand may completely
ofifset this tendency and cause higher prices. The value of raw
products is derived directly from the price of finished goods.
Logs and timber stumpage derive their value from retail and
wholesale lumber prices. Property used for production is valu-
able only because of its products. The value of agricultural
land depends upon its adaptability for certain kinds of farm
crops, and upon the prices these crops will bring. The market
price for Imnber is the source of value for forest land.
Prices for land should therefore depend entirely upon future
income derived from its products or use. Costs already incurred
for clearing or improvements are not considered, for if land is
worth either more or less than the cost of clearing, its value
and not its cost will fix its price. If two grades of land, one
good and one poor, cost the same amount for clearing, they
will still sell for entirely different prices. Both the owner and
the purchaser of land desire it merely for its future use and
income. Sale is seldom forced, since the owner can probably
make a living by developing and using the property. The price
paid for such property thus depends upon expected income whose
value is determined by the prices of the products which the land
yields.
10. Future Costs. — While costs already incurred do not
determine the value of productive wealth, future costs which
intervene between the present moment and the final attainment
of income must be subtracted from the value of this income.
If it can be shown that the future cost of obtaining income
exceeds the future value of the income, the property itself will
be worthless. Thus the value of standing timber is the margin
left after subtracting from the sale value of the lumber the esti-
mated costs of logging, manufacturing and transporting this
lumber to market. At present prices, nearly all standing timber
has a stumpage value, but in the past only the most accessible
6 FOREST VALUATION
trees had any value. Wild land or stump land may be worthless
under present conditions, in spite of a fertile soil, if it is evident
that the labor of clearing exceeds the discounted value of the
income from the crops which may be raised. Most land is cleared
at an economic loss, and there is a tendency to hold cut-over
or stump lands at prices which greatly exceed their real value
as reduced by the future costs of clearing.
11. The Element of Time in Values. — As prices and values
center upon the satisfaction of human needs in the present
moment, the tendency is to avoid delay and reduce as far as
possible the period which elapses between effort and satisfac-
tion. Yet this element of time intervenes in every process of
production. Hunting and fishing supply food within a very
short period, which explains the dependence placed upon this
source of living by primitive people. In agriculture, the period
which must elapse between effort and satisfaction is extended
to cover the crop season, and enough surplus must be produced
to last a year. Modern engineering, illustrated by railroad
construction, requires still greater delay before any use or income
can be derived from the property. If the laborers who construct
such works were also the owners, and dependent for their living
upon the receipts from freight and passenger service, they
would starve long before the completion of the road. The
development of civilization is marked by the lengthening of the
time intervening between the inception of undertakings and
the final realization of income. This time element must always
be considered in the determination of present values.
12. Capital. — Men must live while engaged in production,
and they are enabled to undertake enterprises requiring time,
only when they have enough goods stored up to last them until
iheir completion. The wealth with which to supply them con-
sists of food, clothing and dwellings, back of which are factories,
raw products and land. The amount of energy that can be
diverted from immediate production of food to the task of
clearing unproductive land or constructing other improvements
depends upon the surplus wealth available for these purposes.
A poor man works a lifetime to clear up a wooded farm and at
VALUES 7
first must earn wages by outside labor in order to live. But a
person possessed of a few thousand dollars or its equivalent can
hire this work done and accomplish it in a short time.
The term capital is used to signify a stock of wealth existing
at a given instant of time, and therefore available for future
use. All wealth is capital. Efforts to separate wealth into
classes, such as that which is intended for consumption, and that
used for the production of other wealth, lead to confusion. It
is immaterial whether a man's capital is in the form of food,
buildings, land or money. He will endeavor to secure by ex-
change a proper balance between the different kinds of capital
he possesses. The exchange of wheat for money, its reserva-
tion for seed or its conversion into Hour does not alter its status
as capital.
13. The Capitalist. — With sufficient capital a man is not
only free from immediate personal wants but by employment
and the pa^-ment of wages, can provide for the daily wants of
others. On this basis all modern business enterprises are con-
ducted. The time needed in constructive works may be lessened
by increasing the number of persons employed and the capital
expended, but only to a limited extent. For crop production,
and in the growing of trees, the time required cannot be appre-
ciably reduced. Since it is only by the use of capital that any
enterprise requiring time can be undertaken, capitalists make
possible the entire fabric of modern civilization, and without
this accumulated surplus we would revert to primitive condi-
tions. In forest production the element of time is so important
that the trend is toward state and national forestry, for govern-
ments represent the accumulated capital of the entire community
and can best afford to await the maturing of timber crops by
the slow process of growth.
14. Interest. — The present moment is the basis for comput-
ing and comparing all values. Although use and income, on
which value depends, continue into the future indefinitely,
yet no one will provide for future wants and leave present
demands wholly unsatisfied. To every one the enjo>Tnent of
wealth in the present is valued more highly than at any future
8 FOREST VALUATION
period, and the less capital a man has the greater is his prefer-
ence for its immediate use. This preference can be satisfied
by borrowing. The borrower obtains the benefits he seeks
immediately, but the lender is forced to wait until the capital
is returned before enjoying it. For this gain in " time value,"
the borrower pays interest. Upon money loans interest is
repaid in money, the amount paid bearing a definite relation
to the amount borrowed and to the length of time elapsing
before repayment. Since interest and principal are in the same
commodity, money, the relative amount and value of the interest
can be expressed as a per cent of the principal. This per cent
gives the rate of interest paid or earned. The period for which this
rate is customarily quoted is one year. If the period intended
is less than a year the fact must be clearly stated. High rates
of interest may be based on the month, in order to make the
rate sound less exorbitant.
Interest, therefore, is the price of time differences or the stand-
ard by which the value of immediate possession and enjoyment
of income can be determined, when compared with the value of
the same income if its receipt is postponed to a future period.
15. Discount. — All future values can be standardized by
reducing them to their equivalent present value by means of
a given rate of interest. This process of reduction is termed
discount. The discounting of money loans or demand notes
consists of receiving in advance the value of a sum receivable
in the future, less the difference in value due to the time elapsing
before this pa^-ment is due. In the same way the present value
of all forms of property is derived by consciously or uncon-
sciously discounting its future value which takes the form of
future income. The process of discounting is therefore the most
important element in the valuation of forest property.
16. Compound Interest and Discount. — Interest upon money
loans is due and payable either annually or at shorter intervals.
When received it may be added to the principal at the discretion
of the owner. It may then be loaned and will in turn earn
interest. At the end of each period of payment, provided no
capital has been withdrawn, and interest has been promptly
VALUES 9
reinvested, the total investment will have increased by an amount
representing the interest on the total sum on hand at the begin-
ning of the period. A sum earning interest in this manner
increases at a compound or geometric rate.
Should the annual interest earned be withdrawn annually,
neither the principal nor the interest earned would increase in
amount. Should this interest be saved but not reinvested, the
total \-alue of principal and accumulated interest would increase
by the same amount annually. This is termed simple interest.
In neither of these cases is compound interest obtained. Com-
pound interest is paid by savings banks on deposits which remain
untouched for periods of six months or more.
Since the earning of interest on money, without expenditure
or withdrawal of the earnings, is equivalent to depriving the
owner of this capital of all use of his property for the period
covered by the loan, the difference in value of the capital at
the beginning and end of the period measures the money value
of the period of waiting. When money is loaned for periods
exceeding one year, this difference in value must be computed
by compound interest. Any lesser sum would fall short of the
demonstrated earning power of money capital at a given rate
of interest. Since compound interest is thus required for money
loans it must be accepted also as the standard of time differences
in value for all other forms of income.
By means of compound interest at a given rate the exact
ratio is obtained by which present values may be converted
into future values, or, by discount, future values may be re-
duced to their present equivalents. When both the present
and future values are known, a rate of compound interest may
be found which will equalize the difference in time and convert
the one value into the other.
17. Sale Value. — The sale value of property is indicated
by recent prices for similar property in the same locality. In
the absence of actual sales it is difficult to determine present
sale value.
Sale values arc not uniform for the same kind and quality of
goods, even in the same locaUty, unless there is a complete
lO FOREST VALUATION
general knowledge of current prices and the desire to buy is
approximately equal to the pressure for sales. Should the owner
stand in need of money he will tend to lower prices, and vice
versa. Forced sales for cash or to Hquidate assets are made
at prices much below the market and establish what are termed
wrecking values. The difference in value due to forced sales
is greatest with property used in production or for special pur-
poses, of which real estate is a good example. A forced sale
of forest lands, especially of young timber with no market value,
will seldom secure more than a fraction of the true value of
the property.
18. Appraised Value. — Values must frequently be estab-
lished in the absence of sales, or as a basis for such transactions
when previous sales are either lacking or unreliable as a standard
of value. Instances are found in condemnation proceedings,
in settlements for damages, and in inventories or the valuation of
assets for purposes of determining the financial status of a busi-
ness. The principle underlying appraisals is that the value
to the owner, for continued ownership and use, must be deter-
mined rather than its possible value for sale, since the owner
must not be forced to accept a lower value than that represented
by his use or enjoyment of the property. Appraised values, for
this reason, frequently differ sharply from sale values, especially
in the case of slow-moving assets.
CHAPTER II
OUTLAY AND INCOME
19. Proprietary Accounts versus Specific or Valuation Ac-
counts. — Modern accounting distinguishes two classes of
accounts, proprietary accounts and specific or valuation accounts.
Proprietary accounts deal with the proprietor or owner's in-
terest, and show what his outlay has been, the resulting income
already received and the balance which represents net capital.
These accounts show the owner as creditor of a business venture,
the credit representing his investments. Expenses are debited
and income or profits credited. Such accounts normally show
a credit balance. The credit items are the plus items^ of the
account. Dealing as it does entirely with outlay and income,
it records only actual transactions or past events.
Specific or valuation accounts deal with the assets or goods
for which these expenses are incurred, and from which the income
is expected. In contrast to economic accounts, they determine
the value of these assets, and may thus introduce elements
derived from the future as well as the past (§9).
20. Capital Accounts. — Outlay or expenditure of capital
is undertaken for one of two purposes. Either an exchange
is effected by which the proprietor receives goods or property
of equal value, or the outlay is in return for services and the
equivalent in value must be sought in the effect or results of
such services.
In accounting, these two classes of outlay are rigidly sepa-
rated wherever it is possible to do so. The cost of tangible assets,
especially of those which have a more or less durable character
and permanent value, is entered in a capital account. This
account is corrected by entering deductions from cost for forms
of capital which depreciate in value and may finally become
worthless. This factor of depreciation is common to all forms
12 FOREST VALUATION
of property constructed by human labor, as, for example, ma-
chinery and buildings. The charging off of depreciation, unless
accompanied by an appropriation of income to replace the capital
originally expended, corresponds to a loss of capital. If re-
placed from income, it serves to diminish the net income avail-
able for dividends. In either case it improves the accuracy of
the capital account.
A capital account ought to show at any time the total amount
of capital invested in permanent or durable assets, or the actual
cost of these assets, whether or not there has been any sub-
sequent increase in value. The correction for depreciation,
which is justified by the fact of diminishing value, is in itself
purely a matter of accounting. The amount of depreciation
written off on the books may not, and usually does not, coincide
exactly with the actual loss in value at the time. Should no
account be taken of depreciation, the capital account would
merely show that the owner had neglected to reduce the " value "
or appropriate any of his income as replacement of capital cost.
This is an unwise and dangerous practice, but it is optional
with the owner except where provision for depreciation is pre-
scribed by law for the protection of stockholders in order to
bring the capital account into closer agreement with the actual
value of the assets.
21. Outlay and Income Accounts. — Outlay and income ac-
counts, more often termed profit and loss accounts, deal first
with the expenditures for which services are received and which
are not therefore chargeable to capital account or regarded
as investments. A second class of expenses usually included
in this account is the cost of raw materials to be manufactured,
goods to be resold, supplies to be expended in service, and fuel.
These items represent capital and their value will be included
in an inventory. But in most forms of business this investment
is transitory in character, the raw materials are turned over as
quickly as possible, and the resultant income is expected to more
than cancel these outlays during the current year.
Outlay and income accounts are for this reason kept as open
accounts, to be balanced, usually, at annual intervals. Outlay
OUTLAY AND INCOME 1 3
is debited under such heads as wages, transportation, fuel, in-
surance, light, rent, repairs, interest, taxes, supplies and cost of
raw materials or goods. Income is credited, and in mercantile
business consists almost wholly of receipts from sale of goods,
to which is added incidental receipts from all other sources,
such as rent and interest. The capital account, kept separate
from this mass of fluctuating items of expense and income,
is brought up to date each year by entering against it the net
increase or decrease in actual capital resulting from the trans-
actions of the year. Should any of the assets whose cost is
included in the capital account be sold, the income thus re-
ceived must be credited in the capital account to replace the cost
of this asset. In the same manner, loss in value of capital is
replaced through the depreciation account. Excess of sale value
over cost of assets would be credited as profits.
22. Investments versus Expenses. — The distinctions, or
classifications in accounts, adopted by experience as suitable
for modern business conducted on the basis of annual returns,
should not be allowed to conceal the economic similarity of
all forms of outlay and income. Outlay is undertaken with
the sole purpose of thereby securing income. Those forms of
outlay customarily entered in the capital account, for which
tangible assets are received, are, it is true, regarded in the hght
of investments rather than expense by the owner. But their
acquisition is merely the first step in securing income, and the
culmination of the process is certain to require services or labor.
The income will be the result of both classes of expenditure.
That these are really identical is seen by the fact that improved
property, purchased as capital, is largely the result of the ser-
vices of former owners. The further expenditure for services
by the new owner may have a sale value which a future pur-
chaser would enter not as expense but as capital. Expenses for
all kinds of service and supplies, instead of being an economic
loss as must of necessity be assumed in the practice of account-
ing, is the most important form of investment, without which
there could be practically no income, and the capital would
then be without value. The controlling purpose of the pro-
14 FOREST VALUATION
prietor is to obtain as great a ratio of income as possible for each
unit of capital employed, whether this outlay takes the form of
investment or subsequent expenses.
23. The Relation in Time between Outlay and Income. —
The element of time enters into every process of production
(§ ii). Effort normally precedes satisfaction. Money income is
to business what the satisfaction of personal wants is to an in-
dividual. Since outlay and efifort are synonymous, it follows
that in all forms of business, investment must precede the re-
ceipt of income.
This process is easily recognized in the period of installation,
especially in such forms of business as require the completion
of material structures. But it is equally true of the current
business of a going concern. The receipt of income is reck-
oned from the moment a trade is concluded. Actual payment
may be delayed, but this is a matter of accounting. Upon the
delivery of the goods, all expense connected with the securing
of this income terminates, except where contracts stipulate
future maintenance in good order for a stated period. Conse-
quently, the wages and all other charges incurred in the securing
of this income normally precede the final sale. The postpone-
ment of payment of these expenses is also a mere matter of
accounting. The liabiHty or indebtedness for expenses is in-
curred previous to receipt of income in practically every case.
24. The Total Investment. — The total capital invested in
a business is always greater than that represented by the cost
of the assets listed under the capital account. Were income and
the items charged under expense to occur simultaneously, the
one should cancel the other, leaving the surplus or profit to
apply as interest or dividends on the capital originally invested.
After a business is established, this actually takes place and unless
the scope of operations is enlarged, the capital required should
not subsequently increase. But this apparent coincidence of
income and outlay does not alter the time relation shown to
exist between them. The expenditures of to-day are for the pur-
pose of securing future income, while the income of to-day is the
result of past outlays.
OUTLAY AND INCOME 1 5
These outlays, whether in fonii of services or purchases, must
be paid for by the proprietor at the time they are incurred,
either in money or credit. This evidently requires an addition
to the total capital invested, sufficient to meet all expenses
covering the period of installation or formation of the business,
or the time elapsing between outlay and income. If the income
is regular and continuous, this required capital ceases to increase
as soon as current income exceeds current outlay. But the sum
invested up to this point remains in the business, for whatever
portion may be paid back out of income an equal sum is at
once required to meet the expenses for which the corresponding
future income has not yet materialized.
The capital required to meet these current expenses and carry
them continuously, thus bridging the gap between outlay and
income, is termed working or floating capital, in contrast to
that represented by more durable assets shown in the capital
account.
For business in which income is realized only at long intervals,
expenses continue during the period, and the amount of working
capital tied up in wages and supplies increases rapidly to large
proportions, and is as suddenly decreased when the income is
received. Such a condition is represented by the business
of dri\-ing logs down streams. Contractors engaged in this
work receive their settlement when the logs reach their desti-
nation, which is once a year, while frequently a drive is hung
up and lays over a season. It was formerly the custom in some
states to transfer this indebtedness or outlay to the shoulders
of the laborers, who were paid in time checks made payable
in cash at a date subsequent to the probable delivery of the
drive. The men, being without capital, cashed these checks
at discounts which allowed the bankers or speculators who
furnished the funds to make very large profits. These profits
were in some cases split with the contractor who issued the checks.
Legislation has in most instances required cash payment of
wages, thus requiring the contractor to assume this obligation
and raise the necessary working capital. Where, as in the case
of forest plantations, the period elapsing between outlay and
l6 FOREST VALUATION
income becomes abnormally long, the amount of capital required
to carry the project to completion is proportionally increased.
25. Cost Accounts. — A cost account differs from a general
profit and loss account in that it analyzes the cost of producing
a given unit of output, instead of accounting for the current
outlay and income of the business as a whole. Such an account
traces the history of the product from the time of its purchase
or inception until it is sold. The costs incurred fall into two
groups: specific costs, which include that for raw materials
and labor directly applied in production; and overhead charges,
which include taxes, insurance, light, fuel, superintendence,
rent and other items, which must be apportioned on an equitable
basis over the entire output. Cost accounts in forest production
sum up the cost of growing a crop of timber from origin to matu-
rity. Owing to the great length of the period involved, the
factor of compound interest on invested funds, when introduced
as a cost in such accounts, becomes one of the largest items of
expense.
26. Income. — In § 8 and § 9 it appears that prices for fin-
ished products are the source of value for all forms of property.
Value, as distinguished from cost, depends upon net income and
looks to the future. The income from finished products, which
gives them their value, corresponds with the services they are
capable of rendering by being used or consumed.
The sources of income from productive property consist
either of finished products or materials in a raw or unfinished
state, while the income derived from the business of operating
such properties is the money received from the sale of the output.
27. The Economic Opportunity. — To derive or produce
an income, some himian want must be supplied. The greater
the range and diversity of these wants and the greater the
purchasing power or capacity of the average individual to
gratify them, the more numerous and promising will be the
economic opportunities for business. Inequalities in the dis-
tribution of wealth, and the existence of a pauper class, greatly
diminish the total business of a nation and divert much of it
into wasteful and injurious channels.
OUTLAY AND INCOME 1 7
28. The Business Venture. — Income can be produced only
by risking capital and expending effort on the chance that this
outlay will be returned " with interest." In a properly con-
ducted business this risk is assumed by the proprietor, who
makes himself personally responsible for the management.
Ownership is represented in modern business by capital stock.
By means of this same device, extensive frauds are possible by
which the real managers of a business shift both risk and loss
to the stockholders or owners. Legitimate risk, borne by those
responsible for the results, is unavoidable and is one of the
chief characteristics of the business venture. Aside from the
risk of accidental losses by fire, theft and other factors, the final
ever-present risk is that income will be insufficient to offset the
required outlay, and insolvency result.
29. Exchange. — Income from business (§ 26) is derived
almost entirely from sales of merchandise or manufactured
products, which constitute an exchange of goods for money.
The transaction is in theory completed with the delivery of the
goods, but payment is often deferred and constitutes a debt
on the part of the purchaser, which is a debit or asset to the
business. The losses which occur through ultimate failure of
debtors to pay are finally debited as an expense.
30. Disposition of Income. — With the receipt of income
the cycle of elTort is completed and the purposes of the business
are accomplished. An accounting must now be rendered to
the owner. In case the proprietor's account and ownership is
terminated by a sale of the entire business, the settlement would
consist of:
Payment of outstanding bills, wages and other outside obli-
gations.
Return of outstanding and borrowed capital.
Distribution of surplus as profit to owners of the capital
invested.
In the annual accounting of a going concern the profit and
loss account takes care of the expenses. The surplus or deficit
in annual income, shown as profit or loss, is carried into the
annual balance sheet for future disposal.
l8 FOREST VALUATION
31. Returns on Capital. — Out of the net profits after can-
celling the expenses for the year, provision must first be made for
the replacement of capital assets lost by depreciation or other-
wise. The remainder is available as returns on capital.
Here a sharp distinction must be made between the total
amount of capital required to finance a venture and the persons
or sources from which this capital is derived. From the stand-
point of the business itself, the source or ownership of this
capital has no effect upon the total net profits but affects merely
the apportioning of these profits.
A proprietor who furnishes his entire capital, both fixed and
working, takes all the profits and assumes the risk of loss. But
it is an almost universal custom to borrow part of the needed
capital on the security of the business or of the fixed assets.
In this case profits are earned on the total invested capital as
before, but the division is on a different basis. The borrowed
capital receives a fixed rate, agreed upon at the time of secur-
ing the loan, and guaranteed by the proprietor. He receives
in turn the entire surplus remaining after this obligation is
met.
32. Interest versus Dividends. — The sum guaranteed to
the lender of borrowed capital is interest. This is paid out of
net income and is as much a part of the net earnings of the busi-
ness as the remainder. The residue is either left in the business
as additional capital, or paid to the proprietors as dividends.
Interest, at the rate demanded on borrowed funds, will require
a given sum on the entire capital. Should the business earn a
net income exceeding this sum, the proprietor receives the excess,
which raises the rate earned by his own capital, or his dividends,
above the rate of interest paid to creditors. The greater the
proportion of capital he borrows, the greater will be the rate of
dividends on the lessened capital of the proprietor. But on
failure of the business to earn the rate paid on borrowed funds,
the owner bears the entire loss, and the smaller the proportion
which his capital bears to the whole investment, the greater is
his relative loss.
In an insolvent concern, the owner's capital, as well as divi-
OUTLAY AND INCOME 19
dends, is sacrificed before any loss of either interest or capital
is permitted to fall upon the holder of mortgages or liens. For
this reason bankrupts may fraudulently conceal the assets and
thus defraud cretiitors.
33. Profits. — According to Marshall,* " When a man is
engaged in business his profits for the year are the excess of his
receipts from his business during the year over his outlay for
his business. The difference between the value of his stock
and plant at the end and at the beginning of the year is taken
as part of his receipts, or as part of his outlay, according as
there has been an increase or decrease of value. What remains
of his profits after deducting interest on his capital at the current
rate may be called his earnings of undertaking or management."
According to this definition, interest paid on borrowed money
is excluded from profits, but interest on the owner's capital is
considered as constituting part of the profits. This is the dis-
tinguishing point between a purely economic or impersonal
consideration of a business and a personal account with the
proprietor. In an economic consideration of the general ques-
tion of profits on an industry as a whole, such as is needed, for
instance, in the process of appraising stumpage values for stand-
ing timber (Chapter XI), the distribution of the required capital
between proprietors and creditors has no significance. The
entire net revenue available as returns on capital for the current
year must be regarded as profits.
34. Wages versus Profits. — Wages are an outlay, or an
expense, which serves to diminish profits. The wage or salary,
ultimately met from income, is the share of the wage earner
in the returns of the enterprise.
In most undertakings the owners themselves give at least
part of their time to the management of the business. In very
small enterprises the owner may even do most of his own work,
thus saving the expense of employing labor. The larger forms
of business, in which the ownership is scattered in the form of
capital stock, are managed by pro.xy, through boards of direc-
* " Principles of Economics," by Alfred Marshall, 5lh Ed., Vol. I, p. 142.
Macmillan & Co., London, 1907.
20 FOREST VALUATION
tors who devote but a small portion of their time to these duties.
There is an almost complete separation between wages or salaries,
and income in the form of dividends. Even in such cases,
capable managers are frequently given an interest in the business
and their returns thus include both wages and dividends, although
the two items are separately accounted for. In small ventures
managed by the owner, this distinction is often neglected, and
the owner's profits are the sole source of compensation for his
time. In such cases a sum representing the wages of the manager
or overseer should be charged to expense. Should the business
pay less than this sum it is unprofitable.
CHAPTER III
INTEREST
35. The F^roblem of Interest. — In proprietary accounts,
all items, with the exception of interest, are easily classified as
costs or as income. Interest may be regarded as either cost
or income, according to the point of view. Since these two
conceptions are not interchangeable, a clear understanding of
this problem is necessary to avoid errors in dealing with ques-
tions of valuation accounting.
36. Interest as a Cost. — Interest when regarded as a cost
must be considered in its relation, first to the owTiers of capital,
and second, to the capital itself. In accounting, the interest
paid upon borrowed capital is regarded by the proprietors as a
cost. But it must be noted that the net profits of the business
are first computed, and from these profits, rather than from
gross income, the cost of interest is met (§32). This item of
cost is entirely a personal matter between the owner and his
creditors. Should there be no borrowed capital, this cost item
would disappear from the account, and dividends or additions
to surplus, to an equal amount, would be substituted.
But since borrowed capital is entitled to receive interest at a
standard rate, and this "cost" must be met, the owner con-
siders that his own capital is entitled to receive interest at a
like rate. He guarantees payment on loans, but must depend
on his own exertions to obtain this interest on both the borrowed
funds and on his own investment. Should he prefer the role of
money lender, his capital will earn this rate of interest without
the risks attendant on the business venture. The risks of lending
money upon good security are much less than those accom-
panying other forms of business. Shall he therefore charge
interest upon his entire capital as a cost which must be met?
Those who take this view will include interest, not only on
22 FOREST VALUATION
borrowed funds but on the total invested capital, in the same
category as other expenses, that is, as a part of the so-called
carrying charges of the business.
The interest to which the owner is entitled cannot be entered
in proprietary accounts as an actual charge or cost similar to
interest on borrowed funds. His share of interest is never
actually expended, and the idea of cost exists merely by impli-
cation. But in a cost account, which is intended to present
definitely the relation between total cost of production and
resulting income, interest may be calculated and entered as a
part of the total cost.
37. Interest as Income. — Whether or not interest is re-
garded as a cost, it always represents income on the capital
investment, and in this respect differs from other costs. All
other items of expense, such as taxes, wages and cost of supplies,
while met eventually from income, go to persons or enterprises
other than the capitaHsts who finance the venture. And just
as the creditors of the business, during the formative period,
are paid in advance by the capitalist, who receives returns
finally from income, so the capitaUst who only loans money and
does not assume the risks of ownership may receive his interest
in advance of income, provided it falls due and is paid by the
proprietor. But this cost to the latter is ultimately returned to
him from income, which must also pay him returns on his own
investment. In case the income is continuous and is accounted
for annually, both borrowed and invested capital receive income
directly from the net returns.
38. The "Rate of Interest." — Interest has been defined as
the price of time differences in the enjoyment of income (§ 14).
Since the use or borrowing of capital is the means of anticipating
income (§12), and the value of both capital and interest is ex-
pressed in money, it follows that interest is the price of the use
of money.
This price for money loans is termed the "rate of interest."
As money is more desirable than other forms of capital because
of its universal acceptability as a medium of exchange, and as the
risk in money lending is normally less (§ 36) than in business,
INTEREST 23
this rate of interest, which represents the possible income on
capital in the form of money, becomes the standard by which
the desirability of any other form of investment is gauged.
39. The Profits of the Undertaking. — Unless there is a
chance of earning a larger rate of income upon the capital re-
quired in an undertaking than could be earned by lending this
capital to others, there would be no incentive to assume the
risks of the business. In order to make a business really profit-
able, the net income should exceed this "rate of interest."
This surplus is the goal of the whole operation and is termed the
"profits of the undertaking," as distinct from the term "profits,"
which includes interest (§33). It is the personal reward of the
individual who has borne the responsibility of the business.
There is no good Enghsh word to indicate this person. Un-
fortunately we have appropriated the \vord "undertaker" for
other uses. The French term "entrepreneur" is commonly
accepted by economists. The more recent English substitute
"enterpriser " is rather clumsy, but will be used in this text.
The term "profits of the undertaking" would therefore ex-
clude interest as a necessary "cost" and regard the margin
remaining as the real profit.
40. Annual Profits. — On this basis, a business paying annual
dividends is considered successful if the average dividends are
larger than the rate of interest which the firm has to pay on
borrowed capital. If the dividends are less than this, the busi-
ness is considered unprofitable to the owner, although it may be
relatively more profitable to continue it than to abandon or sell
it, with resultant loss or impairment of capital. As a matter of
fact, only the more capable and experienced managers succeed
in earning an "enterpriser's profit," and one per cent of independ-
ent concerns annually become insolvent, thus failing to earn a
net income sufiicient even to protect the capital investment.*
41. Deferred Profits. — In an enterprise in which outlay
precedes income by an interval greater than one year, the method
of accounting for profits depends upon whether this condition
* The Percentage of Failures, Dun's Revien', May 31, 1913. R. S. Dun & Co.,
New York.
24 FOREST VALUATION
of affairs is normal or accidental, expected or unforeseen. If
profits should normally be earned annually, failure to do so in
any given year would be regarded as a loss by the proprietor,
but this would be mentally "written off" against the current
year and not carried as a debit to be recovered from the income
of a subsequent year.
If the enterprise is planned to extend several years before
realizing profits, as in the case of the voyages of whaling ships,
or the production of timber from plantations, the annual interest
which remains unpaid is not considered lost, since it is the expec-
tation of the owners that this will be more than made up when
the "ship comes in." But the profits of the undertaking may
still be computed separately from the standard interest "cost"
or income. This must be done by calculating compound interest
on all cash expenses as long as they remain unpaid, which gives
the sum that could be earned by the capital as loans in money
form for an equal period.
The deferred income may greatly exceed the total cash outlay
and the enterprise yet fail to earn compound interest at a
standard rate. In this case the deferred "profits of the under-
taking" disappear, and the status of the venture is the same
as that of the business whose annual dividends fall below the
standard rate of interest.
The production of timber as a business is based largely on
the theory of deferred profits, and both the determination of
these profits and the methods of accounting employed should
be made to conform to the essential differences between such a
business and one conducted on the basis of annual profits.
42. Income versus Profits. — In determining the amount or
rate of profit which should be earned in order to properly com-
pensate the enterpriser, the status of interest must be held
clearly in mind. It is a "cost" merely for purposes of sepa-
rating that portion of the income which his capital could earn
from the additional income earned by his personal efforts. In
impersonal consideration of the legitimate profits of a business,
the distinction between borrowed capital and proprietary capital
is rejected, and the interest upon the entire capitalization is
INTEREST 2$
included in the income earned and not in costs. Should the
fallacy be introduced of considering interest as a cost in comput-
ing profits, the apparent profit required would be increased
abnormally. For instance, it is stated that a certain business
should cam a profit of lo per cent, which, with interest at 6 per
cent, indicates an enterpriser's profit of 4 per cent. By consid-
ering this interest as an actual cost, an additional profit of 10
per cent might be expected. But, in reality, this 10 per cent
would be the enterpriser's profit. The total net income must
then be 16 per cent, and the enterpriser's gain is 2^ times as
great as in the original case. If an enterpriser's profit of 10
per cent is necessary, the "profits" of the business must be 16
per cent and not 10 per cent.
The larger the amount of capital invested in a business, the
smaller, as a rule, will be this margin between income and
interest, which represents the enterpriser's gain. Both income
and "gain," while larger in amount, average less in proportion
than on small investments. This shrinkage does not come
entirely on the margin of gain, since funds can probably be
borrowed at lower rates in such undertakings. The longer the
time elapsing before income is received, the less will be this
margin of profit over compound interest at standard rates.
For very long investments, the enterpriser's gain tends to dis-
appear, and is entirely dependent on the rate of interest chosen
as representing the legitimate income on the capital itself.
In both the above cases, in spite of the shrinking of enter-
priser's profits, the income or profit over expenses remains in
the form of interest returns, and, especially on long time in-
vestments, the final results may still be considered by the inves-
tor as highly satisfactory.
This attitude is partly due to ignorance. The owner of un-
productive property, such as unimproved real estate, seldom
keeps a cost account which shows him the total outlay repre-
sented by the purchase price plus taxes and improvements, and
still more rarely does he add the "cost" of the unearned interest
on this total from year to year. When he sells this property
after the lapse of several years, for more than double what he
26 FOREST VALUATION
paid for it, he does not realize that a savings bank at 4 per cent
might have paid him more for the uninterrupted use of the same
capital than his profit amounts to.
Yet this attitude of investors towards deferred profits is not
explained wholly by ignorance. If an investor is in a position to
get along without income for a long period, at the end of that
time the "loss" of annual income has but little significance
and he sees only the accumulated total of his profit. He com-
pares this with his original outlay and judges results on that
basis. This tends to make him satisfied with a return which in
reality represents low rates of interest on such investments.
43. Influences Determining the "Rate of Interest." — The
current rate of interest is a price, determined by the demand
and supply of money for borrowing purposes. This price or
rate has no greater stability than the average prices of other
commodities. It fluctuates during the year, and over longer
periods, in response to changing economic conditions. Nor is
this rate the same for all classes of loans. It varies with the
security offered, the length of the period covered by the loan,
and the personality of the individuals negotiating it. In spite
of these variations, an average rate of interest may be roughly
approximated for a given time and place; but this is determined
far more closely if the circumstances affecting the particular
loan are also known.
44. The Influence of Personality on the Rate of Interest. —
Just as prices are the resultant of human opinions interpreting
desires or demand and weighing them against efforts or supply,
so the rate of interest depends even more completely upon the
human character and mind.
Impatience for income, and preference for present over future
income, tends to raise the price the individual will pay for this
privilege. Persons who lack foresight, are improvident and
are lacking in self-control will borrow at high rates. The same
is true of persons who lack capital and are in need of present
income. On the other hand, individuals who desire to provide
for the future, who possess the power of self-denial and who are
already possessed of considerable capital will borrow, if at all,
INTEREST 27
only at reasonable rates. As investors, the former group desire
to "get rich quick" and by seeking abnormal profits usually
lose what capital they may possess. The latter group are apt
to favor long time investments which give a certain return even
at a low rate.
45. Risk and Expense. — As most loans of money are made
on the basis of a security pledged as a guarantee for repayment,
and worth more than the amount of the loan, the risk of loss
of principal or interest is correspondingly reduced. In case of
imreliable parties, notes are guaranteed by some one who is
able to pay. Risky loans are made at higher rates than safe
loans, the extra rate being intended to cover average losses.
The exorbitant rates charged by loan sharks are not justified on
this basis, although loans of this character require a somewhat
higher rate than business loans. Such rates are due to personal
elements, exaggerated by defective laws and bad economic con-
ditions, which permit the exploitation of a class of persons unable
to protect themselves.
Expense of placing loans and of collecting interest tend to
increase the rate of interest charged. This expense is greater for
short loans, and the funds are apt to be idle part of the time.
It follows that the lowest rates of interest are received on
absolutely safe securities, which run for a long period and upon
which the interest pa}Tnents are made without expense to the
owner. Government securities and bonds of high grade fulfil
these conditions.
46. Fluctuating Value of Money. — Should money fall in
value or in purchasing power, the rate of interest tends to rise
to a degree corresponding to the average annual loss in the value
of the capital. Only by this means can a lender of capital escape
actual loss. If the fall in value amounts to i per cent per year,
securities upon which the normal rate of interest is 4 per cent
will be worth in purchasing power only 99 per cent of their
original value at the close of the year. A rate of 5 per cent
enables the investor to replace this difference by adding it to the
capital.
Such losses usually escape the notice of the owner, who imag-
28 FOREST VALUATION
ines himself as wealthy as before even if he spends the entire
income from his investment.
47. The Rate of Interest for Business Investments. — The
rate of interest for a business is the rate at which money will
seek investment in the enterprise. It is a question whether
or not this basic rate should include an enterpriser's profit.
The rate which the lender of capital will accept on the security
of the business, or what the proprietor can obtain as the basis
for a loan, is a conception tallying rather more closely with actual
conditions. Such a rate may be said to attract capital, but it
may not attract the enterpriser, who hopes to do better. The
*'rate" adopted as the standard for an investment becomes
the basis for computing both the cost of production (§ 25) and
the value of the assets (Chapter IV).
48. The Effect of Deferred Income upon the Rate of Interest.
— A mathematical comparison of simple and compound interest
leads to the conclusion that, since the latter, as applied to de-
ferred returns, is the exact equivalent of the former when returns
are annual, a given basic rate should be the same whether the
investment pays annual or deferred income.
But under the definition that the "rate of interest" means
the rate which will attract money to a business, the above
conclusion must be tested by the "price making" factors
which influence the minds of investors. Should these factors
be found to differ for investments of the two classes, the basic
rate of interest applicable to each case will differ to a corre-
sponding degree.
49. Comparison of Results of Simple and Compound Interest.
— The economic results obtained in actual practice from an
undertaking which produces simple or annual interest are not
the same as those obtained by compound interest, however
similar may be their mathematical relation.
To make the returns from a business which starts with a
definite amount of capital, and earns annual net profits at x
per cent, equal to those from the investment of a similar sum
which will produce compound interest after a term of years at
the same rate, x per cent, requires several assumptions. The
INTEREST 29
entire earnings of the business would have to be retained as
capital and not a cent withdrawn as dividends. This capital
must then be utilized in such a manner that it will produce net
earnings equal in rate to the earnings on the original capital.
Each year this process must be repeated, resulting in an expan-
sion of the business at a geometric rate. If this result is ob-
tained, the total capital at the end of the period will not be
worth one cent more than the funds accumulated in the second
investment, where all income is deferred until the end of the
period.
Should the proprietor withdraw any portion of the earnings
during the entire period, or should the business fail to expand
annually at the required per cent, the resultant rate of com-
pound interest earned by annual profits will be lowered below
that demanded in the comparison.
50. Limitation of Opportunity. — Such compound expansion
of a business is possible only where the economic opportunity
(§ 27) is practically unlimited, or increases at a rate which keeps
pace with the growth of the business. This occurs only as a
temporary condition, both in business and in all other forms of
activity.
Animal and plant life have the capacity for expansion at geo-
metric ratios comparable to enormous rates of compound in-
terest; such events seldom occur, but when they do, the result
is calamitous. English sparrows imported into America found
an environment not used by any existing species of bird. Until
this niche had been completely occupied, the sparrow increased
at a compound rate. The species is now merely holding its own.
In manufacturing, the production of new articles and the
growth of a demand for them, as in the case of automobiles,
creates an opportunity which permits of a trade expansion at
geometric or compound rates for a while. This expansion took
place when bicycles were first made popular. It cannot con-
tinue in^any line at the same rate over an extended period. A
lessening, not of the annual demand, but merely of its rate
of increase, has the effect of preventing further expansion at a
like rate, and with the establishment of equilibrium, not only
30
FOREST VALUATION
will compound interest fall to a lower rate, but annual profits
will be reduced as well. This explains the fact, accepted by
economists, that the larger the aggregation of capital employed
in an undertaking, the smaller will be the annual rate of profits
which justifies the investment.
The conclusion is irresistible, that the mathematical equality
between simple and compound returns does not hold good.
The latter tends to fall below the former, and, what is more
important, this discrepancy is accepted as equitable by investors.
The recognition of this fact will go far towards clearing up
the false impressions which at present obscure the question of
rates of interest applicable to forest investments.
51. Effect of the Rate of Interest upon Accumulations of
Compound Interest. — The cumulative effect of compound
interest bears an intimate relation to the rate of interest. Low
rates cause a very slow increase and may be applied with some
reason to investments which run for a very long period. High
rates cause a very rapid increase which soon passes the bounds of
possible attainment in practice. The following diagram reveals
this relation. (See Diagram I.)
TABLE I
Comparison of the Results of Simple and Compound Interest
ON $ioo AT the End of a Period of 50 Years
Rate of
interest
earned
Value of capital
and interest at
end of period
Rate of simple in-
terest to be earned
and saved to
give equal final
results
Per Cent
1
2
3
$164
269
438
Per Cent
1.28
3.38
6.76
4
710
12.20
5
6
7
8
1,146
1,842
2,946
4,690
20.92
34 84
56.92
91 .80
10
11.730
232.78
A comparison of the economic results of simple and compound
interest is further brought out by the above table which gives
INTEREST
31
DIAGRAM I
Periods Required for $r.oo to Multiply, at Different Rates of
Compound Interest*
20
19
18
17
16
15
-14
§13
£
a
111
O
8
|9
b
o
E 7
o
O 6
5
4
3
2
1
lO-^
»< :<
Cc
1
1
1
ii
/
1
1
/
f
1
/
/
/
/
J
/
/
/
/
/
1
/
/
I
/
/
/
1
f
/
/
1
/
1
/
/
/
/
/
/
/
r
1
/
\ \
'
I
1
/
/
/
/
/
1
/
/
3ft
/
/
/
/
/
/
/
/
/
//
7
'
1
/
/
/
/
/
/
/
/
/
/
/
/
/)
'/
/
r
/
r
/
^
//
V/
/
/
/
/
y
y
^
21.
/
VA
Y.
/
y
■^
^
^
y
^^
^
/
^
^
y
/
^
^
— '
\i
::iJ
—
' 1
■
"
20
30
40
Years
50
GO
* A rate of 10 per cent, compounded, multiplies 20 times in 31 years. A rate of
I per cent compounded, doubles in 70 years. Even 6 per cent would, in 70 years,
multiply the principal 59 times.
32 FOREST VALUATION
the total amount to which the sum of $ioo will increase in 50
years, provided the investor complies with the conditions out-
lined in Article 49.
The final column shows the rate which the original invest-
ment would have to earn annually to get the same results, pro-
vided the entire income were placed in a deposit vault and
saved until the end of the period without reinvestment. Should
the proprietor spend the annual income, he would have merely
the original capital of $100 left at 50 years.
52. The Rate of Interest in Forest Investments. — To de-
termine the basic rate of interest applicable to investments
in forestry, two factors must be analysed, namely, the relative
security of the investment, and the financial nature of the enter-
prise. It is claimed by advocates of a high rate on forest invest-
ments that this is justified by the ever-present risks from fire and
other destructive agencies, and also by the length of the period
elapsing between outlay and income, which makes the invest-
ment less desirable unless it can be shown to be more profitable.
The first of these claims must be admitted. Risk should be
pro\^ded against by demanding higher interest. This subject
is discussed in Chapter XIII. Risks must be judged on the
basis of comparison with those assumed in other lines of in-
vestment, and due weight must be given to the present
development of measures of protection on the part of states
and associations.
The second claim is fallacious. To demand a higher rate of
interest the longer the returns are deferred is a subversion of the
economic laws applicable to all forms of investment. The desir-
ability of the investment as affected by the difference between
annual and deferred returns will not modify the rate of interest
which should apply, but rather, will determine the class of
persons who are apt to choose such an investment. And since
those persons who are the most apt to favor long-term invest-
ments with deferred income are those possessed of foresight,
making provision for their children, and with sufficient capital
for their personal needs (§44), such persons will accept a lower
rather than a higher rate of interest, and in many cases will not
INTEREST 33
even compute the probable rate, being content with the general
prospect of a future value greatly in excess of present investment.
53. Comparison of Interest Rates in Forestry with Other
Investments. — Proper rates for forest investments can only be
judged on the basis of comparison with other forms of enterprise.
If the scope of the comparison is confmed to forest production
and the account covers the period requisite for growth, a com-
parison between forestry and business producing annual income
is impossible. The goal of forest management is the forest
which will >'ield annual returns, but each crop represents the
accumulated outlay throughout its life and must be so judged
in comparing interest rates.
The only enterprises familiar to the public, which are reckoned
on a basis of compound interest, are savings banks and Hfe
insurance companies. The former have paid an average of
3 per cent, but of late years 4 per cent is common. Most banks
do not permit the accumulation of compound interest on accounts
to run more than 20 years without some sign of active interest
on the part of the owner, manifested either by withdrawals or
additional deposits. If the owner is alive and can refrain from
depleting his account for fifty years and the bank remains
solvent, he can obtain compound interest for that period. Such
cases practically never occur.
The average period covered by the risk of a life insurance policy
is not over 13! years,* and most companies calculate that they
can earn compound interest at about 4 per cent on the money
invested in policies for this average period.
For periods longer than fifty years there is no basis for com-
parison by which the rates reasonably appHcable to forest
investments can be judged. Based upon the economic laws
outlined in Articles 47 to 50, it must follow that those rates
will be less than 4 per cent provided the investment offers equal
security with life insurance and savings banks. Should the
security be considered less safe, the increased rate demanded
would ofTset the reduction in rate called for by the length of
the period of investment, and the investment should not require
* The Brown Book of Life Insurance Economics. Edition of 1911-12, p. 13,
34
FOREST VALUATION
a rate appreciably higher than 4 per cent for periods of over
50 years.
If these arguments are admitted, it is possible to show that
the income which may actually be earned by forest investments
covering long periods will be equivalent to the rates demanded
by the character of the investment, even though the earnings
may fall as low as 3 per cent for periods of over 50 years, and
2I per cent to 2 per cent for periods exceeding 100 years.
CHAPTER IV
VALUATION OF ASSETS
54. Valuation Accounts. — A valuation account is a specific
statement (§ 19) of the value of assets, whether material or con-
sisting of intangible rights. It informs the owner of the present
condition of the property, and enables him to compare this con-
dition and value with the total net cost or investment (§22), and
thus determine whether the business as a whole is gaining or
losing (§28). To accomplish this purpose, the account should
show what the business or property is actually worth at the
present moment, not merely what it was worth when the assets
were first acquired.
55. The Inventory. — In order to determine value we must
know the quantity of goods on hand and what each unit is worth.
This process of taking stock is termed an inventory. It is not
complete \\'ith the mere listing of goods, but includes their valu-
ation. In forest management the process of estimating standing
timber and other forest resources, often termed reconnaisance,
is the means of obtaining this data.
56. Cost as a Basis of Value. — Conservative accounting
seeks to avoid inflation of the value of assets, with its corre-
sponding indication of false profits in the balance sheet. If an
asset has been purchased in good faith, the purchase price is
taken to represent its true value. All items of investment
representing assets of such a character that they would be
included in the capital account will be accepted at cost, less
depreciation, in the valuation of assets. This does not mean
that the cost of an article represents its present value, but merely
that cost is definitely known and, when corrected for deprecia-
tion, is accepted as a conservative basis for value.
57. Expenses and Interest versus Value. — While account-
ants approve of the acceptance of capital expenditures or original
35
36 FOREST VALUATION
cost of purchase of tangible assets as a basis of value, they
condemn the assumption- that subsequent expenses, or items
customarily entered under outlay and income, or profit and loss,
add anything to the value of assets or furnish a basis for valuing
these assets. The theory is that such expenditures are made
for the direct purpose of producing income sufficient to offset
them, and that if this result is not secured, the loss must be shown
as a deficit, and not concealed by adding an equivalent of this
loss to the value of the assets.
This theory is justified for business undertakings supposed to
produce annual income, for if the income which should cancel
expenses fails to do so, the deficit cannot be construed to
represent anything but absolute loss, leading to insolvency.
This reasoning is then extended to apply to undertakings
in their formative period (§ 23), and the practice of retaining
investments in the inventory at their original cost is highly
commended, in spite of the fact that practically all expenses
during this period require additions to capital (§ 24) , and this
treatment of assets is thus bound to result in an apparent deficit
or state of insolvency.
Yet no one would undertake such long time investments
unless he expects an increase in the value of his assets in a meas-
ure corresponding to or paralleling the accumulation of cost
and interest. That this fact is assumed has a remarkable con-
firmation in the revolutionary practice of accounting authorized
in case of railroad properties during the course of construction
and before it is possible to earn an income. In Germany and
England it is permitted by law to include as an addition to the
value of the assets, not only the revenue expenditures during
construction, but the interest on bonds and dividends to stock-
holders.* This is the very process so vigorously and justly
condemned in case of business undertakings which should pay
annual dividends, nor would it be tolerated in the case of rail-
roads except during the period of construction.
A case closely parallel to the above is found in forest planta-
* "Modem Accounting," by Henry Rand Hatfield, pp. 76, 77. D. Appleton
& Co., 1Q09.
VALUATION OF ASSETS 37
tions. Shall the value of such property be based on the
purchase price, plus expenses, plus unpaid or deferred interest,
representing the total "cost" or "cost value" of the property?
As in the case of the railroad this might be justified. But such
"cost" is only an indication of value in either of these instances.
Unless the property is of such a character and its promise of
future income is such that this increase in value is sure to occur
and is evidently taking place, no one would be deceived into
thinking that such a cost calculation corresponded in the least
with value. Even then the value might be more, or less, and
there is no reason for assuming that it is accurately gauged by
cost.
58. Essential Difference between Cost and Value. — The
reader must keep clearly in mind that the valuation of assets is
a process essentially different from the account of cost and ex-
penses (Chapter I, Articles 2 to ii inclusive). If costs are taken
as the basis of value, as is done in some instances (§56), they
are merely the source of the information used, but this informa-
tion might as readily be obtained from entirely different sources,
and frequently must be so acquired. Value is determined for
the purpose of comparison with costs to indicate profit or loss.
If it were identical with cost, no comparison would be possible
and the owner could not determine his probable profits.
59. Sale Value as a Basis of Value. — In case a business
changes hands by sale, the sale value so determined is accepted
as the value of the business. In this transaction the price paid
for the assets must be entered as their value on the books.
Such sales thus establish a new recorded or book value for these
assets. The fact of the sale is the most convincing evidence of
value, although even this is not final proof, for one or the other
of the parties may have been deceived or handicapped in the
transaction. Nor will a past sale be accepted as absolutely
determining a future sale value even for the same property;
in fact it is usually the reason for desiring a different value.
Sales of property or business have a profound effect upon pro-
prietary' accounts, in that the former owner receives at once all
his income and capital and can balance his books and determine
38 FOREST VALUATION
his total net profit, while the purchaser is saddled with a cost or
investment which forms the opening entry in a similar account,
and no future acts will serve to reduce this initial cost.
60. Appraisal of Value (§ i8). — In determining the true value
of assets, either as a guide to the owners in negotiating a sale,
or for compensation for damages or in condemnation pro-
ceedings, the appraiser bases his opinion upon the most reliable
sources of information at hand. If a basis for sales is sought,
the average sale value of similar property in the immediate
past is given most weight. But where the owner does not
desire to sell, the appraiser must seek to establish the value
to the owner if the property remains in his possession, and this
rests wholly on its usefulness to him, not on what someone else
would pay for it.
61. Future Income as the Basis of Value. — The only true
basis of value recognized by economists is income (§§4, 26).
When a sale of property occurs, the "income" from the sale
should coincide with the value of the property. The value
which the owner or purchaser places on the property is deter-
mined by the value of all the future income which he expects to
derive from it.
In explaining values on this basis the true nature of income
must be kept in mind. "Final" income takes the form of
actual enjoyment of the uses or services of possessions. Real
estate is valuable to an owner, not merely for its money income,
but for the personal enjoyment which he gets from the rights
of possession. In this must be included the associations and
neighborhood of which it makes him a part. The sentiment
attached to the retention of an inherited homestead, the prej-
udice against leaving surroundings grown familiar by long resi-
dence will, by contributing to the peace of mind of the owner,
enhance the value of his land in his opinion in a manner fully
as concrete as money income. Only poverty or actual want
will counterbalance these very real values. This element of
social income must never be lost sight of in the valuation of
property. But the appraisal of income must ordinarily be based
upon money returns which can reasonably be expected in the
VALUATION OF ASSETS 39
future, and the present value of the property rests upon the
mathematical relation between the future income and its dis-
counted value.
62. Capital Value or Expectation Value. — Capital value, or
expectation value, is the net value of property based upon future
income. It is the capitalized value of future income minus
future expenses. The terms "capitalized" and "discounted"
are s>Tionymous. Therefore capital value is the discounted net
value of future income. Finally, since all future income is
included in present value, capital value is the sum of the dis-
counted values of all items of future net income. This definition
holds good whether the income is received at regular daily,
monthly or annual intervals, or at intervals of two or more,
even of icx) years, or is irregular in amount and paid at irregular
intervals.
An example of regular annual income is the interest on a
money loan. This interest, capitalized, corresponds to the value
of the loan of capital. This relation established between capi-
tal and income through the rate of interest (§ 38) is the means
of determining the capital value of all other forms of property.
For money alone the value of the capital and of its use deter-
mines the value of the income or rate of interest, and the value
of money is neither raised nor lowered by fluctuations in the
rate of interest.
For other property the relation is :
1. Capital or property earns income.
2. The value of this income is appraised.
3. This value is then discounted to obtain the value of the
capital.
4. The "rate of interest" is the measure of discount.
The term "capital value" has so far found no place in the
literature of forest valuation. Instead, such authorities as
Schhch have translated continental terms into the EngHsh
"expectation value." This term is descriptive of the fact
that such values are based on future expectations, not fully
determined; but it is open to objections, since it conveys the
40 FOREST VALUATION
impression that such values are different or obtained in a different
manner from the capitalized values computed for all other forms
of property. On the contrary, the process is identical and it
would be a distinct advantage to recognize this fact in terminol-
ogy. A third term, also identical in meaning with the two above
mentioned, is "capitalized rental value," sometimes abbreviated
to "rental value." Two objections to the term "rental value"
are that it may be confused with rent, which is only one form
of income, and that it may be taken to mean the value of one of
the current or periodical payments of income instead of its
true meaning, which is the sum of the discounted values of all
items of future income. The term "capitalized rental value"
seeks to emphasize this latter meaning, but the use of the word
"rental" might be taken to mean that such values are deter-
mined only for property producing income at regular intervals.
Since it makes no difference what the character or interval of
payment is, the term "capital value" is the most comprehen-
sive. The one great objection to this term is that the word capi-
tal is commonly used to denote the amount of an investment,
or the total funds furnished by capitalists (§§ 12-13), ^^'^ is in this
sense allied with cost rather than value of assets (§ 73). Were all
assets in the form of money, this would make no difference (§ 62),
but as cost and value for other assets diverge widely, some
term should be used which is clearly understood as referring to
value rather than cost. Another possibility is the term "income
value," or "capitalized income value." "Income value" is
open to the same objection urged against "rental value," — that
it might be understood to mean the value of one year's income,
or of one payment. "Capitalized income value" comes nearest
to fully describing the value indicated and the means of ob-
taining it.
The valuation of forest property differs from that of property
earning annual income only from the fact that the income may
occur at intervals separated by long periods. Hence the tend-
ency, expressed by the term "expectation value," to emphasize
this "expectation." As will be shown in Chapter V, the formulae
employed in the capitalization of annual and of intermittent
VALUATION OF ASSETS 4 1
income, such as is received from forest crops, are identical in
character, and it is more important to recognize this essential
similarity than to seek to dilTerentiate forest valuation from other
forms of appraisal. In the text, the synonymous terms "capital
value" and "expectation value" will be used interchangeably,
rather than the more cumbrous term "capitalized income
value."
63. Future Prices and Values. — The determination of
capital value rests upon the abihty of the appraiser: first, to
ascertain the amount and character of the income, its duration
and the total for the entire Hfe of the enterprise; and second,
to appraise the probable value of this income for the time when
it is received, by a conjecture as to prices for the future products
(Chapter XII). But the future is shrouded in uncertainty,
which becomes more impenetrable the longer the period over
which such predictions must extend. The past is an open
book. The knowledge thus obtained by experience is the guide
in the process of appraisal. It is comparatively easy to deter-
mine the probable productiveness of property for any business
which presents the results of past experience. In new and
untried ventures this is uncertain. But future prices are far
more of a problem, since they are the resultant of the complex
of all the economic forces of society. Attempts may be made to
predict changes in prices, due either to changing price levels
based on fluctuation of the value of money, or changes in the
supply and demand for the specific product. Such predictions
can only be based on present tendencies interpreted in the light
of past, especially recent, experience.
When rehable authority is lacking for prophesjing the prob-
able nature and amount of changes in prices, although they are
certain to occur, the appraiser is forced to accept present prices
as the basis for future income. This principle finds its expres-
sion in appraisals for damages, when speculative increase in
future income is not admitted in valuations.
64. Future Expenses. — The net present value of income is
equal to the margin over future expenses (§ lo). These future
probable expenses must be appraised as carefully as income.
42 FOREST VALUATION
Most elements of expense can be judged by past costs for similar
undertakings. Future expenses may and will vary from pres-
ent standards, for part of this expense is determined by prices,
part by wages and part by legislation and taxation. Uncer-
tainties regarding the trend of any of these elements of cost
interfere with the accuracy of the appraisal of value. A fruit-
ful source of uncertainty is future taxation. Legislation tending
to substitute a definite arrangement for this fluctuating item
is a great aid in appraising the value of forest property.
65. The Time Element in Capital Value. — When once the
future income and future expenses have been appraised, the
determination of the capital value of the property is a mathe-
matical calculation, dependent on the rate of interest chosen as
the basis of comparison between the present and the future
values involved. Each item of income is discounted for the
period of time intervening between the present moment and
the receipt of the income payment (§ii). The sum of these
values equals the amount of money which is equivalent in pres-
ent value to the expected future income. The property is there-
fore considered as having this value. For this " time difference "
in value the rate of interest is the measure. In the same way,
future expenses are discounted to get net value.
The greater the time interval between the present moment and
a future transaction, the less will be the importance of this trans-
action when discounted to determine its present money value.
The net capital value of property is practically determined by
events occurring within the next fifty years, not merely because
these events can be more accurately prophesied, but through the
operation of the factor of discount, based as it is on the laws of
compound interest. Not only are profits that are deferred for
fifty years of little significance to the investor (§41), but the
future values themselves are correspondingly small when viewed
from the present standpoint. The immediate future occupies
the minds of men and its relative importance is mathematically
expressed in discounting to obtain capital values.
66. Effect of Rate of Interest on Capital Value. — The rate
of interest is a barometer which measures the fluctuations that
VALUATION OF ASSETS 43
occur between the relative values of future and present income.
An increase in this rate, or measure, increases the dilTerence in
values due to this time element. The greater this difference, the
smaller will be all capital values. A permanent doubling of the
rates of interest would diminish the value of productive capital
to one-half its former worth. This premise is based on the eco-
nomic facts discussed in Articles 60 to 64, which refer value
directly to future income. High rates of interest indicate risk,
unsettled conditions and instability of character, and are thus
directly related to influences tending to depress property values.
Low rates of interest correspondingly raise the capital value of
property, by diminishing the loss or discount necessary in arriv-
ing at the present value of the future income.
67. Uncertainty of Capital Value. — The premise that value
is based wholly on future net income is sometimes questioned,
because of the uncertainty which surrounds every element of
future occurrence. The determination of value on this basis,
by mathematical deductions, is a guess, to the extent that these
future elements are subject to change. Yet every sale of prop-
erty is the result of a guessing contest as to these future ele-
ments, rather than a calculation of past costs. As two minds are
better than one and as the guess is made the basis of an actual
exchange of property, a sale as soon as it is efTected becomes a
new indicator or basis for the next guess. The uncertainty of
future values is identical in nature with other risks incurred in
business and adds the element of chance which becomes the basis
for practically all forms of speculation. The difference between
"legitimate" and "speculative" value lies merely in the degree
of uncertainty surrounding the future conditions upon which the
guess as to present value is based. The value of bonds fluctu-
ates but slightly and then only because of changes in the "rate of
interest," for the income is fixed and secure and the price or
value of the bond is easily calculated mathematically by use of
the desired rate of interest in discounting this income. By
contrast, the uncertainty and fluctuation in the value of indus-
trial stocks is due to a corresponding uncertainty regarding
future dividends.
44 FOREST VALUATION
68. Independence of Capital Value and Past Outlay or Cost.
— It is essential to thoroughly establish the idea of this inde-
pendence of capital or expectation value from all elements of
past cost. It cannot be said that past costs are without in-
fluence on value. In most cases they have been the direct means
of creating this value. This leads to the erroneous conclusion
that such costs are identical with value or are value. The
fallacy of this idea is easily shown. Cost is an individual outlay.
Value is the product of social conditions. Costs are undertaken
in order to obtain value and, when contrasted, are negative
where value is positive.
To illustrate: Two parcels of land are acquired and cleared
at an expense in each instance of $25 per acre. One tract
has such poor soil that it will raise nothing of value and cannot
be sold for $5 per acre. The other is suitable for truck gar-
dening and eventually sells for $500 per acre. Such variations
in value, entirely independent of cost, may be caused by differ-
ences in location or by the development of new crops or new
markets. All such fluctuations are due directly to the prospects
for future income.
The true relation between cost and value is that between a
means and an end. The cost is assumed for the purpose of
obtaining income and the value is derived from the prospect
of this income. If the outlay has been effectual in insuring
the future income the rise in value will follow. If the outlay
is ineffectual for any cause, chiefly through errors of judgment
or through incompetence, there will be no corresponding increase
in value. On the other hand, value will increase and decrease
from social and economic causes not even remotely associated
with the owner's outlay. For these reasons it must be accepted
that past cost or outlay, while it may furnish useful information
for the calculation of value, does not determine value.
69. Efifect of Capital Value on Sale Value. — Sale value
depends directly upon the demonstrated ability of property
to earn income. Whenever this earning capacity is uncer-
tain, especially if it appears probable that it may increase in the
future, sale values move in response to the guesses of those
VALUATION OF ASSETS 45
who exchange property, as to the probable future income.
Inflated ideas of future income, if commonly accepted, result in
inflated sale values, as instanced in real estate booms, high
values for western fruit lands and flurries in mining stocks.
Could sound, reliable information regarding the possible future
income from property be a matter of common knowledge,
inflation of values would become very difficult. Occasionally,
by rapid development of a region, values which at first seemed
high materialize by the assurance of income resulting from
this increase in population. More often the boom is overdone,
and sooner or later, values collapse to a level corresponding to
the measure of income possible. In every case the sale value is
a crude attempt at approximating capital value, and the disa-
greement between them is due to ignorance of the investing
public as to the true present value of the possible income.
70. Effect of Capital Value upon Appraised Value. — The
appraiser must therefore take into account the actual sources
of value in appraising property in order to check the- sale value
and detect any glaring discrepancies betw-een the reasonable
capital value of the net income and the price asked for the
property. If the owners of wood lots are selling their timber at
one-half to one- third of its real value, because they are ignorant
of both the quantity of standing timber they possess and the
current prices for stumpage, or if these current prices mani-
festly are so low that the purchaser is able to make a very large
profit, the appraiser can go back of sale values and determine
the value of such stumpage directly from income (§61). Where
no sale values exist, the determination of capital value is his
only recourse and is fully satisfactory.
71. Inflation of Capital Values. — Value thus depends upon
future income which may never materialize. On the chances
of obtaining this income, investors are willing to purchase prop-
erty at values computed by discounting these chances. The
rate of income earned on the past cost or invested capital of the
owner does not fix the price of the property. The amount and
value of this income are the determining factors. The price is
determined by discounting this value, using a rate of interest
46 FOREST VALUATION
which is satisfactory to both the purchaser and owner. Should
a business be sold which represents an investment of $50,000,
and earns a net income of $25,000 per year, or 50 per cent on
cost, the purchaser would probably be satisfied with 20 per cent
per year. The price wUl then be ~ , or $125,000, and the
former owner has exchanged his income of $25,000 for capital
on which he in turn must earn 20 per cent in order to be as well
off as before.
In the large operations of modern finance, especially in the
formation of trusts and transportation monopolies, it was con-
sidered that unlimited opportunities for future income would
be created by the control of prices and railroad rates. This
beUef was then capitaUzed on a generous scale. The final step
was to sell these securities to the pubHc, thus realizing, for the
original owners, the capitalized income which had not been
earned. This inflated income must now materialize or the
value of these investments will correspondingly diminish, as
has been the case with many such ventures in the recent past.
72. The Regulation of Capitalization. — It is possible to
prevent the fraud and burdens of over-capitalization by giving
to states or the national government the power of supervision
over such semi-public operations. Since income is the key to
capitalization, the exaction of extortionate rates or prices should
be checked. Capitalization may also be regulated to conform
to the reasonable requirements and to the true earning power
of the business. The effect of such regulation will cause dis-
proportionate differences between the capital value placed
upon a business and its actual cost, to shrink to reasonable
proportions, and the balance sheet to show a margin of profit
more in keeping with the best mterests of the public from whom
must come the income upon which these values rest.
73. The Problem of the Balance Sheet. — Accounting prac-
tice is based on an equation in which
goods or assets = Uabilities 4- proprietorship.
The left-hand member of this equation represents the tangible
and intangible assets, at book value, or whatever value is
VALUATION OF ASSETS 47
adopted as correct according to the conditions and principles
employed in determining such values. Accounts receivable
and debts owing to the business are part of the assets.
The right-hand member represents the capital paid in plus the
borrowed capital. Debts owed by the business and accounts
payable plus borrowed funds constitute the liabilities.
In balancing the equation, the "value" of assets is first
determined. The liabiUties are rigid, therefore the balance
represents the proprietorship. WTien this is originally expressed
as capital stock, an excess of value is shown as surplus, while a
deficit is carried to the left member to balance.
Changes in the status of the business, which are constantly
occurring, take one of two forms; a change in value of capital
resulting from net income or loss, or a change in said value
independent of such net income or loss. The cash for the pur-
chase of assets must come either from the proprietors as addi-
tional capital, or from surplus derived from income. On the
other hand, sales are mere exchanges, bringing in an equivalent
asset in cash.
It is evident, then, that the assets are increased only by
Additional capital invested by proprietors.
Net income, from
Excess of sale value over cost of assets. ,
Revenue from use of assets.
Appreciation in value of assets.
The last item is a potential income, which may or may not be
eventually realized. In the same way, assets are decreased by
Withdrawal of capital by proprietors.
Losses or destruction of assets not insured.
Dividends.
Expenses.
All items of current income or expense effect a corresponding
change in the net value of the capital, but as the balance sheet
is not usually made up oftener than once a year, these items are
carried in the profit and loss account, and only the surplus or
deficit entered in the balance sheet.
The commercial balance sheet attempts to show, first, the
48
FOREST VALUATION
status of the assets, and second, the relation existing, as a result
of this status, between assets and proprietors.
The problem of the balance sheet lies in the treatment of
potential income, and its effect on the value of the assets. As
long as the assets are entered at cost, and income appears only
after it has been actually received, no potential or unearned
profits appear in the balance. On this basis, the excess of
annual costs over annual income may be added to capital as
cost of assets, as is permitted in railroad construction (§57), and
by the government in computing the income tax (§ 162). Un-
earned interest on such costs would be excluded in a balance
sheet.
But if the assets are revalued, at "actual" value, based
perhaps on present increased sale value, but due entirely to
increased prospects of income capitalized as expectation value,
the alteration of the value of the assets, thus justified, indicates
an apparent profit to the owners exactly equalling this increase,
not yet realized nor available for the payment of dividends.
Not only does the balance sheet fail to distinguish between
actual and potential profits, but it entirely ignores the element
of time in indicating the relative value of the profits earned,
compared with the capital invested.
The fundamental relations exhibited in the balance sheet,
and its connection with the profit and loss account, may be set
forth in the following framework.
Balance Sheet
Assets Liabilities,
Proprietorship
+ - - +
Cash.
Capital assets in
form of goods
or property.
Deficit.
=
Capital paid in.
Borrowed capi-
tal or liabili-
ties.
Surplus.
The diagram corresponds to an equation in which the opposite
sides may show both plus and minus items. A minus item, by
transfer from one side to the other, becomes plus. The items
included in each subdivision represent a separate equation.
VALUATION OF ASSETS
49
CHANGES IN STATUS DURING YEAR
I. Capital Account
a. Deductions from Capital
I. Depreciation
+
—
-
+
Losses not cov-
Corresponding
ered by insur-
reduction in
ance.
value of pro-
Depreciation in
prietorship
value not off-
constituting
set by income
a loss of cap-
or deprecia-
ital or of sur-
tion fund.
plus.
2. Withdrawal of Capital
Withdrawal of
cash or other
assets by
transfer to
proprietors.
Cancellation,
or reduction
in value of
capital
stock.
These withdrawals may be induced by the sale of certain of
the capital assets, or by their depreciation in value. Instead of
creating a depreciation fund, the investment in a business may
be steadily reduced. This would be the course pursued in
lumbering, should it be found impossible to reinvest the income
in new timber stumpage or otherwise continue the operation.
The cancellation of bonds issued against standing timber must
keep pace with the cutting of this timber.
b. Additions to Capital
. Additional Investment
+
-f-
Purchase of ad-
ditional as-
sets.
Cash.
Additional capi-
tal paid in.
2.
Income
Net income
(gross income
Depreciation
minus annual
fund.
Increase of sur-
plus.
expenses, in-
=
terest and divi-
dends) trans-
ferred from
profit and loss
account.
50
FOREST VALUATION
3. Capitalized Expenses
Increase in book
value, i.e., in
cost of capital
assets already
owned.
Additional capi-
tal to meet
deficit caused
by excess of
expenses over
income.
This last transaction consists in marking up the capital assets
on the basis not of value, but of cost, to coincide with the addi-
tional capital advanced to meet annual expenses in absence of
revenue. Normally the deficit would appear as such in the
balance sheet and not in the capital account.
The appreciation in value of capital, or unrealized profits,
requires no corresponding investment, and should be distin-
guished from increase in cost by a separate account.
4. Appreciation of Assets
+ - - +■
Appreciation or
marking up of
value of capi-
tal assets.
Corresponding
increase in
proprietorship
representing
potential prof-
its.
II. Profit and Loss Account
This account records the cash outlay and income during the year, and
its balance, indicating a net income or deficit, is then transferred to the
capital account, and appears in the balance sheet.
+ - - +
4. Deprecia-
tion fund.
=
1. Cost of cap-
ital assets.
2. Annual ex-
penses.
3. Interest on
borrowed
Gross income, in-
cluding sale of
capital assets.
6. Additions to
surplus.
capital.
5. Dividends.
Item I represents cost of assets sold, and this amount is
credited to the capital asset account. Item 2 includes
the current expenses of operation including taxes. Item 3,
interest on borrowed capital is met before further disposition
of income is permitted. In item 4, the depreciation fund thus
VALUATION OF ASSETS
51
appropriated from income olTsets the loss from this source in the
capital account. Item 5, dividends are then appropriated, and
the remainder of the annual income (item 6) represents profits
remaining in the business.
A deficit, instead of a net income, occurs if the gross income
is insufficient to cancel the first three items. When a regular
annual provision is made for depreciation this may also cause
a deficit. In case this deficit occurs, it results either in dimin-
ishing the surplus, or the value of the proprietor's equity, or
else it is considered as a natural and legitimate cost to be added
to capital expenditure. This difference in the point of view-
coincides with the difference between enterprises yielding annual
income and investments on which income is naturally deferred
for longer periods.
The failure of the commercial balance sheet to fully inform
the investor as to the true economic status of his business, for
the reasons mentioned (page 48), suggests a supplementary
statement, in which the factor of time, and the increase in value
of assets due to future or potential income, may be expressed.
Such a statement is merely a prospectus or forecast, but will be
of great value if its true character is clearly explained. Its
principal use is found in connection with a business in which the
actual returns are deferred rather than annual.
III. Prospectus or Forecast
Debit
Credit
+
-
-
+
Expectation
Total cash in-
value of future
Future costs to
Past income.
Interest cred-
ited on past
vestment for
income, capi-
be subtracted
all purposes.
talized as val-
from income
=
Interest defer-
ue of assets.
previous to
red on cash
capitalization.
income.
investment.
Potential loss.
Potential profit.
To obtain this last balance, the cost of assets must be shifted
to the "credit" column, thus comparing cost with capitalized
or expectation value and revealing the potential profit by which
the true economic status of the business may be gauged.
The sources of confusion in the treatment of assets by
accountants are now revealed. Costs and value are diametri-
52 FOREST VALUATION
cally opposite in character, yet custom and the practical
necessities of commercial accounting compel a consolidation or
compromise between these elements, as a result of which the
valuation of assets is sometimes based on cost, with or without
" expenses," sometimes on capital value, and often on both
cost and value. Sprague* both sums up and explains this
practice by the statement: "The aspect of assets as the present
worth of future services (capitalized income)! is entirely based
on opinion, while the aspect which regards them (assets) as the
resultant of services (cost) is based upon facts."
It is evident that the proprietor is at liberty to compute his
potential profits by capitaHzing future net income on any basis
which he sees fit, and may charge against this value a cost on
which he adds the unearned interest on his capital. He may in
this manner satisfy himself as to his economic status, and deter-
mine whether to sell, buy, or continue to operate. But in public
accounts a limit must be placed both upon inclusion of costs
not actually incurred, and of profits not yet realized. Hence
the full and perfect expression of economic status is seldom per-
mitted or secured by the commercial balance sheet, and must
be left to supplementary calculations in the nature of forecasts.
In this economic comparison, the proprietary or right-hand
member of the ordinary balance sheet does not appear, and the
account deals entirely with the material assets. The balance
is struck between past costs, with interest, less past income,
and future value, discounted, less future expenses. Instead of
being upon the same side of the equation, necessitating an
arbitrary choice between absolutely opposite elements, the
equation lies between cost and value, and the balancing quantity
is the potential or unearned profit or loss, expressed as capitalized
or expectation value.
The incorporation of a portion of this potential profit into
the regular balance sheet, previous to actual sale of the business,
is an action dictated entirely by motives of expediency.
* " The Philosophy of Accounts," by Charles E. Sprague, 54 West 3 2d St., New
York, p. 41, Art. iii. Published by author (at above address). 1908.
t Material in parentheses inserted by author.
CHAPTER V
FORMULiE OF COMPOUND INTEREST
74. The Discount Factor. — The mathematical relation be-
tween present and future values is expressed by formulae. By
substituting the desired rate of interest in the formula the ratio
is found by which the one value may be converted into the other.
This ratio may be termed the "discount factor."
75. Rentals. — The term "rental" is used to denote a
definite sum recurring as income at regular intervals. The
interval may be of any length, even one hundred years, provided
the payment is assumed to recur periodically. Since income
to one person means outlay to another, the amount of an expense
occurring at regular periods is obtained by treating it as a rental.
The sum of the future values of a series of payments consti-
tuting a rental must frequently be determined, as well as the
discounted or present value of this sum.
The formuljE needed in valuation are those which will deter-
mine:
The future value of single sums.
The present value of future sums.
The future value of the sum of rentals.
The present value of the sum of future rentals.
The ratio between present and future values.
76. Future Value or Cost of Single Sums. —
V = value of capital or sum.
Vo = value at beginning of period.
F„ = value at end of period.
Vi, V-2. = value at end of years indicated by numeral.
n = period intervening before final reckoning.
P = rate of interest adopted.
-^ = CO/), interest expressed decimally.
lOO
53
54 FOREST VALUATION
The expression o.op is an arithmetical term, in which the letter
p is substituted for the numeral representing the rate of interest.
For a given rate, as 4 per cent, the expression reads 0.04; for 10
per cent, it reads o.io.
o.op is the ratio between capital and interest for one year.
Therefore i + o.op, or i.op, is the ratio between the capital at
the beginning and end of the year, assuming that the interest is
added to the principal.
Fi : Fo : : i.o^ : i.
Fi = Fo X i.o^.
At the end of the second year
F2 : Fi : : i.op : 1.
F2 =Fi X I.op
= (Fo X I.op) I.op
= Fo X i.op\
¥3= {VoXi-op^)i.op
= Fo X i.op^
and F„= (FoX i.o/>"-i) i.oi?
= Fo X i.c/?". (I)
This formula is used to determine the accumulation of cost on
an investment which does not produce income until the close of
a stated period. In such a cost account (§§ 25 and 36) all in-
vestments are charged with interest. Sums representing expend-
itures which occur only once and cannot be treated as rentals,
as, for instance, the cost of planting trees, are totalled for n
years by this means.
All formulae dealing with future values of present sums show
also the present cost of past expenditures. They reckon forward
from beginning to end of an investment.
77. Present, Expectation, or Capital Value of Future Sums. —
In computing future sums, the value at a future period has no
special significance until it is discounted to the present.
If F„ = Fo X i.op^
then ^o = -^„- (11)
I.op"
FORMULAE OF COMPOUND INTEREST 5$
The arithmetical equivalent of — - may be expressed as a
decimal.
Discount formulas are used in valuation of assets. The
discounting of future "profits" or net income is identical with
the determination of capital value. There can be no value in
excess of this discounted net income (§ 62).
To obtain this net present value, future costs may be first
discounted and then subtracted from discounted gross income.
Or this subtraction may be made at any future period and the
net income discounted. If the values arc properly computed
to the same year, before striking the balance, the discounted
results are identical. For instance, an expense c occurs in the
year d, which lies between the years o and n.
The present value or equivalent of c will be •
The future equivalent of c at the end of the year « will be
c X I •o/?""'^, since ft — d is the period over which interest on c
would accumulate.
The present equivalent of c X i .op"''' will be
c X i.op"''^ __ c X i.o/?" _ c
I. op" ~~ i.op"^'' ~ 1.0/
Hence, to determine the net present value of future income,
future expenses may be computed fonvard to the year in which
the income is received, and subtracted from this income, and the
resultant net income discounted to the present. This accom-
plishes the same purpose as discounting each item of expense
to the present before subtracting it from gross income. The
choice of these methods is merely a matter of convenience.
78. Use of Logarithms and Tables. — The arithmetical
equivalents of these fomiulae are calculated by the use of loga-
rithms. The numeral representing the desired rate of interest
is substituted for p, and the number of years in the period for
n. For 4 per cent and 50 years, i.op" becomes 1.04^°. The
logarithm of i .04 is multiplied by 50. The result is the logarithm
of 1.04^, from which the ratio is obtained. In the case cited,
the ratio is 7.1067, which indicates that $1.00 will increase in
56 FOREST VALUATION
value to $7.1067 if placed at compound interest at 4 per cent for
fifty years.
The value of all other formulae are derived from the expression
1 .0/)". The values for discount, , are obtained by reducing
the fraction to a decimal. In the above case, gives a
7.1067
discount factor of 0.1407, which means that $1.00 payable in
fifty years has a present value, at 4 per cent, of $0.1407.
These values may be expressed in tables, which make such
calculations unnecessary. (Table VI, appendix.)
79. Future Value of Temporary Annual Rentals. — The
future value, or cost, of a rental continuing for a temporary
period represented by n annual payments, equals the sum of
all these items plus interest upon each from the date of pay-
ment to the end of the year n.
The payments are regarded as occurring in each instance at
the end of the year, although they might be made during the
year. The final pa^nnent thus incurs no interest charge.
Let r = annual rental.
Then, final rental for year n = r.
Rental for year n — 1, in year n = r X i.op.
Rental for « — 2, in year « = r X i.op'^.
Rental for first year, in year n = r X i.o/?""^
These terms form an increasing series showing a geometrical
progression. The ratio of increase or multiple is the factor i.op.
The sum of these terms gives the total value or expense of the
rental at the end of the period. The calculation of these separate
values is unnecessary. The sum may be obtained by formula.
Let Vr = total value of rental.
(i) Vr=r + r(i.op)-\-rii.op-)-\-r(i.op^) -\-' • • +r(i.o^"-i).
Multiply the equation by the ratio i.op.
(2) Vr (i.op) = r (i.op) +r {i.op^) -\-r (i.op^) -\- ' • •+ rCi.o/?").
Subtract (i) from (2).
Vr (i.op) - Vr= r (i.op") - r,
Vr (i.op — i) = r (i.op" — i),
^,^_^.(i.o/>"-i)
I.O^ — I
FORMULA OF COMPOUND INTEREST 57
Since i.op — i = 0.0 p,
V, = '±^e^^A (III)
o.op
= -^(i.op" - l).
o.op
Outlay lor tire protection or sums paid annually for adminis-
tration serve as examples of annual rentals. As income we may
have receipts from grazing or hunting privileges. The above
formula holds good only during the period that such rentals
remain equal in amount and value as is the case with actual
rent. Should they fluctuate annually, each item must be sep-
arately computed.
If rentals remain the same for a period and then rise or fall
to a different level for a second period, the above formula is
used to compute the total to the end of the first period. This
value then bears interest for the remaining period as a definite
sum (I), and the value of the new rental n for this second
period is computed in the same manner as before and added to
the total. For two periods termed a and 6 this reads:
,,.^^|Hi.o^--i)j r.(..o^>-,)
( O.op ) o.op
80. Formulae for Geometric Series. — In the series whose sum
is obtained by Formula III, the ratio i.op is greater than i,
which gives an increasing series.
Let g = first term of series.
q = ratio or multiple (such as i.o/>).
Q = sum of series.
Then, by demonstration above (III),
Q=^f^- (QO
The sum of future values of rentals forms such a series.
Should the ratio be less than i, each succeeding term will be
diminished in value, which gives a decreasing series.
The sum of this series is obtained by the same formula, but
a more convenient form of expression, obtained by multiplying
both numerator and denominator by — i , is
58 FOREST VALUATION
The sum of present or discounted values of rentals forms such
a descending series.
These formulae apply either to temporary rentals, with a
limited number of terms, or to perpetual rentals, with an infinite
number of terms.
For an infinite increasing series
Q = ^ ^^°°_~ '-* = 00 (infinity). (Q3)
For an infinite decreasing series, since the value of ^" dimin-
ishes in direct proportion to the exponent used,
g°° = o.
Therefore
Q=^-^^-^^ = -l~. (Q,)
I -q I -q
81. Present, Expectation, or Capital Value of Temporary
Annual Rentals. — Let R = present, expectation, or capital
value of the sum of a rental.
Should each rental be discounted to the present by Formula
I, the sum of the resulting terms is
R=—. + ^^ + ^.+ ---+-^.-
i.op \.op^ i.op^ I.O/>"
Applying Formula Q2 for the summation of decreasing
temporary rentals,
r
g = ,
^ i.op
I
q = >
R=^^
i.op\ I .op"/
I —
I.op
Multiplying numerator and denominator by i.op X i.o/)",
ji r{i.op"-i)
{i.op — i) i.o/>"
^r(i.or-i)^ (IV)
o.op X i.o/>"
FORMUL.^2 OF COMPOUND INTEREST 59
The same result may be obtained by discounting the final
future value of the sum of these rentals to the present (II).
This future value Vr = dL^^lZLii.
o.op
Hence r(i.o/>" - i) i ^ y(i.o/>" - i)
o.op i.op" o.op X i.o/>"
Since capital value is the net value of income discounted to
the present, the application of this formula is evident. It may
be used to discount either annual income or annual expenses.
Should the two occur simultaneously, only the net annual
profit or loss is thus discounted.
82. Future Value of Temporary Intermittent Rentals Due
First at n Years, and f Times at Intervals of n Years There-
after. — A rental which occurs at intervals greater than one
year is termed intermittent, although if the interval is regular
it does not differ in character but only in degree from annual
or monthly rentals.
Let n = period between rentals.
t = number of pa^^ments expected.
nt = total period covered by the investment.
/ = intermittent rentals due at intervals of n years.
Vr = total value of intermittent rentals at end of period.
The future value of the sum of these rentals, if computed in
the year of pa>Tnent of the final rental, is
Final payment = r',
Pa>Tnent, n years preceding = / (i.o/>"),
Payment, 2 ?i years preceding = r' {i.op^"),
First payment = / (i.o/>('-^>").
By use of Formula Qi, the sum of these terms is found by
substituting the ratio i .op" for q and the factor t for n.
The formula then reads:
i.op" - I
Either income or expenses which terminate at a definite
date are far more apt to occur annually than at longer intervals
6o FOREST VALUATION
(III and IV), and if intermittent and terminating, such as a
succession of thinnings from a crop of timber previous to final
cutting, they are also apt to be of different values, requiring
separate valuation. If assumed to be equal in value, they may
usually be assumed to recur perpetually (IX).
83. Present, Expectation, or Capital Value of Temporary Inter-
mittent Rentals, Due First at u Years, and t Times at Intervals
of n Years Thereafter. — The present, expectation, or capital
value of intermittent rentals limited in number is found as
in the case of annual rentals.
The series decreases.
For rentals due first after n years and / times at intervals of
n years thereafter, this series is
/ / / /
I.O^" I.O/>^" LOp"^" I. Op'
Then (Q2),
Q =
I .op"
I
i.op"
r
I —
I.O/?"\ I.O/>^
I.O/>"
Multiplying numerator and denominator by i.op" X i.o/>"',
(l.O/)" - l) I.O/>"' ^ '
The same result is obtained by discounting the future value
of the series (V) to the present (II) using the factor ~ as
the substitute for
I. op"
^ ^ r'd.op"' - i) ^ I ^ /(i.o/>"'-i)
I. op" — I I.O/>"' (i.o/>" — l) I. op"'
84. Future Value of Temporary Intermittent Rentals, Due
First in a Years, and t Times at Intervals of n Years There-
after. — When the value of the sum of temporary rentals is
FORMULA OF COMPOUND INTEREST 6l
determined for the date of the final payment, falling in the
year nt, the interval elapsing subsequent to this payment is
zero. When this payment falls at some previous date, a, the
total value at that date accumulates interest during the remain-
ing period. This period is equal to » — a years.
The series forming the sum of the rentals is
Vr = / {i.op"-") + / {i.op-"-") • • • + / (i.c/)'"-").
By use of Formula Qi, substituting the ratio i.op" for q, and
the factor / for n, this becomes
/(i.or--i)i.o/>-^ (VII)
I.op" - I ^ ^
By multiplying Formula V by i.op"'" (see Formula I), the
same result is obtained.
85. Present, Expectation, or Capital Value of Temporary
Intermittent Rentals, Due First in a Years, and t Times at
Intervals of it Years Thereafter. — The present value of the
first payment, due in a years, is (II). The period a may be
I.op"
of any length and may exceed n. The present value of subse-
quent payments diminishes by the constant ratio , form-
ing the series
*' »' -' J
■p __ ' _| ' I ' [
T ,-^y^<^ t rs/iO+n t /^Aa+2 n '
I.op" I.Op"^" I.Op"'^'-" LO^^+C"^)"
To obtain the sum of present values (Q2),
g =
I.op"
9 =
I
I.op"
Q =
/
I.op"
I.op" \
I
I.op'
\
~7
I —
--r'ii.op-
I
I.op"
62 FOREST VALUATION
Multiplying numerator and denominator by i.o/>" X i.o/>"',
^^/(i.or-.)i.or-. (VIII)
This formula is also derived from Formula VII by discounting
the final value to the present (II), substituting ■ for
i.o/>"' i.op"
Formulae V to VIII are seldom used in forest valuation
(§82).
86. Present, Expectation, or Capital Value of Perpetual
Rentals. — Under the assumption that a rental is perpetual
(§ 80) , the intermittent rental r, payable every n years, forever
will have a future value equal to infinity (00).
Its present value (Q4) is
/
Q =
I.O/J"
I
I. op"'
Q = ^^
I —
R = . (IX)
If the first rental is paid in the year a instead of at n years,
as in case of revenue from thinnings, the present value of the
sum of a perpetual series due every n years thereafter (Q4) is
s -
I. op"'
q =
I
I. op"
r'
Q =
I.O/>«
I
\.op"
R =
/(i.o/>"-«)
I. op" - I
(X)
FORMUL.E OF COMPOUND INTEREST 63
But should the period of discount lie between the year a and
the final year «, when the crop is harvested, as it does when
the value of growing timber is computed at a years, this formula
(Q4) is
r'
s
=
I
.Op"-"'
I
I
.Op"'
r'
Q
I. op"-"
T
I
i.op"
I.op" - I
When the first rental is due in the present year, the series
becomes
••' -' f
I.op" I.op-" I.op"
Q =
r
I —
I.op"
j^^i:u^p±. (XI)
I.op" — I
By separating the first payment from the series, the remaining
terms equal (see IX) , and the sum is
^ I.op" - I ^ ^'
i? = /+ . (XIa)
I.op" - I ^
An annual rental, payable perpetually, has a present, expecta-
tion, or capital value (Q4) of
64 FOREST VALUATION
^ I
I —
i.op
r
R =
I.op — I
= -^. (XII)
o.op
Formulae IX to XII are of great importance in forest valuation.
The conception that a rental may be perpetual is difficult to
grasp. But this is merely another way of stating that the prop-
erty producing the rental does not depreciate in value. Grant-
ing this premise, the receipt of income for any given period
leaves the property capable of yielding another return of equal
value. Since this assumption can be extended indefinitely, the
expected income may be regarded as perpetual.
Formula XII is customarily used to determine the money
capital which will produce an annual income of r. If we assume
that money remains of the same value, and nothing occurs to
impair the integrity of the capital, it can be imagined that
this income is perpetual. In the case of land whose fertility is
maintained by proper methods, so that the net income does
not represent a drain of capital, or soil depreciation, the same
conditions are true, and the capital value of the soil may be
found by use of Formula XII.
This premise will hold for forest lands producing crops at
long intervals. The trees maintain the productiveness of the
soil. In this case, the net income, being intermittent, is cap-
italized by Formula IX.
For practically all other forms of investment, revenue is
apt to be accompanied by depreciation of capital, which causes
the income to diminish and finally terminate, thus requiring,
instead of the simple formulae just quoted, the use of the formulae
IV, VI or VIII for the present value of temporary rentals.
r' r
These values are less than those obtamed by or
I.op" — I o.op
FORMULAE OF COMPOUND INTEREST 65
and the erroneous use of these latter formulie leads to over-
valuation of assets.
87. Relation Between Future Value of Temporary Annual
Rentals and Present, or Capital, Value of Same. — In the
formula for future value of temporary annual rentals, expressed
as (i.o/?"— I ) (§79), the portion -represents the capital
o.op 0.0/?
value of a perpetual annual rental (XII), or the capital which
will produce an annual income of r. This formula might be
expressed {i.op") •
o.op o.op
Substituting R for >
R = capital value of annual rental r.
Then -^ (i.op") — ^ RX i.op" - R
o.op o.op
= Rii.op'^ - i). (Illb)
This expression gives the sum of the compound interest, or
deferred income, earned by the capital R in n years, and is
obtained by computing the value of i? at w years at p per cent,
and then subtracting the original capital.
The numeral i substituted for R indicates that at any future
period the original capital remains intact. Since the sum of
the future values of an annual rental is thus shown to equal
the compound interest or income on its capitalized value, the
formula R (i.op" — i) may be used to compute the total cost
not only of annual rentals, but of interest on invested capital
whenever the capital so invested remains intact at the end of
the period, as is the case with land.
88. Conversion of Intermittent into Annual Rentals. — To
convert an intermittent rental occurring every n years into its
equivalent annual rental, it is incorrect to divide the amount
of the intermittent rental by the factor n. The intermittent
rental is not received until 11 years from date, while the annual
rental is received in installments over the entire period, which
makes the average period of deferred pa>Tnent less than half
as long.
66 FOREST VALUATION
r'
The capital value of an intermittent rental is and
^ i.o/>" - I
of an annual rental . Since the annual income for each is
o.op
required to be equal, these expressions must have the same value.
If =-^'
i.o/>" — I o.op
J
then r = X o.o^. (XIII)
i.o/>" — I
The annual rental equivalent to an intermittent rental falling
due first at an interval shorter or longer than n is found in
the same way by multiplying the capital values given in for-
mulae XI and XII respectively by o.op. The results show that
notwithstanding the fact that the intermittent rentals are
equal in amount and paid at equal intervals, the capital value,
and its equivalent in permanent annual income, constantly rises
until one of the intermittent payments is received, which at
once diminishes this capital value by the exact amount of the
payment. If exchanged for an annuity at this time, the per-
manent income thus secured is the lowest for any portion of
the period, while a similar exchange effected just previous to
receipt of intermittent income secures the maximum annual
revenue.
89. The Ratio of Income or Earnings. — The "rate of inter-
est," p per cent, is accepted as a fixed standard in computing
cost (I); or in discounting for value (II). But when both cost,
or investment, and income are known, the ratio of this income
to cost represents the earnings of the capital invested, or divi-
dends. A rate of interest can be found by which the discounted
value of income is made to exactly equal cost, or the accumu-
lated costs to just balance income. This rate is the per cent
earned by the investment.
To distinguish this rate from the "rate of mterest" p, the
term x will be used.
X = per cent representing income earned.
FORMULA OF COMPOUND INTEREST 67
Then i.ox" =
I .OX = I + o.oa:,
+ o.o:c =\/t7"'
o.o.v- = vf"-i'
(i/g-)
x = ioo(^Vfr-ij. (XIV)
The rate x enables the owner to compare the earning power
of his investment with enterprises which produce annual divi-
dends (Chapter VIII).
Instead of solving the above equation, the value of x may be
found by inspection of Table VI. The value of i.oo;" is calcu-
lated, and the nearest equivalent figures must be found opposite
w years in the table. By interpolation, x may then be found to
within one-tenth of i per cent.
CHAPTER VI
INVESTMENTS AND COSTS IN FOREST PRODUCTION
90. The Business of Forest Production versus Lumbering. —
Lumbering is a term applied to that portion of the business
of forest utilization which begins with the removal of the forest
products from the soil and is completed when the wood is
placed upon the market as lumber, ties, shingles or other products.
The stage dealing with the felling and transportation of the raw
product to place of manufacture is termed "logging," while the
manufacture itself is spoken of as "milling."
Forest production is a separate undertaking, which precedes
lumbering, and deals entirely with the growing of forest crops,
principally wood products. Until recently, the raw material
on which the enormous investments in logging and milling are
dependent, was drawn entirely from virgin stands grown with-
out human aid or expense. Ultimately, forest production must
rank in importance with lumbering, for under modern condi-
tions, forests will seldom renew themselves unaided. The only
large and complete organization of forest production as a business
in this country at present is found in the administration of the
national forests. The operations of certain states are gradually
taking on a systematic form. But, as a whole, the productive
side in the management of private timberlands has not yet
been organized into a systematic effort, and takes the form of
tentative or experimental measures, completely overshadowed
by the operations of lumbering.
Logging and milling are indispensable adjuncts to production,
but without it they are self-destructive. These three operations
complete the chain of effort by which the income from forestry
is finally secured. Owners of large tracts of timber usually
undertake to log them in order to produce income from their
holdings, and professional lumbermen prefer to own their stump-
68
INTESTMEXTS AND COSTS IN FOREST I'RODUCTIOX 69
age. When stumpage is owned, logged and manufactured by the
same person or coq^oration, both costs and net profits are based
on the total operation. Frequently an owner of stumpage will
contract the logging and do his own milling. Both logging and
milling may be contracted, the owner receiving the linal net
revenue from sale of lumber. Or, the owner may sell his
stumpage, permitting the logger and mill man to make what
profit they can. On the books of a firm operating with their
ovm. stumpage, a technical separation of costs is made between
stumpage, logging and manufacture. The total profits as well
should theoretically be distributed between these three depart-
ments, but for practical purposes this is unnecessary. Where
desired, the "value" of stumpage is charged as a cost against
logging. By increasing this value, logging costs are advanced
in the same proportion, and the profits disappear into stumpage
values, without in any way altering their amount or character."
But should stumpage be owned separately, and its sale constitute
a transaction taking place between different firms, the costs and
profits arising from sale of stumpage are actual.
Forest production as a separate business, or even as a separate
department of the general business of lumbering, is completed
with the sale of the timber or products on the stump. This
separation from lumbering is illustrated by the operations of
the United States Forest Service, which performs no part of
the logging or manufacturing.
WTien an owner of forest property finds it necessary to engage
in logging and manufacturing, he should separate the costs
and profits of these enterprises from the profits on growing or
holding his timber. Often the owner is in position to log his
own timber. Th*is may result in securing a combined or total
profit far in excess of the receipts obtainable from sale of stump-
age. In general, lumbering, to pay as an enterprise, requires
large tracts and a supply of timber which will last for a reason-
able period, and the owners of small tracts must either sell
their timber on the stump or contract for its manufacture.
91. Proprietary Accounts in Forestry. — Proprietary accounts,
showing the amount of capital invested, and the income and
70 FOREST VALUATION
outlay, or profit and loss in the business of forest production, will
deal with the operations of the owner as a unit, and not with the
stand. If such accounts are kept according to the customary
forms, only actual cash outlay or income can be recorded.
The expenditures might be separated into capital account for
such items as land, and profit and loss for wages, taxes and
other current expenses.
Unfortunately, both for the accountant and the proprietor,
such a business may fail to pay dividends for an extended period.
Whether it does so or not depends upon the condition of the
forest, for if the timber is already produced or grown, the income
is within reach. With a young forest, or plantation, additional
capital is required to cover every item of annual outlay in excess
of income. Since no dividends are produced, interest on bor-
rowed capital increases at a compound rate, actually when this
interest is also borrowed and paid, or by analogy, when its pay-
ment is merely deferred.
Unless this condition is foreseen, and the enterprise floated
without borrowing, or the loan is negotiated on the basis of
deferred instead of annual interest, which is not customary, the
proprietor must pay this interest or bankruptcy ensues. No
existing custom of book-keeping will permit the charging of
unearned interest as a cost or actual expenditure, unless it is
paid out as above indicated. Hence, in the absence of borrowed
funds, the accumulating "costs" represented by deferred in-
terest (§ 36) are not shown on the books.
For a forest investment, representing, as it usually does,
timber in all stages of growth, some capable of yielding income
at once, while other portions require outlay for many years, it
will be necessary to keep a proprietary account in the usual
form, omitting the item of deferred interest on the owner's
capital. Such an account will eventually show net profits,
regarding interest as income (§37), but it will not reveal actual
"cost," nor the profits of the undertaking (§39) or enterpriser's
gain.
92. Cost Accounts in Forestry. — A serious defect in such
proprietary accounts is that the value of the element of time is
INVESTMENTS AND COSTS IN FOREST PRODUCTION 7 1
wholly neglected (§11) and profits received after many years are
shown in amount only, as though of equal value with profits
of the year. In contrast, cost accounts (§ 25) seek to eliminate
such inconsistencies and express costs in their true economic
relation to income. This is accomplished by the adoption of a
rate of interest (§§ 52 and 53) by which all expenditures are cal-
culated forward to the year when the income, for which the cost
was incurred, is" finally received (§ 23). In practice, a separate
cost account could be kept for each stand, lot or subdivision.
The summary or total to a given date (the present) of these
accounts would reveal to the proprietor his exact investment,
including the "unearned" interest. This summary should differ
from the corresponding items in the proprietary account by just
the amount of this interest.
93. Investments, or Permanent Outlay. — Expenditures for
property of a durable character in forestry are confined to land
and to permanent roads, houses, telephones or other improve-
ments. The original cost of these may be considered a capital
expenditure.
94. Expenses, or Temporary Outlay in Forestry. — Temporary
or current expenses would ordinarily include raw materials as
well as items like wages (§21). But when wages are expended
on planting trees and when the raw material consists of stand-
ing timber, which will remain as property for a period of years,
this treatment is open to question. After the forest property
has passed through its initial stage of construction, and is pro-
ducing annual revenue, many items, such as reforestation, which
at first call for an initial investment, can be regarded as current
outlay. In this class will fall all expenses for upkeep of im-
provements.
95. Land. — Land is the one investment which can be credited
as capital not ordinarily subject to depreciation, and indispen-
sable to forestry. It remains after the timber is harvested.
The purchase price of land is the only land value which can
legitimately be entered in the cost account, and this valuation
can remain the same as long as the owner retains the land for
forest production. A sale of the property, terminating the
72 FOREST VALUATION
ownership and cost account, calls for a revaluation of land (§§ 6i
and 62).
Bare land suitable only for forest crops does not command
a high price (§ 96) .
96. Standing Timber. — By definition, real estate comprises
land and all that stands thereon. A purchaser of land acquires
all permanent improvements. These improvements may be
sold separately, but always with the stipulation that they are
to be removed within a given time.
Standing timber is part of the real estate, and a purchase of
land includes the timber, unless excepted by the owner subject
to removal by him. Timber stumpage is sold by the owner on
contract which allows the purchaser a definite time for removal,
failing in which, the purchaser, in certain states,* loses his right
to the timber. These timber rights sometimes run for periods
of twenty years and while in force constitute a lien on the
property.
By the time a crop of timber is large enough to cut, its value
greatly exceeds that of the land. Virgin timber, containing ma-
terial of high quality, shows a still greater excess of value (§ 184).
In the past, lumbermen were quite indifferent to land values,
regarding the title as desirable only because it made them inde-
pendent of restrictions as to time and rate of cutting. What
they purchased was the timber. Yet timber, whether young or
old, is a "vanishing" asset. It must be converted eventually
into income, and is subject to losses. Owing to the difficulty,
in some cases, of distinguishing between the value of the land
and of the timber, and the great preponderance of the latter
value, the cost of standing timber is usually regarded as a cap-
ital expenditure. Bonds may be issued, with this standing
timber as security, provision being made to retire these bonds at
a rate to more than keep pace with the cutting of the timber.
Such bonds are in this sense paid out of "capital," as this "capi-
tal" is converted into income. Bonds could not be floated on
timber which was not about to be, or in process of being, cut.
* This subject has caused extensive litigation, and has resulted in conflicting
practice. State supreme court decisions must be ascertained in each locality.
INVESTMENTS AND COSTS IN FOREST PRODUCTION 73
97. Permanent Improvements and Equipment. — On any prop-
erty managed exclusively lor forest protluclion, and of suflicient
size to demand continuous care and administration, buildings
must be provided for the permanent force, both officers and
laborers, especially since these tracts are not often conveniently
near towns. Special telephone construction is often required.
These are legitimately classed as capital expenditures. Stables,
draft animals and tools come in this category, but proper allow-
ance for depreciation must be made.
In cost accounts for individual stands, it is proper to dis-
tribute these overhead charges over the entire territory which
they cover, pro-rating them on a per acre basis. The initial
cost for these items may be included with the cost of land and
timber. The annual charge for upkeep, or its equivalent in
depreciation, must be entered as a current annual expense on
the same acreage basis.
98. Roads and Transportation Systems. — Lack of perma-
nent roads or other means of transportation is characteristic of
American forest conditions. To }'ield a steady income, a forest
must produce wood annually for market, which requires the
transportation system to be in continual repair.
In inaccessible regions, timber must exist in sufficiently large
bodies to justify construction of a system of transportation for
its removal. The cost of transportation contains two elements:
first, cost of construction; second, cost of transport. Con-
struction cost, no matter how cheapened, cannot be reduced
below a certain limit. Cost of transport is lessened by improv-
ing the means of transportation. WTien railroads, roads or
flumes are built for merely temporary use, the entire cost of
construction, as well as transport, falls on the timber removed
at the time, and is pro-rated for each unit of product as, for
instance, per thousand feet of lumber.
Since transportation is a feature belonging strictly to logging,
it affects forest production through its influence on the value of
stumpage. It is the universal practice in America to allow the
cost of construction, as well as transport, to fall upon the logger,
who takes it out of the price of stimipage.
74 FOREST VALUATION
In permanent forest property, this construction cost may be
assumed by the forest owner, whether or not he intends to do the
logging. This is necessary in order to permit of the radical
change in logging from the removal of practically the entire
crop at one time to the system of continuous removal of smaller
quantities over the entire area. Under the latter system, no
logging contractor could afford to construct his own transpor-
tation facihties.
Such permanent systems are a capital expenditure similar
in character to land, and the overhead costs thus incurred
should be pro-rated by area and charged as an addition to the
cost of acquiring the property. The maintenance of transpor-
tation systems is an annual expense to be pro-rated in the same
way. The owner's benefit from thus assuming costs belonging
to logging is obtained by appropriating a larger share of the
general profits through increased value of stumpage.
99. Silvicultural Operations. — All labor expended directly
upon the forest crop constitutes a charge against the particular
area or stand which is benefited. Such costs include planting,
with the cost of the plants; weeding or removal of injurious
"weed" trees or brush when the plantation is young; protection
from insects by measures requiring expenditure of labor on the
area; and thinning, provided this is done at a cost exceeding
the value of the product obtained. Costs incurred in natural
reproduction, by leaving a portion of the stand to serve as seed
trees, correspond to the cost of planting and should be charged
against the new crop. Practically all silvicultural expenses
occur as single or initial costs, and not as annual expenses, when
reckoned in cost accounts for the stand. In a forest under
perfect management, costs of most of these operations consti-
tute a nearly constant annual expense for the forest as a whole,
and would so appear in the proprietary account.
100. Protection Expenses. — Initial expenses for protection
from fire take the form of measures for disposal of slash left from
logging. This expense is chargeable to the cost of the new
crop and may be so treated in a cost account. But in practice,
where the owner is not doing his own logging, as in the United
INVESTMENTS AND COSTS IN FOREST PRODUCTION 75
States Forest Service operations, this cost is transferred wholly
or in part to the logger, and taken out of the price of stumpage.
By this means, the true nature of the expense is concealed.
The loss in stumpage value is a present cost or investment in the
new crop as surely as if the owner received full value for the tim-
ber and re-expended the amount required for brush burning.
This initial cost, then, accumulates interest until the new crop
is cut (§ 107). For this reason, it has been advocated as an
alternative, that a sum representing merely the annual interest
on this initial expense could be expended annually on the area
to secure better protection from fire, without increasing the
total outlay.
Fire lines will frequently be necessary, particularly where a
bad hazard occurs and where an investment has been made in
plantations. This constitutes a capital expenditure, especially
where the initial cost of the Hues greatly exceeds their subse-
quent cost of maintenance. The charge must be pro-rated
over the area benefited, dated from the year it waS incurred.
Subsequent maintenance of these lines, a necessity often lost
sight of, is an annual charge per acre.
Lookout towers and installation of telephones used in fire
protection are of the same class of expenditure as fire lines.
The labor employed in fire protection for patrol constitutes
an annual charge.
Extra costs of extinguishing fire, if borne by the owners, con-
stitute losses, entered against the area burned, and recoverable
in some cases as damages.
101. Administrative Expenses. — With a large area and
well-developed system of forest production, the administration
of the tract involves not only all business matters dealing with
sale of products, taxes, protection and silviculture, but includes
as well the proper technical direction of the work to assure
the success of the measures for forest production which are
the basis of the business. The salary of a technical forester is,
therefore, a necessity, and this must be pro-rated on an area
basis. Should the tract be too small to justify such expense,
the owner must seek occasional technical advice and trust the
76 FOREST VALUATION
management to a foreman who can follow directions. Such
advice is best obtained, for very small areas, through the State
forester. For larger areas it is practicable for several owners
to co-operate and employ a forester.
102. Taxes and Insurance. — Taxes are separately discussed
in Chapter X. Under present systems of taxation they tend to
increase and this, coupled with the uncertainty as to the amount
and time of these increases, makes it difficult to predict the total
cost of this item or prescribe the exact method of calculating
it. In this chapter, taxes will be assumed as a fixed annual
expense, to be added to that for administration and protection.
Insurance is not as yet available in this country on growing or
standing timber. The owner bears his own risk and losses.
103. Interest Charges. — These do not appear in proprietary
accounts except when money is borrowed (§91). In cost ac-
counts, past interest may at any time be calculated at whatever
rate is considered equitable. Since the periods intervening be-
tween outlay and income may extend to over 100 years, the
interest charges will often be found to far exceed the sum of all
actual expenditures.
104. Classification of Costs in Forest Production. — Follow-
ing the suggestions in the above analysis of costs, the invest-
ments in forest production may be grouped, for computation,
into three classes:
Group A .
Capital expenditures for
Land.
Permanent improvements and equipment.
Permanent roads and firelines.
Group B.
Crop expenses for
Standing timber, which is often included with cost of land.
Planting or cost of regeneration.
Brush disposal or initial fire protection.
Weeding.
Protective operations.
Thinning.
INVESTMENTS AND COSTS IN FOREST PRODUCTION 77
Group C.
Annual or current expenses for
Protection.
Administration.
Taxes,
^laintenance of permanent improvements.
105. Calculation of Total or Final Costs. — To compute the
total final cost, with interest included, at the end of a given
period, the items under each of these three classes may be
totalled.
The "cost" of each is the amount which should be charged
against the resulting income, which in forestry is the stumpage
value of the timber plus the revenue from other sources.
In Group] A, the original capital, if maintained properly, re-
mains intact at the end, and only the interest can be charged as
an expense to the crop. Let S, = cost of soil and permanent
improvements. Then total cost is
5,(i.or)-5,. (§87, Illb)
In Group B, only those crop expenses which occur in the same
year may be computed as one total. These expenses must
eventually be met entirely from income and do not constitute
capital expenditures. With the cutting of the timber, no por-
tion of the remaining assets are available from which to return
these costs.
. The total cost of all such items is found by Formula I in which
C = initial investment,
C (i.o/>") = cost at end of period.
Expenses incurred in year d will cost
Cii.op"-").
Let Co, Cd,Ce,Cf = Initial expenses incurred in the beginning
and in the years d, e and /. The sum of these costs is
Co (i.o/>") -\- C, (i.o/>"-<^) + Ce (i.c^-O + C/ (Lop^-O.
In Group C, all annual expenses are totalled. The sum of this
expense with interest is found by Formula Illb (§ 87).
Substitute e for r to represent annual expense.
78 FOREST VALUATION
Then = R = E, capitalized annual expense.
The sum of these expenses, provided they remain at a constant
annual amount, is
E {i.op") - E = E {i.op" - i).
The analogy of this calculation to that used in Group A is
evident. The difference is that in A, Sc represents existing
capital which remains as an asset, while in C, £ represents
a fictitious capital which may have no existence and is never
expended. It represents the capital which would be tied up,
in order to produce an income to just balance the expense e.
This capital might, if the owner desired, be actually deposited
at interest, when the expense e would be permanently taken
care of and the capital remain intact at the end as in Group A.
But the proprietor usually meets this expense out of income
from other sources. The capital represented by E is, therefore,
.6
merely a mathematical device, and the expression better
expresses the status of the item, as it emphasizes the annual
expense.
Should expenses increase, the modified Formula Ilia is used,
by substituting E' for — ^ (§ 79).
0.0^
The total actual cost of production for timber grown under
management covers the period from its origin to its removal.
Adding the summaries for the three groups, we have
Gc = C {i.op") + 5, (i.o/>" - i) + £ (i.o^" - i)
= (C + 5, + £) i.op^ - (5. + E). (A)
This formula suffices when all initial crop expenses occur in
the first year.
Income during this period serves to cancel an equal value of
accumulated costs in the year in which it is received. Annual
income usually serves merely to reduce the net annual cost, and,
therefore, does not appear in the formula. But income received
from the sale of products obtained from advance cutting, or
thinnings, bears no constant relation to the total expenses for
INVESTMENTS AND COSTS IN FOREST PRODUCTION 79
the year. All income is equivalent to negative costs, and in
this case the item is best carried with interest to the final
year, when its total may be subtracted (§77). Otherwise a
separate balance would be required for the year of receipt of
this income, which would serve no useful purpose.
Let Tp, T,„ Tr = value of thinnings or other incidental rev-
enue received at p, q and r years. The future value, at end of
period, will be
T, (i.o/^"-") + T, {i.op"-") + Tr (i.o/>"--).
Subtracting this income from total cost, including Cj, C^ and
Cf, we have the net cost of the growing stock, G',.
G, = (C + 5. + E) i.o/)" + Q {i.op"-')
+ C, (i.o/>"-0 + Q (1.0^-0 - T, (i.o/^"-")
- T, {i.op"-") - Tr (i.o/>— ) - (5,. + E). (Ai)
There is no way of avoiding these separate calculations for
single sums occurring in odd years. As each item is independent
of the others, the apparent complexity of these forrriulae need
not be a source of confusion.
To obtain the cost of a forest, including both soil and timber,
the cost of soil is not subtracted.
Let Fc = cost of forest.
Then Fc = (C + 5c + E) i.op" - E,
and for the year a,
°Fc = (C^ + Sc-^E) I. op'' - E. (Ao)
106. Total Cost of Investments in Standing Timber. — Only
a few instances are found in America where forest crops have
been brought from seed to maturity under management, and
it is still less frequently that actual total costs of production
have been recorded. Practically all past transactions in land,
for forest purposes, dealt with property which already contained
standing timber.
Cost accounts for such property begin with the purchase price
and carry all subsequent 7tet expenses to the present, to final
sale of the property, or to the year when the timber is sold.
Since such property is purchased in a partially or fully developed
8o FOREST VALUATION
condition, with respect to the timber crop, and may include cer-
tain permanent improvements, the cost to the purchaser may not
coincide with the cost of production, for the sale is usually the
means of realizing profit on the part of the original owner (§ 90).
This initial cost is usually a lump sum, which includes the value
not only of all separate stands of timber, but does not often
separate the value of the land from that of the timber crop. An
analysis of this cost must precede any attempt to institute a
cost-keeping system separately for different parcels or stands.
Separation of the cost of land and timber, while usually
postponed in such instances until actual separation occurs
through cutting, is necessary if the true cost of holding the timber
is to be computed, and the land permanently devoted to for-
estry. But if the purchase is a timber speculation, and the
land, after the timber is stripped from it, is to be sold or aban-
doned, there will be no need of this distinction.
In the former case,
C+5<. = cost of timber and land, or purchase price of property.
The purchase price of the property is substituted for cost of
land plus silvicultural operations, in Formula A. The net cost
of production for timber depends now upon the value agreed
upon for the land at time of purchase, for this must be subtracted
as representing a capital investment. The formula is in all re-
spects identical with A, and interest accumulates for the period
elapsing between date of purchase and date of final sale or in-
come, which is assumed as n in the problem.
When interest is thus computed as a cost on the investment
in stumpage, as well as on taxes and other expenses, a rate of
6 per cent will cause this "cost" to double in twelve years.
The stumpage value must double in a shorter period or there
will be no income to replace current expenses. This raises the
important question as to the length of time which it is possible
for private owners to hold stumpage without cutting it (§181).
For periods of forty years or over, it might easily be shown that
the costs of raising a new crop of timber leave a higher margin
of profit than those incurred in carrying a mature crop with a
high initial value, for the same length of time.
INVESTMENTS AND COSTS IN FOREST PRODUCTION 8 1
107. Costs of Forestry Compared with Destructive Lum-
bering. — Owners of timberlands have the choice of two lines
of policy. They may desire to retain the lands only until the
timber is removed, when every efTort will be made to sell or
dispose of them. Or they may plan to hold these lands indefi-
nitely, with the intention of producing or securing a new growth
of trees. The former policy is usually accompanied by destruc-
tive lumbering, so termed because the purpose of the operation
is to remove every tree of merchantable value, at the same time
undertaking no measures to reproduce or perpetuate the forest.
The linancial distinction between these two policies lies in
the character of the investment required for forestry. Destruc-
tive lumbering squeezes the last cent of capital from the forest,
wrecking it as a productive enterprise, and converting it into
money profits. In this process, the cost of transportation is
reduced to a minimum by use of temporary structures and com-
plete removal of the timber, by elimination of all care in felling
and skidding needed in preventing injury to }oung timber, and
by neglect of the fire trap caused by the slash, and abandonment
of the land to promiscuous broadcast burning. Under such
conditions, stumpage brings its highest prices and the profits to
logger and owner are greatest in amount. But there they cease.
In any other form of business, similar results may be obtained
should the owner close out the enterprise by the sale, not only
of the net product, but of his reserve stock, fixtures and capital
assets. The profits obtained on stumpage under destructive
lumbering are higher than the business of forest production
can earn or is entitled to, and the entire structure of lumbering
as it is carried on to-day will crumble away with the exhaustion
of the raw materials, having converted the chief asset, produc-
tiveness of forest lands, into money.
The investment which forestry may require, and which de-
structive lumbering avoids, consists of
Additional cost of transportation in logging.
Additional felling and skidding costs.
Brush disposal.
Cost of seed trees.
82 FOREST VALUATION
With the entire cost of building roads charged against the
logging, and pro-rated over the amount of timber logged, any
reduction in this quantity, especially if the area is not corre-
spondingly reduced, increases the unit cost of logging by nearly
the same ratio. It is not often possible to cheapen the means
of transportation to conform to the lessened cut (§ 98).
Felling and skidding will cost more in proportion to the care
needed in avoiding damage to young timber.
Brush disposal (§ 100) is almost always needed. It frequently
happens that as a result of this measure, the costs of skidding
are correspondingly reduced.
A question may well be raised as to whether the sum of these
extra expenses constitutes a loss of profits on the crop being cut
or a diversion of profits into initial investments on the next
crop. Should the total extra cost, thus incurred, be charged as
initial cost or silvicultural expenses, to accumulate at compound
interest, it would constitute a heavy burden on the succeeding
crop. Viewed from the standpoint of destructive lumbering,
this cost, taken from profits, is a deliberate reduction of ordinary
profits and must be charged against future income. But from
the standpoint of forest production, this excess profit is not a
true profit at all, but the wrecking value of .the "plant" added
to legitimate profit. Normal profit is that which will leave the
productive capital intact. From this standpoint these "extra"
costs of logging would be considered as "ordinary" costs, falling
on the logging and cancelled by income from sale of logs, and
would not be regarded as an additional investment in the new
crop. These two opposing tendencies are best illustrated by
the expense of burning brush (§ 100).
The investment represented by the stand of timber left after
logging is more easily classified. Should this consist merely of
seed trees, it can be regarded as a loss only in case these trees
will not live until the harvesting of the next crop. If they
survive, they represent an investment from which the returns
will be:
The future value of the trees themselves;
The value of the new crop.
INVESTMENTS AND COSTS IN FOREST PRODUCTION 83
This investment feature is even more conspicuous in the case
of stands in which a large per cent remains after logging.
In either case, the sale of the greater portion of the merchant-
able stand gives the basis for an appraisal of the remaining timber.
A balance may be struck between past costs and income and
the remaining crop credited with its present value, which is
then charged as an initial investment for the ensuing period.
This would show profits on the entire crop, and a reinvestment
of the portion left standing. If this appraisal is not used, the
profits are confined to the timber actually cut, and the invest-
ment would not be charged against the new crop or period.
The former method of accounting is preferable. The use of
profits to cancel investment may be pushed to illegitimate
lengths, as when income from the sale of timber is allowed to
" wipe out" the cost of the land, which is then carried as having
no "cost" or "value" for a succeeding period. In this case,
income from sales should be permitted to offset only the cost
of the timber sold, while the land (§ 96) must be separately
valued, and will be charged with interest in the future reckoning.
108. Cost of Many-aged Forests. — Proprietary accounts of
investment for large forest properties are kept very simply (§91).
The same is true of such an account when dealing with single
stands composed of trees of many ages. But the question
arises as to whether income from such a stand should cancel
original capital investments, or be regarded purely as interest
or dividends on this capital.
If the forest is established and is renewed, so that, whether
the cutting be annual or at intermittent periods, it may be
maintained in amount and value indefinitely, the cost of the
stand can be considered as a unit, regardless of the separate
age classes (§ 161). This cost may be the price of purchase or
the cost of production (§ 109). In a stand of all ages, producing
armual income, this cost does not increase and the net income is
merely the annual dividends on the investment. None of this
income is needed for the replacement of capital.
In a forest yielding an intermittent rental, the cost or total
investment continues to increase (§ 92) until a pa>Tnent of
84 FOREST VALUATION
income is received. This payment must be regarded as can-
celling the additional capital invested since the last pa^Tnent.
Where yields are irregular in time and value, and yet there
always remains a considerable stand of timber on the ground,
the relation between cost and income becomes a matter of judg-
ment or adjustment. The object should be to insure the return
of the capital invested in the timber which is removed, and carry
as a cost or further investment only a reasonable balance of
original cost against future income. The cost of a forest is the
sum of the net costs of the separate stands or parcels.
109. Cost of Producing a Normal Forest. — A normal forest
is one from which an annual income may be obtained without
diminishing the amount and value of the capital or assets. This
requires the presence of equal productive areas in each age class.
Granting that the cost of each parcel of land is charged to
this forest in the year in which the crop upon it is started, and
that it takes n years to establish the forest, an area equal to
- of the whole must be reproduced each year. The total annual
n
expense e applies to the entire area of the forest. C is required
to plant the parcel. The capital tied up in the investment
for the year will then be C + 5"^ + -E (§ 105).
Since an equal area and capital investment is added each year,
on which interest accumulates till the year n, the sum of costs
forms a series, with {C -\- Sc -\- E) as the first term and i.op
as the ratio of increase. See Fomiula III.
The sum of these costs is
(C + 5. + £)(i.o/>"- i)^
o.op
But the capital E is fictitious (§ 104) and this has been intro-
duced n times. In the same way, Sc may be deducted as a
capital asset, totalling nSc.
This makes the net cost of production for the timber alone as
G. = (C + ^. + £)(..or-0 -„(S, + E). (A3)
o.op
CHAPTER VII
THE VALUATION OF FORESTS
110. Valuation Accounts in Forestry. — Just as the proprie-
tary and cost accounts in forestry (Chapter VI) deal with the
personal investments of the owner and past elements of cost
and income, so the valuation accounts in forestry deal entirely
with material assets (§ 54) and determine their value. The
basis of this determination is the forest inventory (§55) which
shows the area of land of different qualities, the amount and
kind of timber and of other resources, and any other property
included in the forest.
111. Income as the Basis of Value of Forests. — This phys-
ical property must be valued or appraised (§§ 18, 60). Follow-
ing the conservative systems of accountants, the values entered
for land, timber, buildings or other forms of property cannot
exceed what was actually paid for them (§ 56). Such an asser-
tion does not mean that the actual value of the property remains
at cost, but that growth in value is not considered equivalent
to realized income. An increase in value of assets may and
does occur, and, with growing timber, is the rule; but the ac-
countant in all such cases desires to await the actual sale of the
product, and credits this increase in value only when received
in the form of money returns.
\\Tiile this custom protects the proprietor or stockholder, no
pretense is made that the book values, based on cost, represent
the actual value of the property. In Chapter IV the basis of
value is seen to be future income (§§6i and 62) and the true
value of all assets is derived from this income, discounted to
the present, minus future costs.
In order to grasp the principles employed in appraising for-
est values, the relations between physical assets, income and
value must again be emphasized. First, the forest land, with
86 FOREST VALUATION
its growth or stand of timber, is the property to be valued.
Second, this land, by producing timber, and the timber, by grow-
ing, yields saleable products whose final sale produces income.
Third, the income, expressed in money, has an appraised value.
As the final step, the value of the income is discounted to deter-
mine the value of the physical capital which will produce it.
This process cannot be short-circuited. The sale value of
forest land or timber does not represent any quality inherent
in the land or timber except the capacity to produce income,
and the value of the property must first be based on the valua-
tion of the income.
The income from forests is principally the value of timber
sold on the stump, or the proportion of profits from logging
which is due to the owner of stumpage. Secondary income is
obtained from thinnings or advance cuttings, and from pastur-
age, or hunting and fishing rights. Other sources of income are
by-products, such as naval stores, or tree seeds, nuts, bark,
sugar, shrubs, herbs and litter.
The present value of the forest is the sum of the present or
discounted values of all items of income expected in the future,
less the present value of all items of anticipated expense (§62).
Sale value bears the same relation to capital or expectation
value for forests as for any other form of property (§ 59). But
since sale values are the expression of average general opinion,
the sale value of forest land and young timber will be apt to
depart widely from the capital or expectation value of such
property in regions where the business of forest production is
not recognized, and lands are abandoned after logging or de-
voted to agriculture and grazing.
112. Value of Forest Property for Destructive Lumbering. —
When the owner intends to remove the timber and devote the
land to other uses, his income will consist of:
Yield of timber;
Value of land for other purposes after timber is removed.
As long as the timber remains, the land cannot be utilized
fully for anything but the timber crop. Grazing is only a sec-
ondary source of revenue. When cleared, its value is considered
THE VALUATION OF FORESTS 87
as depending solely on the net future income from other uses,
such as agriculture or grazing. Since these are enterprises not
directly connected with forestry, it may be technically assumed
that the forest owner sells the land, and the sale value received
completes his income and terminates the enterprise.
The total present value of forest property based on the
income from destructive lumbering is determined as follows:
Fg = sale value of forest property, including both land and
timber.
Y = yield or net stumpage value of timber in fmal cutting.
Tp, Tg, Tr = yield or value of thinnings or timber removed
before final cutting.
S, = sale value of land when finally cleared of standing timber.
e = annual expenses.
E = capital value of annual expenses.
a = present year, or the year a dating from the origin of the
stand.
n = year in which final cutting is made, dating from the origin
of the stand.
The period of discount will then hen — a years.
In the year of sale, and previous to its consummation, a and
H coincide. The value of the property for immediate sale is
then
Fs = Y-\- 5,. (B)
When the year of valuation a precedes n, the value is as
follows :
Value of Y for year a
i.op"-"^''
icc xxy.
Value of Tp, T^, Tr for year a
T
i.op^"
T
I. Op"-"
i.op"-"
Value of Sg for year a
s.
I .op"-
88 FOREST VALUATION
Cost of e for n — a years = -^ (see Illb, II), which
becomes £
I .o/>"~"
Omitting the item of thinnings,
ap _ F + >S. -£(i.o/>"-°-i)
I .o/>"-"
F + 5, + £
I .o/>"~"
- £. (Bi)
Including thinnings whose income is expected in the future, or
between the years a and n,
ap^ ^ y + S, + E _ ^ ^ T, ^ T^ ^ T,
I. op"-" I. op"-" i.op"-" i.op'-"
_ Y+.S, + E+T, (i.o/>"-^) + r, (i.o/>"-^)+ Tr (i.or~0 ^
(B2)
113. Value of Forest Property for Continuous Forest Pro-
duction. — The substitution of sale value of land for its value
determined from income was a makeshift justified by the
change in its use. True forest land, devoted permanently to
producing timber, must be valued on the basis of the sum of all
future income which it is capable of producing. This will in-
clude the net value, not merely of the present stand, but of a
succession of timber crops, extending to infinity (§ 86).
The relative present value of the first crop compared with
others to follow is very large, but merely because the interval
between payments is correspondingly long. The income from
sale of a crop of timber does not differ in character from the
monthly pa>Tnent of rent, and the value of the forest is as truly
the sum of all present values from future crops as that of the
house is the capitalized net rental or income. In the same way
that the value of the house represents, not the gross rent, but
the rent minus all outlay such as taxes, repairs and depreciation,
so from all future income from timber, deductions for expenses
must be made to get total net value.
THI-: VALUATION OF FORP:STS 89
114. Value of a Forest of Even Age Just Previous to Cutting. —
A forest or stand of even a<;c may be cut clear at one time and
replanted. During the period immediately following the cut-
ting, the soil is bare of trees, while at all other times it is occupied
by timber of constantly increasing size.
Since every item of either income or expense must be assumed
to recur for each future timber crop, the total present or dis-
counted value for each item is found by FormuUe IX to XII.
For the year n, and just previous to receipt of income Y, the
value of income Y, being the sum of all future payments dis-
counted to the present year, is
Y Y V Y
'-'■'■ ■ ' -■ (§85,XIa).
I .op" I .op- " I .o/?* I .op" — I
The cost of planting or reproduction, which in destructive
lumbering does not occur, falls here in the same year as Y and
recurs every n years.
Value of expense C, totalled in the same manner, is
C C C C
l.Op" I.O/>2" i.o/?" l.Op"- I
The annual expenses e recur at intervals of i year, by defini-
tion, and are computed from the end of each year.
Value of the sum of annual expenses e\
i.op i.op- i.op^ I.O/>" I. Op— I o.op
Let F,. = expectation or capital value of forest property for
continuous production.
Then
F, = F + Z f C + ^
I.op'* — I \ i.o/>" — I
= Y+ ^\-^ -(C + E), (C)
i.o/>" — I
which is the value of forest property just previous to removal
of the timber.
In this formula, no account has been taken of other items of
90 FOREST VALUATION
expense corresponding to C but falling at different years, nor
of income from thinnings corresponding to Y but received
previous to this final cut.
The present value of these items is found by Formula X, since
each single payment, while not repeated during the rotation, is
assumed to recur in the next rotation, and the total of all future
payments forms the series.
Let Tp = income from thinning in year p, recurring every n
years forever.
T
Then — ^ is the value of Tp in the first year, n.
i.opp ^
The series is
-^ P I -^ P I -^ P I . . . _L P .
I.Op^ I.O/>P+" I.O/)P+2n ■ ■ ■ i.o/>»*
The sum is (Formula Q4)
Tp
I —
I. op" _ Tp (i.o/>"-^)
I I. op" — I
i.op"
By substituting q, or r, for p, the present capital value of
other items of income or of expense, for any year, is obtained.
The present value of forest property just previous to removal
of a final cut of timber is summed up as
Y + Tpii.op"-'^) + T,{i.op--')
+ r.(i.or--) - C - CA^-op""-')
-C.(i.o/>— )-C,(i.or-0 (Ci)
F„ = F - (C + £) +
i.o^"— I
115. Value of an Even-aged Forest for Any Year. — The value
of the forest for any other year, or during its growth, is ob-
tained by discounting the above value for the period previous
to this final cut. The forest has its maximum value just before
the principal yield is removed. The further into the future this
income is postponed, the less becomes the present value of the
property.
THE VALUATION OF FORESTS 9I
Should the value be sought for the year a, and this year be
but one year previous to the cut, the value of the forest is dis-
counted n — a, or one, year. As a is dated earUer and earlier
in the life of the stand, the discount period n— a increases, until
when a = o, just after the felling of the old crop and previous to
the starting of the new one, we get the smallest value to which
the property shrinks in the entire rotation.
With the advance of the date of calculation to the year a,
both the future yield Y and the cost of planting C occur first
in n — a years. The annual expenses, since they are calculated
for the same interval, and extend to infinity in both cases, have
the same capital value E.
By Formula Xa, the value of the forest is
„^^ ^ Fd-o/)") _ C(i.or) _ £^
i.op" — I I. op" — I
^(F-Oi.or_g (D)
I .Op" - I
Items of either income or expense occurring at other than n
years will fall either previous to or subsequent to year a. Those
preceding a are not considered in the value of the standing crop
(§ 68) , but their occurrence in the subsequent rotations afifects
the value of the forest.
A thinning occurring in the year r subsequent to a has a value
at present (year a) of ^ —
^ -^ ^ i.o/>'-"
The sum of future values (Q4) is
I I.O/>" — I
I —
i.op"
A thinning occurring in the year p previous to a^ has a present
T
value (year a) of r
92 FOREST VALUATION
The sum of future values (Q4) is
I I.O/>"— I
I ^
I.O/>"
These expressions are equally applicable to costs occurring
before or after the year a. The present value, in year a, of an
even-aged forest or stand, is summed up as
F {i.op") + Tj, {i.op"-") + T, (i.o/>°-*)
+ Tr (i.o/>"+"-'-) - C {i.op") - Q (1.0^°-'^)
-C.(i.o/>— )-Q(i.o/>°-0
"F =
i.o^"-
-£.
This formula may be expressed in another form.
"Fv =
\ I.OpP LOp"^ I.Op'' l.Op'^ I-Op^ I.O/>V _p,
I.Op"-I
(Di)
The chronological relations of these items are set forth in
Diagram II. The present year is the basis of valuation. Past
occurrences are ignored. But in the terminology, the numerical
value of a is reckoned from the past year o, or date of origin
of the crop, which is also the basis for the other dates.
The year 2a is just n years in the future. The Formula Di
expresses the value of the items computed at compound interest
to the year 2a, when the balance is struck which gives net
value. This net income recurs at intervals of « years from
date, and its present value is , hence the above result.
' ^ i.o^" - I
116. Value of Forest Soil. — The value given in Formula C
was for a forest just previous to removal of the final cut. This
value steadily diminishes as the date of this cut is assumed to
be further into the future until the lowest ebb is reached, just
before the discount period overlaps the date of the previous cut.
A similar fluctuation in value occurs in the case of an account
THE VALUATION UF FORESTS
93
9,
' '
0
•
^i
.a u.
is
^^
,'
•s
T)
1
t=.
i<^
8
9
a
i
q
.
^
+
E
t)
1 S
I
1
t
a
q
P_
-a-
3
q
1
0
o
'
.
3
1
1
1
U
3
a
o
0
a
a
:5
^
a
a
>
a
a.
"
V
""
5
q
1
"l
1
I
i
i
^ ■«
S
■J
u
o
s
5
o m
S s
o.c.
s
i~
S s 2
c
c-
o
c
Ob
H
JUDSJ
•Id
t-
>
15,
q
~
S
1)
-
iS
1
1 •"-'
1
L- fi""
«
1 ec>
Q TO 4_>
i2
4> O.
T3 -O "O
rt (3
S. -2 5
(J "t? «
O 4)
.15 t« -a
^T* rt c
c c —
r g i2
u? C C
8 S 2i
-)-C,(lor-0 r^ , ^^ (El)
i.op" - I
5„, the expectation or capital value of forest land bare of trees,
may be likened to the value of bare land suitable for farm crops
or orchards. In the case of farm land, it may happen that the
sale value of one annual crop will equal or exceed the value of
the land, and farms are usually sold subject to crop removal
or in the winter. With orchards, the value of the bearing trees
greatly enhances that of the bare soil. Even a young orchard
increases land values. In the latter case, it is of small moment
whether value is separated into the value of the land and that
of the fruit trees, for both are sold together. With forest trees,
the relation between land values and ultimate income is exactly
the same, but the period covered by the growth of the stand is
so long that one is apt to lose sight of the fact that this so-
called value of land is merely the discounted value of the future
crops of timber.
This soil value S, represents the value of all future income
dating from a point just subsequent to the complete removal of
THE VALUATION OF FORESTS 95
a crop of timber. It is the value of all future crops exclusive
of the one occupying the ground.
But 5„ represents this value correctly, only for the year of
cutting, or just previous to planting. Dismissing the idea that
5„ represents the actual "intrinsic" value of the soil itself, and
regarding it solely as the discounted net value of the future re-
ceipts from timber, it is seen that this value S„ holds good only
for the one year. Just previous to the cut, the property is worth
Y + S„. Just subsequent to cutting, the value is S^. But when
this net income is discounted to any previous year a, its value
S
ceases to be 5,, and becomes The value of the entire
I .op"-"
property, soil and timber, as determined from the net revenue
(see § 112, Formulae Bi and Bo), is the sum of the net income
from the standing crop plus the discounted net income from
future sources, represented by ^ • The value of the stand-
ing timber is (E — ■ • )
* I. op"-" \ i.op"-y
The sum is, therefore,
But since S^. reappears every n years as the net value of bare
soil, it may be assumed that this represents the value of the soil
during the interv^ening period, and that the excess of value for
the property represents the value of the trees or growing stock.
Under this assumption, S^, might be regarded as the fLxed capi-
tal, corresponding to a sum of money, and the value of the
timber as the accumulating interest earned by this capital.
To determine what annual interest this soil capital is earning,
it is necessary merely to multiply 5„ by the rate of interest p
used in calculating it.
S,. X o.op = soil rent (§ 162). (E2)
Expectation value of soil is merely an expression of net income.
Instead of being permanent or fixed, it is a prediction or forecast,
and changes constantly (as do all values) not only with every
96 FOREST VALUATION
change in economic conditions affecting the price of products,
but with the opinions of property owners as to the amount and
present value of the anticipated income. Since it is the furthest
removed from actual income, soil value is the most unreUable of
all forest values, and is subject to greater proportional fluctua-
tions than values of standing timber.
117. Value of Many-aged Forests Producing Regular In-
come. — The true character of this capital value of bare forest
soil is further emphasized in the valuation of stands of timber
composed of trees of many different ages.
Two cases may be presupposed. First, the existing age classes
are so distributed that an amount of timber can be cut at
equal intervals of time, and of approximately equal quantity
and value. Second, the age classes are irregular in quantity
and unevenly distributed as to age. This second example is
the prevalent type of many-aged forest.
In neither case is the land ever clear of timber, unless the young
age classes are destroyed by fire or logging. It follows that for
a forest of this character the value of bare land cannot be deter-
mined, except by making an artificial assumption of an even-
aged stand of equal total yield with that of the many-aged
forest, and in which the trees take an equal time to develop.
But the trees in the all-aged stand take longer to grow than
they would if even-aged, on account of suppression or shading.
The correct determination of soil value, apart from the stand,
for such forests is therefore quite unsatisfactory. With a slow-
growing species the values indicated for bare soil may be nega-
tive and are usually very low.
But the forest itself, or total property, both soil and timber,
even after a cutting has just been made, has a positive and often
a high value.
Whether the interval between cuttings m is long or short,
the value of the forest just after the cut is
F. - ^~^ - (C + E). (F)
I .op"' — I
But in this case, the formula, although similar to that (E) for
THE VALUATION OF FORESTS 97
bare soil, differs in the period m and gives, not the value of soil,
but of the soil and timber remaining; after the cut. It is the
value of the real estate or forest.
The term F„ is thus used to indicate the \alue of the forest
just following a cut.
For any year previous to a cut, the value of the property may
now be found by discounting the net value of this yield to the
present, and adding the discounted value of F^.
This gives
V -\- F F
I. op'"'" i.o/?™""
= ^-^^"-^^ _ E. (Fi)
I. op'"'"
The value of a forest producing a regular annual income is
• • • • • T
found by capitalizing this net income, using Formula XII, .
o.op
The annual income will be F + Tp + T, + Tr.
Annual expenses are C -\- n X e, since e is the annual expense
for but one area or age class and there are n age classes in the
forest.
Other expenses, as Q, C^ and Q, also occur annually.
P _ F + Tp + r, + r. - (C + Crf + C, + C, + ;/ X g) (^.
o.op ' ^^^^
The net income, which is thus capitalized to obtain value, is
termed the forest rent (§ 162).
118. Value of Many-aged Forests Producing Irregular In-
come. — Should the value of irregular many-aged forests be
sought, the period must first be determined, which is required
by the average trees to become merchantable. The stand must
then be roughly grouped into its age classes, and the approxi-
mate per cent of total area agreed upon which each age class
occupies. Each of these jields must then be discounted to the
present, with a value determined by its area. To get the net
value of each crop, the future expenses must be pro-rated ac-
cording to the same distribution of area. Finally, the total value
98 FOREST VALUATION
is obtained if each yield is treated as a recurring rental (Formula
X, Diagram II). An example of such a valuation would be:
Crops cut
in year a, - total area,
in year h, - total area,
y
in year c, - total area.
.2
If total value of all crops is Y and total expense e is capital-
ized as E, and there is no expense for reproduction, the value of
the forest is:
V Y Y
— (i.o/?"-°) +- (i.o/?"-*) + - (i.o/>"-0
''F„=^ y- '- E.
I. op" - I
Should an expense for reproduction, C, occur at the time of
cutting, or any other initial expense be incurred at that time,
this expense is subtracted from Y in that year.
As
V — r V — r Y — c
{i.op--") + (i.op--") + -{i.op--')
»F =-^ ^ E.
I. Op — I
(Fa)
Formulae are merely convenient methods of calculating re-
sults after the facts are obtained. Any large area of forest
requires careful analysis and separation into its component
parts before any of the methods of computing value can be
applied.
119. Value of Timber Separate from Land. — When for any
reason the value of the timber must be separated from the value
of bare land, it may be done by subtracting this latter value
Sv from the formulae giving the total value of the property.
Formula D2 then becomes
THE VALUATION OF FORESTS 99
and Formula Fi reads
°G.= ^"^^:-'!'^-(>S„+£), (GO
provided in this case that the value of the soil can be determined
or agreed upon apart from that of the poles, saplings and seed-
lings which increase the value of F„ over that of S,.
For a normal forest (§ 109) producing annual income, the ex-
pectation value of the standing timber, separate from the land,
may be found by subtracting n X S„ from Formula Fo which then
reads
■op
CHAPTER VIII
FOREST STATICS — THE BALANCE SHEET — PROFITS
120. Determining the Profits of a Forest Investment. — Forest
statics is defined by Schlich * as "the science which weighs and
considers the comparative merits of the different methods of
treatment to which forests may be subjected. The financial re-
sults, or income-yielding power of an undertaking, are expressed
by the proportion existing between the yield and the capital
which produces it."
Two distinct methods are possible in preparing a financial
statement in forestry (§ 73). The first may be termed the spe-
cific balance sheet and conforms to the principles of accounting,
by recording only the actual cash investments as credits, and
valuing the assets preferably at actual cost. By means of the
supplementary profit and loss account, the net income, or loss,
is annually transferred to the balance sheet.
This specific balance sheet does not reveal profits until they
are actually realized. It is therefore extremely conservative.
For a business based on deferred income as in forest production,
the annual net deficit of expenses over income may continue for
many years, requiring continuous increase in invested capital,
which would be further increased by borrowing, and adding to
expense the actual cost of interest on these borrowed funds.
The balance sheet indicates an increasing deficit, up to the time
the timber is cut.
With the receipt of this income, the total assets are suddenly
increased to several times the total investment, showing an ap-
parent profit of hundreds of per cent in case of even-aged stands
harvested after from 40 to 60 years.
* " Manual of Forestry," Volume III, Forest Management, by Sir William
Schlich, 4th Ed., Chapter VI, p. 149. Bradbury, Agnew Co., Ltd., 10 Bouverie
St., London. 191 1.
100
FOREST STATICS— BALANCE SHEET - PKOI 11 S lOI
Such results evidently do not fully accomplish one important
purpose of a balance sheet, which is to reveal to the owner the
true financial status of his investment. Two elements of eco-
nomic importance have been neglected, which entirely alter this
status. The expectation value, not the cost of the assets, is
the true measure of the debit entries, while the profits finally
credited are not revealed in their true relation to costs unless the
time required to earn these profits is given proper weight in
the balance by exhibiting the interest at p per cent which should
have been earned on the invested capital during the period.
A statement which includes these two factors, expectation
value and interest on costs, may be termed the "economic fore-
cast.'' Revaluation of assets to coincide with present value
rather than cost is practiced in commercial accounting when
circumstances seem to justify it (§73). But the addition of
unearned interest as a cost is universally excluded in specific
accounts. The economic forecast would include such interest
on costs, for in no other way can the owner inform himself of
the relative value of the profits derived from income, or whether
there is any enterpriser's gain. The apparently enormous final
profits shown by the specific balance sheet may, when tested by
this economic comparison, be revealed as equivalent to less than
p per cent, which is no profit at all as measured by the standard
of enterpriser's gain (§ 42).
In this economic statement the proprietary side ordinarily
shown as credit is excluded altogether, and the costs are shifted
to the right-hand column in order to compare them with actual
value (§ 73), and reveal potential profit or loss. The statement
formulated in this manner is thus purely impersonal, and does
not distinguish between borrowed and personal capital. It is
similar to that which would be formed by comparing a cost
account for manufactured articles, as credit, with the sale value
of the article as debit. But in the case of productive property,
this comparison must be made far in advance of the receipt of
final or total income and is a balancing of cost against expecta-
tion value for the entire enterprise.
That the economic statement will show entirely ditt'erent
I02 FOREST VALUATION
results from the specific balance sheet is evident. When the
accountant insists on retaining land and timber in the balance
sheet at their original cost, the credits will exceed the debits
by the amount of annual expenses not entered as a capital ex-
penditure. This deficit is further increased by interest paid
on borrowed capital if such expense has been incurred. By
contrast, the economic statement shows an even greater "cost,"
since interest is added as a cost item to all capital invested,
whether borrowed or not. The assets, on the other hand, are
treated without any regard for actual cost, their value being
determined entirely on the basis of future income (Chapter VII).
The value of forest property, which is used in the economic
statement, is its expectation or capital value, until it reaches
maturity, when the capital value of the standing timber is
merged in the sale value from which it is derived. The com-
parison for timber property at any year previous to maturity
of the timber will show.
Debits.
Credits.
Expectation value of
property, consisting of
Young timber,
Forest soil.
Indicated or potential
loss.
Cost of property, consisting of
Cost of soil 1 • , J.
Cost of crop r"^l"d^"g
Interest on all items of cost.
Indicated or potential profits.
The economic forecast in forestry thus consists of balancing
past costs, with compound interest to date, against future
income (§ 62) discounted to date, as represented by expectation
value of assets. By thus comparing the relative values of past
net outlay and future net income, for any year a, the exact
economic status is revealed for that date.
This method of valuation for forest assets may be compared to
the appraisal of the property and business of a lumber company
for purpose of sale. Cost would not finally determine the value
placed upon any item of such property. The mill and logging
road, machinery and stock, would be valued on the basis of
their future usefulness to the purchaser and present owner.
The timber would be appraised at going prices for equally
FOREST STATICS - BALANCE SHEET - PROFITS 103
good stumpage. Should the sale be consummated these ap-
praised values are realized, and the profit shown in this tenta-
tive or economic statement becomes an actual profit, entered
specifically on the books.
To what extent the value of assets in a specific balance sheet
should be increased above cost of purchase, is a question to be
determined by the character of the business. Unless these
increased values are eventually realized, the profit shown by
reason of such increase exists merely in anticipation, and until
it is secured, this profit cannot be distributed as dividends.
There is considerable difference between the financial status
of a lumber company conducting an extensive operation with
stumpage held merely as a timber mine to furnish wood until
exhausted, and that of a forest owner engaged in growing timber
as a business. The former concern is obliged to adhere rigidly
to the accounting principles commonly accepted in business
circles. Its timber will be entered at cost, unless a bond issue
is floated, when it is customary to appraise the timber at its
present stumpage value and to make a far more complete esti-
mate of its amount. Bonds are secured by value, not by cost
of property bonded. The interest on these bonds must be met
annually or foreclosure follows. Taxes, protection and interest
are, therefore, formidable items of expense and timber must be
cut each year to produce sufficient income to cancel these costs
for the entire remaining body of stumpage.
But because of these conditions, the actual status of the
lumberman's investment tends to follow a similar course to
that of an investment in growing timber. The first years will
tax all the resources of the owners to keep ahead of their obli-
gations. Need for income is urgent. The tendency is to
greatly increase the size and capacity of mills and operations.
This universal tendency causes overproduction of lumber and
defeats its own ends by lowering prices.
But once a concern has weathered this initial period, and
reduced its indebtedness and carrying charges, the final years
of the operation become more and more profitable. It follows
that those operators who have the greatest amount of capital
104 FOREST VALUATION
behind them, and who do the least borrowing and maintain
operations in a region after others have ceased, reap large profits,
while the small investors, or firms attempting too much with
limited capital, are often bankrupted in the first stage of the
business.
The investor must, therefore, distinguish sharply between the
conmiercial or specific trial balance, and the economic forecast
which accounts for time, includes interest on the investment as
a cost, and bases the value of assets not on cost but on income,
by the process of discount. • Such a " balance " informs the owner
of his true economic status, thus enabling him to determine his
future policy — whether to sell, purchase or continue to operate.
Economic, and not specific, profits are discussed in this chapter.
121. The Rate of Interest in its Relation to Profits. — In
securing an accurate statement or balance between past costs
and future income or capital value, the effect of the element of
time upon such relative values must be eliminated or equal-
ized (§ ii). This is done by employing the same rate of inter-
est (§ 38), p per cent, on both sides of the equation.
The total amount of compound interest is increased by em-
ploying a higher rate, while the same increase in the rate has
the opposite effect of lowering the present or discounted value
of assets. This effect is due in each case to increasing the
difference in value caused by the element of time. It follows
that an increase in the standard rate of interest, p per cent,
tends to obHterate the margin of profit on the credit side of the
balance, and replace it with a debit deficit or loss. In other
words, if the investor is satisfied with 3 per cent, and that rate
is used in computing values for the balance sheet, the statement
might indicate a profit, but if he uses 6 per cent as the necessary
basis of comparison with other investments, the resulting bal-
ance may indicate a loss, although the cash income and expenses
remain the same in either case. The change is wrought wholly
in discount or expectation value and in the accumulated "cost "
of compound interest.
A rate of interest maybe found for any given total of expense,
on the one hand, and of income, on the other, which will just bal-
FOREST STATICS — BALANCE SHEET — PROFITS 105
ance the cost or credit side with the asset or debit side of the
balance sheet. This rate would in most instances include a
fraction or decimal, such as 4.27 per cent. The rate which
thus balances cost and income is the rate of interest earned by
the investment. And since money is never borrowed at odd
rates, and the earning power of an investment does not deter-
mine the rate of interest used in calculating its value (§62),
these items of cost and value seldom balance exactly, but always
show a profit or loss.
Yet the fact that this rate exists indicates a second method
of determining enterprisers' profits. The rate earned, expressed
in terms of compound interest, eliminates the element of time
as elTectually as does discount, and enables the investor to com-
pare the income rather than the expectation value of two in-
vestments. The forest investment must earn p per cent before
it becomes as desirable as the money it represents. If x per
cent is earned, then when x per cent > p per cent the excess
represents the ratio of profit or enterpriser's gain, per dollar
of investment, in excess of the standard rate. If x per cent
< p per cent, the rate x per cent still indicates net income,
but compared with p per cent, there is a loss, or rather a failure
to realize the amount desired.
122. Profits in Destructive Lumbering. — It is assumed that
owners who do not intend to continue in forest production will
sell the land or devote it to some other purpose. Its sale or
appraised value for this purpose is credited as income.
Let P = profit.
P = r + 5, - (C + 5J i.o/>" - E {i.op^ - i)
= r + 5, + £ - (C + 5, + £) i.op\ (H)
This formula is expanded, by the addition of other items of
both cost and income, to the form,
P = Y ^S.^-E^T, (i.op--^) -\- T, (i.o/>"-«)
-f- Tr (i.op--^) -{C-{-S,-\-E) I. or
- C, (i.op"-') - C. (i.o/^"-') - Q {i.op^-0. (Hi)
This formula gives the profit on a single stand of timber,
for the year of sale, assuming that both timber and land are
Io6 FOREST VALUATION
sold, or that the timber is immediately removed and the land
sold or appraised.
Actual profits on the investment in land and timber exclusive
of lumbering, for a large operation, must be based on actual
sale of land rather than appraisal at time of sale of timber,
and if this sale is delayed, as it may be, for many years, the
transaction is not closed. A new account may be opened for
the denuded land, crediting it to the original account preferably
at the cost, not the present sale value of land, and debiting
the land account with this investment. If a "cost" account is
kept as before, the land will be charged with interest until sold.
123. Profits on a Stand of Timber. — Whether or not the
owner intends his land for future crops of timber, the profit on
the existing stand may be separately stated, by charging interest
on the cost of land as an expense against the timber, and credit-
ing the land at its original cost, when the timber is sold.
p = F + 5, - (C + 5,) i.op- - E {i.op- - i)
= F + 5, + £- (C + 5.+£)i.or. (K)
This formula differs from H only by the introduction of Se
as an asset in place of 5j, and may be expanded in the same
manner as Hi.
124. Anticipated Profits on Young Timber. — Assuming that
Sc is credited at the time the timber is cut, the profits of that
year may be anticipated for the year a in one of two ways.
The net profit (K) may be discounted to the present (II), or
the balance may be struck for the given year by direct compu-
tation of value and cost for that year. In the latter case,
Value = y + S, + E _ ^ ^^
Lop'"-"
Cost = {C + S, + E) i.o/»« - (5, + E).
P = ^^t-t^ - (C + 5, + £) i.op'^. (KO
This formula may be expanded by the addition of income
and cost items, regardless of whether these costs occur after
the year of valuation, or income occurs previous to this year.
FOREST STATICS — BALANCE SHEET — PROFITS 107
T
The expression ^ gives the present equivalent of Tp in the
year a whether a > p or the reverse. Therefore,
P = ' '' + -^±7. +
I. op""" l.Op"'" I.O/?""" LO/J*""
- (C + 5, + £) i.o/)" - C, (i.op-")
-C(i.or-') -Q(i.o/^°-0. (K2)
125. Profits from Continuous Forest Production. — If in-
stead of abandoning the business, forest production is to be
continued, the sale value S, credited for land does not express
the true conditions. The value S,., representing the expectation
value of the soil or the value of all future crops, must be sub-
stituted for S,.
Formula H then becomes
P = F + 5, + £ - (C + 5, + £) i.op\ (L)
The net profits from future crops, expressed as
Y -C
i.op" — I
- (C + E),
may be substituted for the expression 5„ in the formula, which
does not alter the result. Both the net profit on the present
crop, and on the future crops, S^, should include all items of
cost and income which appear in Formula Hi, but the repetition
of these terms in Formula L has been omitted.
126. Anticipation of Continuous Profits. — To anticipate the
total net profit, for the year a, including net income from all
future crops, the value S,., once determined, is substituted for
Sc as an asset in Formula Ki which then reads
P = ^^"^i-"l^ -(C-hS^-hE) i.or. (Li)
i.o/>" "
This formula is modified by the same additions for extra items
of cost or income, as Formula Ko. But Formula Ki gives the
profit on the present stand of timber, exclusive of future crops
or of profit on the sale of the land, while Li includes these
Io8 FOREST VALUATION
future profits. Should Formula Li be derived in the same way
as Ki the result stands
^ = ^tor-^ - (C + 5. + £) i.or - {S. - 5o),
which indicates a means of separating the profits on the stand-
ing timber from that on the future crops, or "soil," parallel to
the method employed for sale values in § 123.
The true derivation of Formula Li is from value (§ 116, D2)
and cost (§ 105, A2) of the entire property, timber and soil.
Then
P = «F, - "Fc (L2)
127. Profits Expressed in Soil Values. — In the year in
which the enterprise of planting or reproduction is undertaken,
and previous to the actual planting, the net value of all future
income is 5„, or, expressing this value as discounted from future
crops, it equals
Y — C
I.O/)" - I ^
The cost includes merely the price paid for the soil Sc. Then,
P =S^- 5c. (L3)
Since this profit is shown for the year previous to undertaking
forestry, it is taken as an indication of the advisability of such
an enterprise. This relation shows clearly the nature of 5„,
which is merely a calculation of discounted net income. S„
does not indicate what a purchaser should pay for land. It
indicates the highest price which he can afford to pay and still
expect to earn the desired rate, p per cent, on his undertaking. If
more than this is paid, a prospective loss is incurred, i.e. he
cannot expect to earn as much as p per cent. If the land costs
less than 5„ he has good prospects of earning a profit at p
per cent, or a rate of income, x, exceeding p per cent on his
investment. If a purchaser is so foolish as to deliberately
convert his expected profits (5„ — Sc) into costs, by making
Sc = S^, he is merely handing over these profits to the one who
sells him the property.
FOREST STATICS — BALANCE SHEET -- PROITTS 109
5i, increases in value with every change in prospective in-
come or expenses which alters the net value of this income,
and is much larger for soils of good than [)()or equality. But
there is evidently no profit in devoting to forestry lands which
will sell for other purposes for a sum larger than 5„.
In countries where forestry is extensively practiced on lands
owned by states, or on private estates which have practically
never changed hands, there is no way of determining the cost
of land. The value of the soil, S^, is calculated for the pur-
poses of taxation and as a necessary step in valuing growing
timber. This value may be recalculated at any time. It is
evident that the soil value may always be placed at a figure
which will permit the investment to earn exactly the rate of inter-
est agreed upon as the standard for forest investments. And
in practice, if during the crop period it becomes evident through
price changes or other influences that the investment, with its
former soil value, will earn more than p per cent, this value
is promptly raised, and the rate of earnings is thus arbitrarily
reduced to p per cent once more. The real status of the in-
vestment is thus concealed in the capitalized value of the soil.
Applied practically to a private operation, this process would
consist of entering the land in the capital account as an asset
having a value in excess of its cost. If this value were made
great enough, the investment never could earn more than p per
cent upon said value. But figured on the original cost, a much
greater rate of profit may be shown. This practice of capital-
izing income as soil value is universal in European forest finance,
and the profits of forestry, standardized to p per cent, may be
discovered only by comparing the values of land computed for
different sites and species, and by a knowledge of past changes in
these soil values.
If S„ equals Sc, it may be substituted for Sc in Formulae A,
Ai and Ao. This is done under the conditions just discussed,
where Sc is not determinable. The effect of this substitution
is to make the computed cost of timber in any year of the rota-
tion just equal to its expectation value in that year, and to
reduce profit, outside of soil value, to zero.
no FOREST VALUATION
In the same way, it can be shown that for definite costs and
income, the profit determined for any year may be converted
into that for any other year by the use of Formulae I and II.
Substituting 5„ for Sc in Formula Li, thus reducing profit
to zero, this formula becomes
i.o/?"
Then
- (C + £) = 5„.
I. op"
Resuming the value of Sc as cost of land, the profit is
P = ^ + ^'^ + ^ -(C + E)-Sc
I. op"
= 5„ — Sc. (See L3.)
Since Formulae Li and L3 are thus derived from Formula L
by discount (II) , the reverse is true, and for any year a
. P = iS,- Sc) I. or. (L4)
128. Profits Expressed as a Ratio of Income to Capital. —
The economic forecast shows profits as a net sum or balance
between assets and cost, which sum cannot be realized in money
without a sale of ownership. But the net future income which
is accountable for this balance of profit shown may be also
expressed in terms of interest earned on the cost instead of as
capitalized value (§121). The rate or ratio of income to capital
depends directly upon the period of time elapsing between ex-
penditure and income (§ 23), a fact often lost sight of. In quick
profits, earned largely by the sale of property at an advance in
capitalized value rather than by awaiting the slow realization
of income, the element of time is lost sight of; yet every profit
should be standardized by reducing it to the rate of interest
which it represents on the investment for the period of waiting.
Should a property be sold at double its cost, the profit is
100 per cent on cost. But with the element of time intro-
duced, the rate earned would be as follows (Formula XIV) :
FOREST STATICS — BALANCE SHEET — PROFITS
III
Sale at end of
Rate earned,
per cent.
1 year
5 years
lo years
20 years
50 years
100 years
100
14 9
7.2
1-4
•7
129. Earning Power of Capital Invested in Forest Produc-
tion. — In no form of business does the per cent earned by the
total amount of capital invested equal the per cent earned by
the proprietor's investment unless he furnishes the entire capi-
tal without borrowing (§32).
In business receiving annual income, the capital needed to
carry the current expenses is usually borrowed, and therefore
does not share in the profits but receives p per cent only.
These arguments are used as a justification for separating the
capital invested in a forest crop into two portions, one of which
shall be computed at p per cent, and not share in the profits,
while the remainder is the basis upon which the rate of income
is computed. By thus reducing the amount of profit-sharing
capital, the rate of profit is increased or reduced on this capital
as the earnings exceed or fall below p per cent on the total in-
vestment.
For instance, it may be arbitrarily assumed that the o\\Tier
acquires the land, but borrows the funds needed for all expenses
of crop production (Group A, § 104), as silvicultural expenses,
and maintenance or annual charges. It has been shown that
such a transaction would seldom occur. But if it does, these
expenses must first be returned from income, with compound
interest at p per cent. The remaining sum is net income
earned by the owner's capital, Sc. ■
Net earnings = F -f 5„ - \C{i.op^) -f E (i.o/>" - i)|
= F-f 5„ + £- {C + E)i.op\
The substitution of Sc or of S, for 5,. will adjust this formula
to any desired condition (§§122, 123 and 125).
112 FOREST VALUATION
In this formula, E = , and as p is determined, this term
o.op
has a definite value (but see Formula N2).
Capital invested by owner = Sc,
Rate earned = x per cent,
Period of time = n years.
By use of Formula XIV (§ 89),
Sc (i.ox") = Y + S,+E- {C-\-E) i.op%
,,,„ . (F + 5.+£)-(C + £)x.or (N)
^c
or X = 100
This division of capital is purely arbitrary. An equally
justifiable assumption is that the owner also invests the capital
needed for silvicultural operations and all initial expenses (Group
B, § 104). In this case, the borrowed capital E is first repaid
with p per cent interest from the gross income and x per cent
determined for the remainder.
Net earnings = F + 5„ - £ (i.o/>" - i),
Capital invested by owner = Sc -\- C.
Then (5c + C) i.ox" = F + 5„ + £-£ (i.o^"),
„ F + 5, + £-£(i.or)
"°^ = s:^
(Ni)
or X = 100
"/F +5, +£-£(! -or)
Sc + C )
Both of these solutions (N and Ni) give a value for x,
greater or less than that actually earned by the entire capital
investment. The difference is greatest when only the investment
in soil is used as a basis. Method Ni has been advocated for use
in this country.*
The true "economic" per cent (§121) earned by an investment
is the rate paid on all capital invested for periods of one year or
* Forest Management of Loblolly Pine, Bulletin 11, U. S. Department of Agri-
culture, W. D. Sterrett, Jan. 23, 1914, p. 21.
FOREST STATICS — BALANCE SHEET — PROFITS 113
over, regardless of ownership. This investment must include
the annual expenses which are not cancelled by annual income.
In this case,
Net earnings = F + 5„,
Capital invested by owner = Sc + C -\- n{e) (see § 105).
Then net earnings = F + 5„ - ](Sc -hC -\- E) i.ox" -El,
Y-\-S,-\-E
i.oa;'* =
or X = 100 1 y 7; — , ^ , ^ — I
Sc-\-C + E
i :/Y + 5, + £
Sc^C-\-E
m
6 •
But in this formula, E = , and as x appears on both sides
o.ox
of the equation, a solution is not reached. The value of x may
be obtained by trial. A trial per cent x' is first substituted for
X in the expression and the value £' determined. The
o.ox
solution then gives a value a;". This new value is then sub-
stituted for x' and 77 gives £". The second solution of the
o.ox
equation will give a value for x usually within one-tenth of one
per cent of true value.
This result is satisfactory, for the rate, x, is a prediction or
estimate in most instances; or where results are at hand, it is
merely a calculation intended to gauge the relative merits of
the investment compared with others. For such purposes, even
§ per cent is sufficiently close.
In the solution of the value of x, the use of logarithms is not
usually necessary. The value may be found in Table VI, op-
posite n years, and interpolated to one-tenth of one per cent.
This method of gauging the profits of forest production is far
more suitable to new conditions characteristic of the industry
in America than the method of capitalizing income in the form
of soil value or computing the "forest per cent." In almost
every instance, except for lands owned by the nation, the cost of
acquiring the property is known, or is a determining factor to
be decided previous to undertaking forestry. It is upon this
114 FOREST VALUATION
investment that profits must be computed whether or not the
capital invested in future expenses is also entitled to share in the
profit. The rate of interest earned offers an intelligible standard
of comparison with the common forms of business enterprise.
The profit (§ 39) or enterpriser's gain is then found as a ratio
instead of a lump sum, by subtracting p per cent from x per cent.
European methods of computing the rate x earned by capital
invested in forestry differ from those advocated above. The
capital investment is regarded as the cost of the forest soil,
in accord with Method N. But instead of computing the rate
of compound interest which is earned on Sc, the first step is to
calculate the annual "rent" earned on 5„, which is equivalent
to 5„ X 0.0^. This, divided by Sc, gives o.ox, and x is termed
the mean annual forest per cent. As expressed by SchHch,
x = ^Xp. (N3)
The per cent x in this formula is more sensitive than in
Formula N. When x > p,2L higher rate is shown for x than that
given by method N. This is due to the effect of using different
rates of interest, x versus p, in discounting by the two methods.
Formulae N to N3 express profits only for the beginning of
the enterprise, as forecasts or as summaries. When the poten-
tial annual or current rate of interest is desired, termed the cur-
rent annual forest per cent, this may be found, after the timber
becomes of merchantable value, by first determining the annual
increase in this stumpage value (Chapter XII, § 182).
Let F„ = stumpage value in year n.
Yn+i = stumpage value in year n -\- 1.
From the increase thus shown must be deducted the annual
expenses e. The investment consists of the cost of the forest
for the year n, consisting of soil and timber, and represented
(Formula A2) by "Fc
The formula for current forest per cent is
-(^
\n-Y^-e^
"^Fc
100 (N4)
FOREST STATICS — BALANCE SHEET — PROFITS 1 15
for which may be substituted
For a normal forest (§ 109) the forest per cent is obtained by
methods identical with those applied in Formuku N3 and N4. The
value of such a forest (F2) divided by its cost, which is either
the cost of purchase or of production (§ 109), gives the basis for
the following formula
x = ^Xp. (Ne)
re
130. The Relative Importance of Profits in Private versus
Public Forestry. — In Chapter III it was emphasized that for
very long periods the operation of the laws of compound in-
terest requires the lowering of the rate of interest, ''/> per cent,"
used to gauge the relative value of investments. It is easily
shown that enterprises running for periods of over 50 years
cannot earn to exceed 4 per cent except under the most favor-
able circumstances, although the specific net profits above
cash outlay may exceed this outlay by several hundred per
cent (§§53 and 128).
Private industry caimot be expected to undertake the business
of forest production on a scale commensurate with our future
needs, for the following reasons:
1. A higher rate of interest is required on private than on
pubUc undertakings.
2. The average business life of an individual is shorter than
the period required to produce a forest crop.
3. The private enterprise depends for its existence solely on
profits, while the pubHc undertaking includes the benefit to the
community as the principal item of income, and may therefore
be conducted at an actual money loss and still be justified.
4. In many instances, lands are already the property of the
state or nation, and no cost or interest on land need be charged.
The sole cost of public forestry in such instances is the sum of
actual outlays for protection and silvicultural measures.
5. PubHc forestry can and should be conducted on a very
Il6 FOREST VALUATION
large scale as it is on the national forests, with resulting economy
in all measures of protection, technical administration and
improved efficiency which will increase future revenue.
6. Private ventures are based on the assurance of an enter-
priser's gain or net profit above p per cent, which is a matter
of indifference in public enterprises. The necessary lowering
of the interest rate on long investments, the postponement of
results and the increasing importance of the governing rate of
interest as affecting the size of the indicated profits lessen the
individual's interest in forest production as a business venture,
and strengthen the reasons for state or national enterprise.
After the forest capital has been destroyed, its restoration by
planting or seeding can be of interest to private owners only
for species, regions and sites which promise reasonably quick
returns and high values, such as are shown for white pine in New
England or Loblolly pine in Maryland. But before destructive
lumbering has made such restoration necessary, especially for
forests which show a succession of age classes, such as spruce in
the northeast, the private owner may often continue to operate
indefinitely, with profit, by removing only the more mature
timber. This difference is due to the fact that such a forest
produces income annually with which to cancel expenses. Under
such circumstances the specific balance sheet shows an annual
profit; there is no accumulation of unpaid interest, and by fore-
going the "profits" he might obtain at any time by withdrawing
the entire capital, the owner substitutes a permanent annual
income.
In considering questions of public policy, no sound conclusions
can be reached if the financial questions involved are neglected.
The difficulties of inducing private owners to voluntarily enter
forest production as a definite business are evident. If this
course is made mandatory by legislation, as is seriously contem-
plated in some states, it must first be shown that the expenses
thus required are in reasonable relation to the income that can
be expected from forestry. Otherwise it would appear that the
state is attempting to shift onto private shoulders a responsibility
which it should publicly assume.
FOREST STATICS — BALANCE SHEET — PROFITS
117
This public sentiment for regulation is the expression of an
instinctive protest against destructive lumbering as a policy,
for it is far more expensive and wasteful to tear down a busi-
ness and then rebuild it than to continue it as a going concern.
Whether or not forest owners can afford any other policy than
destructive lumbering, they should in any case use every effort
to do as little harm as possible to reproduction, protect cut-over
lands from tire, and induce the formation of a new crop of natural
seedlings on absolute forest soils. In proportion to the effective-
ness of such measures for perpetuating the productiveness of
forest lands in private hands, the desire on the part of the pubhc
for drastic interference with private rights will lose its force.
131. Forms for Specific Accounts in Forestry, — The accounts
kept by the proprietors of a large business, involving the owner-
ship and management of many separate parcels of forest land, and
a more or less continuous annual income and outlay, must show
specifically the cash transactions and actual cost of the property.
The capital accounts should record cost of permanent assets.
But to this cost may be added the annual excess of actual cash
expenses over annual income, incurred for the care and mainte-
nance of the property (§57). The only alternative is to exhibit
a corresponding deficit in the balance sheet. The choice between
these methods will be based on the character of the assets.
For property increasing in value by natural growth of timber
there can be no serious objection to the process of adding actual
costs to the capital account.
A depreciation fund is seldom required for such an enterprise.
The equipment subject to depreciation is of such small total
value that it will usually appear as expense.
Assets
Capital assets:
Land.
Timber.
Other property
less depreciation.
Current assets:
Cash.
Accounts receivable.
BALANCE SHEET
Liabilities and Proprietorship
Capital paid in.
Surplus.
Loans (liabilities).
Current liabilities:
.Accounts payable.
ii8
FOREST VALUATION
TRADING, AND PROFIT AND LOSS ACCOUNT
A. — Land
DeUi
Cost, to date of sale.
Balance, gross profit, to general outlay
and income account.
Credit
Sales.
Balance, loss, to general outlay and in-
come account.
B.
Debit
Cost, to date of sale.
Balance, gross profit, to general outlay
and income account.
Stumpage
Credit
Sales.
Balance, loss, to general outlay and in-
come account.
C. — General Outlay
Debit
Silvicultural operations.
Protection.
Maintenance.
Administration.
Taxes.
Loss, from lands.
Loss, from timber stumpage.
Balance (profit).
AND Income Account
Credit
Leases.
Grazing.
Secondary forest products.
Tiiinnings.
Profit, from lands.
Profit, from timber stumpage.
Balance (loss).
Balance (loss).
Interest on loans.
Depreciation.
Surplus (profit for period).
Balance (profit).
Deficit (loss for period).
CAPITAL ACCOUNTS
D. — Land.
Debit
Cost, by parcels.
Additions to cost by reason of annual
cash expenses.
Credit
By cost to date of sale.
Balance.
E. — Stumpage
Debit
Cost, by parcels.
Additions to cost by reason of annual
cash expenses.
Credit
By cost to date of sale.
Balance.
F. — Distribution of Annual Loss, from Profit and Loss Account
Debit
Deficit.
Credit
By increase of capital assets.
FOREST STATICS — BALANCE SHEET — PROFITS
G. — Distribution of Slrplls
119
Debit
To dividends.
Credit
Surplus, profit and loss account.
H. — Changes in Value of Capital Assets
Debit
Appreciation or marking up of value of:
Stumpage.
Land.
Credit
To appreciation of assets.
Depreciation of assets.
To losses of timber by reason of fire,
etc.. not insured.
132. Forms of Economic Accounts in Forestry. — During
the formative or constructive period of a forest investment,
previous to the receipt of the principal income, the economic
status of the entire investment may be shown by a cost account,
in which accrued interest is charged against all outstanding
capital investments.
Debit
Outlay for all sources.
Accrued interest on outlay,
Outlay and Income Account
Credit
Income from all sources.
Accrued interest on income.
Balance, representing net investment
or cost.
Since such an account is intended merely for the owners' in-
formation, the "interest" cost is a legitimate one. In the same
way the "economic" balance sheet (§ 73) can be made up by
discounting the value of future income and entering the assets
on the basis of their capital or expectation value.
"Economic" Balance Sheet
Credit
Total net cost of land and timber from
outlay and income account.
Net cost of improvements (original
cost, less sums returned for de-
preciation).
Potential surplus.
It is this balance which is the object of nearly all the calcu-
lations discussed under forest finance.
Debit
Expectation value of land and young
timber.
Value of improvements.
Potential deficit.
CHAPTER IX
THE APPRAISAL OF DAMAGES
133. Principles Underlying Appraisal of Damages. — In ap-
praisals to determine damages, the principles underlying the
valuation of forest property reach their fullest development
and receive their most complete application. When the eco-
nomic basis of forest valuation is understood (Chapter IV) it
will be seen that the guiding principles of legal practice indicate
a consistent effort to apply this basis in determining compen-
sation for damages.
The uncertainty and difficulty of authoritative determination
of future values is here, as elsewhere, the most serious drawback
to the unqualified adoption of expectation values as the basis
for measuring losses or damages. Whatever substitute methods
are adopted, as, for instance, the determination of cost, are dic-
tated by the greater relative certainty of the figures thus ob-
tained, which consideration may outweigh in importance the
fact that these figures do not accurately represent actual value
or loss.
These legal principles may be summarized as follows:
a. Damages are payable in money. Compensation, not
physical restoration, is required.
b. The difference in value of the property before and after
the damage is the measure of damages. The value of the por-
tion destroyed is not in itself the measure of damages, but is
a means of ascertaining this difference in total value. Soil and
timber are real estate. The value of this real estate as a whole,
before and after the injury, is the measure of damages.
c. Damages must be appraised on the basis of the most prof-
itable use to which a property is adapted, as indicated by the
use of similar contiguous property. Sale value may or may not
be a correct index of real value.
THE APPRAISAL OF DAMAGES 121
d. Values must ordinarily have a commercial or utilitarian
basis, but aesthetic values, or the value of "legitimate gratifi-
cation" (§ 4), must be recognized whenever based on elements
generally accepted by the pubUc at large. Sentimental value
peculiar to the owner cannot be admitted.
e. Loss of income may be made the basis of damages; but
this loss should be discounted to the present, and will then equal
the loss in capital value.
/. Cost of restoration, while frequently ruled out, is admitted
when shown to be less than value, or when value is difficult to
determine.
g. Ordinary ''profits" or income is the basis of damages.
Excessive profits, which do not allow for normal losses, and
speculative or contingent profits, which depend upon uncertain
future factors, such as increased prices, are not admitted. The
element of time, intervening between the damage and the real-
ization of profit, does not bar the consideration of these profits
provided they are reasonably certain to occur and are properly
discounted.
//. Damages must be actual, present, imminent or reasonably
certain to occur. The damage itself may be indirect, but it
must be proximate, or traceable directly to the offending cause,
as, for instance, the destruction of crops, due to cattle, through
leaving a gate open. The physical destruction of property by
fire is an actual present damage. The cause may be a spark
from a defective locomotive igniting the debris upon an improp-
erly cleared right of way, several miles from the property
destroyed. The determination of the money value of the dam-
age is the only element of uncertainty in the process.*
* The entire subject of damages is the source of wide dififerences of legal opinion
and practice in different states. Precedents and rules adopted in one state are
frequently at variance with the decisions in other states. The measurement of
damages is largely a determination of facts rather than of legal principles; the
ascertaining of the amount and character of the injury done to the property and
consequent income of the plaintiff. The above rules appear to agree with the
principles laid down in Sedgwick on Damages, gth Ed., Vol. 3, §§ 931 to 933.
The contention of foresters that expectation value, where it can be determined, is
the basis of damages, finds its clearest legal expression in rule b above, in which
form it is receiving increasing recognition in state courts. See reference above for
citations of cases.
T22 FOREST VALUATION
134. Elements of Damage to Forest Property. — Damage
may occur to forest property through injury or destruction of
timber, soil or permanent and temporary improvements. For
permanent improvements, the cost of replacement or repair is a
fair basis of valuation. For temporary improvements, the present
value would be found by subtracting depreciation from cost, or
estimating the future usefulness of the improvements destroyed.
The problems discussed in this chapter are those which deal
with damage to timber crops and forest soil.
The separate elements which may constitute damages are
itemized as follows:
Mature timber.
Young or immature timber.
Forest soil.
Watershed protection.
Reduction in total value of property not otherwise damaged.
^Esthetic values.
135. Physical Separation of Timber from Soil. — Damage
to forest property may take many forms, but only those sources
of injury traceable to human agencies financially capable of mak-
ing good the loss, are of interest in appraisal of damages. All
losses involving actual destruction of property are irreparable
in the sense that the entire value destroyed is lost to some
person. Losses from insects, wind or disease must be appraised
for the information of the owner. But when the loss is to be
shifted to another, and collected by legal processes, its appraisal
must rest upon facts that can be accepted by a jury.
Timber trespass takes the form of removing forest products
from the soil without the consent of the owner and, incidentally,
of injury thereby caused to unmerchantable trees. The main
element of damage is the value of the timber destroyed or taken.
Damage by fire results in the destruction, or partial destruc-
tion, of the tree growth, or merely in injury and retardation of
growth. Except in the most unusual conflagrations, the timber
even if completely killed is not consumed or removed in the sense
that it is in lumbering. Much of this fire-killed timber, if large
THE APPRAISAL OF DAMAGES 1 23
enough to be merchantable, can be salvaged. After the great
fires of 1910 in the Pacific northwest about 90 per cent of lire-
killed timber owned by private parties was marketed. If not
merchantable, the inflammable dead material, rotting and fall-
ing, greatly increases the tire hazard (§ 200). In practically no
case does tire bring about a complete separation of the tmiber
from the soil.
136. Separation of Value of Timber from Value of Soil. —
As a step in the appraisal of damages it may be necessary to
determine separately the value of timber and of soil.
By Formula G the separate value of timber is
F + 5„ + £
I .op"'"
-(5„+£)
which gives the value in the year a for the timber by sub-
tracting the value 5„ from the total value of the property.
The residual value, land, then equals S^, and if the damage just
equals the value of the timber, it may be appraised by this
means. But this assumes that the physical separation actually
takes place, and that the soil or property 5„ is left, as a result,
in the same condition which it would be in after lumbering and
brush disposal. This premise becomes evident by analysis of
the above formula which equals
= (
I.O/>"~" \ i.op"'"/ \ i.op"'
F + 5„ + £
I .op"'
-E -S,.
In this form the separate values of land and timber are clearly
shown. But the expression 5„ ^^ is equivalent to the
difference in value of 5„ if freed for use now, and its present
value if freed for use only after the lapse of n — a years.
This difference is equal to the present, discounted or capital
value of the interest on 5„ for n — a years, or
5, (i.o/)"-" - i)
i.o/?"""
124 FOREST VALUATION
It is important to understand the significance of this treat-
ment of soil value in valuing timber. One way of describing
this "expense" is that the owner of the timber is charged with
the interest on the soil value, or ''soil rent," as a cost of bringing
the timber crop to maturity, dating from the present year.
This is the assumption made by Schlich.* This would class
soil rent as an actual future cash expense similar to taxes. But
soil rent cannot be an actual future cost or outlay, unless a differ-
ent person owns the soil and rents it to the one who grows the
trees. The capital value of the property, timber and soil, takes
no account of this cost (Formula D2), for — is the dis-
^ I. op"""
counted net income, which constitutes soil value.
A separation of the present net value of the standing timber
from the value of subsequent crops (soil 5„) gives
Y 4- E
■ — E = value of timber,
I. op"-"
S ...
"-3- = present value of soil if released inn — a years.
i.op
Comparing this with
F + 5„ + £
— {S„ -\- E) = value of timber,
I.op"''
Sj, = value of soil,
the sum of values for soil and timber, or the value of the property,
is identical, but the proportion of this total value assigned to
the timber is greater by the first method than by the second,
by just the amount of the discounted interest on S^.
In the second method, instead of assuming that the timber
owner is charged with interest on 6'„, a much clearer conception
is that the land owner, who in fact is the same person, benefits
by the release of his land value from its necessary use for w — a
years to produce the revenue Y. He therefore cannot de-
Y 4- E
mand the full value E for the crop, but accepts a
i.op"-"
value smaller by the exact amount of the excess in value of
* Schlich's " Manual of Forestry," 4th Ed., Vol. Ill, Part II, Chapter III, p. 133.
THK APPRAISAL OF DAMAGKS 1 25
5
Sv over ^^- The trespasser, in settlinj^ the damages, thus
" purchases " the tmibcr separately and is given the benefit of
subtracting the discounted future expense of "soil rent" in re-
duced damages. It is now possible for the owner to obtain
this soil rent on another crop of timber that can be planted
immediately. He is not justified in collecting it in the form of
increased net damages.
The subtraction of soil rent from present value of standing
timber in appraisal of damages is therefore a mere matter of
book-keeping between the owner and the trespasser, by which
the owner is the loser in damages, but is compensated by the
release of the land.
It is evident that unless these conditions are actually secured,
and the land not only released from the crop but left in the con-
dition which would normally result from logging, such an as-
sumption absolutely fails to appraise the true damages, which
are in excess of the amount indicated.
In European practice, the expectation value for thie soil 5„
is first computed. This value is then introduced not only in
determining expectation value of standing timber, but is also
substituted for the cost of the soil.
The eff'ect of using 5„ as the so-called "cost" of the soil is to
eliminate "profit" or enterpriser's gain, and to balance costs and
income at p per cent (§ 127). Not only will the costs balance
the income at the final year, but, by formula Ki, substituting
5p for Sci
^ lor-^ ^ ~ ^^'' ^^) = ^C'rS, + E) i.op" - (5„ -f E),
which indicates that this so-called "cost" is exactly equal to
expectation value of timber for any year during the growth of
the crop. This means that if actual cost of soil is not known,
or does not enter into the problem, as in the case of govern-
ment lands, and the returns from forestry are computed on the
basis of a fixed rate of interest, p per cent, throwing all "profit"
into terms of soil value (§ 127), standing timber of a given age
126 FOREST VALUATION
will have the same value whether computed as a cost or as a
capital value. To compute this value under actual conditions
in this country, either the standard rate of interest for many
sections must be very low or a negative soil value may have
to be used, which is perfectly practical. The method is so
foreign to our ideas of finance that it should be discarded in
favor of the more intelligible plans of utilizing actual costs and
sale value, or of discarding altogether the subtraction of inter-
est on soil as a deduction from damages.
137. A Basis of Damages : Cost of Replacement. — The
objections to the use of cost of replacement as a measure of
damages are that it does not represent the true value of the
property nor measure the loss (§§i33Z>, 68). Its merits lie in the
certainty of the figures, derived as they are from past experience.
Very young timber or reproduction may be completely de-
stroyed by fire. It has no sale value, except, rarely, for Christ-
mas trees. The expectation value of such young stands is
difficult to compute. But the cost of planting and the annual
charge for protection and administration can be easily deter-
mined.
Assuming that the trees have been completely killed and that
no further expense is needed to prepare the ground for a new
crop, the cost, including interest on soil, the use of which is
lost, will be, for a years,
(C + 5. + E) I .o/>« - {Sc + E) . (A)
By substituting the capital value of soil for Sc, this cost be-
comes equal to the expectation value of the young timber
(§ 127). But this value 5„ is even more unreliable than the ex-
pectation value of the young stand (§116). If Sc is charged
as a cost, it will be determined by the price paid for the soil,
or the sale value of similar bare land in the vicinity.
Where, as in government forests in the west, land has no
purchase price, the practice is to omit this item from cost. The
cost of the crop then becomes
{C + E) i.op'' - E.
THK APPRAISAL OF DAMAGES I27
The effect of this omission is to decrease the damages demanded.
The cost C is included except when natural reproduction is
sure to occur. In this case, C may be omitted, and the damages
would then amount merely to the annual expenses
Eii.op" - i).
In ordinary cases, the entire annual charges, including admin-
istration, taxes and upkeep, would constitute the cost. But hi
national forests, administration expenses are frequently offset
by revenues from grazing, while taxes are not paid. The item
e may then include only the cost of fire protection. The rate
of interest adopted in government forestry is seldom over 3
per cent. For these reasons, damages based on cost for private
forests usually exceed those claimed for government timber of
the same quahty.
Excessive costs of replacement are sometimes demanded on
the basis that the trees burned should be physically replaced
with others of Hke size. An owner who has a young grove
destroyed feels that the small value represented by the cost of
growing the trees does not compensate him for the loss of the
grove. His trees are gone and he will have to wait an equal
period for a new plantation to attain like size. If repeatedly
burned, he would never secure his grove. The excess value
indicated in such a case actually exists, both as sentiment on
the part of the owner and as an addition to the value of the
entire property (§ 133^). Neither of these elements are best
valued by attempting to estimate the cost of immediate physical
restoration of the property, but are discussed under other head-
ings (§§ 138 and 147).
With increasing age of the timber, the relative merits of cost
as a basis, compared with value, become less and less. Wherever
there is a marked divergence in the two, whether cost exceeds
or is less than value, the collection of damages based on cost
cannot be justified by any principle of law. Its use is clearly
a make-shift and will be confined to young timber whose age
does not exceed one-half the period required to bring the trees
to maturity.
128 FOREST VALUATION
138. A Basis of Damages : Sale Value. — Sale value is a far
more reliable indication of damage than cost. In forest property,
it is always a question as to whether the timber destroyed or
removed can be valued separately, and by this means the loss
in value to the property as a whole be determined.
The ultimate sale value of the timber is a reliable basis for
damages, as it is the basis of capital value not only for the tim-
ber but for the soil as well (Chapter VII). Whenever timber
is destroyed which has a present sale value, this value must be
ascertained, and will be accepted as the measure of damages
for the timber destroyed, unless it can be proved that other
damage has been suffered. If the timber is young and growing
rapidly, or if it is at present inaccessible but certain to be de-
veloped in the near future, its present stumpage value or sale
value may not represent its true value to the owner, who intends
to hold it. By' proving with reasonable certainty the existence
of this higher value, sale value even for merchantable timber
can be set aside. But the burden of proof is on the owner, and
courts will accept sale value for timber unless a strong case for
higher values can be shown.
The loss in sale value of the entire property is not so easily
gauged. It is a great advantage to be able to value the income,
in the form of timber, rather than to judge of the effect of this
loss of timber upon the selling value of the property. In theory,
the latter loss more accurately gauges the damage (§ 1336).
There are cases when the value of the materials destroyed is
wholly inadequate as a measure of the loss resulting to the
owner.
The most direct case is where a portion of a large stand is
destroyed, appreciably reducing the total amount that may be
logged. This raises the cost per thousand feet, or unit, for
logging the remainder (§§ 98 and 174). The increased cost is
subtracted from stumpage value of the remaining timber. The
total loss is equal to the sale value of the timber burned plus
the loss in sale value for the entire remaining body of timber.
A woodlot frequently adds materially to the sale value of a
farm. Its destruction would represent a loss many times greater
THE APPRAISAL OF DAMAGES 1 29
than the value of the wood, and, under definition b, this difference
in value for the entire property must be the basis of damage.
For such losses, affecting the value of the entire property,
the appraised loss in sale value is the safest guide, as it eliminates
sentiment or personal considerations (§ 12,3d).
Were the general public fully alive to prospective values of
young timber and of forest lands, and agreed upon the rate of
interest which should apply to forest investments, and if a suffi-
cient movement in forest real estate existed so that these opinions
could be crystallized by sales, there is no doubt that sale value
for immature timber would approximate its real value so closely
that it might be accepted as a basis for damages as readily as
the sale value of mature or saleable trees. This would be an
immense advantage, as there is never any objection to accept-
ing sale values whenever they are evidently just to the owner.
But with the growing of trees as a business still in its infancy,
or perhaps not practiced at all, the sale value of such young
timber is likely to be far below its capital or expectation value.
Under principle c (§ 133) a great injustice would be done the
owner by accepting such a basis of settlement.
In regions where immature timber is commonly regarded as
having little if any value, the claimant must prove the injus-
tice of such valuation by demonstrating his intention and ability
to bring the young trees to maturity and to realize the ultimate
revenue. It would be difficult for a lumberman who customarily
abandons his lands to fire, to do this. But the United States
Forest Service has no trouble in proving the value which it
places upon such young growth. In regions where forestry is
extensively practiced, and upon lands which the owner has had
under management, such as plantations, not only will sale value
more nearly approximate real value, but it will be easier to secure
the true expectation value independent of the standard set by
sales.
139. A Basis of Damages: Expectation or Capital Value. —
Not only does sale value fail to establish the value of property
to the owner for his own use, when this value is unfamiliar to the
public at large, but it frequently happens that there are no sales
130 FOREST VALUATION
of similar property on which to base such values. There is a
further difhculty in judging of the loss in sale value resulting
from the damage. For these reasons, and in order to base the
damage fairly upon loss in income or use, the capital value or
expectation value of the property, as well as of the portion de-
stroyed or income lost, must be calculated, in spite of its uncer-
tainties.. These uncertainties (§ 67) lie in the determination of:
Future yield of merchantable material.
Date of maturity or final cutting.
Future price of products.
Rate of interest adopted.
Authoritative studies of the yields per acre for important
commercial species are becoming available which indicate not
only the amount of merchantable material to be expected,
but the proper age at which to cut the stand. In the absence
of such data, experience of farmers and woodlot owners in re-
gions of second growth can be cited.
It might seem that the certainty of the upward tendency of
prices for wood products would justify the adoption of higher
stumpage values as a basis of damages for destruction of young
timber (Chapter XII). This argument is ingeniously used by
the Forest Service to justify valuation of very young timber on
the basis of cost and thus secure higher values than would be
shown by capitalizing income on the basis of present stumpage
prices. It is probably true that owners forced to accept settle-
ment on terms of expectation value based on present prices,
for timber which will not mature for several decades, are losing
a profit which in all reason they may expect. But the deter-
mination of the amount of this increase introduces a speculative
element into a calculation already sufficiently complicated, and
runs directly counter to principle g (§ 133). Damages are in-
tended to fully compensate the owner for reasonable profits,
and no objection can be raised to admitting the effects of the
growth of the timber or its increase in quality, but the fluctua-
tion of stumpage prices will not ordinarily be admitted by a court
and it is the part of wisdom to base the evidence upon prevailing
prices. In such calculations as an owner may make for his own
THE APPRAISAL OF DAMAGES 131
information, he is at liberty to speculate on the increase in
prices as he sees fit.
The rate of interest will remain a matter of dispute until
forest production takes its place as a recognized business. The
higher the rate used, the smaller and more conservative will be
the value placed upon the damage. This is directly opposite to
the effect of a high rate used in calculating cost of replacement.
In such a case, the higher the interest rate, the greater will be
the cost, and the smaller the value of the crop (§ 121).
140. Damages to Merchantable Timber. — Timber killed by
fire is saleable if accessibly located and a market exists capa-
ble of absorbing it before it deteriorates from rot and insects.
If sales can be made, the damage is the difference in value of
the timber before and after the fire. To this loss must be added
the loss in stumpage value of timber not burned but whose
logging costs are increased as a result of the diminished quan-
tity of stumpage (§ 138).
Let V = value of damaged timber,
L = total damage.
The loss is expressed as
L = Y -Y'. (0)
Timber cut illegally may be settled for with or without suit,
on the basis of the stumpage value.* But it is poor satisfaction
to an owner to collect merely the present value for small timber
which he desired to preserve. Additional damages can be ob-
tained by the owner, if he can prove:
a. That the expectation value of the timber is greater than
its present stumpage value. Unless increase in prices is per-
mitted, this is not always easy to show.
b. That the sale value of the entire property has been in-
jured by the cutting.
* An important principle of damages widely recognized is that in case of
wilful trespass, the value of the products wherever found, is the measure of the
damages. In such cases the value of the timber after feUing, transportation, or
manufacture may be the basis of damages. Sedgwick on Damages, 9lh Ed.,
Vol. m, §934.
132 FOREST VALUATION
c. That its value for other uses, as park purposes, has been
injured.
He may also instigate a criminal action against the perpetrator
provided the trespass is wilful. In case of a logging contract
under which the contractor is required to leave trees of certain
sizes, constant inspection by the owner, cancellation of the
contract, or perhaps a clause requiring payment of double
value for forbidden timber is more effectual than damage
suits.
Merchantable timber injured by fire but not killed must be
appraised on the basis of its present saleability, and the extent
and character of the damage to its sale value. If it can be sold
at once, the loss will be measured by deterioration in grade
and quantity due to the fire. If it must remain for some years,
a further deterioration may be expected as the result of fungi
and insects. If this can be measured, it should be allowed.
Timber whose sale is necessarily postponed, even if of mer-
chantable size, should be valued by the same method as young
or immature timber. Its expectation value, as reduced by rot
and insects, and not its present sale value, should be the basis
of damage.
141. Damage to Immature Timber: Partial Loss. — For
reasons given in § 138, sale value for immature timber de-
stroyed does not compensate the owner, and it rarely happens
that the sale value of the property, either before the damage
or after it occurs, is a safe index of the damage. Cost of
replacement may be used, as suggested in § 137. But for
timber more than half grown or approaching maturity, capital
or expectation value must be the means of approximating the
loss in value to the property, and this method should always
be used as a check on cost, even for very young stands.
Where a stand is injured but not killed, the trees will continue
to occupy the soil until they reach merchantable size and are
cut. The damage to the crop is measured by the loss in value
of the timber when cut, traceable to the fire.
Y = original expected value of timber when cut,
Y' = expected value as reduced by fire damage.
THE APPRAISAL OF DAMAGES 133
The future net value of each of these crops in the year n is,
respectively, when 5 represents either Sc, S„ or S„
Y-{S-^E){i.op"-'-i),
r -(S-\-E){i.op"-''-i),
as the expenses continue undiminished. The difference in net
value, representing damages, is F — Y'. Discounting this loss
Y — V
to the present year a gives 3^- (Oi)
Under normal conditions, the expected value of the crop cannot
exceed
Y - (5 + £)(i.o/>"-"- i).
But if F'< (5 + E) (i.op"-" - i),
then Y -Y'>Y -{S-\-E) (i.op"-" - i),
and damages will exceed the expectation value of the timber.
That this result coincides with actual conditions can be easily
shown. A damaged crop of timber which will just pay expenses
can be left till mature. But what is to be done with a stand
damaged so severely that it will not meet these future expenses?
Its presence prevents the use of the land for a new crop, yet the
cost of removing it is a net loss. Assuming that the timber
Y -Y'
will be left standmg, ■ should be used whenever Y' can
^ I. op"-"
be determined. The total loss to the value of the property
rather than to the timber is thus measured (§ 1336).
142. Damage to Immature Timber: Total Loss. — When
immature timber is totally destroyed or so badly injured that it
must be removed if any further profitable use is to be made of
the soil, two factors influence the method of appraisal. The
soil is released by this removal, and its value advanced from
5
^^ to S^ (§ 136). But the. value 5^, is materially altered
to the injury of the owner. As S„ is merely the value of the
discounted net income, all future expenses directly diminish
this value, as is seen in the formula for S„ or
Y - C
I. op"— I
134 FOREST VALUATION
The initial expense C includes brush disposal, soil prepara-
tion, and the cost of securing reproduction. The removal of
burned and worthless timber increases C abnormally. The
expense E representing includes fire protection. A fire
trap, caused by debris, must either be removed as an initial
cost or an additional annual expense e' be incurred, propor-
tionally increasing E to E' for at least a few years.
If the value of the burned timber is appraised as
i.o/>""'
the owner must be left in possession of a value for land, 5„, un-
diminished by such expenses (§ 136). The expense of restoring
the original value of S^ is C — C, in which C represents
the costs of securing and protecting the new crop after the
fire.* For instance, should natural reproduction, by sprouts or
seed, be the normal method, but as a result of the fire, planting
becomes necessary, the cost of planting constitutes a damage.
If the owner would have had to plant anyway, the damage in-
cludes only the cost of removing the debris or protecting the
plantation from extra fire hazard.
The damage where young timber is totally destroyed may be
summarized as:
Timber destroyed = ^ "^ \^^ ^ - (5„ -\- £),
Further damage to property = S„ — S'^,
Total damage . = ^ "^ ^l^ ^ - (5'„ + E).
In other words, the value of the soil resulting from the fire can
be substituted for its value previous to the fire, thus covering
the total loss in value of the entire property. But as the item
* This formula is technically incorrect, since an additional expense e' — e
occurs probably for but a limited period b. Hence the increased cost of this
(£' — E) (i oi/> — i)
item is • i—^ . This alteration may be made in formula O2.
i.o^
THE APPRAISAL OF DAMAGES 135
(C' — C) as an expense is the equivalent of 5„ — 5'„ in future
value, the practical application of this problem consists in es-
timating the costs of restoring the soil to its original condition,
5,„ and adding these future costs to the value of the timber
destroyed. It must be emphasized that this is not an awarding
of double damages but that the two items are absolutely distinct
and their sum represents the loss in value of the property. The
formula should, therefore, be expressed,
L = ^' + -^^ + ^ _ (5^ + £) + (C - C). (Oo)
i.o/>"~°
The cost of removing dead timber and debris and any extra-
ordinary cost of securing reproduction is thus seen to be a legiti-
mate damage wholly apart from and in addition to the value of
the timber destroyed.
143. Damage to Forest Soil. — Damage to the soil results
frequently from fire, and sometimes this is so serious that the
soil is entirely destroyed. This damage takes two forms,
actual physical injury by destruction of litter, humus and
beneficial bacteria with resulting impoverishment of the soil,
and loss of profits or net income from either present or future
crops of timber, without necessarily injuring the soil itself. Both
results usually occur and there is no accurate way of measuring
the injury to the soil, in terms of money, except through loss in
probable income from timber crops.
Damage to soil resulting in destruction of litter and humus,
but which does not kill the standing or growing trees, results
in retarding their growth. This decreases the volume and value
of the crop. The damage is measured by the reduced value of
the standing timber (§ 141, Oi).
Damage to soil accompanied by complete destruction of
timber can be measured only by the probable efifect of this
injury on the value of a nrcv crop of trees. WTien the soil is
largely vegetable, as in swamps or on high mountain slopes, its
destruction, especially on slopes, may prevent all further tree
growth. The damage then equals 5,. in addition to the value
of the timber burned. WTien the soil is partially destroyed,
136 FOREST VALUATION
it will be difficult to estimate accurately the probable loss on a
new crop, unless the effect of similar burns can be cited.
The cost of restoring soil value by removal of debris (§ 142, O2)
is wholly apart from the appraisal of physical damage to the
soil itself. Except in unusual cases, this physical damage is
exceedingly difficult to measure in terms of value, and, where
timber is destroyed, destruction of soU represents but a small
proportion of the total loss. This item of damage is, therefore,
neglected in most instances.
144. Damage to Single Trees. — When the expectation
value of young timber is made the basis of damages, and the
present value of future crops is calculated, the future expenses
deducted from value are based on the acreage protected and
utilized by the crop. The yield of the timber is also computed
on the basis of area, and in this way the normal loss in numbers
which occurs in all stands with increasing age is allowed for.
In scattered stands of timber, the individual tree becomes
more important, and this importance increases in stands com-
posed of trees of many ages. Damage or loss in such forests
cannot as easily be appraised as for crops of even-aged trees.
The mature timber can be estimated according to its merchant-
able contents. If these trees are still small, though merchant-
able, it may be possible to show that their future increase in
volume and quality, with consequent increase in value, is such
that this discounted value exceeds the present value of the
trees.
If it be assumed that all trees now merchantable will remain
standing, and future expenses are neglected, the expectation
value so obtained will be too high. Such figures must be reduced :
By allowing for loss of numbers;
By pro-rating the crop expenses among the reduced stand, per
tree, according to present volume.
The immature portion of such stands cannot, with any degree
of accuracy, be valued on the basis of individual trees. The loss
in numbers previous to maturity increases with decreasing age,
and the proportional expense to be charged to each tree becomes
wholly problematical.
THK APPRAISAL OF UAMAGKS 137
145. Damage to Many-aged Stands. — The value of damage
to a many-aged stand is determined by the character and value
of the stand. Should the timber be entirely destroyed, its value
corresponds to that given in § 117 or § 118, according to the
age classes represented. The keynote in valuing damage to
stands containing both immature and mature trees of different
ages on the same area is to attempt to separate the stand into
its age classes according to the area which each really occupies.
This permits of the distribution of future costs and avoids
double valuation.
For instance, suppressed and stunted reproduction growing
under old timber may be considered as occupying little if any
area. But if this reproduction would have been the means
of forming a second crop after logging, it must be valued. Its
age should be taken not as the actual age resulting from sup-
pression, but as the age of trees of similar size grown in open
land. Means of determining accurately the proportional areas
occupied by age classes in such forests are not yet perfected.
But an approximation of the area and average "economic"
age of the crop, or age of an even-aged stand of equal volume
and sizes, is the only satisfactory basis for arriving at damages.
The first step is to decide upon the area which should be
assigned to immature timber as a whole. The remaining area
is that occupied by mature trees. The appraiser then decides
whether to divide this immature timber into several age classes,
or to assume an average age for the entire crop and treat it as
an even-aged stand of that age. If more than one age class is
required, the area and average age for each is determined. In
this manner the even-aged stand and area become the basis of
appraisal of damages for many-aged forests (§ 140 to 142).
146. Damage to Watersheds. — The protective value of
forest cover affects, first, the soil itself and its ability to produce
timber crops, and second, the property and interests affected
by stream flow.
Soils subject to erosion may be completely ruined, even for
tree growth, by the effect of removing the timber cover through
fire or logging. This loss would be measured as in § 143.
138 FOREST VALUATION
But the damage inflicted on other property caused by the in-
creasing irregularity of stream flow, floods followed by almost
complete cessation of flow, the silting up of streams and reser-
voirs, and the consequent damage to navigation, waterpowers,
irrigation and agriculture are additional to the loss of the timber
and soil on the property itself. DeHberate ruin or removal of
necessary timber cover, and destruction of grass and brush by
over-grazing, probably renders the owner of such lands Hable for
the resulting damages to others. But the connection between
cause and effect, whfle proved beyond a doubt, is very difficult
to express in money value. Large areas of watershed contribute
to the result, and the damage extends over many years and
varies according to rainfall and other circumstances. To deter-
mine the proportion of this ultimate probable damage for which
the denudation of one acre is responsible, is a mere guess. Such
protective areas should be acquired by national or State govern-
ments and the damage prevented, rather than to attempt to force
private owners to preserve the forest for the benefit of others,
or endeavor to collect damages from such owners for the in-
juries caused by their abuse of the forest cover.
In the absence of commercial value, as where forests are in-
accessible and cannot be cut, the cost of re-establishing the
protective cover, either by natural or artificial means, and of
protecting this area from fire until it reaches the same state of
effectiveness as that which was removed, can properly be con-
sidered as a measure of damages. It is also possible in the case
of forest users, such as lumbermen, to set an arbitrary value per
acre for the protective influences of the cover, and bind the user
by private contract to pay this sum in case of fire occurring
through the carelessness of his employees.
As knowledge of the effect of forests on flow of streams is ob-
tained, it will become possible to arrive at a value per acre of
the protective influence of the forest cover on different water-
sheds. This value may then be used in damage suits.
147. ^Esthetic Values. — The fundamental character of the
value represented by an appeal to the aesthetic sense must be
recognized in appraising damages (§ 4). The gratifications for
THE APPRAISAL OF DAMAGES 139
which mankind will pay money are by no means confined to the
material demands of the body. Simply because it is ditlicult
to place a money value upon such gratification is no reason
for denying its existence. Scenery and beauty are capitalized
by those who provide hotels and camps for visitors, and the
common rights in scenery, especially in the enjoyment of woods
and forests, clash repeatedly with the private property rights
of those who own and may wish to cut the timber, usually to
the loss of the public, without recourse to damage suits. Such
rights, just as in the case of watersheds, are best protected by
public ownership of lands and forests which have peculiar or
exceptional value.
But the private owner who has acquired property of scenic
and aesthetic value is not obUged to accept merely the commer-
cial value of the income from wood products as full settlement
for damages caused by fire or theft. The additional value is
as real to him as similar values are to the public at large. It is
just this common or universal acceptance of this form of value
which permits of its appraisal as an element of darnages. Pur-
chasers can usually be found for estates possessing such advan-
tages, and at prices which would probably compensate the owner
for any reasonable cost he has incurred to secure the results.
For this reason, the aesthetic values destroyed may frequently
be gauged roughly by the loss in sale value of the entire prop-
erty. Where landscape features are afifected the damage can
best be appraised by experts familiar with landscape gardening
rather than forestry.
148. Punitive Damages. — Damages in excess of loss in
value are sometimes provided for by law in case of destruction
of property belonging to the state. This is not justified by
any principle applicable to private owners, but is rather an at-
tempt to enforce punitive measures as a matter of public edu-
cation. It lies halfway between civil judgments and criminal
penalties, in which the offender is punished as a public example.
The state of Xew York has such a law, providing a penalty of
$10.00 per tree destroyed on the Forest Preserve. The advantage
of combining punitive measures with civil suits for damages is
140 FOREST VALUATION
extremely doubtful, and in suits instituted by New York, this
provision, while held as a club over the heads of the offending
parties, has not been used as the basis of determining the dam-
ages. Even in private contracts it has been found advisable
to secure compliance with contract terms by other means than
the enforcement of punitive damages for unauthorized acts.
CHAPTER X
FOREST TAXATION
149. Sources of Revenue from which to pay Taxes. — Taxes
are levied to raise funds with which to meet the expenses of gov-
ernment. They therefore constitute an annual charge against
the wealth of the community. In both theory and practice
taxes are levied against persons instead of property, and are
gauged according to ability to pay, and not on the basis of
benefits received. But the effect of taxation upon the value
of productive property may best be studied by regarding the
enterprise as the source of the revenue required to pay the
taxes. The expense of taxes must be met eventually from
income, as are all other annual expenses. Taxes must be paid
whether or not this income from the taxed property is forth-
coming, and in the absence of such revenue, or previous to its
receipt, must be met by the investment of additional capital
(§ 131)-
Such investments of capital add nothing to the value of the
property, and must eventually be recovered from income.
Should the taxes reach a proportion where the entire net income
is absorbed, the property becomes worthless to the owner (§61)
and will be abandoned, as was the case with much cut-over
timberland in the Lake States in the early '90's when owners
could see no prospect of income sufficient to pay the annual
taxes.
150. Tax on Income. — A tax on income is the most logical
method of preventing excessive taxation. The relation between
the income and the tax is definite and the collection of the tax
follows the receipt of income, thus reheving the owner of the
necessity of borrowing or making additional unprofitable invest-
ment of capital. The determination of net income raises the
question as to the character of expenses to be permitted as deduc-
141
142 FOREST VALUATION
tions from gross income. A tax levied on gross income must of
necessity be at a lower rate than one levied on net income, and
is more easily computed. But net income is a more scientific
basis of taxation since the net, after subtracting expenses inci-
dental to securing it, is the only portion of gross income which
becomes the property of the owner available to meet taxes.
151. Tax on Value of Property. — Value of property is de-
rived from net income (§ 64) and may therefore be taxed directly,
without injustice, provided the assessed value of the property
does not exceed its expectation or capital value, and the rate
of taxation on this capital value bears the proper ratio to the
legitimate tax on income.
This ratio is dependent on the rate of interest used as the
standard for determining the capital value {p per cent). The
annual equivalent of intermittent income may always be found
(XIII). The relation between this annual income and value is
,, , Income
Value =
.op
= Income X ••
The expression is the ratio between a tax on income and on
capital value. It follows that a tax equal to a per cent of value
must take X a per cent of income. A tax rate of 10 mills, or
P
I per cent, when the rate of interest is 5 per cent, will require
X I per cent, or 20 per cent of the income, while a 20-mill tax
absorbs 40 per cent of income. With a rate of interest of 10
per cent the proportion of taxes to income would in this case be
respectively 10 per cent and 20 per cent.
The amount of the annual tax is the product of the assessed
value and the tax rate. The annual tax, rather than either the
rate or the assessed value alone, determines the relative per cent
of income demanded. A low valuation permits a proportion-
ally higher tax rate, while high tax rates may be lowered with
FOREST TAXATION 1 43
no corresponding reduction of taxes by increasing the assessed
valuation.
In practice, sale value is made the basis of valuations for
assessment purposes, and since sale value may not coincide with
expectation value (§§ 17, 59, 69), this may cause both assessed
value and taxes to depart widely from the desired ratio.
A tax on sale value secures the desired ratio of net income
most accurately when property is producing this income annu-
ally. When the income is intermittent and deferred, great dis-
crepancies and inequalities are almost certain to exist in the
ratio between taxes and final income.
152. Taxable Value of Property. — The taxable value of
property is the value determined from future net income, or its
capital value (§ 62) calculated by disregarding the future expenses
represented by the proposed taxes, but deducting the discounted
value of all other future expenses. The net income which rep-
resents this net value is then divided between the owner and
the taxing power, and the owner's final net income is what is
left after paying his taxes.
153. Effect of Taxes on Property Values. — This net taxable
value is merely the sum of values belonging jointly to the owner
and the taxing power or public. Nominally the complete
ownership is vested in the proprietor. Practically the power
to take income carries with it and is a manifestation of the sov-
ereign right of ownership, and on failure of the owner to pay
taxes this right is exercised by confiscating the propert}-. But
the payment of the tax results no less in an actual transfer of
value from o^^^ler to public. The residual value after sub-
tracting the taxes from net income is the real value of the prop-
erty to the owner, who is justified in considering it as worthless
when the total net income is absorbed by taxation.
It might be assumed that in absence of taxation, property
would be worth the additional value represented by the capi-
talized taxes. This is literally true when property is exempted
from taxation and at the same time receives all the benefits of
governmental activities. Just as business expenses are expected
to result in income greater than the expense, so the benefits of
144 FOREST VALUATION
a government conducted by and for the people, and respect-
ing the rights of property, should, on the whole, give a full
equivalent in service for the taxes collected. Whatever the
effect may be upon the individual property owner, the entire
level of values is raised and the pubHc or common share in this
increase should absorb less than the total gain.
Perfect equaHty of taxation on all forms of income and capital
value would have no visible effect upon relative values of dif-
ferent forms of property. But if the burden of taxes is un-
equally distributed, either by deliberate intent as is proposed by
the advocates of single tax on land, or by exemptions of certain
forms of private property from taxation, or merely by reason
of the imperfect working of the machinery for assessment and
collection of taxes, this balance is disturbed. The value of
property over-burdened with taxation is then confiscated in
actual reality and to just the extent of the excess of taxes above
the average level. This serves to depress the sale value of the
property and lower its apparent taxable value, resulting either
in diminished taxes or an increased tax rate which still further
depresses values. The end of the vicious process is physical
confiscation of the property, destruction of the private enterprise
dependent on it, and the cessation of public revenue from taxes
formerly received. Meanwhile, property bearing less than its
share of taxes is automatically increased in value and made
prosperous at the expense of the over-burdened forms of enter-
prise, but only to a certain extent, for the effect of the destruction
of any form of industry is a general lowering of the value of
all forms of property or of the total wealth of the community.
Universal equality in taxation on the basis of ability to pay
(§ 149) is, therefore, the goal of all genuine efforts at tax reform.
154. The General Property Tax. — The general property
tax is a direct tax levied on the assessed value of all forms of
tangible and intangible property on the theory that equality
in taxation is thereby secured. In an agricultural age and
region results were fairly equitable. With increasing complica-
tion of modern industrial development, the method has become
less and less effectual, since it fails to secure equal proportions
FOREST TAXATION 145
of net income from dilTcrcnt forms of property and industry.
As a means of taxing standing timber, it is a conspicuous failure
in this respect, as the tax rates and the total taxes paid on
timber bear no fixed relation whatever to the ultimate value of
the income.
155. The Problem of Taxation for Timberlands. — The
failure of the general property tax when applied to timberlands
is due to several causes. Imperfect and unequal valuations
are more prevalent with this class of property than with other
forms, owing to the inherent difficulty of estimating and apprais-
ing standing timber and the unfamiliarity of tax assessors with
this work. This is not a defect of the system, but merely in
its application.
There are three fundamental difficulties in securing equitable
taxation of timber under this system, namely:
The difiiculty of distinguishing capital from income for pur-
poses of taxation.
The practice of collecting taxes in advance of the receipt of
income.
The element of time and the resulting problem of interest in
its effect on the relation between taxes, income and taxable
value.
156. Distinction Between Capital and Income in Timber
Property. — Regarded as a crop, artificially produced, the en-
tire value of timber represents the income earned by the capital
invested in the soil. In the form of an even-aged stand, the
increasing value of the crop is merely the accumulating income
which, when finally cut, exposes the soil capital once more
(§ 116). In determining the value of this soil capital, all future
expenses are deducted at compound interest. The annual in-
come equivalent to this final income (Formula XIII) is termed
soil rent, and the point of view which regards soil alone as capi-
tal, timber as income, and requires all values to be based on
compound interest, is termed the theory of soil rent.
In contrast to this conception, land and timber together may
be regarded as capital. A forest which has been brought to a
condition of complete normality (§ 109) capable of jielding a
146 FOREST VALUATION
continuous annual income without diminishing the value of the
capital, has an actual capital or property value which includes
the entire value of all standing timber. The annual net cash
income from this forest represents interest on this entire forest
value, and is termed forest rent. As this income cancels annual
expenses, compound interest on the forest as a whole has no
chance to accumulate. The point of view which regards the
forest, including timber, as capital, and does not deduct com-
pound interest on costs but treats the entire forest as a business
capable of producing annual net returns, is termed the theory of
forest rent.
The latter conception more nearly approximates the attitude
of investors in American forest property. Yet both the con-
ditions and the thoughts of investors occupy a position midway
between the extremes of soil rent and forest rent. Timber is
almost universally acquired in the form of native or virgin
stands, already grown, and is purchased as capital. The entire
business, rather than the stand, or parcel, is the basis of annual
income, if such income is secured. The source of this income
is largely the increase in value of the timber, rather by price
increment than through growth, and in the realization of this
income the capital itself is liquidated (§132). The operation
thus resembles a speculation similar to the holding of unim-
proved real estate, rather than a productive business as contem-
plated by the idea of forest rent. Under such conditions, the
distinction between capital and income cannot be co-ordinated
with the physical distinction between wood and soil, or between
wood capital and wood increment. It is a mere matter of book-
keeping based on cash investments and cash returns.
157. The Problem of Interest in Forest Taxation. — But the
problem of interest appears in such investments in the form
presented by the distinction between the theories of soil rent
and forest rent (§35). When the investment as a whole pro-
duces no annual income for a period of years, unearned interest
on the annual expenses accumulates and this time element affects
both final "cost" and capital value of the property.
The capita] value of a forest which will produce a sustained
FOREST T.\XATION 147
income which is realized at intervals greater than one year, may
be less or greater than that of a forest producing income of the
same total value, but in annual installments. The difference
in value is due to the same factors which cause the difference
between soil value and forest value, i.e., the income is discounted
by compound interest, and the discounted total of future or
intervening annual expenses is deducted from value.
As touching taxation the question assumes this form: Shall
taxes be levied on actual present value of property, or shall
deductions from this value be permitted, including interest on
past costs, in arriving at the net taxable value? And shall
taxes paid in advance of income be computed as if drawing
compound interest in calculating the per cent of final income
which such advance payments of taxes absorb?
158. Effect of Present Condition of Forest upon Choice of
Methods of Taxation. — These problems are best presented by
a concrete example in which the effects of the two opposing
theories are illustrated.
A stand of Loblolly Pine in Maryland * yields products
worth on the stump:
At 20 years of age ..." $17.81 per acre.
At 30 years of age 61.14 per acre.
At 40 years of age T08.91 per acre.
At 50 years of age 168.49 P^r acre.
Land costs 85.0)0 per acre. Annual expenses, exclusive of taxes,
are 3 cents per acre. The cost of securing reproduction is placed
at S5.00 per acre.
An interest rate of 5 per cent will be assumed for the problem.
A tax rate of 20 mills on full value will be assumed. This
is nearly twice as heavy as the average rate, yet it is exceeded
in many forest regions, especially in new and poorly developed
localities.
The area of the forest will be taken as 50 acres, and the total
yield in 50 years will be 50 X S168.49 or $8424.50. Three
cases are assumed. Case A is for an even-aged stand cover-
* Bulletin 11, U. S. Dept. of Agriculture, Jan. 23, 1914, Table 15. page 19.
148
FOREST VALUATION
ing the entire area, and cut at the end of 50 years, thus giving
the conditions described under soil rent. Case C is for a stand
of all ages. There are here 50 age classes, each occupying one
acre. The yield on one acre is cut each year perpetually.
This crop may either occupy a separate area as an even-aged
stand of one acre, or be scattered as single trees throughout the
forest. The results will be identical. Case B is for a forest
giving an intermittent yield every 10 years, thus presenting
five age classes of 10 acres each.
Except for this difference in the arrangement and present
condition of the age classes of timber, the financial results for
these forests are assumed to be identical. The capital value
(expectation value) of each forest can be computed as a basis
for taxation.
Table II presents the relation between a tax of 2 per cent on
capital value and an equivalent tax on income from sale of timber
in each case.
TABLE II
Comparison of Results from Taxation of Capital Value of Forest Soil
AND OF Soil and Timber on a Forest of 50 Acres
Basis of taxation.
Character of
forest.
Cutting
area.
Period be-
tween
cuts.
Value of yield
for period.
Cash expenses
for period.
Total
for
period.
Per
acre.
Total.
Per
acre.*
A
Forest soil.
Soil and timber.
Soil and timber.
Even -aged.
S age classes.
All-aged.
Acres.
50
10
I
Years.
50
10
$8424 . 50
1684.90
168.49
$168.49
168.49
168.49
$325.00
65.00
6.50
B
6.50
c
• The cash expenses, $5.00 per acre for planting, and $1.50 per year, or $.03 X So for protection
of the entire tract, are charged against the area cut over within the period.
Receipts less
expenses.
Cash expenses
compounded to
year of cutting
at 5 per cent.
Net value of
stumpage.
Capital value
of property
after removal
of yield.
Annual taxes
at 20 mills
on capital
value.
Total.
Per
acre.
Total.
Per
acre.
Total.
Per
acre.
Total.
Per
acre.
Total.
Per
acre.
A
$8099.50
1619.90
161.99
$i6r.99
161 99
161.99
$3180.87
100.31
6.50
$63.61
10.03
6.50
$5243.63
1584.59
161.99
$104.86
158.46
161.99
$ 500. 95
2519 62
3239 80
$10.02
SO. 39
64.79
$10.02
50.39
64.79
$ .20
B. .
c
1.29
FOREST TAXATION
149
TABLE
II, — {Conlinuedj
Total cash taxes
for 50 years.
Taxes compounded
to year of cuitint;
at s percent.
Compound interest
on taxes.
DiflTerence in taxes
and interest paid
on forests A and B.
compared with C*
On total
area.
Per acre.
Total.
Per acre.
Total.
Per acre.
ToUl.
Per acre.
A
B
C
A'
$ 500.95
2519.62
3^39 80
2178.50
$10.02
50 39
64.79
43. 57
$2097.46
3169. CO
3239 80
4326.50
$41.95
63 38
64.79
86.53
$1596 SI
649 38
2148.00
$31 93
12 99
$1142.34
70.50
$2284
1. 41
(A'. Taxes levied on sale value, revalued at 20 years and every 10 years thereafter.)
* This saving is largely due to the fact that the capital values of forests A and B are com-
puted for the year in which these values are lowest, and remain at this valuation for fifty years.
See §161.
Per Cent of Values Taken by Taxation, Computing Taxes with Compound
Interest to Year of Final Yield
Full stumpage
value.
Net cash profit
on stumpage.
Net value of
stumpage.
A
Per cent
24 5
37.6
38.4
51-3
Per cent
25 9
39 0
40.0
S3 4
Per cent
40
40
40
82.5
B. .
C
A'
In the problem discussed, the tax rate of 2 per cent on full
value is nearly twice the average rate of taxation on present
values of forest property. But the crop of timber chosen as
the basis of the problem is more profitable than that produced
by most species and localities. The coincidence between total
cash taxes for 50 years at 2 per cent and capital value would
hold good only for the same period and rate, since 2 per cent X
50 = 100 per cent of value.
159. Scientific Taxation : Forest Property Tax. — The value
given for the forest in case C is found by deducting the annual
cash expenses, $5.00 for planting and 3 cents X 50 acres or
Si. 50 for protection. This gives $161.99 as the ''net" value
of the annual crop, which, capitalized at 5 per cent, equals
S3239.50. (Formula XII.)
The tax, 2 per cent, yields $64.79 annually. This is just
40 per cent of "net" stumpage value and a slightly smaller
per cent of sale value. The annual profit or net income of
15© FOREST VALUATION
the forest coincides with net value of the yield, and the tax, there-
fore, takes 40 per cent of this profit.
Since no one would dispute the desirability of subtracting these
current cash expenses previous to taxing stumpage value, it is
evident that for forests producing an annual income, the tax on
forest capital and on forest products are equal in value and inter-
changeable.
160. Scientific Taxation: Forest Land Tax. — The value
given for forest soil in case A is found by discounting the value
of the final crop for 50 years, treating it as a recurring income,
and subtracting the discounted cost of planting and annual
expenses in the same manner (§116). This gives $500.95 as the
capital value of the soil just after removal of the crop.
The tax of 2 per cent on this value for 50 years amounts,
in cash, to but $10.02 per acre, as against a cash total of
$64.79 P^^id by forest C. A study of the table explains this
discrepancy. The sum of $31.93 represents compound interest
on these taxes during the 50-year period. The further sum of
$22.84 represents a saving due to the fact that the capital value
adopted as a permanent basis for taxation is determined just
subsequent to the removal of the periodic cut of timber. This
requires that the future costs for planting and protection, amount-
ing with interest to $63.61, be deducted from stumpage value
previous to discounting (§ 105) to obtain capital value.
As a result of this latter deduction or allowance, the total
taxes with interest, paid on forest A, amount to but 25,9 per
cent of the stumpage value minus cash expenses, or 24.5 per cent
of sale value. The ratio of 40 per cent applies only to the
reduced value or net profit on the investment in land.
Forest B presents conditions midway between these two
extremes. The capital value is found by discounting the de-
cennial yield and deducting the discounted lo-year accumulation
of expenses, giving a value of $2519.62 (§117, Fi). Upon this
value a 2 per cent tax gives a total cash payment of $50.39
per acre during the 50-year period, which is increased by com-
pound interest to $63.38, leaving a small margin of $1.41 as a
saving due to the factors explained for forest A.
FORKST T.VXATIOX 151
In computing the comparative per cents of stumpagc value
taken by a 2 per cent tax on capital value, compound interest
has in each case been added to the taxes, although this item does
not constitute a cash outlay. It represents, rather, the equiva-
lent to the community of receiving taxes in advance of income,
or may be considered as the discounted value of a 40 per cent
income tax paid in annual installments throughout the growth
of the crop instead of at the close of the period.
161. Comparison of Taxes on Forest Rent versus Soil Rent. —
The point at issue between these two systems, both based on
the taxation of capital value, is evidently the double deduction
from income, first, of the future costs of production with in-
terest, exclusive of soil, and second, of the interest on taxes
paid previous to receipt of income. A forest created by plant-
ing or human effort passes through stage A before it can be
brought to condition C. Shall it. at the latter date, be taxed
as for C or continue to pay the reduced taxes computed for A?
This problem depends for its answer upon whether future
conditions, or past conditions, are permitted to determine the
burden of taxation. Both cases, A and C, as well as case B,
represent actual present value, based on future conditions.
When forest A is brought into condition C, its present value
is no longer A but C and, based on value, it would pay the
taxes demanded of C.
Taxes are based upon value and not upon cost. Future
costs diminish value (§ 64) but past costs are disregarded in com-
puting value and do not directly affect it (§ 68). By this reason-
ing, the increasing tax which would accompany increased capital
value is apparently justified (§ 165). But just as property may
have a definite value and still represent a net loss to the owner
(§ 68), it may be shown that an owner of timberland cannot afford
to pay taxes continuously for 50 years and then have these
back taxes completely ignored and be taxed on the full value
of his crop. The public, basing the tax on present value, may
ignore past taxes, but the owner, looking ahead, is not so apt to
overlook this future possibility. This situation can only be
met by a contract or tax agreement by which the public consents
152 FOREST VALUATION
to forego taxing the full final value C and confines its tax to
present value A, in return for which concession the owner
agreed to undertake the growing of the crop. Past errors in
taxation will ordinarily have to stand.
162. Scientific Taxation : Income or Products Tax. — The tax
on income, correctly appHed, is the mathematical equivalent
of the tax on capital, provided the controlling rate of interest
can be agreed upon. But the same difficulty is encountered
in computing this tax as was detected in comparing taxes on
forests A and C. Table II shows income taxes purporting to
represent the equivalent of 2 per cent on capital value, yet vary-
ing from 24.5 per cent to 38.4 per cent of the gross income.
Net cash income from either form of forest. A, B or C, is the
same, provided interest on expenses is neglected, and totals
$161.99 per acre. The "net" income corresponding to the capi-
tal value is diminished in cases A and B by deductions for
interest, which accounts for these discrepancies. The question
is, will such deductions be permitted in levying an income tax
on present incomes?
This question is open to the same solution as that proposed
for the taxation of capital values. If the income tax is to be
substituted for an annual capital tax on standing timber, the
full rate can be levied without injustice. But if the income is
not available until a distant future period on crops still immature,
the lesser rate should be promised and contracted for as a future
system of taxation binding on both parties. Future expenses
must be considered in a scheme of taxation. Past accumula-
tions of interest "cost" may be successfully ignored.
This view is confirmed by the attitude of the U. S. Collector
of Internal Revenue in interpreting the income tax on corpo-
rations deahng in timberlands.* The ruling reads: "In cases
where lands are purchased for cash, the cost being the proceeds
of the sale of the capital stock of the company, the earning
value of the rnoney invested, that is, the interest which might
have been received on this money had it been otherwise employed,
cannot be added to the initial cost of the land to represent its
* Letter, Jan. 6, 1914, to P. S. Ridsdale, Sec. American Forestry Association.
FOREST TAXATION 1 53
aggregate cost at time of sale. The compensation for such
investment is the anticipated dividends which will be paid to
the stockholders out of the profits when the lands are sold. The
addition of the earning power of the money invested to the orig-
inal cost of the lands would operate as a deduction of the divi-
dend from gross income. Dividends are not deductible, either
directly or indirectly. Interest purported to accrue on invest-
ments of this character, made by stockholders, cannot be added
to the initial cost of the assets for the purpose of fixing a cost
price as the basis for determining the profits accruing to the
corporation when such assets are sold."
Since these regulations state previously that "the cost of
assets (land and timber) for the purpose of determining the
amount of income resulting from a sale is held to mean the pur-
chase price of the lands plus the taxes and other carrying charges
paid thereon prior to the sale," it is clearly the position of the
government that interest on such carrying charges will not be
permitted as a deduction from income. The national income tax
on timberlands would, therefore, be based upon the theory of
forest rent, ignoring interest, in spite of the fact that this income
is deferred until some future year as in case A , and not earned
annually as in case C.
The tax would thus take the same per cent of income, whether
this income were received in six months or sixty years. For a
speculative business, where profits are not dependent on a definite
period of time, this method of taxing income may not act as a
deterrent. But with the production of forest crops, the announce-
ment in advance that "no deductions from the income tax will
be permitted for interest on future costs incurred in advance
of income," would have a direct influence on future profits and
act to prevent the undertaking.
The controversy as to whether interest is a cost or an income
as affecting taxation either of income or capital values cannot
be settled, but may be dismissed, with this summary; past
interest accrued on the capital invested by the proprietor or
owner is not an actual cost, but merely a method of gauging
profits and will usually be neglected in taxation. But future
154 FOREST VALUATION
interest, in the form of discount, cannot be neglected for it
vitally affects present values, which are the basis of present
taxation. Whether or not an income tax to be collected at a
future period shall be reduced on account of deductions from
income of interest on costs, depends upon the desirability of
encouraging industry by granting this absolutely just conces-
sion in advance.
163. Scientific Taxation: Combined Capital Tax and Income
Tax. — The two systems of taxation, capital tax and income
tax, are thus seen to be interchangeable for property producing
annual income (C), but to give widely divergent results for
property whose income is intermittent {A). In the latter
case, either system is open to grave objections. The capital
tax can properly be computed only for the year following the
yield, when it is most difficult to determine it exactly (§ii6).
The income tax wholly fails to satisfy the need for current
revenue for which taxes are levied. The third difficulty is that
during the growth of the timber and in absence of definite pro-
vision to the contrary, the constant tendency will be to levy
the capital tax upon the existing value of capital including the
timber as if this temporary capital value were permanent and
capable of producing permanent annual income (§156).
In order to secure regular annual revenue from taxation
in the absence of regular income from lumbering or cutting,
and at the same time convince the public that owners of timber
property are paying their full share of taxes, it is theoretically
possible to assess the capital value of the property at a portion
of its value and postpone the collection of the remainder as an
income tax.
In case A, the soil has a capital value of $10.02, but can be
purchased at $5.00 per acre.* A tax on $5.00 at 2 per cent
will amount in 50 years to $20.93, leaving $21.04 available as a
tax on stumpage at time of cutting. This amounts in each case
to 12.5 per cent of the "gross" value, or 20 per cent of the
"net" value of the yield.
* This discrepancy in values is possible in regions where the value of land for
forest production is not fully appreciated.
FOREST T/VXATION 1 55
The true equivalents between capital tax and income tax,
and the ratio of division between them, depend hrst upon the
proportion of capital value which is taxed, second, upon the
rate of taxation applied to it, and third, upon whether the com-
munity is willing in the future to abide by its agreement and
permit the owner to continue to pay taxes on the basis of
capital values which no longer represent the present value of
the property. If the rate is full, the only margin left for an
income tax is due to a low valuation of the land. If the land is
valued at its full capital value, only a reduced rate will leave
a margin for income tax on stumpage. And in case the full
rate is collected for the full period on its original capital value,
the public is entitled to an additional income tax only by re-
pudiating the owner's claim to deduction of interest on costs
from gross stumpage value. In practice, capital values of land
tend to advance and the stumpage tax might well be levied on
the increased value of timber which is the cause of this advance
in land value.
In European systems of taxation both capital tax and income
tax are usually levied, but the scientific relation between them
is not determined. Each tax is assessed independently, but
the combined taxes are sufficiently low so that the property is
not over-taxed.
164. Taxes under the General Property Tax. — Under the
general property tax, the principle of taxing capital value, theo-
retically the basis of the tax, is actually entirely superseded
by the plan of taxing sale value regardless of income. While
standing timber may be legitimately taxed as capital when,
as in case C, only the annual growth is removed, the efTect of
annually taxing the sale value of even-aged crops is entirely
different. The distinction between capital and income cannot
be drawn with any accuracy. Case A presupposes that the
entire timber value represents income only and not capi-
tal.
The injustice in the system consists in taxing annually, on
its full capital value, a property which is not producing annual
income, and which is being held and increased in value by a
156
FOREST VALUATION
process similar to that of savings.* It is as if the owner of
property capable of yielding a definite annual income of $168.49
(Table II) allows this income to accumulate, although by so
doing the earning power of the property is not increased. The
tax assessor promptly adds this increment to the assessed value
of the property, whereupon the owner, if he can, as promptly
withdraws the surplus to escape this excessive tax. By inspec-
tion of Table II it will be noted that the value of the yield just
previous to cutting, for an even-aged forest, is $8424.50, which
would be the "full" assessed value of the property at that time.
After cutting, the assessed value should not exceed $500.95,
and in practice will be nearer $250.00 if land sells for $5.00
per acre. The average value for the whole period would corre-
spond closely to $3239.80.
The tax assessor, under the present plan, bases his increases
upon market or sale value, and as the value of young timber is
seldom recognized, this sale value usually equals the value of
the soil for other purposes, plus the market value of the timber.
In this way the property escapes the full effect of repeated
taxation of capital value.
A comparison of values for the crop used in Table II gives
the following results.
TABLE III
Comparison of Sale Value with Expectation Value of an Even-
aged Stand, Including both Land and Timber
Age, years.
Sale value with
land at $5.00.
Expectation value
with land at $10.02.
10
20
30
40
50
$5.00
22.81
66.14
113. 91
173.49
$24.83
40.83
66.90
109.36
178.51
The expectation value is based in each instance on the value
of the crop at 50 years (Formula Gi) , and on an interest rate of
* The Economic Problem of Forest Taxation, by Fred Rogers Fairchild, Yale
Review, February, 1909. See also " The Nature of Capital and Income," by Irving
Fisher, pp. 249-255.
FOREST TAXAPIOX 1 57
5 per cent. Basing the taxes on sale value and revaluing every
lo years, the total cash taxes paid during the 50-year period
amount to $43.57 per acre, which is slightly less than the amount
paid on forests 5 or C for the same period and over four times
as large as the sum paid by forest A , which is taxed solely on
the value of soil.
Adding compound interest to these annual taxes (Formula
Ilia), the total tax, with interest, amounts in 50 years to $86.53,
equalling 51.3 per cent of gross stumpage value, or 53.4 per cent
of net cash profit on stumpage. But basing the net value of
the stumpage on the margin over costs with interest or $104.86,
we find taxes and interest absorbing 82.5 per cent of this margin.
These taxes are computed as follows:
Let e = annual tax on original assessed value.
e' = annual tax on revaluation at 20 years.
e" = annual tax on revaluation at 30 years.
e'" = annual tax on revaluation at 40 years.
e e' e" e'"
Then £, £', £", E'" = -^ , -^ ^ -^ , -i— .
o.op o.op o.op o.op
Sum of taxes (Formula Ilia) ,
UiE-i .op^-E-\-E') I .op'^ -E' + E"\i .op''-E"-\-E'"]i.op'''-E"'.
$5.00 X 0.02 = $0.10, annual taxes for 20 years.
^^ = S2.oo(£).
0.05
$2.00 X 2.6533 ~ $2. 00 = $3.30, taxes at 20th year.
$22.81 X 0.02 = S0.45, annual taxes for next 10 years.
— ^- = $9.12 (£') (discrepancy due to decimal values, omitted
0.05
in text).
$(3-30 + 9-12) 1.6289 — $9-12 = Si I.I 2, taxes at 30th year.
$66.14 X 0.02 = $1.32, annual taxes for next 10 years.
1-32 ^
0.05
$(ii.i2 + 26.45) 1-6289 ~ S26.45 = $34.76, taxes at 40th year.
= $26.45 (£").
0.05
158 FOREST VALUATION
$113.91 X 0.02 = $2.37, annual taxes for last 10 years.
'-^ = $47.56 (£"').
0.05
$(34.76 + 47.56) 1.6289 — $47.56 = $86.53, taxes at 50th year.
165. Effect of the General Property Tax on Forest Production.
— The cjffect upon the owner's profits of the system of taxing
sale value annually depends upon the length of time the present
owner has held the property, the purchase price, the amount
of back taxes already paid and the period which must elapse
previous to cutting. The relation of taxes to the value of the
property, regardless of ownership, is independent of the purchase
price or of back taxes, and deals only with the future. A rapid
rise in prices for timber products so enhances the value of stand-
ing timber as well as of forest soil that taxes previously paid,
on very low values, do not absorb an unfair percentage of pres-
ent value. Whatever over-taxation would have occurred with
stationary values has been offset by reason of this increase in
capital value of the property. A continuous increase in value
of forest property at the same rate as in the past would continue
to absorb a large portion of the over-taxation due to reassess-
ments based on sale value. But it does not absorb the compound
interest item which accumulates on past taxes in absence of
income from sales.
Should the owner have paid practically no taxes up to the
present year, he can pay annually on full value for a definite
period before the amount of his tax with interest becomes
equivalent to the taxes paid on forest A. Should he cut his
timber sooner, he pays less than this tax. For every year which
the timber stands beyond this period, the tax becomes propor-
tionally greater than its just equivalent.
Assuming that the tax of $41.97, the total paid in 50 years on
forest A , is just, how long can an owner permit his timber to
stand before incurring over-taxation. The sum of annual taxes
with interest must equal $41.97.
E {i.op' — i) = 41.97.
Omitting all consideration of back taxes, the results are as follows:
FOREST TAXATION
TABLE IV
159
Periods within which Proi'Iirty Tax on Timber becomes Equivalent
TO T.\x ON Soil Valuk
Aaeof
timber at
present.
Present value.
Annual tax
2 per cent of
present value.
Tax capitalized
{£).
41.97 -i- E.or
I. op' — I.
Period indi-
cated.
Years
50
40
30
20
Dollars
173-49
113. 91
66.50
22.81
Dollars
3-47
2.28
^■33
0.46
Dollars
69.40
45-56
26.60
9.12
0 . 6048
0.9212
I 576
4.600
Years
9 to 10
13 to 14
19 to 20
35 to 36
The indicated period is found by looking up the factor i.op''
in the table of values for 5 per cent (Table VI) . The value cor-
responding to the factor is found opposite the year indicating
length of period.
In the owner's mind these periods will be lengthened if he
bases his standard of value on the capital value of the forest
rather than on the soil, and would be shortened in proportion to
the back taxes which he has paid. Increasing prices for forest
products would lengthen the period, and future increases in the
assessed value of the property would shorten it. But at some
future date, not very far distant for mature timber when taxed
at full value, the timber must be cut or the process of confisca-
tion begins. After the year in which the accumulating cost of
annual taxes equals the equitable proportion of value available
for taxation, the tax steadily confiscates an increasing per cent
of the capital value.
With the tax of 2 per cent on soil value, the per cent of "net"
income appropriated was shown to be 40 per cent. This in eflfect
appropriates 40 per cent of S^, so that for forest land worth
Sio.cxD the owner's equity amounts to but $6.00, and the state
has taken $4.00 in value for taxing purposes.
But with assessed value increased at lo-year periods the per
cent of the net future income taken for taxes is 82.5 per cent.
Since this net income is the basis of capital value of soil, the
state thus appropriates $8.25 in land value, leaving the owner
a residual value of $1.75 exclusive of the sum required to reim-
burse his costs and taxes with interest at 5 per cent. But if he
l6o FOREST VALUATION
has paid $5.00 for this land he cannot afford to give the state
in taxes two-thirds of this cost price as well as his entire net
profit over 5 per cent. Such a method of taxation therefore
tends to prevent the private owner from undertaking the business
of forest production.
Upon mature timber the effect is to stimulate cutting in order
to save taxes, whether or not over-taxation has already occurred.
Few owners stop to compute how much taxes timber should bear.
They know that the way to escape paying any more taxes is to
cut the timber. If this is the purpose of the tax it accomplishes
its object thoroughly, and is a great stimulus to over-produc-
tion of timber. The only incentive to hold mature stumpage
under this system is the hope that increased prices will offset
the taxes. The injurious effects of a bad tax system are not
reflected fully by depression of values (§ 153), since the resulting
losses are pocketed by the owners as past costs, and values for
stumpage continue to reflect only future elements of cost and
profit. But upon the business of lumbering, in a region of
large surplus supplies of stumpage, the effect is disastrous, forc-
ing the weaker operators into bankruptcy and stimulating rapid
and wasteful cutting on the part of even the strongest holders.
166. Tax Reform for Forest Property. — From the analysis
of the financial relation of taxes to values, the most serious flaws
in the system of taxing forests on their sale value appear to be:
1. Actual over-taxation through taxing annually the value of
the entire property including timber, during periods when no
income is produced, resulting ultimately in confiscation of an
inequitably large proportion of ultimate or total income.
2. Uncertainty as to the extent of this over-taxation through
the arbitrary power vested in local assessors to raise valuations
at any time.
Tax reform must remove these two obstacles by substituting
some system of scientific taxation which will secure equality
between forest taxes and those imposed on other property when
gauged by the per cent of income taken, and thus remove the
element of uncertainty which is even worse than the over-taxation
itself.
FOREST T.VXATION l6l
But in effecting this reform the annual local revenues from
taxation must be maintained. Reduced revenue at present,
even if made up in later years, causes heavier taxation of other
forms of property (§ 153). This is the explanation of the failure
of many attempts to encourage forestry by granting tax rebates
and exemptions, a form of privilege quickly resented and ren-
dered ineffectual by assessors through the simple device of
increasing the assessed valuation of other property belonging
to the beneficiary. From the facts discussed in Article 161 it
appears that tax reform must of necessity look to the future
rather than attempt to correct past errors. On this basis, the
problem divides itself into:
The taxation of forest land not containing merchantable
trees.
The taxation of land bearing merchantable timber.
The efforts to secure an equitable tax on forest land devoid
of merchantable timber are best directed, at present, along the
lines discussed in Article 163. A combined land and products
tax best meets the needs of the situation and is most easily
understood. It must not be forgotten that the products tax is
justified only when land is not taxed at its full value, and to the
extent of the margin of accumulated value remaining untaxed.
Efforts to secure this result have recently been made by several
states in the northeast. Connecticut permits no increase in
assessed value of land for fifty years and limits the tax rate to
10 mills. An additional income tax of 10 per cent is then assessed
on the stumpage value of wood products when harvested.
Massachusetts permits the revaluation of land exclusive of timber
at any time so that it is probable that the assessed value will
be raised to correspond closely with expectation value of the
bare soil. Taxes are paid annually at local rates. An income
tax is then levied on forest products at 6 per cent of the stump-
age value. This tax is equitable only in case the assessed value
of land will average lower than expectation value, to an extent
sufficient to make up the difference represented by the tax on
stumpage.
Pennsylvania arbitrarily fixes the value of land at Si. 00 per
l62 FOREST VALUATIONS
acre. The state then pays local taxes at 2 per cent of this valu-
ation, thus assuming the burden of annual taxation for the joint
benefit of the owner and community. These taxes are never
refunded by the owner. The owner pays a 10 per cent stumpage
tax when timber is cut.
In all these laws only land voluntarily offered by the owner
and approved by the state forester, or in Massachusetts by
the local assessors, for classification, comes within the operation
of the law. This will result in a very gradual application of
the system.
No valid objection can be urged to the adoption of similar
measures in any region, for they do not reduce the present taxes
and will result in greatly increased revenue in the future by
bringing into productive use forest lands which may otherwise
remain waste.
The future taxation of lands bearing merchantable timber
is not so easily provided for. The immediate substitution of
an income tax which takes the same proportion of income as
the existing capital tax does of value, is entirely impractical,
owing to the condition of the capital (§156). Not only would
the annual taxes from a given forest vary from the former
amounts paid annually, being either greater or less according
to rapidity of logging, but this variation would be general; and
regions where logging is being actively conducted would be in
receipt of largely increased temporary revenue, while districts
as yet untouched would be entirely without income from timber
values. Under the general property tax the local revenue is
secured only as long as the timber remains standing, after which
the land alone may be taxed. The loss of current revenue after
cutting is inevitable under any system.
A plan proposed * for securing equaUty of revenue between
counties, for conditions prevalent in regions of heavy virgin
stands and large operations, contemplates the postponement
of the annual taxes on timber until the timber is cut, when they
will be paid in one sum but without compound interest. To
* Report of Forestry Committee, 5th Conservation Congress, November,
1913, page 12S.
FORKST TAXATION 1 63
equalize local revenues the state shall act as banker, collecting
the tax, advancing funds to counties as yet undeveloped, and
recouping itself from counties where active logging is in process.
In eastern states a different plan has been adopted. Logging
is largely in second growth and scattered, so that the problem of
equahzing the revenues from income is not urgent. The plan
is to continue the existing valuation of property containing
timber of taxable value, but to permit no further increase in
assessed valuation of this timber. When the timber is cut,
the property is revalued and thereafter taxed only on the value
of the land. In Connecticut this protection from increased
valuation is offset by a slight tax on yield, increasing i per cent
for each decade, for 50 years, so that the advantage to the owner
of standing timber is not very great.
Massachusetts has adopted a plan which is worthy of special
mention. The land containing merchantable timber may be
revalued at time of classification and pays a land tax similar
to non-forested land. This tax is subtracted from the total
tax paid on the entire property previous to classification. The
balance is the additional amount of tax which the property
must continue to pay if local revenues are to be maintained.
This is termed the commutation tax. The amount of this tax
cannot be subsequently increased, by reason of increased value.
The principle is that the timber is exempt from annual taxation,
yet the property pays this commutation tax to tide over the
gap between the present year and the receipt of the income tax.
On cutting, the timber pays a 10 per cent income tax, which
extinguishes the commutation tax. A particularly valuable pro-
vision is that as soon as timber having a total value equal to
that of the stumpage originally assessed, has paid a products
tax, the timber remaining or the increase resulting from growth
is freed from annual taxation. The community has in the mean-
time suffered no loss of local revenue and is in receipt of an
income tax in lieu of increased taxes on advancing values.
An additional advantage of this plan is that it permits of the
consolidation, for taxing purposes, of areas of any size and con-
dition of timber, with land bare of merchantable timber. The
164 FOREST VALUATION
amount of the commutation tax is made a lien on the entire
consolidated tract and extinguished by cutting on any portion
of it.
Some such plan of taxation is recommended as possessing
greater merits than an immediate substitution of income tax
for capital tax in timbered regions.
No law providing for proper taxation of forest lands should
give arbitrary powers to a state official to prescribe or regulate
the scientific methods to be followed by the owner in growing
trees. The one condition to be insisted on must be that the
land, especially that without merchantable timber, shall be
brought under forest cover composed of useful species, and
maintained as forest land. Cancellation of classification should
follow failure of owners to comply with these basic conditions.
To prevent owners from taking advantage of such laws in
order to escape taxation on property which they may ultimately
intend for some other purpose, two precautions are used: the
limitation imposed by classification of lands suitable for forest
purposes, and provision for payment of a penalty upon cancel-
lation of this classification. Connecticut and Vermont prescribe
that lands above a certain value per acre, not including timber
values, cannot be classified. Massachusetts, in permitting any
lands to be classified regardless of value, protects the public
by permitting revaluations, which is perhaps the better
plan.
On cancellation of classification the penalty imposed should
not exceed the difference saved on taxes by the classification.
Connecticut determines whether the property at time of cancel-
lation has increased in value and assesses this increase at one-
half the average rate of 10 mills, or 5 mills per year, multipHed
by the period of classification. The owner thus pays his back
taxes (without interest), on the theory that the increase has
been uniform throughout the period. Massachusetts releases
the owner by the payment of the products tax on all timber
standing at the time of cancellation.
The apparent difficulties of securing the adoption of rational
tax systems for forest property, not the least of which are the
FOREST TAXATION 1 65
constitutional provisions of many states requiring all property
to be taxed "equally" under the general property tax, should
not discourage efforts at genuine reform. The future practice
of forestry by private owners must be accompanied by the
adoption of a reasonable and adequate system of taxation for
forest property.
CHAPTER XI
STUMPAGE VALUES
167. Definition of Stumpage Value. — Stumpage value is
the sale value of merchantable standing timber — its value on
the stump previous to felling and removal. The term " mer-
chantable " is not so easily defined. Timber is merchantable
when it is of sufficient size to furnish wood products suitable
for definite commercial purposes. There can be no fixed
standard of sizes to coincide with the general definition of
" merchantable " timber. Trees merchantable for cordwood or
paper pulp are not large enough to yield saw timber. It follows
that stumpage value is the sale value of timber intended for
certain specific uses. The industry which can pay the most
for the timber determines its stumpage value. In the form of
stumpage, timber is a portion of the real estate (§§ 134 to 136).
When purchased with land it may be held indefinitely, but when
bought or sold separately it must usually be removed within a
stipulated period. The value of stumpage is ordinarily sepa-
rated from that of the land, even when both are purchased,
though in the past the land was often considered of no value
except for the timber.
168. Sale Value of Stumpage. — Small bodies of timber, such
as woodlots, are frequently sold for a lump sum. The value of
the timber is thus agreed upon without determining its price
per unit, which is known only to the purchaser after he has cut
the timber. Areas of considerable size may be sold on the
basis of a price per acre.
This crude method is giving place, for large tracts or timber
aggregating considerable value, to the determination of quantity
and agreement upon a price per unit, thus arriving at total
value. But neither quantity nor price are easily ascertained
166
STUM PAGE VALUES 1 67
for standing timber. Products already harvested and measured,
like wheat or coal, resemble logs or lumber, but the standing
trees are like the grain before the harvest, or the coal yet in
the mine; yet not quite the same, for the trees can all be seen,
and their contents, quality and value ascertained with some
deliniteness. This requires agreement upon a unit of measure-
ment for the product, as, for instance, board feet by a given
log rule, cords or posts. The methods of determining the
quantity of stumpagc are discussed in Chapter XIV.
169. Stumpage Prices. — Prices for stumpage are deter-
mined by actual sales, whenever a price per unit of product is
quoted. But the price obtained for one body of stumpage is
seldom a safe basis for appraising the value of another stand.
For no other product is there such need of checking sale values
by a careful appraisals as for timber stumpage. Practically
every body of timber should have a separate price, determined
by the factors which are peculiar to the stand in question.
Standard or uniform prices are often established in a region,
for small bodies of stumpage bought by a single company,
but this uniformity is usually explained by the fact that the
purchaser is in position to dictate the price, and could, if he
wished, pay more for the better lots.
170. Factors Determining Stumpage Prices. — The value of
stumpage is derived directly from that of the fmished products
into which it is finally manufactured (§9). The stages in this
process, in reverse order, are:
Income from
retail lumber
Cost of retail business
Retailers profits
Freight charges
Cost of lumber ) _ , , ....
- , .,, J = Income from manufacture or miUing =
f .o.b. mills ) "
Cost of manufacture
Milling profits
Per unit of product
Overrun
Cost for logs at mill = Income from logging =
l68 FOREST VALUATION
Cost of transportation
Cost of felling and skidding
Logging profits
= Income from timberlands, or
Cost of stumpage , „^ ,
) Stumpage value =
Cost of production, or carrying charges
Profits
It is evident that the gross income at any stage in this eco-
nomic series just equals the total costs plus profits incident to
the entire chain of processes underlying this income and pre-
ceding it in point of time, and that the profits, or losses, are
the factors which balance the successive equations. Stumpage
value is equivalent to cost of purchase, and tends to increase
by higher prices for lumber, and to decrease by higher costs or
by larger profits in retailing, manufacture or logging.
There may be a great difference between what is paid for
stumpage and what should be paid. This difference is added
to the profit of the logger or lumberman (§ i68).
But actual values for stumpage, as established by sales of
merchantable timber, do not fluctuate with the annual changes
in lumber prices. Increased prices for lumber are not imme-
diately followed by similar increases in stumpage prices, nor
do the depressions in price, which are so characteristic of the
lumber trade, make themselves felt at once in a lowered price
for stumpage. Stumpage prices are sluggish rather than sen-
sitive.
Three factors serve to explain this apparent failure of stump-
age to behave as indicated by the economic relations set forth
above. The first is the human element in price making (§§ 5-7),
At best, it takes an expert thoroughly familiar with the costs and
reasonable profits of such technical and diversified industries as
logging and milling to determine the proper relations between
prices f.o.b. at mill for lumber and prices for stumpage. The
purchaser possesses this knowledge but the stumpage owner
may not have it. Since it is to the purchaser's interest to keep
the owner in ignorance, prices are allowed to remain as long as
possible at the level set by previous sales. This condition is
disturbed only when competition between two purchasers brings
STUMPAGE VALUKS 169
prices up to their proper level to the benefit of the stumpage
owners. The same condition is secured when timber is
sold by a lumber company which is fully acquainted with its
value.
The second factor is the controlling influence of transportation
and logging costs. Logging alone frequently requires a large
investment in railroads, flumes and equipment. It is often im-
possible for the owner of a small body of timber to market it,
except by means of the facilities owned by a lumber company.
The owner feels entitled to the stumpage value which results
from these increased transportation facilities. The lumberman
endeavors to secure the stumpage at the value which it had
before his improvements were constructed. When he is the
only purchaser, his price, rather than that desired by the
owners, is usually determined upon as the value of the
stumpage.
The third factor is the element of time. Present prices of
finished lumber can under no circumstances determine present
stumpage prices absolutely. In the first place they do not
appl\- to present but to past stumpage values, and the value of
present stumpage will depend upon the price obtained when
its product, in turn, reaches the market (§11).
But the period required to bring the timber from the stump
to the retailer, or even to the cars, is not the most important
element of time involved, and neither the discount factor nor
the speculative probability of a change in value for this short
period would have much influence on stumpage prices. A
more important fact is that large bodies of stumpage cannot
be logged at one time. The operation must extend over several
years. Therefore the prices finally received for this lumber will
not be this year's or next year's prices, but an average of many
years. Averages tend to eliminate annual fluctuations. Stump-
age values do not fall when lumber prices decline because the
owners of stumpage expect that before they have finished cutting,
these lumber prices will have risen again.
171. Appraisals of Stumpage Value. — An appraisal of
stumpage value requires:
lyo FOREST VALUATION
(a) Acceptance of a definite class of products or stage of
manufacture as furnishing a basis of prices from which to under-
take the appraisal. The further removed this basis is from
stumpage value, the greater will be the difficulty of correctly
appraising the intervening elements of cost and profit. But
the more stable and widely accepted are the prices which fur-
nish this basis, the more reliable will be the result.
(b) Appraisal of expenses of the intervening operations as
logging, or logging and milling, including depreciation of capital
assets employed in these enterprises.
(c) Determination of legitimate profits for logging and mill-
ing, and of the proper basis and method of computing what
such profits should be.
{d) Residual or stumpage value after subtracting elements
b and c from a, and correcting for the error caused by
overrun, in order to express value of stumpage in terms of
log scale.
172. The Price Basis in Appraisals. — The acceptance of the
retailer's price as the starting point for appraising stumpage
values would interpose retail costs and profits as an element
in the appraisal. This would result in appraising the value
of lumber f.o.b. cars at mill, instead of accepting the current
prices already determined for this lumber by sales; such a course
is obviously undesirable.
Were the prices of logs standardized, and determined in open
competitive market as are wholesale lumber prices, there would
be a similar argument for accepting log prices instead of sub-
stituting an appraisal of the value of logs. This method has
been used on Puget Sound where such a log market exists.
Whenever logging is conducted as a separate business, and not
merely by contract for the manufacturer, the price of logs does
determine what may be paid for stumpage, and must be taken
as the basis of appraisals.
It is claimed that in markets established for logs, prices for
the logs are not as high as an equitable appraisal would indicate
owing to the ability of the mill owners to keep these prices
under control. Where the log market is the only outlet for the
STUMPAGE VALUES 171
logs, this fact would not justify an appraisal of stumpage based
on higher log prices, unobtainable in practice, although it might
justify holding rather than selling the timber.
But in the majority of cases, the business of logging is either
conducted by the same firms which manufacture the timber,
or the manufacturer purchases the stumpage, contracts the log-
ging and thus bases the price which he can pay for the stumpage
on the price of lumber at the mill. Stumpage appraisals must
thus conform strictly to the prevalent economic conditions, and
must be based on the value of the product put forth by the
operator who purchases the timber, provided he conforms to
general customs in the locality.
^lill prices for lumber fluctuate not only with the season
and condition of the market, but are afTected by freight charges.
In certain localities, prices at large central markets for lumber
may be taken as standard, and the proper discounts made for
local freight rates.
The main source of variation in mill prices lies in the variety
of products, and of grades of the same product, into which the
timber is manufactured. This difference exists originally in
the quality of the trees or logs, and is increased by the methods
of handling the raw material or logs by the millman. One mill
may, from the same material, produce a much greater per cent
of the more valuable grades than another, whose principal out-
put may be dimension lumber.
These differences in the quality of the grades produced vitally
afifect stumpage value and give to old timber a value at present
prices which second growth timber may never obtain in the
future because of inferior quality.
Two plans may be used in obtaining a price basis for the
appraisal of a given body of stumpage. The first, advocated
by the U. S. Forest Service in Washington and Oregon, is based
on grade prices at a central market, discounted for freight
rates to the required locality.
The first step is to estimate in the field the per cent of each
of certain standard grades which will probably be yielded by
the body of timber to be appraised. The average price of each
172 FOREST VALUATION
grade is obtained and a per cent of this price taken equal to the
per cent of the total stand represented by the given grade.
These fractional prices, when totalled, give an average price
weighted both by quantity and value for the grades ex-
pected.*
The second plan depends upon "mill run" prices. In the
absence of stable central markets, average prices for the total
dutput of mills, termed mill run prices, are advocated. This
method is defective for several reasons. The higher the average
prices for lumber, the more profitable it becomes to manufacture
low grades. In periods of depression these grades may be left
to waste in the woods. An increased output of cheap grades,
which always follows higher prices, may actually lower rather
than raise the average mill run prices for lumber. Again, when
prices are based on average mill run, the per cent of grades
sawed may not coincide with those which can be produced from
the timber to be appraised, either because the mill may have
been cutting in timber better or poorer than the average, or,
because the timber to be appraised may be better or poorer
than the average. Mill run prices for timber known to be of
* The following figures, used in determining the average price of lumber in con-
nection with a recent timber sale in Washington, were furnished by Asst. District
Forester, F. E. Ames, U. S. Forest Service, and serve to illustrate this method.
Douglas Fir Grades, Prices and Average Value
No. I V. G. Flooring 3% @ $26.00 $
No. 2 V. G. Flooring 5% @, 23.00
No. 2 and Bet. F. G. Flooring 3%@ iS-oo
No. 2 Clear and Bet. Finish 5% @ 26.00
No. 2 Clear and Bet. Siding and Rustic. 4% @ 17.00
No. 3 Clear Flooring. Siding and Rustic 8% @ 13-50
No. I Shop 4% @ 16.00
Car Sills 6% @ 16.50
Timbers 1 5% @, 10.30
Dimension 28% @ 9.10
Boards and Shiplap 12% @ 8.75
Dunnage 7% @ 6.00
$1.
64
The grade prices represent the average of the quarterly averages from July i,
191 1 to July I, 1914. Underweights not included.
STUMPAGI-: VALUKS 1 73
similar quality to that appraised removes this objection. Aver-
age mill run prices for several mills in a region are serviceable
only when the timber is remarkably uniform in quality and
grade.
173. Depreciation. — Depreciation plays so much more im-
portant a part in stumpage appraisals than in forest pro-
duction that it should be given special consideration in this
chapter.
Depreciation is a sum written off or subtracted from the cost
of capital assets, to correspond roughly or approximately with
a shrinkage or disappearance of value through diminishing use-
fulness. An investment in a fixed or durable asset is not an
''expense " at the time of purchase, but an exchange of cash for
another form of property. The real expense is incidental to
the use or service which this property yields, by reason of which
it diminishes in value. Depreciation on property for which
there exists a continuous need corresponds to actual deteri-
oration and final discarding of the article as worn out. But
where the period and amount of use is limited and the property
will outlast its usefulness, the residual value will coincide with
the value of the material of which it is composed, for removal
or use in some other line. This shrinkage in value not accom-
panied by physical deterioration may be termed "amortiza-
tion."
When depreciation is added to other expenses, the sum gives
the total actual outlay or cost of the business, in which total
the investment in capital assets subject to depreciation is ex-
cluded, as not constituting a cost.
A depreciation Jund is a fund created by the setting aside
annually, from net income, amounts intended to eventually
equal the total depreciation (§ 73). When the period is known
with reasonable certainty, the amounts annually needed to
accomplish this purpose can be computed in advance.
Let A = original capital investment.
W = final or wrecking value.
D = total depreciation or A — W.
n = years in period.
174 FOREST VALUATION
Four methods may be used in determining depreciation.
Method A. The total depreciation may be refunded by de-
positing each year in a savings bank, at p per cent, or investing
and reinvesting, annual sums in such a way as to earn compound
interest, so that the total of principal and interest at the end
of the period equals the depreciation. This fund is not returned
to the owners until the expiration of the period. Their capital
investment remains at its original figure, and the annual divi-
dends are declared on this basis.
Let X = annual sum for depreciation.
Then JL(^_op'^- i) = d, (See III.)
o.op
^ _ Djo.op)
I. op" — I
(P)
This method is seldom, if ever, employed in connection with
annual business, although it is practical as the basis of a sinking
fund for the payment of bonds.
The other three methods neglect the factor of compound
interest on the annual payments, and undertake to repay,
through a series of years, sums whose cash total will just equal
the total depreciation.
Method B. This method proposes to pay the total depre-
ciation in equal annual instalments covering the requisite
period. The formula is
^ D A-W ,p.
X = — or • • (Pi)
n n
The method is used more widely than any other and is easily
understood and applied. Actual return to investors of this
annual appropriation for depreciation would have the result of
diminishing the capital investment annually.
Method C. Instead of depreciating the capital by equal
amounts annually, the depreciation may be made to equal a
fixed per cent annually of the residual value of the capital;
its value less previous depreciation. By this means, depre-
STUMPAGE VALUES 1 75
ciation expense is heaviest in the earlier years, and steadily
diminishes.
Let 2 = per cent of depreciation, and
o.os = per cent expressed decimally.
Then ^(i - o.os)" = W,
"/w
^ A
z = 100(^1 -\/^y (p,)
This method is seldom employed as it is inconvenient to write
off large sums for depreciation in the earUer stages of the business,
especially in lumbering.
jNIethod D. This method proposes to increase the amount
charged to depreciation annually, and combine it with an annual
interest return on the diminished or residual capital, in such
amounts that the sum of interest and depreciation will require
equal annual payments. Depreciation, by reducing the invested
capital, correspondingly lowers the interest returns required
by a given rate of interest- This reduction in interest may be
added annually to depreciation. It only remains to determine
what annual sum in excess of interest on the original investment
is required for the first payment, to secure this balance between
the two elements of interest and depreciation, so that the
sum of the increasing payments on account of depreciation will
at the close of the period just equal the total amount to be
written off.
In this case, either of two solutions is possible to determine the
annual payment.
Let Z = annual payment for interest and depreciation.
I o^" I
Let d = -^-^ , when p = rate of interest to be earned on
o.op ' ^
capital A.
176 FOREST VALUATION
Then 2= ^ ^'■°P'] ' "^ * (P,)
a
or Z = A{o.op)+^''^ (P4)
The first formula utilizes the wrecking value, while the
second introduces total depreciation, and is somewhat simpler.
The factor d is easily computed from Table VI, or, for values of
p not given, by logarithms, in which the logarithm of i.o^ is
multiplied by n to obtain the logarithm of i.o/>"4
* "Modem Accounting," by Henry Rand Hatfield, page 132.
{ {A • i.op — X) x.op — X\ i.op ... to H terms = W.
A (i.op") - X (i + I.op + i.o/>2 . . . i.o/)'^i) = W.
A ii.op'') - X ^•°'^" ~ ^ = W (by Formula Qi).
I.op — I
A (i.op") - W
~ I.op"— I
op
^ A (i.op") - W
d
t Proposed by W. B. Hunter, formerly special e.xaminer in U. S. Bureau of
Corporations.
Let X =A (o.op) + e.
Then, in second year,
(A ' o.op — e) o.op = interest on capital.
e (o.op) = increase in depreciation,
e + e (o.op) = e (i.op) = depreciation.
In third year,
(A • o.op — e ' I.op) o.op = interest.
e (i.op) X o.op = increase in depreciation.
e (i.op) — e (i.op) X o.op = e (i.op^), depreciation.
D = e +e (i.op) + e (i.op"^) . . . i.o/>"-i
_ e (i.op" - i)
o.op
I.op" — I ,
o.op
e = X — A (o.op).
D = (X -A- o.op) d.
X =A(o.op) +y
X The objections urged against this method are: first, that it allows interest on
invested capital as a cost (Hatfield); second, that a plant depreciates more rap-
idly during the first few years than thereafter, and loss during that time would
STUMPAGE VALUES 177
174. Milling Costs and Profits. — The cost of milling or
manufacture may be standardized for operations of a given
size. The current expenses, or operating costs, do not vary
greatly. For operations involving a definite quantity of stump-
age, the duration of the operation is largely determined by the
capacity of the mill.
The factor which indicates the most profitable size for a mill
is the relation between the depreciation of fixed costs or capital
expenditures for the plant and machinery, and the period and
quantity of output over which this cost must be distributed.
The value of the mill when there is no more timber to cut is
practically nothing, and that of second-hand machinery, very
small. The difference between these final values and initial
cost, which represents depreciation, is one of the principal
elements of expense (§ 173).
The size of this item of depreciation and the relation which it
bears to the total output, and to the total cost of producing
each unit of product, evidently depends more upon the total
length of time over which the plant can continue to operate
than upon its daily capacity. With mills of equal efficiency,
the one with a twenty-year cut may be considered as having
about half the depreciation expense per unit of output that one
with but ten years' cut must write off.
Pro\aded the supply of logs is assured, and the period over
which to distribute the cost of depreciation can be approxi-
mated, the requisite profits in manufacturing may be gauged
with reasonable uniformity. Uncertainty as to future timber
supply makes it necessary to guard against a shortage or com-
plete exhaustion of raw material by a correspondingly large
appropriation from gross income for depreciation. Should
this shortage not materialize, the concern would later find its
find the proprietors without adequate provision for meeting this loss. The first
objection does not apply when the purpose of the computation is to determine
profits in advance, since these are not treated as costs. The second objection
holds good if it is considered necessary to make the amounts written off for de-
preciation agree closely with actual loss in value. The results obtained by
this method agree more closely with those of Method A than with Method
BorC.
178 FOREST VALUATION
financial position and average profits correspondingly, and justly,
increased by these earlier sacrifices.
The costs and profits of manufacture are both included in
contract prices for sawing or manufacturing products, which
is the basis of operations of many portable saw mills.
175. Logging Costs and Profits. — It is in the logging, rather
than the milling end of lumbering, that the greatest variations
in costs occur. The cost of felling and bucking the trees into
logs, ties or poles may be standardized. But the cost of trans-
portation of the product from the site to the mill is determined
by a number of exceedingly variable factors, and is the prin-
cipal part of logging.
These factors are: accessibility and quantity of stumpage,
and methods of transportation adapted to climate, to the topog-
raphy and to the size of the timber. The direct relation of total
quantity or volume upon the cost per unit of the combined
expense of constructing the transportation routes and moving
the product needs to be emphasized (§ 98) , and explains the
great dift'erences in value of timber of equal quality but differing
merely in quantity available.
Accessibility is a relative condition depending upon the total
cost per unit of product to bring the timber to the mill, and the
margin of profit remaining for distribution between the owner
of stumpage and the logger. When the logger sees so small a
margin that he demands it all, the timber is for the present
inaccessible. Accessibility depends, then, upon the total volume
available as well as upon the location of the site and the diffi-
culties and costs of transportation intervening between site and
mill.
Methods of transportation exercise a profound influence
upon logging costs. The factor of climate exerts its chief influ-
ence upon the bottom, making ice roads possible in some regions,
while in others rain greatly increases the difiiculties by soften-
ing the soil. The driving of streams, supplemented by the
sleigh haul, may be superseded by rail transportation involving
an investment of an entirely different character. For short
distances, in regions of second growth, wagon haul is the chief
STUMPAGE VALUES 1 79
dependence of the operator. The overhead cable to supple-
ment the railroad may prove cheapest, as in cypress swamps or
over broken gorges, while elsewhere, skidding by ground cables
or with animals is most efticient.
In appraisals, average logging costs for the specific body of
timber, based on the methods accepted by experience in that
region as best and cheapest, will be the basis of costs. Excessive
costs due to deliberate use of methods shown to be antiquated
or expensive, when the operator is in position to use better
methods, or when others can be found who will do so, cannot
be permitted to influence or increase the factor of logging costs.
An additional cost is incurred in logging under forestry prin-
ciples (§§ 107 and 176).
The profits in logging are less easily gauged than in milling.
The great variation in conditions, which makes each logging job
or "chance" a separate venture, prevents the standardization
of methods and increases the uncertainty of the total estimated
cost, and consequently of the risk of loss. Added to this is
the risk from natural agencies, as floods, fire, drought, lack of
cold weather, too much snow or any other variation from normal
which either directly damages the timber or the means of trans-
portation, or unduly increases the labor and cost of logging.
Logging work is less closely supervised from the main ofiice
than is milling. Hence woods bosses are more largely thrown
on their own resources. The main attributes of woods foremen
even now is brute force and practical experience. This type
of boss lacks abihty to apply methods of scientific efficiency.
The average risk in logging is probably double that incurred
in manufacture.
Depreciation as an item of expense in logging chiefly concerns
the means of transportation. The entire initial cost for tempo-
rary railroads, flumes or roads, which will be abandoned on com-
pletion of the operation, is depreciated or charged off as a cost
of logging. The costs for railroads, or roads which will after-
wards be used for permanent traffic, will be maintenance and
the difference in value of the road at the beginning and end
of the operation. A logging company which subsequently sells
l8o FOREST VALUATION
the road to a railroad company for continuous operation may
secure a price equal to the cost of the road, in which case no
depreciation is incurred. Such a result cannot be assumed, and
depreciation must always be charged against the transportation
system.
The cost of all logging equipment, such as cables, engines,
horses, and other supplies, should be reckoned not in the form
of a capital expenditure but as depreciation.
176. Stumpage as a Capital Investment and as a Cost of Raw
Materials. — Methods of appraising the value of stumpage on
the basis of the present net residue, after subtracting logging
and manufacturing costs and profits, are based on the supposi-
tion that this timber will be removed within a short time, not
exceeding three to five years. Such values are appHcable to
short-term contracts or to small bodies of timber, and to pur-
chases in which land is not included. But the purchase for
cash of large bodies of stumpage introduces an additional ele-
ment of cost which must be considered by the purchaser. The
time which must elapse previous to the actual completion of
cutting necessitates the holding of this stumpage, with accom-
panying annual expenses (§ 1 70) . This would apparently lower
the price the purchaser can pay, in the same manner that the
absence of a market at present, even if it is sure to develop
later, depresses present values. When transportation facilities,
mills and markets are ready, the price will be correspondingly
higher than in regions where development must follow purchase.
It is not possible, however, to arrive at a proper appraised
value for large areas of standing timber by the method of com-
puting the value for immediate cutting, and then discounting
this value for the average period which the timber must
stand.
In spite of the impossibility of immediate cutting, the timber
will usually sell for the value shown without such discount.
This is explained by the element of increasing prices, to which
may be added growth of timber and improvement in quality.
It would be unfair to discount a future stumpage value based
on present sales, when everyone, purchaser and owner alike,
STUMPAGE VALUES l8l
expects stumpage to increase in value (§ i88). Were it definitely
known that no such increase would occur, the expectation value
of the revenue from cutting the timber would be less than the
present sale value for immediate cutting. As it is, the expec-
tation value of the stumpage is based on this probable increase
and its present sale value is not depressed by the postponement
of cutting. Again, the great advantages accompanying the
ownership of large bodies of timber and the reduction of depre-
ciation costs (§ 173) and transportation charges (§ 174) in them-
selves more than offset such possible discount in value.
The value of stumpage for immediate purchase as a capital
investment may therefore be appraised on the basis of what
it is worth on the completion of the necessary transportation
and milling facilities, or, if these are assured, it may safely be
based on present value.
For stumpage which is paid for in small instalments just
previous to or following the cutting of the timber, the value is
manifestly that existing at the time of payment. On long-term
contracts, as a result of such postponed payments, a readjust-
ment of stumpage values is required at reasonable intervals,
on account of the expected increase in future prices of lumber.
This method of payment, by which the operator is relieved not
only of the investment with its attendant annual expense, but
also of the risk, and of any losses which may result from fire
or any other agency, puts stumpage in the same class as that
of raw materials, rather than capital. The attendant advan-
tages to the purchaser, corresponding to the prospective loss
and risk of holding timber, are recognized as having a value
great enough to form a material inducement in sales of timber
on National Forests. It is usually sufficient to offset the addi-
tional cost of brush burning and other silvicultural measures
required by the government.
177. The Determination of Legitimate Profits. Overturn
Methods. — Costs must be gauged in relation to the quantity of
product resulting from a given expenditure, and a cost account
seeks to determine the cost and the resulting profit on each
^"lit (§25). All factors of cost, including depreciation, may be
l82 FOREST VALUATION
expressed on the basis of a thousand board feet, cord or other
unit of product.
The surplus after subtracting costs from the average price
of the product is the net profit, from which is paid the returns
on the invested capital and the enterpriser's gain for services
(§39). If the cost of stumpage is fixed, this, added to other
costs, determines the logger's profit. In appraisals of stumpage,
on the other hand, the net surplus after paying all other expenses
must be divided between stumpage and profit, and the deter-
mination of legitimate profit must precede that of stumpage
value.
On small ventures, where the enterpriser depends almost en-
tirely on his individual efforts and the amount of capital invested
is insignificant, most of the annual costs are met from income,
depreciation is a small item, and profit is usually gauged by the
margin of income over costs for each unit. Logging contractors
are satisfied if they realize, say, $1 profit per thousand board
feet log scale above their computed expenses. Profits may
always be expressed in this manner, whether or not the calcula-
tion stops at this point. This has been termed the overturn
method of expressing profits, since the working capital used for
wages and other current expenses is turned over or used once
for each unit of output.
The contractor bases his profit on costs of logging, exclusive
of stumpage.
Let Lc = logging costs.
Mc = milling costs.
D = depreciation costs ] ,,^ , .,,.
[ MD for millmg.
5 = sale value of lumber or of logs.
P = profit.
Ym = stumpage value of 1000 board feet of
manufactured lumber.
q% = legitimate profit.
Then P = g%(Lc + D).
Yrr. = S-(Lc^D) - q% {Lc + D).
STUMPAGE VALUES 183
That is, if the price for logs is taken as the basis of prices,
and the logger computes his requisite profit roughly as a per
cent of average logging costs, stumpage value is the residue
after subtracting costs and profit from sale prices.
In the same way, milling costs and profit may be subtracted,
and (Method A)
F„. = S-{Lc-\- Mc + £>) - q% (Lc + Mc + D) . (R)
Should milling require a different profit from logging, these
costs and profits may be separated, using r per cent for profit
in milling.
Ym^S - (Mc + MD-^Lc-\- LD) - r% (Mc + MD)
-q7o{Lc-\-LD). (Ri)
The computation of profits as a per cent of operating costs,
if based on the results of individual operations, would place a
premium on extravagance. But when gauged by average costs
of well-conducted operations of similar size, and applied in deter-
mining appraisals in advance of cutting, no such objection can
be urged.
Method B assumes that stumpage is a part of the total
operating costs, and that the money invested in it is entitled
to share in the profit. By thus adding stumpage to the sum
of the other expenses, the total of costs plus profit equals gross
income, or sale value. Profit thus becomes a fixed per cent
of this sale value, and is independent of operating costs. Any
increase in operating expense of logging is subtracted from cost
of stumpage, and vice versa.
The formula is:
Y,„ = S - {Lc -\- Mc + D) - q7o {Lc + Mc + Z) + F„),
which reduces to
Ym = ^ ^ - {Lc + Mc + D). (R2)
I + q%
This formula was formerly advocated by the Forest Service
for use in small sales where but little capital is invested, but has
been set aside in favor of Method A. The profit q7c should be
exclusive of a salary of $1200 to $1500 for the operator (§ 34).
l84 FOREST VALUATION
Method C is to share the profit or margin between the owner
of stumpage and the operator. Such a plan requires complete
confidence in the integrity of the operator or a right to inspect
his books, and is not generally practiced, though one of the most
equitable of methods.
It is the only one of the three methods proposed above,
which can be based on the actual costs of a given operation,
with safety to both parties. Letting q per cent equal the per
cent of net income taken for stumpage value, the formula is
Ym = q%\S- (Lc ■^-Mc-hD)l. (R3)
In the following diagram the basis and results of these three
methods is shown, and the effect of an increase of operating
costs upon profits and stumpage values.
DIAGRAM III
Comparison of Costs, Profits and Stumpage Value by Overturn Methods
Sale Value 17.00
Method A
Method B
Method C
Costs 11.00
1 Profit 2.20 1 Stumpage 3.80
Costs 13.00
1 Profit 2.60 fi'^S^'
Profit 20 « Qf Costs
Costa 11.00
1 Stumpage 3.45
Profit 2.55
Costs 13.00
1 Stumpage
Profit 2.55
Profit IS/, of Sale Value
Costs 11.00
1 Profit. 3.00 [ Stumpage SM
Costs 13.00
1 Profit 2.00 1 '^■^T'^'
Profit 50^ of Net lucerne
Operating costs, profits and stumpage value based on i Af board feet of lumber,
scaled in the log.
178. The Investment Basis for Profits. — Although profit
may be expressed in terms of per cent of cost, or of sale value
for a unit of product, it can be correctly gauged only as a return
on invested capital in which is included the enterpriser's gain
(§§ 32, 33)- The knowledge that a profit of $i per thousand feet
has been earned does not suffice as a basis for dividends. The
reward for personal services, which is so large an element in small
undertakings, disappears with large enterprises, and net income
STUMPAGK VALUES 1 85
or profits must be converted into annual dividends earned on
invested capital.
The capital upon which this income is earned is the entire
amount of fixed and working capital employed in the business,
including that which is borrowed. It is of no significance that
working capital is turned over several times in a season, as is
done in railroad logging, except as it increases the total net
income which is the product of the profit per thousand feet
multiplied by the year's output. This income is not the product
solely of the working capital, but of the total investment.
Interest on borrowed capital is paid out of this net income,
and it is immaterial whether the capital entitled to share in
the income is taken as the entire investment, or as the portion
owned by the proprietors, excepting that the latter are entitled
to a larger rate of profit in proportion to the lessening of their per
cent of total capital and corresponding increase of risk (§32).
In stumpage appraisals it is advisable to compute the profit on
the total investment, thus eliminating the purely personal ele-
ment as to what proportion of the capital is borrowed.
It must be self-evident that interest is not a "cost" in stump-
age appraisals, but it may be so regarded without harm, pro-
vided it is not added to operating costs in Methods A, B and C
(§ 177), and is subtracted from income allowed by the investment
method. To permit profits to be earned on income represented
by interest on owner's capital, results in serious inflation of
profits and resultant heavy losses in stumpage values (§ 42).
The main difficulty in computing profits in the form of a
return on the average annual investment arises from the ele-
ment of depreciation, and its effect in reducing the capital
invested year by year.
It is possible to earn annually about the same net surplus,
available for depreciation and profits. To base the amount
of these profits upon the maximum investment, which occurs
normally in the first or earlier years, results in a steadily in-
creased rate of profit on the capital remaining invested in sub-
sequent years, and an average rate considerably greater than
intended, with corresponding loss in stumpage value.
1 86 FOREST VALUATION
By the use of either of the formulae given in Article 175, Method
D (P3, P4), a fixed rate of profit may be found, which will apply
to the residual capital actually invested annually. This is
accomplished through the increasing payments for depreciation.
The sum of interest and depreciation, or Z, calls for equal income
annually. This conforms with the financial conditions which can
normally be secured in lumbering. To the owners, it makes
very Httle actual difference whether their annual income is
termed dividends or depreciation. They expect to allow the
larger portion of their capital to remain invested throughout
the life of the enterprise, and this result is accomplished by
increasing depreciation from small beginnings. Apparently,
there is no valid objection to the adoption of this method of
determining the average per cent of profit to be allowed on
invested capital.
Should the method of allowing equal annual amounts for
depreciation be adopted (§ 175, Method B) the average amount
of capital invested during the prospective life of the enterprise
must be determined. The investment for each year is taken
at the beginning of the year. The average for the period is then
equal to the residual or final investment (W) plus one-half the
total depreciation, plus one-half the annual depreciation. For
an investment of $20,000, with a residual value of $10,000, over
a period of five years, the values at the beginning of each year are
First year $20,000
Second year 18,000
Third year 16,000
Fourth year 14,000
Fifth year 12 ,000
Average investment $16,000
which equals
Residual investment $10,000
One-half total depreciation 5,000
One-half annual depreciation 1,000
Average investment $16,000
STUMPAGE VALUES 187
This amount would be taken as the basis for computing the
per cent of annual profit to be allowed.
179. Overrun. — When the amount and per cent of profit
have been determined, the remainder, or stumpage value, is a
definite proportion or per cent of the sale value of the manu-
factured products, and equals a stated price per thousand
board feet. Should stumpage appraisal indicate a value equal-
ling 20 per cent of the wholesale price or mill price of lumber
worth S20 per thousand, the price of stumpage will be $4 per
thousand feet of sawed lumber.
But this does not indicate that the true price of stumpage
is $4. It is probably considerably more. The contents of
logs, and not the measured products, is the basis of payment,
not only when the timber is bought on the stump, but when it
is paid for after being felled and measured.
Only in case the logs are measured by a rule which will give
the actual sawed contents, will the appraised stumpage value
per thousand feet be the same when measured by log scale
and by sawed contents. All log scales in extensive commercial
use give less than the contents ordinarily sawed from logs, and
this discrepancy increases as utilization becomes closer. The
excess of manufactured lumber over the contents measured by
the log scale is termed overrun.
With certain log rules, notably the Doyle and Doyle-Scribner,
this excess amounts to 25 per cent and over, and increases with
small timber.
Should the overrun be 25 per cent, it indicates that for timber
worth S4 per thousand, each thousand feet log scale produces
1.25 thousand feet of lumber. The value of the stumpage is
therefore 1.25 X S4, or S5 per thousand.
K
Ym = stumpage value per thousand feet of sawed lumber,
5 = per cent of overrun per thousand feet of log scale,
Y = resulting stumpage value per thousand feet log scale,
then
Y = Yrr^X 1.0s.
l88 FOREST VALUATION
180. Stumpage Values for Different Species in Mixed Stands.
■ — In a mixed stand containing two or more species, the sale
value of the products of these species usually differs considerably.
Often only one valuable species will be removed from a mixed
stand. As values increase, other species become profitable, and
finally, all may be taken.
At a point just before the inferior species become sufficiently
valuable to be logged, the operator is under the necessity of con-
structing his transportation system, and incurring his entire
cost for equipment and overhead expenses, in order to log a
portion of the stand, thus moving a smaller volume of lumber,
at relatively greater expense per unit.
Assuming that the total costs, including depreciation, amount
to $12 per thousand board feet, and the most valuable species
is worth $20, the margin for profit and stumpage is $8. A
species worth but $12 on the market could apparently not be
marketed at all. But there is very little additional investment
involved in logging this second species. By doing so, the total
average cost of logging may be reduced, by lessening the trans-
portation expense per unit, the average of overhead charges,
and the depreciation, to $10 per thousand feet for the entire
operation. This adds a profit of $2 to the more valuable species,
and leaves a margin of $2 for the inferior one, for profit and
stumpage.
But such a cost distribution is unfair to the inferior species,
since the operation does not depend on its presence and the
capital expenditures must be incurred without its inclusion.
It has been suggested that the more valuable species or group
be made to bear both the entire cost of depreciation, which
represents the capital expenditures, and the overhead charges.
The inferior group is left to bear merely its proportion of oper-
ating costs. This plan is rather crude where there are several
species, all of different values.
The following method is quoted verbatim from the Manual
of Stumpage Appraisals, U. S. Forest Service, November, 1914.
This plan offers an equitable solution of the problem.
" The most satisfactory method is to pro-rate the gross annual
STUM PAGE VALUES
189
depreciation and profit over the difference between operating
cost and selling price, for each species, in the quantities entering
into the annual cut.
To illustrate:
A yearly cut is made up of 4 million feet of sugar pine, 3 mil-
lion feet of yellow pine, and 2 million feet of white fir (giving a
total of 9 million feet).* The margins between selling prices and
costs of production, exclusive of depreciation and profit, are:
Species.
Selling price.
operating cost.
Margin.
Sugar pine
Yellow pine
White fir
$20.00
18.00
(lO.OO)
$10.00
10.00
(10.00)
$10.00
8.00
6.00
The total net value, or sum of the margins over which depre-
ciation and profit may be pro-rated, is thus:
Sugar pine $10.00 X 4000 M = $40,000
Yellow pine 8.00 X 3000 M = 24,000
White fir 6.00 X 2000 M = 12,000
Total $76,000
The annual sum of depreciation and profit (investment
method) which must be paid out of this total has been computed
as $34,200. Hence -^^^^ = $0.45. That is, every dollar of
76,000
margin between operating costs and selling price must pay
45 cents toward profit and depreciation. Put in quantitative
terms, by species, we have the following charges per M feet for
depreciation and profit:
Sugar pine 10 X $0.45 = $4.50
Yellow pine 8 X 0.45 = 3.60
White fir 6 X 0.45 = 2.70
By this method inferior species which yield no margin between
operating costs and selling price, or a negative margin, but
which must be included in the sale for silvicultural reasons,
* The bracketed material does not appear in the original quotation and has
Ijeen inserted as additional explanation.
IQO FOREST VALUATION
are automatically relieved of profit and depreciation, and the
charge upon the other timbers for these items proportionately
increased.
The same result is readily obtained on a thousand foot basis,
using the per cents of the different species in the cut. That
is, to obtain the average margin (of sale value above operating
costs), multiply the margin for each species by the per cent of
this species in total cost:
45 per cent sugar pine at $10.00 $4.50
33 per cent yellow pine at $8.00 2.64
22 per cent white fir at $6.00 1.32
Total $8.46
Depreciation and profit per M feet ( 34>20o\ $3.80.
\ 9000 /
;:'■ ^ = $.04=5, to be taken from each dollar of margin for
8.46
these items.
This method of adjusting the prices of the more and less
valuable species is believed to accord with customary business
practice. Volume of money handled, rather than quantity
of this or that product, is the usual basis for figuring carrying
charges, depreciation and returns. In logging, improvements
are frequently constructed primarily to take out certain valua-
ble species. Inferior timbers may be cut or left as the market
warrants. In such cases operators will usually cut inferior
species' if a profit can be netted over bare operating costs, figur-
ing that the cost of improvements is borne wholly by the better
stuff. The foregoing is believed to be a logical and rational
application of this principle."
For a mixed stand, the method proposed is, therefore, to com-
pute the operating costs on the basis of the total amount to
be logged, including inferior species. The profit and deprecia-
tion are then determined as a lump sum, sufficient to pay the
required per cent on the total investments. Finally, this sum
is charged as an additional "cost" against the sale value pro-
rated as outlined above between the different species. The
STUMPAGE VALUES 191
remaining margin between the sale value of a species and these
total charges is its appraised stumpagc value.
181. Carrying Charges versus Profits, on Stumpage, — In
Chapter X (§ 158), it was demonstrated that a forest capable
of producing annual income was also capable of paying increased
taxes, for the reason that compound interest did not accumulate
on such a forest. The owner may, for his own information,
and to gauge the advisability of reinvesting income, compute
the interest on his investment for the interval elapsing between
cost and the income directly resulting from such cost. But the
total cash investment in the business does not increase by reason
of this interest. Neither the unearned interest, nor the actual
cash expenses for taxes and protection serve to increase the capi-
tal cost of stumpage, as long as sufficient income is secured each
year from some portion of the forest or business to cancel these
costs.
There is the same difference between tracts of mature stumpage
held for speculation without cutting, and tracts on which an
operation is conducted, as there is between an even-aged and an
all-aged forest, Cases A and C (§ 158). The first case is paral-
leled by the young forest; the second, by the forest already
capable of revenue. For timber, or that portion of the timber
holdings which cannot be cut for from 20 to 40 years, a separate
cost account based on economic factors (§ 106) would show iden-
tical costs, whether or not the specific stand is a part of a large
holding which produces annual revenue, or is part of a specula-
tive holding producing no income. But there is an enormous
specific difference in the financial status of the owners of the
respective tracts, which has an important bearing on the problem
of carrying charges and increased stumpage values.
The non-productive speculative holding requires an increase
in stumpage values sufficient to ultimately offset all annual
e.xpenses, and earn compound interest on the entire investment,
up to the year when cutting begins, in order to show a profit
sufficiently large to include an enterpriser's gain (§ 33).
The productive holding, which is being operated, and is pro-
ducing annual income at the present time, will under certain
192 FOREST VALUATION
conditions continue to pay a profit as great as it pays now, if
stumpage does not increase in value, or, rather, if the margin of
prices over cost of operation does not increase in per cent (§ 187).
Were the forest itself composed of stands of all ages, which
are cut upon reaching maturity, this condition would actually
occur, and advancing prices for stumpage would simply increase
the profits.
The conditions confronting the holder of stumpage, who is
also an operator, partake of both of these extremes or lie between
them. The total investment in stumpage is not maintained,
except through extending the area by purchase, but diminishes
constantly by cutting, with a corresponding lightening of the
annual carrying charges, and a reduction of the capital invest-
ment (§175).
It is hardly to be expected that a company planning extensive
operations over a long period, will inaugurate a scheme of cut-
ting so comprehensive that they will be enabled to earn their
carrying charges for the first few years, and at the same time
pay dividends on the total capital investment. The actual
annual outlay may absorb every cent of annual income for a
while. When interest on bonds is added to other carrying
charges the burden in the earlier years is still heavier, and it
may require additions to capital to meet these charges. Some
companies owning extensive timber properties have lost this
timber by foreclosure, because of non-payment of interest on
bonds through inabihty to obtain this additional capital.
With reduction in interest on bonds, in taxes and in other
expenses, a company comes sooner or later to a condition per-
mitting of the payment of dividends. Up to that time, it might
be assumed that the value of stumpage must increase, in order
that the dividends when received shall be large enough to com-
pensate for their absence in earlier years. From then on, with
both the annual expenses and dividends paid from the annual
net income, an increase in stumpage value or in net income
means a corresponding increase in surplus and dividend rates.
When a company is able, by operating, to secure a sufficient
net income to meet all expenses and pay dividends from the
STUMPAGE VALUES 193
start, stumpage value does not need to increase beyond the
amount needed to meet any increased costs, in order to maintain
the dividend rate. Furthermore, this rate is certain to in-
crease, on account of reduced carrying charges, even if the value
of stumpage remains stationary.
The claim that the value of stumpage must increase at a
rate sufficient to return compound interest on all costs, or the
result will be financial loss or bankruptcy, must therefore be
flatly rejected except for purely speculative holdings, or for
operators attempting to carry far larger holdings than they
can take care of with their own capital. An owner of stumpage
must either have sufficient capital to carry all. charges for an
indefinite period, or he must operate and obtain revenue annu-
ally. In either case, if he expands his operations by borrow-
ing on the security of the timber, he must conduct such a
transaction with considerably greater caution and conserva-
tism than is necessary in many other forms of business, or
he may lose his holdings. For a concern which is earning
annual dividends, increased costs, especially taxation, is the
only factor which will necessitate the realization of higher values
in order to maintain profits. Very strong combinations of
capital holding timberlands and operating, may, by a policy
of cutting calculated to cancel carrying charges, put themselves
annually in a better financial condition, until, after the period
of pressure and over-production has passed, they will reap
relatively large profits, representing more than average divi-
dends on outstanding capital investments.
This distinction between the separation of a business into
parcels, and the treatment of the business as a unit, is recog-
nized by the U. S. Commissioner of Internal Revenue in inter-
preting the income tax law as applied to corporations dealing in
timberlands. A cost account is to be kept for each parcel of
land as the basis for determining net income (§25), and on sale
of this parcel the value received can be reduced by the amount
of the original cost of the parcel, but cannot be absorbed by
applying it to cancel capital cost for any other parcel. On the
other hand, net income is treated as applying, not to the parcel,
194 FOREST VALUATION
but to the entire business of the concern. If actual cash ex-
penses in any year exceed actual income, such expenses can be
added to capital cost, and pro-rated among the parcels. The
net income, after subtracting capital cost of the parcel sold,
may be used, as far as needed, to cancel actual outlay on the
entire tract for the year, the surplus income remaining after
this total expense is met being the only portion subject to the
federal income tax.
CHAPTER XII
FUTURE VALUE OF FOREST PRODUCTS
182. Factors Affecting Future Value. — Since the value of
forest property is derived from income, an appraisal of the future
value of forest products must precede that of the property
itself and forms the basis for this appraisal. The examiner
must base his conclusions, first, on the character and present
condition of the property and its probable productiveness, and
second, upon the factors which will affect the value of the prod-
ucts secured. The elements demanding consideration are:
The Stand.
Growth in volume.
Improvement in quality of products.
Deterioration of standing timber.
Closeness of utilization.
Price Levels.
General price changes.
Changes in prices for forest products.
Effects of substitutes for wood.
Future Operating Costs.
Local Factors.
Future transportation facilities.
Industries and markets.
Future supply of timber.
183. The Stand; Growth in Volume. — The future growth
in volume of a stand of timber may be predicted for short periods
by measurements of past growth on average trees. For periods
exceeding a decade this method becomes unreliable by reason
of the progressive loss in numbers and altered rate of growth
of single trees which takes place in all stands as they increase
195
196 FOREST VALUATION
in age. Yield tables attempt to state the actual results in volume
per acre, produced by stands at different ages. When applied
to young timber growing upon sites of the same quaUty, and of
approximately equal density or degree of stocking, the growth
and future volume of such stands is predicted with sufficient
accuracy. For scattered timber or poorly stocked stands, a
reducing factor is required to prevent over-estimates. Methods
of studying and predicting yields per acre form part of the
subject of forest mensuration. Tables of growth and yield
are published by the U. S. Forest Service and in various state
bulletins, but are still very deficient in number and reliability.
184. The Stand; Improvement in Quality of Products, —
Volume alone does not measure the increase in value of a stand
of timber. As the trees become larger, the quality of the prod-
ucts which may be cut increases, for two reasons. The lower
branches on young trees form knots as long as they remain
attached, either alive or dead. After the branch falls and the
scar heals, the wood laid on is free from knots, or clear, and
produces the most valuable grades. The slabs contain the
greatest per cent of clear lumber of any portion of the tree, and
old trees contain enormously greater per cents of high-grade
products than young timber. The second factor of increase
in quahty is due to the larger sizes which can be cut from older
trees. Both in length and breadth, higher prices are paid for
increased dimensions.
Both volume and quaUty increase the value per acre entirely
independent of changes in prices due to economic conditions
outside the stand.
185. Deterioration of Standing Timber. — After timber
reaches a certain age and condition, the stand as a whole ceases
to increase in volume, and at a much later period it begins to
diminish in quality as well. The trees continue to grow as
long as they hve, but the total growth of the stand is offset by
the loss of trees through windfall, insects and disease.
The remaining trees are putting on clear lumber, but in old
stands, decay caused by fungi becomes increasingly prevalent,
and finally offsets this increase in quality.
FUTURE VALUK OF FOREST PRODUCTS 197
In Washington it was shown that Douglas fir stands yielding
65 thousand board feet per acre at their maximum, deteriorate
to 25 thousand feet in 100 years, an average annual loss of 400
board feet in volume alone. Similar losses are occurring in all
over-mature stands regardless of species or locality.
186. Closeness of Utilization. — Present volume of standing
timber is expressed in terms of the quantities actually utilized
rather than the cubic contents of the stand. A future increase
in the closeness of utilization thus has the effect of increasing
the apparent volume of the stand. Its effect on future income
is of similar importance to that of actual growth in volume and
quality. In regions where markets for the poorer grades are
uncertain, these grades are seldom manufactured or included in
an estimate (§172). The future increase in merchantable volume
from closer utilization alone is a large factor.
In addition to the gain in volume per tree the total merchant-
able yield of the stand is increased by removal of smaller trees
and of species formerly unprofitable.
187. Price Levels; General Price Changes. — General changes
in prices, caused by fluctuations in the value of money (§3)
would raise the cost of logging and milling in equal ratio to
the value of the product. When the ratio of profit to costs
remains the same, stumpage values will increase at the same rate
or per cent as will prices for lumber. For instance, should
lumber, now worth $15, increase to $20, or 33^ per cent, stump-
age value worth at present $3 should then be worth $4. In
this case costs might be assumed originally as $9.60 and profit
$2.40, or 25 per cent of cost. An advance of ^^^ per cent in
prices of supplies and labor would bring costs up to $12.80, and
25 per cent profit would equal $3.20, or a total of S16, thus
leaving the required margin of $4 for stumpage.
Prof. Irving Fisher predicts an average annual increase in
general prices of 2 per cent per year for the next fifteen years.*
188. Price Levels ; Changes in Prices of Forest Products. —
The prices for a given product will depart from the average
* American Economic Review, Sept., 191 2, Vol. II, No. 3, p. 553. Managing Edi-
tor, Prof. Davis R. Dewey, 491 Boylston St., Boston.
198 FOREST VALUATION
price level when the demand for the specific goods increases
relatively faster than the supply. Both demand and supply may
be increasing, or both decreasing, or demand may increase while
supply diminishes. In any case, the effect on prices is gauged
by the difference rather than by the direction of these forces.
When population is increasing, while the area occupied by
timber tends to decrease, the maintenance of the same per capita
rate of consumption for timber causes demand to progressively
outrun supply; and this factor has resulted in the past two
decades in an increase in lumber prices approximately twice
as rapid as the movement of prices in general. This increase
has had a pronounced effect on stumpage values. Instead of
increasing by the same per cent as the price of lumber, the value
of stumpage tends to absorb the entire surplus not taken by
increased costs (§170). The profits of the logger and millman
tend to maintain a fairly constant ratio to cost of operation,
except where, by retarding the advance in stumpage values,
they are able to appropriate a larger share of this increase.
In the above illustration, the price of lumber can be assumed to
have increased from $15 to $25, or 66f per cent, while general
prices and the cost of logging advance but 33! per cent. If a
profit of 25 per cent on operating costs is still considered satis-
factory, these costs advance only to $16, and the margin of value
for stumpage becomes $9, an increase of 200 per cent.
In regions where timber was formerly barely accessible (§ 174)
this increase in value sometimes amounts to several hundred
per cent on cost. Stumpage in general doubled and trebled
in value in most regions of large supplies in the decade of 1898-
1908.
189. EfiEects of Substitutes on WGod Prices. — Increasing
prices for lumber and other wood products act in two ways
to diminish consumption of wood. Less wood is used merely
because it costs more and the enterprises depending on wood
are curtailed; and substitutes appear, made possible by this
same increase in price.
The extent to which substitutes will succeed in permanently
displacing wood as a raw material depends upon three factors:
FUTURE VALUE OF FOREST PRODUCTS 199
The relative adaptability of wood and its substitutes for
the services demanded.
The relative cost, measured in first cost of raw material,
labor of construction and durability or cost of deprecia-
tion.
The habits and customs of consumers as influenced by
advertising and imitation.
When no substitutes can be found which will give the kind
of service demanded, the use of wood will be continued, at
constantly advancing prices, until the supply is completely
exhausted, when the need for which this wood was used will
remain unsatisfied. But ordinarily, high prices will force the
use of some substitute which, while not so satisfactory, is so
much cheaper that it is accepted.
Formerly wood was used for many purposes because it was
cheaper than substitutes. Board fences and sidewalks have
been replaced by wire and cement, since the combined cost of
labor, material and depreciation is less for the latter materials
and they give better satisfaction.
Wood for buildings has until recently been much cheaper
than brick or stone, there being a saving in labor and material.
Old, well-constructed wooden houses depreciated slowly. At
present it is still cheaper to build wooden houses, but there
is less difference in the cost of materials, while the poor quality
of much of the lumber used increases depreciation in favor of
brick, cement or stone. A further element of cost is the insur-
ance of w^ooden buildings demanded by the extra fire risk.
The use of wood for boxes and crates has been considerably
lessened by substitutes in the form of fibre and cardboard,
which are cheaper and fully as satisfactory for many purposes.
Shingles have been extensively replaced by patent roofiing which
is cheaper in both labor and material, although possibly not
as durable.
The effect of advertising and habit is especially noticeable in
the last two instances. Manufacturers of patent roofing and
of cheap boxes have expended large sums to capture the trade
and educate consumers into using their products. Such changes
200 FOREST VALUATION
are made with reluctance and suspicion, but once undertaken,
the imitative faculty, which plays so strong a part in human
affairs, may cause a very rapid extension of the substitution
and force producers of lumber to fight for the retention of trade
formerly theirs by right of original possession.
In spite of the inroads which substitutes have made on
consumption of wood as the result of high prices and trade de-
velopments, there remain many uses for which wood is so pre-
eminently adapted, that the total consumption is almost certain
to increase in the future rather than to diminish. For railroad
ties, the resilience or elasticity of wood, which absorbs the shock
of traffic, combined with the small labor cost of track repairing,
and increased safety of travel, when compared with the sub-
stitutes so far employed, make it certain that the price of rail-
road ties will be much higher than at present before the railroads
discontinue the use of the wooden tie.
A still more striking case is the use of wood for paper pulp.
Formerly confined largely to spruce and poplar, pulp is now
made from many hardwoods and from southern longleaf pine.
Paper can be made from many other materials, such as rags
or corn stalks, but the cost of assembling sufficient quantities
at the mill is greatly in favor of wood.
The general effect of substitutes is to diminish the use of
cheap grades of wood, and to increase the supply available for
more important uses. This tendency is illustrated in the case
of fuel. Wood for domestic fuel is still used in enormous quan-
tities, but only at points near the source of supply. Its bulk
and weight prevent its transportation by freight for long dis-
tances to large centers of consumption. It is probably worth
as much, if not more, for this purpose in most localities than
it ever was. It would have been impossible for our forests to
supply enough fuel for the entire demands of modern industry.
The substitution of coal has relegated wood to the position of
a luxury for the fireplace in most large cities; has ruined the
hiarkets for cordwood formerly existing in connection with cer-
tain manufacturing enterprises, and in some regions near such
factories has caused the value of woodlands to decline. Yet the
FUTURE VALUE OF FOREST PRODUCTS 20l
general effect of this substitution, where the market has been
spoiled for corclwood, is to encoura<];e the growth of timlxT of
larger dimensions, suitable for ties, telegraph poles and lumber,
from which the owner may realize eventually as large a profit
as from, his cord wood. Substitutes thus tend to bring about
longer rotations, greater diversity of wood products, higher
values per acre, and increased usefulness of each acre of forest,
and do not, in general, interfere seriously or permanently with
the industry of wood production. Radical changes in the man-
agement of forests may become necessary by these economic
changes in utilization and markets, and the rate of interest
earned in private forestry may be diminished by the necessity
of longer rotations and more specialized products. New uses
for wood spring up to take the place of former demands now
obsolete.
The use of substitutes will undoubtedly prevent wood prices
from rising as rapidly as in the decade 1898-1908 and probably
explains in some measure the slower increase which has occurred
since that date. But substitutes will never do away with the
use and demand for wood, nor cause the average value of wood
products and timber stumpage to be lowered to any appreciable
extent. Prices are still far below the level established in Europe,
and it is reasonable to expect that these prices will continue
to increase slightly faster than those for other goods, for some
time to come.
190. Future Operating Costs. — Future costs of logging and
milling will increase approximately at the same rate as general
prices. Added to this are the special factors which may cause
operating costs to vary from this general trend.
The cost of labor is the largest item in logging. Throughout
northern regions the effectiveness of woods labor is rapidh' di-
minishing. Old-time American lumberjacks are very rare, and a
large part of the work is performed by inexperienced foreigners,
or shifting labor from the city slums, resulting in an increased
cost considerably greater than can be accounted for by increase
wages. This tendency is offset by improved efficiency, as
operators learn from experience the use of the best technique.
202 FOREST VALUATION
The recent development of logging engineering as a profession
on the Pacific Coast is in response to a recognition by operators
of the possibility of greater efficiency and economy in trans-
portation.
Extraordinary increases in cost, if general, must ultimately
be taken from the value of stumpage. In the same way, a gen-
eral reduction of costs, even if due solely to improved methods
and greater efficiency, will increase the value of stumpage.
191. Local Factors: Future Transportation Facilities. —
With increasing population, transportation facilities are certain
to improve. Tracts of timber of considerable extent and volume
will be certainly reached in time by the construction of railroads
or other special means of transportation. A far more serious
question arises as to the permanence of such facilities. If there
is not sufficient use for them to justify their continuous main-
tenance after the present merchantable stand is removed, they
will be abandoned. The rails and ties are removed, the flumes,
bridges, trestles and corduroy rot away, the grades become gul-
lied and the roads grow up to brush. To remove any timber
in the future these structures must be replaced. There must
be a sufficient stand of second growth not only to furnish the
material for reconstruction but to warrant the expense (§98).
The original stand of virgin timber may have been several hun-
dred years old, and far more valuable per thousand feet than
this second growth (§ 184). There are many districts where a
second operation will be financially impossible, and timber
grown after logging will remain inaccessible unless a very con-
siderable increase occurs in the value of stumpage in general.
This condition applies to mountainous or non-agricultural re-
gions. Elsewhere, increasing population assures a future market
for all timber.
A similar increase in average transportation costs per thousand
board feet occurs with the exhaustion of the more accessible
bodies of virgin timber. This tendency was for a long period
overcome by a corresponding expansion of the size of operations,
the amount of capital invested, and the quantity of timber
tributary to a single transportation system. The old days of
FUTURE VALUE OF FOREST PRODUCTS 203
hand logging, short drives and heavy timber were succeeded
by large operations, which tapped reservoirs of timber of great
extent, and distributed the costs over enough stumpage to bring
them even below those of the simpler undertakings. When
this increasing cost is no longer ofTset by increased volume to be
transported, it at once depresses stumpage values. This means
that average quoted prices for stumpage may not rise as rapidly
as lumber prices, because the later quotations are for stumpage
differently situated. The rise in values occurs, but is evident
only for the same or similar timber.
An important consideration in forest production is the pos-
sibility of substituting the cost of growing trees in accessible
situations, for the cost of transportation from regions much
farther from markets. As accessible timber disappears, the
difference in stumpage value between timber easy and difficult
to obtain will become larger and larger, and this margin of value
can be expended upon forest production on accessible sites.
192. Local Factors : Industries and Markets. — Transpor-
tation charges are subtracted from income in arriving at stump-
age value. It follows that the farther from the mill the timber
lies, the less will be its value. In the manufacture of lumber,
portable mills brought to the timber greatly reduce the cost
of hauling this lumber to the market by leaving the waste from
sawing in the woods. But the greatest value for many woods
lies in their use for special products, such as spools, excelsior,
boxes, match stock and other specialties. These factories
pay larger prices for stumpage since they utilize the tree far
more completely and obtain much greater returns on a given
amount of wood. Local industries of this character must
operate continuously in order to be profitable. They remain
in a region as long as they can obtain a sufficient supply of raw
material. The reduction of the supply to a point where the
mills can only run part time, or must suspend operations for
several years, results in driving out these industries. The
remaining stumpage must then be marketed at more distant
points, perhaps for a less intensive use, and there is a very con-
siderable loss in value.
204 FOREST VALUATION
193. Local Factors : Future Supply of Timber. — From the
factors discussed in Articles 191 and 192 it is apparent that the
local value of timber stumpage in the future depends largely
upon the total quantity of timber produced in that locality,
and the continuity of the supply. If virgin timber is being
appraised, its value must often be based on the premise that it
will be logged at the time the remaining stumpage is cut, since
it is worth more now than it may ever be again. If the timber
is of second growth, or is in a region of second growth, the extent,
average age, vigor and utility of this second growth is of the
greatest importance in appraising the value of any separate par-
cel or tract. Where most of the cut-over areas are ravaged by
fire, or otherwise rendered worthless, an isolated patch of repro-
duction or plantation not only costs more to protect, but its
stumpage value is permanently less in such a region than if it
were a part of an abundant second growth. It may pay better
to plant trees in regions where natural reforestation is abundant
than under the reverse conditions. By following out this argu-
ment it will be seen that extensive operations on the part of
states or the national government to protect and reproduce
large areas of forest will have the effect of raising stumpage
prices for those private owners who grow trees in such
localities.
194. The Rate of Increase in Stumpage Value. — By care-
fully weighing both general tendencies and the equally important
local factors, the examiner may appraise the probable stumpage
value of timber with considerable accuracy for a period of 10 to
15 years in the future. Beyond this period, so many unforeseen
events may occur to affect prices that only a semblance of accu-
racy can attach to such appraisals. One of two suppositions
can be made. The value may be assumed to remain constant
beyond a certain year. The tendencies of prices and the
history of wood consumption justify so conservative a con-
clusion.
The second assumption is that prices will continue to advance
at the same per cent as in the past. The validity of this con-
clusion depends upon the meaning attached to the phrase;
FUTURE VALUE OF FOREST PRODUCTS
205
whether simple or compound interest is meant, that is, whether
the original value or the increasing value is the basis of the
annual percentage. Stumpage as a residual value is subject to
more extensive proportional changes than the price of timber
products which causes these changes (§ 188). Then, while prices
and stumpage value may rise at a rate equal to simple interest
on the value at a given date, the rate of interest, simple or com-
pound which this rise represents, when based on increased prices
or values, becomes less and less.
Table V illustrates these relations. Should stumpage rise
from an original value of $5 per thousand, by the sum of $5
every 10 years, or 50 cents per year, the rate of increase would
be equivalent to 10 per cent simple interest annually on the
original value.
TABLE V
Rate of Annual Increase in V.^lue of Stumpage
Period,
years.
Value of
stumpage,
dollars.
Rate of simple
interest on
original value,
per cent.
Rate of com-
pound interest
on original
value,
per cent.
Rate of simple
interest on
value for each
decade,
per cent.
Rate of com-
pound interest
on value for
■each decade,
per cent.
0
5.00
10.00
15.00
20.00
25.00
30.00
10
20
30
40
50
10
10
10
10
10
7.2
5.6
4-7
41
3-65
10
5
3 3
2-5
2
7.2
41
2.9
2-3
1.85
Values of stumpage are more apt to follow the law of increase
set forth in this table than to increase continuously at a fixed
rate of compound interest. It follows that as prices and values
advance, the rate of increase must fall. By first predicting the
amount of the increase, or the rate expressed in terms of simple
interest on original value, the rate of compound interest for
these values may be computed if desired (§89, Formula XIV;
see also § 49) .
The true rate of increase in stumpage value depends upon
the sum of increased values due to growth in volume, improved
quality, closer utilization and price increment. These sources
2o6 FOREST VALUATION
may be expressed separately, as if each represented a rate of
interest, as
Fo(i.oa)(i.o6)(i.oc) = Fi,
which is slightly greater than
Vo 'i.o{a + b-^c) = Vi.
In ascertaining the values of the factors a, b, etc., for a period of
some years, these values must either be taken as representmg
simple interest, or, if compounded, the rate quoted for the
entire period must be much lower than the probable annual
increase in the earlier years.
195. Increasing Future Values as a Basis of Appraisals. —
As set forth in Article 139, the elements of increase in value
inherent in the character and condition of the property itself
must be accepted as reliable and occurring in the natural course
of events, and will be recognized in appraisals for public purposes,
such as damage suits and condemnation proceedings. These
include growth and quality increment. But the factors of
closer utihzation and rising prices depend upon outside influ-
ences shown to be affected by a complex of causes and therefore
not capable of reliable diagnosis.
The acceptance of such increased prices as a basis of appraisals
must be determined by the purpose of the appraisal, and by
the evidence on which the conclusions rest. Reasonable con-
servatism is required in appraisal of damages. A more liberal
construction is permitted in condemnation proceedings. In
either case, evidences to prove the probability of rising prices
must take into account both the general and local factors dis-
cussed in this chapter, and it will usually be found advisable
to make very moderate claims on this score.
As a basis of valuation to determine a tentative sale value,
it is equally necessary to treat the element of future prices
conservatively. The purchaser is entitled to this source of
future profits, and should base his price for the property upon
present rather than future prices for products. As tending
merely to show the probable amount and present value of these
FUTURE VALUE OF FOREST PRODUCTS 207
profits, for the information of the owner, no objection can be
urged to any assumption which he can reasonaljly justify.
196. Revision of Stumpage Values in Long-term Contracts. —
In timber sale contracts, where timber is paid for at time of
purchase, the owner of the stumpage, in return for the risks
incidental to carrying this investment, is entitled to share in
the increased values which may materialize (§ 176). For periods
of less than five years this factor is immaterial. If the contract
is for longer periods, at a fixed price, the purchaser is usually
willing to operate at a loss during the earlier portion of the term,
in expectation of realizing increasing profits later on. In this
way the increase may be shared with the owner even on the basis
of a fixed contract price. Contractors desire certainty in the
element of cost of raw materials, even at some sacrifice of possible
profits.
The ideal arrangement is some form of revision at stated
intervals, by which the value of stumpage is readjusted to
changing conditions. Such a revision may be based on a reap-
praisal. This would take into account the element of closer
utilization, as well as advancing prices. The factor of growth
is accounted for by the scale, while changes in quality are usually
neglected, but can be considered in reappraisal. This method
is advocated in the Forest Service for regions where close compe-
tition exists for government timber.
A second plan for revision confines the changes to the single
factor of prices for lumber, neglecting those of utilization and
quality. The point to be determined is the per cent of increase
in lumber prices which should be appropriated by stumpage.
On the basis that timber prices have advanced in the past
more rapidly than costs, the Forest Service has claimed as much
as 75 per cent of this increase for stumpage. Their present
basis is to appropriate 50 per cent of increased prices as stumpage
value. Revision, without reappraisal, is undertaken at intervals
of five years. The prices of lumber accepted as a basis (§172)
are averaged for three years previous to revision.
CHAPTER XIII
RISKS
197. Risks versus the Rate of Interest in Forestry. — The
risks to which forest property is exposed tend to discourage
the investment of funds in forest production, in the same manner
that similar risks restrain investors in other enterprises. This
tendency is expressed by an increase in the basic rate of interest
at which capital will seek investment in forestry {p per cent).
A high rate of interest is the expression of a fear entertained for
the safety of the principal. The use of such a rate gives very
low expectation values for probable future income.
When the per cent which can be earned by forest enterprises
is lower than the rate of interest demanded, capital is presum-
ably unwilling to invest in forestry because the average risk
of loss exceeds the probable income. Should individuals still
be willing to undertake forestry, they do so because they place
a lower estimate upon this risk than that commonly prevailing,
or expect to combat it by effectual preventive measures; hence
their individual "rate of interest" is gauged proportionally
lower and indicates possible profit.
198. The Character of Risks in Forestry. — Risks may be
classed as physical, moral and financial. ' Physical risks are
those incurred through the operation of the forces of nature.
In case of fire, the physical risk is greatly increased by the addi-
tion of a moral risk. Moral risks are those arising through
possible human actions, either deliberate or accidental. Finan-
cial risks include both physical and moral elements, since all
risks are measured by the probable financial losses that may be
inflicted. But the risk of loss of profits exists quite independent
of these other factors, and is influenced by changing economic
conditions, such as demand, prices, future taxation and any other
208
RISKS 209
element which serves to diminish profits below the expected
amount.
199. The Gauging of Risks. — There are two elements to a
risk: the hazard, or degree of probabiHty that damage will
occur, as indicated by past history and present conditions; and
the liability, or value of the property subject to damage. The
liability, in forest investments, is measured by expectation
value for partially mature stands; but for plantations, cost is
the basis considered, and extra efforts will be made to protect
such plantations because of the investment which they represent.
The hazard must be gauged, during the growth of the crop, by
the increasing or decreasing susceptibihty or resistance of the
trees to fire, wind, insects and fungi, and by the probability of
these events occurring, through prevalence of the causes.
When the liability is large, and the hazard is extreme, active
preventive measures involving considerable expense are jus-
tified.
With a small present liability and extreme hazard, the ques-
tion arises whether protective expenses will pay for themselves.
When liabihty is large, but the hazard negligible, protective
measures may involve a needless expense, and diminish profits
and value.
With small present liability, and negligible hazard, the ex-
penditure justified for forest protection is still further reduced.
The financial character of the risk thus indicates the expense
which should be incurred for protection. The largest expen-
ditures are justified when property of considerable value is in
great danger of being destroyed.
200. Physical Risks : Fire. — Fire is by far the greatest
risk in forest production. The resistance of trees to fire damage
depends on the character of the bark, which differs with the
species, and on its thickness, which increases with age for all
species. Sandy soils in all regions are far more subject to fire
than soils which retain moisture. In many localities fires burn
annually on such sites. As a consequence, the tree species
which inhabit these situations have developed a fire-resistant
bark which often renders them immune to the effects of ordinary
210 FOREST VALUATION
fires. This immunity is attained at an early age, but seldom
covers the period of reproduction, or the seedling stage of growth.
On soils and in locaHties where fires burn only at long intervals,
most tree species are very susceptible to injury, and, as the
fires which do occur on these sites are unusually severe, practi-
cally the entire stand may be killed. The younger the stand, the
greater the per cent of mortality and consequent proportion of
value destroyed.
The fire hazard is largely due to the inflammable character
of the forest floor. The entire mass of accumulated litter and
humus will burn when dry enough. Most of the undergrowth
is also extremely inflammable. Shade thrown by a dense cover
reduces the risk by preventing extreme desiccation, and keeping
out brush and grass. Of the materials forming the forest floor
and undergrowth, grass, when dry, is the most inflammable.
Pine needles come next, while hardwood leaves do not cause a
serious blaze. Humus or duff, when dry enough to burn, causes
a slow and very destructive ground fire, difficult to extinguish.
The hazard is reduced by atmospheric moisture. Except on
the sandiest soils, belts of heavy rainfall will give rise to rank
vegetation. These are^ regions of slight hazard. Over most of
the forest areas in this country droughts occur either annually
or at greater intervals, of sufficient severity to create an exces-
sive fire hazard.
This risk is enormously increased by logging, because of the
great increase in litter and slash incidental to the operations.
As the Uability is reduced in like proportion, the temptation
to ignore the hazard and abandon the attempt to protect the
residual forest values is very great.
201. Wind. — Wind resistance is greatest with small timber,
and becomes less with increasing bulk, weight and age. The
form, distribution and penetration of the roots of different
species determine their resistance to wind-throw. Shallow,
rocky soils, or those underlaid by hardpan or water, induce
windfall. Regions subject to frequent tornadoes present a
wind hazard which must be reckoned with in planning the
sequence of logging operations. This risk is excessive only for
RISKS 211
mature and over-mature timber, and is a serious factor in opera-
tions where a portion of the stand is left for a second crop or as
seed trees. If all parts of a tract are accessible, wind-thrown
timber can be marketed without loss, provided the quantity
thrown does not exceed the capacity of the operation as gauged
by the length of time the down trees can be left without deterior-
ation.
202. Insects. — Imported insects as, for example, the gypsy
and brown-tail moths are far more dangerous to forests than
native insects, as they are practically without any natural
parasites. The introduction of these enemies now promises to
keep the g>'psy moth in check.
Native insects occasionally develop possibihties of injury,
and may destroy great areas of forest. They are finally checked
by disease or parasites. The worst of these insects are the bark-
boring beetles. Defoliating insects, like the larch sawfly or
spruce bud worm, may kill timber over entire regions. The
destruction of native birds explains the increase of certain
forms of injurious insects. Woodpeckers are very useful in
keeping boring larvae under control.
203. Fungous Diseases. — The only conspicuous instance of
widespread destruction of an American species due to fungous
attacks is fovmd in the ravages of the imported disease of the
chestnut, Diaporthe parasitica, which threatens to exterminate
what is considered the most important commercial hardwood
over wide regions east of the Appalachians. Great damage is
done to the heartwood of all species of trees by fungi which
gain entrance through wounds or knots. These fungi do not
kill the trees as they have no effect on the living tissue. This
damage is greatest in old timber and is not a serious factor in
second growth.
204. Climatic Injuries. — Excessiv^e drought in rare instances
kills many trees of the more susceptible species in exposed
regions or localities. Trees unused to swampy conditions are
killed by prolonged flooding of the roots.
Minor injuries are caused by breakage in sleet storms or hea\^
snows, permitting fungi to enter. Reproduction is especially
212 FOREST VALUATION
sensitive to frost, drought and excessive moisture, but the
young trees soon become hardy.
205. Injurious Fumes. — The physical injury caused by
fumes is due to human activities. The fumes from copper
smelters will sometimes kill timber seventy-five miles from the
location of the smelter.*
206. Moral Risks : Trespass. — Timber products are fre-
quently stolen, but the theft is easily discovered, and it is not
difficult to identify the trespasser. Losses from this source are
the result of neglect of the property, and are easily eliminated by
proper marking and posting of boundaries, and the employment
of a custodian. The expense of such protection is serious for
small tracts whose owners reside at considerable distances, but is
immaterial for larger holdings. The character of the population
and ease with which small quantities of timber can be transported
determine the degree of hazard.
Trespass is frequent in connection with logging operations,
where only a portion of the stand is to be cut, or where the logger
attempts to enlarge his operation at the expense of adjoining
owners. Reputable firms incur considerable expense in relo-
cating boundaries not only to prevent others from trespassing,
but to avoid accidental encroachment on adjoining lands by
their own employees.
207. Moral Risks : Fire. — Some fires are started by light-
ning, but the great majority are due to human agencies. Most
of these fires are caused by careless or unintentional acts, but
in some regions the habit of burning is firmly flexed, and occa-
sionally fires are set through mahce. The moral risk thus in-
curred is so great in some southern states that it presents
an almost insuperable obstacle to forest production. In other
localities this risk is chiefly due to avoidable factors, such
as railroad operation, and yields to preventive measures and
education.
208. Financial Risks. — The risk of excessive future taxa-
tion is discussed in Chapter X. Unless this risk is removed, it
will prevent the practice of private forestry in the regions affected.
* Deerlodge National Forest, Anaconda, Montana, 191 2.
RISKS 213
The financial risk is in reality a summary of the factors
enumerated above plus the economic risk of failure to
secure remunerative prices (Chapter XII). The economic
situation, except in certain inaccessible localities, is so
favorable that the only serious risks are those discussed in
this chapter.
209. Control of Risks: Insurance. — Insurance against losses
follows rather than precedes other measures for the control of
risks. When the risk is large, and the probable amount of
damage uncertain, the premiums will be prohibitively high.
At the present time, no insurance against tire is in force on
standing timber in the United States, and no companies will
accept such risks. Lloyds of London have insured a large
tract of timber in Canada.*
The unreUability of appraised values in case of damage, and
the great variation in value of stumpage, adds to the difficulty
of such insurance projects. Standing timber in European states
is widely insured at low rates. Tornado insurance on timber
is available in the United States, but has not been taken ad-
vantage of by owners of timber stumpage.
210. Public Measures. — Within the last decade it has been
demonstrated that the fire risk can be largely eliminated in
northern and western states by the enforcement of efficient
fire laws and the organization of state and local forces of fire
wardens. These systems are as yet not completely successful,
but promise to become so, especially in states where politics
has been eliminated from the organization. Education of the
public, punishment of offenders, and prompt detection and sup-
pression of incipient fires form the groundwork of these systems.
Through their operation, risks will eventually be reduced to
the point where it will become possible to insure standing
timber from fire.
These state forces are aided materially by semi-pubUc co-oper-
ative associations of land owners, which expend large sums in
fire patrol and suppression. The operations of these associa-
* " Logging," by Ralph Clement Bryant, p. 37. John Wiley & Sons, Inc., New
York, 1913.
214 FOREST VALUATION
tions are conspicuous in the Pacific Northwest, and have ex-
tended to Michigan and New England.
The importation of injurious fungi and insects is now guarded
against by national statutes and inspection. One serious fungous
disease, the white pine blister rust, has been checked by this
means. State inspection and control of injurious insects and
diseases, supplemented by the activities of the national govern-
ment, furnish a means of preventing future outbreaks similar to
that of the chestnut bark disease. Such aid should be chiefly
preventive in character, and can be invoked but seldom for the
control of native insects.
211. Private Measures. — Private owners may be forced by
state legislation to take measures to eliminate unusual fire risks
caused by their own operations. Laws making brush or slash
burning compulsory, especially along rights of way, are already
adopted in some states. Top-lopping is intended for the same
purpose.
In addition to these compulsory private measures, owners of
forest property must expect to take extra precautions against
fire, similar to those adopted by factories and stores to supple-
ment the work of the fire department. Firebreaks should be
constructed and maintained for the protection of plantations,
and to guard against excessive hazards. The owner and his
tenants and employees should be prepared for fire fighting and
equipped with the most suitable tools for the purpose.
212. Effect of Risks on the Business of Forest Production. —
Mature timber, while in danger of being killed by fire, insects
or disease, or blown down, can usually be salvaged with only
partial loss. To the greatest danger of all, fire, it is moderately
resistant. Since systematic fire protection has been instituted in
the North and West, losses have averaged less than two-tenths
of one per cent annually, on the value protected. The risk has
never deterred investors from making purchases and speculating
on values of stumpage.
With young, immature timber and reproduction, the same
cannot be said. A comparison of risks shows that the hazard is
less on small or young trees, from practically all sources excepting
RISKS 215
fire. But the risk of destruction from this source has in the
past been so great as to constitute a prohibitive hazard. De-
struction of young timber is a total loss, for there is no salvage.
The dead trees are quite worthless, and even constitute an
additional expense (§ 136). The period over which the invest-
ment is exposed to risk is correspondingly longer for young
timber than for mature trees, which can be removed at the
owner's convenience.
As long as the public and the land owners themselves remained
completely indifferent to young growth, and regarded tires on cut-
over lands as of no consequence, the risk incurred in the business
of forest production was prohibitive. One could as well expect to
succeed in a mercantile business when thieves, incendiaries and
dishonest debtors abounded, and there existed no efTective law
or public sentiment to check their operations. The first step in
establishing the social conditions which are now making forest
production possible was the creation of a new public conscience
and understanding on the subject of forest property and forest
fires. The elimination of theft of national and state timber, the
tremendous progress in fire protection in northern states, and
the large sums spent in eastern states for suppression of forest
insects and diseases indicate that this constructive work is
succeeding. Under proper social conditions, such as have been
secured in France and Germany, the element of risk in forest
production becomes less than that incurred in almost any other
form of enterprise. The employment of a high rate of interest
in forestry is merely the expression of this undeveloped state
of civilization as touching forest property, and should not be
confused with the returns or earning power of forest invest-
ments.
CHAPTER XIV
FIELD APPRAISALS OF TIMBER STUMPAGE
213. The Scope of Field Appraisals. — The value of timber
stumpage, while based on the species, quantity and quality of
the timber, is determined only when the value of the products
f.o.b. at mill and the intervening costs of logging and milling
have been appraised (Chapter XI).
The field appraisal thus deals first, with the reconnaissance
of the timber (§ no), and second, with the appraisal of logging
costs. The cost of milling, depending as it does on the size of
the mill and duration of the operation (§ 173), is affected by the
total volume of timber accessible to the mill, and its ownership,
and this cannot always be determined when examining a given
tract. Appraisals, except when they cover a large area, are
therefore most definite when made in connection with mills
already operating.
The choice of general means of transportation must occasion-
ally be left to the field examiner, but more often this is already
indicated by local custom, and it remains only to determine on
the ground whether any modifications of the plan are necessary
because of the nature of the topography and the transportation
problems which arise. The scope of the actual field appraisal
of costs is usually confined to ascertaining the local costs of
logging. These costs should be appraised separately for each
so-called "logging chance," or separate body of timber forming
a logging unit. In flat regions, the division of a larger area
into units is not important and depends on the convenience of
locations and routes for main spurs. But in a rough or moun-
tainous country the "chance" is a distinct topographic unit,
such as a gulch or small basin, containing enough timber to
furnish employment for a camp of reasonable size for one or
216
FIELD APPRAISALS OF TIMBER STUMPAGE 21 7
more seasons. The timber on such a unit normally comes out
over the same route — a branch railroad spur or road.
Of lirst importance in the examination is the necessity of
sizing up this local transportation problem, deciding upon the
best method of removing the timber, and estimating the diffi-
culties of construction and cost of overcoming them. The cost
is gauged, not on the basis of the total expense of construc-
tion, but with relation to the amount of timber reached (§ 174).
In high and precipitous mountains it is necessary to decide
how far up the slope the operator can go without exceeding
the permissible cost of getting out his logs.
This transportation cost is thus directly dependent upon
the estimate of the standing timber. The field examination
necessary to determine it is either a part of the work of timber
reconnaissance, or some additional work is done following the
completion of the cruise, to make sure of the salient points.
214. Timber Reconnaissance : The Map. — In the timber
examination the tract is ordinarily crossed and recrossed at
intervals of 40 rods or less, and the intimate and systematic
knowledge of the topography and surface thus gained permits
the formulation of the plan for logging. The main drainage
and its tributaries are located and the character of the slopes
and surface noted.
This knowledge, when necessary, may be systematized in
the form of a topographic map which shows all features that
affect logging. If the topography is so level that transportation
presents no difficulties, such a map serves no useful purpose.
If the map does not indicate conditions with sufficient accuracy
and detail to enable the manager to plan the general location
of his transportation system, it fails of its purpose. Actual
lines of railroad or road must be located on the ground, but the
entire system can nearly always be roughly planned from a
good map. Since such a map can be made as a part of the work
of timber estimating, the expense is minimized and the effort
justified. Otherwise the information so vitally necessary to
the planning of transportation routes exists only in the mind
of the field examiner or in the form of incomplete notes.
2l8 FOREST VALUATION
215. Estimation of Standing Timber. — The estimation of
standing timber presents one of the most diifficult problems in
the business of lumbering. This might not be true were there
no limits to the cost which can be incurred in making such an
estimate. But it is quite possible for a careful detailed measure-
ment of the timber on a tract to cost over $i.oo per acre. It is
a recognized precept in business that the cost of stock taking
must be kept as low as possible, for the work adds nothing to
the value or the profits of the business, and is necessary merely
as a basis upon which to plan actual operations.
Methods of timber estimating are determined by the relation
between the cost of doing the work and the value of the timber.
The amount of care and expense justified increases with rising
stumpage values. Timber is always estimated in terms of the
product which has the highest market value, or is most readily
saleable. When pulpwood is used, the cord is the customary
unit. But should the stand be situated in a region where cord-
wood is used only for fuel, the number of ties or poles and the
contents in lumber of suitable trees would be first estimated
and only the residue expressed in cords. By far the greater
quantity of timber is estimated in terms of board feet, since
it is used in this form.
216. Log Rules. — The measurement of standing trees for
board foot contents is beset by the fundamental difficulty that
no commonly accepted standard of measurement has been or is
lik.ely to be adopted in this country which will properly express
this contents. Innumerable log rules are in use, of which a
few are now widely recognized. But these rules are very de-
fective, seldom giving a sufficiently large contents for logs (§ 179).
In spite of this fact, it will seldom be possible to adopt the actual
sawed output as a basis for timber estimating, as long as logging
contracts and other woods operations, such as felling, are based
on the old standards as expressed by the log rules in common
local use. Any great increase in the measured volumes of the
logs would require reduction in the scale of payment or result
in loss of profits by the millman. The only safeguard is a
knowledge of the amount of overrun usually obtained with the
FIELD APPRAISALS OF TIMHFR STUMPAGE 219
given rule in the class of timber estimated (§ 179). Quantities
estimated will therefore be expressed as log contents measured
by the local rule, but in computing values the overrun on each
thousand feet of logs will be allowed for. Log rules have been
devised which give very closely the actual sawed contents of
logs. The use of such a rule insures a proper standard of meas-
urement for the contents of standing trees.*
217. Closeness of Utilization as Affecting Timber Estimates.
— Another factor which influences timber estimating is the
closeness with which the timber is utilized (§ 186). Cheap lumber
necessitates the wasting of the poorer grades of boards, as the
cost of manufacture exceeds the sale value. Under this condi-
tion, limby tops, defective logs and small trees are left in the
woods. In such forests as exist in Washington State, the differ-
ence between utilizing only the highest grade product and taking
common and low grade lumber may make 50 per cent difference
in the total quantity removed (§ 186). In general, an estimate is
made on the basis of present market conditions, and does not
attempt to anticipate future values, though this will have weight
with a far-sighted purchaser. Estimates made in past periods
were low compared with present estimates and must be revised
as utilization becomes more complete.
218. Field Methods of Timber Estimating. — With these
points decided, the problem remains of how to cover the area
with the least possible cost. It is desired to obtain the total
quantity of timber, by species, with a knowledge of sizes and
quality. Cruisers of considerable experience in a restricted
locality can size up timber by walking through it, and from their
general knowledge of what similar stands have cut out, will
make a guess at the total stand. This method is comparatively
useless for large tracts, or with men of lesser experience or un-
familiar with a region, and is always subject to large errors.
On the other hand, the cruiser may go to the trouble of meas-
uring the contents of each tree separately. To justify this course
the trees must be very valuable and the area small. Woodsmen
* '■ Forest Mensuration," by Henry Solon Graves, Chap. Ill, pp. 27-35. John
Wiley & Sons, Inc., N. Y., 1906.
220 FOREST VALUATION
almost invariably guess at the contents of the tree, either as
a whole or by their knowledge of the contents of logs of cer-
tain sizes. A better method is to use tables giving volumes in
board feet, or in other units, for average trees of given diameters
and heights, when such tables are available and are known to be
reliable.
219. Strip Methods. — By far the greater amount of timber
estimating is done by methods involving the measurement of
only a portion of the stand, in an effort to get an average which
will apply to the whole area. Even if all the trees on a tract
are observed, they may be merely counted, and an average
volume obtained by guess or by tallying the sizes of a certain
proportion of the stand.
The most widely used methods consist of running parallel
compass courses through the area at definite intervals, and meas-
uring the trees standing on a strip of a definite width with the
course as a center. In dense brush, or with small timber, this
strip may be but 4 rods wide. Where tree callipers are used
to get the diameter of each tree and the men employed to do
the work have but little experience in timber cruising, this
width of 4 rods is seldom exceeded. More experienced woods-
men, who estimate the timber by eye, usually cover a strip
8 or 10 rods wide. The number and contents of the trees on
these strips form the basis of the estimate. Should the strips
so measured be accepted without question as giving an average
stand for the whole area, the total estimate is found by using
the multiple determined by the per cent of the area measured.
220. Errors in These Methods. — But this is seldom the case.
Timber is never uniformly distributed even over small areas,
but varies enormously from acre to acre in size and density.
Topographic and site factors exercise a marked influence on
the stand. The timber tends to run in belts along stream
bottoms and slopes. Chances of obtaining a better average
are improved by arranging the strips to cross these belts, which
object is most frequently attained by running up and down
slopes rather than along them.
For a given per cent of the total area estimated, the chances
FIELD APPKAISALS UI' TIMBER STUMPAGE 221
for accuracy are imi>r()ved in direct ratio to the size of the area
units separately measured. Should the figures be desired by
separate forty-acre tracts, an estimate covering lo per cent of
the total would leave opportunities for large errors, while for
a section of 640 acres, 10 per cent might give quite close results.
Large and scattered timber requires a more complete estimate
than small trees densely stocked. Very irregular or bunchy
stands may require greatly increased work to arrive at a fair
result. One method of dealing with this fundamental difficulty
is to merely accept the result as within the allowable error for
such work. Astonishing errors creep into timber estimates,
even with experienced men.
221. Types. — A second plan is to subdivide an area into types
by means of a sketch map. In timber estimating, these type
divisions are for the purpose of improving the possibility of
getting a fair average stand. They are really stand classes.
Blank or open areas are mapped and excluded in computing
the total estimate. Only the area of strips run within a given
t^pe is used in determining the stand on that t^pe. The amount
of work which this method entails is somewhat greater than when
the timber is calculated on the basis of the whole area, but this
is often justified and the plan is used in a rough form by nearly
all woodsmen.
222. Correction Factor. — Another method of improving the
final estimate without measuring every tree is the correction
of the computed total, whenever the observations and judgment
of the cruisers indicate its necessity. This correction must be
based on actual inspection of the entire body of timber. When
running strips, short side trips are made to view the timber which
lies outside the strip. Should this timber run heavier or lighter
than that measured, the total will be reduced or increased by an
estimated per cent. This plan must not be confused with the
method of guessing at the total stand, for it is based on a careful
estimate, tree by tree, of a portion of the area. Should it be
impossible for any reason to actually inspect the remaining
timber, there can be no basis for correcting the result, which
must stand for what it is worth.
222 FOREST VALUATION
223. Quality of Timber. — To judge of the quality of the
timber, attempts have been made to grade logs, according to
the relative value of their contents, into perhaps four classes.
This is actually done in Puget Sound where a well-established
log market exists and logs are purchased on the basis of the log
grade or class. The difficulty with such a basis ordinarily is
that logs vary in value from several sources; knots or sap in
young timber, rot and wind shake in old trees. A dividing
line or standard is not sufficiently definite, nor, except under
the conditions cited above, are logs ever sold on this basis.
They are paid for at a fiat rate, according to the average value
of the contents. The only recourse of the cruiser is to attempt
to size up the quality of the trees by their size, apparent age,
clearness or freedom from knots, and soundness or freedom from
interior defects. With a knowledge of the average per cent
of grades produced in mills cutting similar timber, the cruiser
estimates the per cent of each grade that the stand will cut.
Should the timber be older, larger or better than the average
stands, he increases his estimate of the higher grades to corre-
spond.
224. Reports. — The information which should be given in
a satisfactory report on a tract of timber is shown under the
following heads.
I. Area.
1. Description or location of specific tract.
2. Area.
3. Subdivisions of area.
a. Blanks.
Water.
Barren.
Burns.
b. Reproduction or immature timber.
c. Forest types.
d. Age classes, where distinguishable.
FIELD APPRAISALS OF TLMBFR STUMPAGE 223
II, Volume.
1. Species: Separate estimates for conifers and
hardwoods, and for each commercial species.
2. Volume in merchantable units.
a. Board feet.
h. Cords.
c. Pieces (poles, ties, etc.).
3. Deductions from gross volume.
a. Dead timber (probable durability).
h. Cull, due to defects (rot, wind shake).
III. Damage.
1. Rot: Extent, character and amount of damage.
2. Fire: Standing dead timber, damage to live
timber.
3. Insects: Location, prevalence, character of
damage.
4. Windfall: Location, amount and condition.
rV. Quality.
1. Size (if necessary, for two or more size classes).
a. Average diameters, at 43 feet (or at stump
height) .
h. Average heights.
Number of merchantable i6-ft. logs.
Total height of tree in feet.
2. Form of bole.
a. Straight or crooked.
h. Taper, expressed in inches per i6-ft. log.
c. Clear length. Limbs, character of knots.
3. Grades.
Per cent of probable output in each of several
standard grades for species and locality.
V. Young timber.
1. Species.
2. Area, in acres or in per cent of total area
224 FOREST VALUATION
3. Average age. Range of ages.
4. Sizes. Average and range of diameters and
heights.
5. Condition. Thrift, damage, with causes.
6. Chances of survival. Competition with older
timber, and with worthless species, or brush.
7. Probable commercial value at maturity.
VI. Soil. Quality. Agricultural value.
VII. Logging conditions; summary for ^^ logging chance ^^
rather than for each subdivision of estimate.
1. Topography. By map or description.
Character of slopes. Obstacles to logging.
2. Surface.
a. Underbrush.
b. Rock.
c. Character of bottom.
3. Transportation.
a. Streams, character for driving, cost of im-
provements.
b. Routes for roads, or railroad spurs.
c. Methods of skidding and hauUng.
VIII. Modifications of logging required by silvicultural demands.
Summary for logging chance.
1. Amount and character of merchantable timber
to be left standing.
2. Methods of brush disposal, and precautions re-
quired for protection of young timber (if not
summed up for larger areas as a whole).
IX. General conditions affecting appraisal.
1. Market value of lumber, or price basis.
2. Size of mill, and cost of milling, with profits.
Investment required.
3. Cost of main transportation system.
FIELD APPRAISALS OF TIMBER STUMPAGE 225
X. specific conditions ajfecting appraisal.
1. Specific costs of logging the "chance."
2. Specific appraisal of value of standing timber
per unit of log scale, based on total cost
and total quantity, or distributed according
to value of species (§ 180).
XI. Appraised value of standing timber, by species, for
specific units of product, modified for overrun to
apply to standing timber.
CHAPTER XV
COMPARISON OF FOREST VALUES WITH AGRI-
CULTURAL VALUES
225. Agricultural Soils. — Agricultural soils are soils which
will produce agricultural crops continuously in paying quan-
tities, under proper cultivation and treatment. Many classes
of soils will produce scant crops for short periods, after which
they must be abandoned. Such soils should seldom be used
for crops at all but kept under forest cover. Permanent agri-
cultural fitness of soil is determined by six factors: quality of
the soil itself, topography or slope, climate, water supply, the
personal or human factor, and the economic factors.
226. Quality of Soil. • — Soils to be agricultural must be free
from excessive quantities of rock, and not too sandy, since
loose-textured soils will not retain sufficient moisture or soluble
plant food to permit satisfactory growth. They should be
underlaid by a permeable subsoil which permits sufficient drain-
age. Deep sands, and stiff clay underlaid by hard-pan, are
familiar types of non-agricultural lands.
227. Slope. — The slope is important, since crops must be
cultivated, and upon steep slopes, if not terraced, the loosened
surface washes away, deep gullies are formed and the land is
permanently ruined for agriculture. Slopes varying from lo to
20 per cent, according to rainfall and quahty of soil, will prevent
permanent cultivation.
228. Climate. — Crops will grow in all but the coldest climates
if given sufficient water. But in mountainous regions, lands
at high elevations resemble regions near the arctic circle. Frosts
occur every month in the year, and the growing of all agricul-
tural crops, except a poor quality of hay, is prevented. Such
lands are non-agricultural, regardless of the quality of soil.
226
COMPARISON OF FOREST WITH AGRICULTURAL VALUFS 227
229. Water. — In regions of sufficient rainfall, low-lying
lands arc often swampy. Drainage transforms such soils into
permanent agricultural lands of high value. In dry regions,
irrigation brings otherwise desert soils under cultivation. Trees
ordinarily recjuire fully as much soil moisture as crops. Desert
lands are therefore of no value for forestry, but undrained
sw^amp land will produce valuable though slow-growing species.
230. Personal Factors. — The personal element is a large
factor in successful agriculture. Experience is the foremost
need, but industry, economy and good business capacity are
equally helpful. The advancement of agricultural knowledge
by experiment stations, and the general trying out of new
methods, often make success possible on soils and in climates
which w^ere once thought too hostile to permit of agricultural use.
231. Economic Factors. — The development of transporta-
tion, and increasing values for farm products, have a stimulating
effect on agriculture, and farms can be made to pay in regions
near large markets, which would be too poor to cultivate in less
accessible localities. This last factor, coupled with the advance
in knowledge of farming methods, tends to bring more and more
land into agricultural use, and the standard of classification
between agriculture and forestry, for this reason, can never be
a hard and fast one.
But the differences between good and poor soil will remain
as great as ever and some soil will always be too poor to farm.
In densely populated eastern states sandy and rocky land in
abundance is found, upon which the inhabitants eke out a mis-
erable existence and which no amount of skillful management
will make into profitable farms.
232. Comparison of Agriculture with Forestry as a Source of
Livelihood. — The use of land for the production of agricultural
crops diff'ers in many important particulars from its use for the
production of timber crops. Agriculture, the direct source of all
food supplies, yields immediate livelihood to the farmer, w^hose
returns are based on an annual cycle. A large element of labor
enters into crop production, both for preparing and clearing the
soil, and in actual cultivation and harvesting. Added to this is
228 FOREST VALUATION
the investment in buildings, fences, machinery and hve stock-
Agriculture requires large continuous outlays per acre, and in
return must produce adequate income to compensate the farmer.
If the soil is unsuited to agriculture, this outlay, which is as
necessary on poor soil as on good, is inadequately rewarded,
and the farmer impoverished.
Trees grow best on good agricultural soils and produce their
greatest values in such situations. But timber crops do not
provide as stable a source of livelihood as agriculture. The
revenue from sales of timber is reaHzed only after the lapse of
the long period of growth. Mature stands may be sold or held
at will and the income varied largely at the discretion of the
owner as long as there are trees of suitable size for cutting.
Over long periods, even at best, the net annual revenue from
forest property is much lower than from agricultural crops.
Relatively, forestry may be far the more profitable business.
The expenses per acre are correspondingly lower than in agri-
culture. While not giving a solid basis for continuous liveli-
hood except in the business of lumbering, which requires large
areas of land, forestry on the other hand does not require con-
stant time and attention. Timber if given protection from fire
will grow without cultivation. It therefore forms an ideal in-
vestment for surplus income, but a poor basis for an individual
living.
The economic advantage of forestry over agriculture becomes
evident only on poor agricultural soils. Trees of fair quahty
will still grow on soils utterly unfit for farming, and owing to the
small expense attandent on this crop, will yield profitable returns
on such soils.
233. Non-agricultural Soils. — Since food and livelihood and
permanent homes are more important to mankind than fuel
and timber, soils which will repay the farmer should be devoted
to farm crops. But the attempt to cultivate soils essentially
non-agricultural leads to very serious results both for the indi-
vidual and for society. Soils are non-agricultural when they
cannot continue year after year, with proper care, to produce
paying crops. Non-agricultural soils, when cultivated, either
COMPARISON OF FOREST WITH AC.RICULTURAL VALUES 229
wash away by erosion, blow into sand dunes, lose their small
store of fertility by too active drainage, or for other reasons fail
to respond to the elTorts of the farmer.
234. Exploitation of Land Purchasers. — Intelligent farmers
refuse to buy or work such lands. Uninformed purchasers,
either foreigners or city emigrants unused to farming, buy
these lands because they are cheap. They are even less able to
make a living upon them than are the more experienced farmers
who have passed them by. The effort results in financial and
often in moral bankruptcy. Lands of this character thus change
hands often, and since the real estate business is based on land
transfers, it thrives on such conditions.
WTiatever hurts the individual hurts the whole community.
The exploitation of well-meaning land-hungry investors by
professional land locators and real estate sharks is a business
closely akin to more pronounced forms of swindling. Local
sentiment in such communities will be largely molded by these
selfish predatory interests and will resist attempts to properly
classify such land as non-agricultural. Thus a condition is
created containing Umitless possibilities of e\-il to the public at
large.
235. Land Classification. — The solution of this problem lies
in the scientific classification of lands, to determine whether or
not agriculture is possible. If unsuitable for farms, then the
lands fall naturally into the class of forest soils, and should be
removed from the market as agricultural land, and devoted to
forest production. The best way to accomplish this removal is
for the states to purchase such soils for forest reserves or for the
national government to acquire them for stream protection.
236. Basis of Comparison of Agricultural and Forest Values of
Land. — To compare the value of land for agriculture with its
value for forestry, each value must if possible be expressed in
money. In each case the basis of value is future net income
capitalized (§ 62). If we include for both'uses all items of future
income, minus future costs, and can appraise this income and its
present value accurately, the comparison will reveal the relative
value of the property and determine whether the soil is best suited
230 FOREST VALUATION
to farming or forestry. Unfortunately, the uncertainties affect-
ing the determination of these future items, in both cases, prevent
a satisfactory mathematical comparison of such values. Yet
whatever the basis on which the comparison is made, it is
founded on the economic relations which such calculations set
forth.
237. Expectation Value of Agricultural Land. — The basis
of agricultural value is the net revenue from crops. The actual
cost of labor and use of machinery is deducted from the sale
value of the crops and the average net return is capitalized.
Owing to the fact that on small farms the proprietor puts in
his own labor and raises food for his family, this net income is
not often accurately computed. Cash rent paid for farm land
separates the costs from the income, since the tenant presumably
gets only his just share, including profit, and the rent represents
the net income earned by the soil. Since this is annual, it is
capitalized by the formula (XII), on the basis that the
o.op
farm will produce this rental without deteriorating. A farm
earning $5 per acre rent will, at 5 per cent, be worth $100 per
acre.
238. Sale Value of Agricultural Land. — Improved farm
land is transferred with sufficient frequency to establish sale
values, in any region where farming is a well-developed industry.
These sale values will, on the whole, coincide quite closely with
the capital or appraised values of farms based on net income.
But traditions, demand, and increasing or declining population
affect farm values and prices to a great extent. Values of farm
property are sluggish at times and again, in boom periods, out-
strip conservative appraisals of income. In this the human
element in price making is seen to play a large part (§§17,
59. 69.)
239. Timber as an *' Agricultural " Value. — Improved farm
land is not the true basis of comparison with forest land.
Land in its wild state ranges from heavily timbered tracts
through all degrees of stocking and of young timber, to natural
prairies needing only to be broken for a crop. Land which
COMPARISON OF FOREST WITH AGRICULTURAL \'ALUES 231
has been stripped of timber, but is covered with stumps which
interfere with the cultivation of the surface and prevent the use
of machinery, is the condition in which the prospective farmer
in most cases has to accept property in timber regions to-day.
In former times, timber itself had no value, hence the cost
of removing it, including the burning of the logs, gave such
lands a low initial value. It is still necessary to cut and remove
standing timber from agricultural soils, but the timber now has
a stumpage value and its removal will cost the owner nothing,
while its sale supplies him with capital with which he can un-
dertake the work of clearing the land of stumps. The presence
of merchantable timber upon such soils thus aids, apparently,
in establishing agricultural use.
In heavily timbered regions, this seldom works out. Stump-
age caimot be marketed at will and in many regions must await
the slow development of transportation and the gradual cutting of
the more accessible timber. The owner cannot aflford to sacrifice
it for agriculture, except on a small portion of the area and,
consequently, sells this land with its timber to some lumber
company. In time, the land is stripped of timber and the
stump land is offered to purchasers for agricultural use.
Timber values on agricultural soils cannot be regarded in any
sense as agricultural values, but are the equivalent of so much
money capital to the owner of the land. Granting that pur-
chasers who secure timber obtain more valuable property than
those who get only stump land, it is still evident that the agri-
cultural value of. forest land must be based solely on the land
bare of all timber.
240. Stump Land versus Cleared Land. — The value of
stump land is less than that of open meadow or prairie land
in its wild state, by the amount of the extra cost of clearing and
preparing it for cultivation. The crops are the only source of
value, and since improved land is now bearing crops its value
rests on a firm basis. Between this value and that of stump land
is interposed the future costs of clearing and breaking, and the
time necessary to do the work. Fencing, development of water,
and buildings must be added, before agriculture can be sue-
232 FOREST VALUATION
cessful. These future costs depress the real value of stump
land, and cause a wide divergence between the true values of
wild land and improved farms.
241. Cost of Clearing Stump Lands. — The appraisal of the
cost of clearing land is not difficult, but if based on the actual
cost of wages for the labor required in clearing up ground at
one operation, it is apt to be too high. Land is seldom cleared
in that way, except by land companies supplied with large
capital. The settler clears gradually, using his own labor at
slack seasons, cultivating between the stumps, grazing the
land, and allowing the stumps to rot. The roots of hardwood
and sap pine stumps decay in from three to ten years and the
stumps are easily gotten out. The stumps of heart pine and
certain other conifers do not rot readily but will pull much more
easily after a few years than at first. The loss in time is great,
since the full utility of the soil for crops is not attained for years.
The settler may even be investing an amount of labor and capital
in the clearing for which, judged commercially, he will never
be repaid. But clearing will be attempted successfully even on
lands on which its cost apparently exceeds the final value of
the land. Therefore the cost of clearing, provided the soil is
good, should not be regarded as indicating a negative expectation
value for stump land. Should the cost exceed the value of
cleared land, a very low value for stump land is indicated, but
this value will still be positive in most cases.
242. Sale Value of Stump Lands. — Sale values for stimip
lands are often falsely or inaccurately determined and are set
at far too high a figure. This is due to the lack of general
knowledge of the costs and delays of clearing. The values for
highly productive improved lands, perhaps bearing orchards,
are compared with stump lands, to the enhancement of value
for the latter in the minds of purchasers, many of whom
know nothing of the problems involved. It is safe to say that
without the necessary additional capital to hire the clearing
done, such lands can never be developed by this class of inves-
tors out of the income from the property, while persons of
small means cannot buy stump land at high initial prices and ever
COMPARISON OF FOREST WITH AGRICULTURAL VALUES 233
expect to lift the mortgages which they must usually accept.
In contrast, to boom sale values upon such lands, the appraised
value of stump land should be reasonably low compared with
improved tracts in the same neighborhood.
243. Summary of Elements of Value for Forest Land. — The
elements of value which must be considered in arriving at the
value of forest lands arc:
Value of mature or merchantable timber.
Expectation value of young timber.
Value of land based on future timber crops.
To these values must be added:
Value of improvements as roads, fire lines.
Value of protective influence of the forest.
The determination of value for merchantable timber is dis-
cussed in Chapter X. Actual prices received for similar timber
are commonly accepted as indicating this value.
The value of young timber and of land is found by the methods
described in Chapter VI, when an appraisal is necessary.
Roads and other improvements do not influence value on
the basis of what they cost, but by their effect in cheapening
transportation, lowering fire risks and increasing the net income
or lowering the rate of interest (§§211 and 68). In proof of this
statement it is recognized that in agricultural appraisals the cost
of dwellings and other improvements on farms is not the basis
on which the farm is valued, although they add to its value by
providing the immediate faciUties for deriving the incom'e by
cultivation.
The value of the protective influence has been discussed in
Chapter VII (§ 146). This value benefits adjoining property
rather than the land itself, but is an important factor when
weighing the relative merits of agricultural versus forest use.
Fortunately, slopes valuable for their protective forest cover
are usually too steep to be tilled without inducing erosion, and
the demonstration of this fact would at once prevent the
classification of such soils as agricultural by an intelligent
investigator.
234 FOREST VALUATION
Of these five items of value only the revenue from sale of
mature timber is immediately available. This is comparable
with the revenue from the current crop on agricultural land.
When ready to harvest, it greatly exceeds the latter as it rep-
resents a long accumulation.
244. Value of Young Timber as a Part of the Value of Forest
Soil. — When comparing the value of land for forestry with
agricultural values, we assume that the land has some value
for agriculture. Absolute forest soils, whose agricultural use is
impossible, need not be valued in order to determine the class
to which they belong.
Where agriculture is possible, but its profitableness is ques-
tionable, and the cost of clearing is high, the value of the land
for forestry may greatly exceed any value for farming. Here
a calculation of forest values will be of great assistance in deter-
mining the best disposition of the land.
Agricultural soil is always regarded as bare land and the value
as that of the soil itself, not including crops which may be grow-
ing. This is merely because of the short crop period. In
reality the standing crop increases the value of the property
while present and is the source of this value, and a purchaser of
the land must either permit the former owner to harvest the
crop or pay him for it. Forest land to be compared with agri-
cultural land on the same basis must be bare of timber. But
it is the timber crop that gives the land whatever forest value
it has (§ ii6). In actual practice, forest land is seldom in this
bare condition. As seen in Chapter VII, the actual value of
forest property depends upon the closeness of the date of realiz-
ing the income from the timber. The value of the timber may
be separated from land if necessary, but this separation is arti-
ficial (§135). The real value of forest property is based on the
actual condition of the stand, its age and size. Forest values
differ from agricultural values in that they fluctuate over long
periods with the growth and removal of the crops instead of
maintaining a reasonably constant relation from year to year.
The lowest ebb is represented by bare land, and in a system of
dear cutting this condition is attained but once in the period of
COMPARISON OF FOREST WITH AGRICULTURAL VALUES 235
growth of the crop, just previous to planting. In any system
of natural seeding, and especially with selection cutting, the value
of forest **land" never reaches this low point, but is maintained
at a higher level by the presence of partly grown timber which
will bring in revenue in a shorter period than a full crop
rotation.
If voung timber is present on forest soils, it is not possible
to consider this timber as having no value without rejecting the
basis of all values, which is future income. We cannot consider
merely the forest value of the land itself, for this is derived
wholly from timber. The expectation value of the young
timber is more definite than the same value calculated for the
soil itself (§ 116), as it is nearer and more certain than that from
non-existent future crops, or "soil." If land bearing young
timber is cleared for agriculture, the forest value sacrificed is
greater than that of forest land by just the difference that the
age of this timber makes in the present value of the income
expected from it. To ignore this value would be the same as to
consider a half grown crop of wheat as adding nothing to the
sale value of agricultural land.
Nor can we ignore the future income from young timber as
an element of forest value on the grounds that this is not a
present but a future value, perhaps not attainable for several
decades. If agricultural values were based merely on the revenue
from the next year or decade, the capital value of farm land
would be much lower than it is. All future revenue is included
in such agricultural values as surely as it must be included in
finding the present value of forest property (§85). The mere
fact that forest income is irregular makes it no less necessary to
value the entire future income in finding the value of the prop-
erty for forestry.
245. Sale Value of Forest Property. — As in the case of
agricultural soils, sales are the generally recognized basis of
value for forest property, soil and standing crops included.
But the sale value of forest property may suffer from ignorance
or lack of recognition of the true worth of the property (§111).
If young timber has been allowed to burn up in the past, or if
236 FOREST VALUATION
insufficient time has elapsed since logging began on the virgin
forest, the fact that young timber will grow into a valuable
merchantable stand, or second growth, is not generally appreci-
ated. The forester, a specialist on appraisal of growing timber,
can estimate this value on its true basis. But the public will
place a much lower estimate on the property, or may ignore
altogether the element represented by the young timber and
value the land itself on an arbitrary basis not related to its
use for forest production, but based on grazing or other uses.
Purchasers of land follow a sound policy in acquiring it at as
low a value as possible, and if bought for forestry they gain
by this condition of undeveloped sale values. But as a basis for
classification, the acceptance of existing sale values of land and
young timber, merely because the public are not familiar with
true values, is wholly inexcusable. When this condition is
further aggravated by accepting an inflated agricultural value
for unimproved stump lands, the comparison is unfavorable to
the securing of a true and lasting classification.
246. Discrimination against Forest Values. — Where eco-
nomic pressure is strong for the listing and opening of lands for
new settlers, the tendency is to deliberately ignore the expec-
tation value of young timber as well as of the land, and to con-
sider only the mature timber as indicating the sum of forest
values. Or, perhaps, the forest value of the land is recognized,
but not that of young trees. This is even more inconsistent
than the first plan. The argument is advanced that the value
of young timber will not be realized for many years while that
of agricultural crops applies to the present moment. But if
these timber values are based on present stumpage prices (§ 195)
and properly discounted to the present, it must be evident from
the discussion in Chapter VI that expectation value is a true
present value, strictly comparable with that for agriculture
(§ 244). Rejection of such appraisal can be justified only in two
ways, — when forest values are actually less than agricultural
values for stump land, or on the basis of poHtical expediency.
247. Discrimination in Favor of Forest Values, — The rec-
ognition of increasing future prices brings an element of specu-
COMPARISON OF FORKST WITH ACRICUl.rURAI. VALUES 237
lation into such appraisals, and when this is done, the present
values thus found are no longer based on present but on future
conditions. It is this element, and not the discounting of future
income to the present, which would unfairly alter the basis of
appraisal in favor of forest values. A parallel case would be
found were it estimated that prices for farm crops would in-
crease and that the value of land at present should be based on
an appraisal of this future increase in annual income.
Future growth in volume is a justifiable assumption, as is
also an improvement in quality of timber and of unit price based
on this quality, to conform to the higher prices now received for
similar grades (§§ 183, 184). But the discounting of future in-
creases in the general price level for timber is as little justified
in the case of valuation for comparison with agriculture as it is
in valuing damages to young timber. In either case, present
values must be based on present prices, and future increases may
be used only by the owner in computing possible or speculative
profits.
248. Results, when Values of Bare Land are Compared. —
From the above discussion it is assumed that a true comparison
of forest with agricultural values is based on a computation or
appraisal of the expectation or present capital value of the
property for each use, the forest values present in the form of
timber and land being compared with the value of stump land
for agriculture. The highest value for both purposes will always
be found on the richest agricultural soils. But it will seldom
if ever be true that the forest value of bare soil will exceed its
agricultural value if the soil is fairly adapted to crop production.
Only upon the poorer or non-agricultural soils will land itself,
even at a low forest value, be worth more for wood crops than
for agriculture.
249. Results, when Full Value of Property is used in
Comparison. — With the growth of the timber, however, a
corresponding increase takes place in the forest values of the
property or "land," until at some point during this growth the
actual present value of the timber and land exceeds the agri-
cultural values. At any time previous to this, it is justifiable
238 FOREST VALUATION
to destroy the young timber and clear the land, although in doing
so a greater value is sacrificed or wasted than if stump land only
were so used. The destruction of merchantable timber in
former days was justified on this basis, since the value of the
land for agriculture exceeded the total timber values present.
But pioneer conditions have passed, and the destruction of
merchantable timber values is no longer thought of except
where these pioneer conditions are reproduced by lack of trans-
portation and markets. Even as the former settlers found
that with increasing values the uncleared portions of the farm
became a source of unexpected wealth, so in the future it will
pay the settler to protect young growth and keep a portion of
his farm in timber.
The mature timber upon agricultural land adds a forest value
to the value of the stump land. The land is worth just as
much more to the settler as the price he can get for his standing
timber. The only drawback is that until this is sold and re-
moved he cannot begin his clearing. But upon most claims there
is enough poorly timbered soil to occupy the time and energies
of the settlers until such sale is effected. Should there be no
such openings, and the entire claim be heavily timbered, agri-
cultural use is inevitably postponed until logging commences,
for the relative value of the timber is so great as to preclude
any other course.
250. National Forest Policy in Land Classification. — In
classifying national forest land in pursuance of the policy of
granting homesteads, land should not be listed for settlement
while the total forest values exceed the agricultural value of
stump land. This necessitates the sale and removal of mature
timber from agricultural soils, previous to listing. But owing
to the pressure for land throughout the west the tendency is
at present to ignore the appraised value of immature timber
and even the capital value of forest land, and to permit the
listing of lands containing a certain amount of merchantable
timber. This reservation is beneficial to the settler for it gives
him a subsidy or value in addition to his land.
Since this procedure clearly sacrifices all forest values except
COMPARISON OF FOREST WITH AGRICULTURAL VALUES 239
the present saleable timber, it will inevitably result in listing
rapidly all lands of agricultural value whether or not they are
covered with young trees, provided only that the merchantable
stand is not too dense or valuable. If this policy is demanded
by dearth of farm land in these regions it should be carried out,
but the basis upon which the classification is made must be
frankly recognized as expediency rather than sound appraisals
of value.
251. Reciprocal Values in Forestry and Agriculture. — Forest
and agricultural values cannot be considered as wholly sepa-
rate. On every agricultural unit there is need of a certain
amount of forest land to furnish wood for fuel, fence posts and
even lumber, and as shelter for stock and windbreaks. In
treeless prairies the planted grove greatly enhances the desira-
bility of the whole property as a residence and -adds in this way
far more to the sale value of the farm than is accounted for
by the possible revenue which this grove could produce. In
wooded regions the labor of clearing is so great that two or even
three decades must elapse before the entire farm will be brought
under cultivation by the efforts of the farmer, unless aided by
investing the necessary capital in clearing on a large scale.
Meanwhile the woodlots will grow at an appreciable rate and
young timber at first but a few feet tall will become large
enough for use. In many regions this wooded portion may also
be grazed without undue injury to the trees, if the latter have
sufficient height.
Every effort should be made by owners of such tracts to spare
and encourage areas of reproduction and of young timber, more
especially when such growth occurs on the poorer portions,
steeper slopes and more inaccessible parts of the farm. In
this way each part of the farm unit is put to its best use, the
maximum returns are obtained, and the sale value of the entire
property will usually exceed the sum of the forest and agricul-
tural values when separately considered.
APPENDIX
Formulje.
Summary of Formulse of Compound Interest.
Definitions of Symbols.
Summary of Formulae of Forest Valuations.
Compound Interest Tables (Table VI) .
Tables of Logarithms (Table VII).
SUMMARY OF FORMUL.S: OF COMPOUND INTEREST
Character of payments.
Single sums.
Temporary rentals,
annual
intermittent . .
Perpetual rentals,
intermittent
annual
Values at the end , future
values, cost.
VoX i.o/)"
(I)
r
(I
op--
I)
r
(i
o.op
.o/>"« -
-I)
'
I
(i
op" -
.op"' -
I
op"^
I. op"
(III)
(V)
(VII)
o.op (i.op")
r'(i.o^"'- i)
Values at the beginning, present
values, capitalized income, capi-
tal value, expectation value.
Vn
I .Op"
(11)
r (i.op"- i)
(i.op"- i) I. op"'
r'(i.op"' - i)i.op"-°
(i.op" - i) I. op"'
I .op" — I
r'(i.op"-^)
I.op"- I
r' (i.op")
I .op" - I
r
o.op
Conversion of intermittent into annual rentals.
I.op" - I
Ratio of income to capital investment, .r = loo I V y^
(v/f:-)
(IV)
(VI)
(VIII)
(IX)
(X)
(XI)
(XII)
Xo.op (XIII)
(XIV)
240
APPENDIX 24 1
SUPPLEMENTARY FORMULiE
\ -^ (i.o/>" - i) I i.op" + -^ (i.o/- i). (Ilia)
( o.op ) o.op
R{i.op"-i). (Illb)
-^^1^^ . (Xa)
i.o/>" — I
I. op" — I
DEFINITIONS OF SYMBOLS
a — Year, previous to n, for which value or cost of property
is sought.
I ot)" I
d '—^ , ratio used in Formulae P3 and P4 in deter-
o.op
mining the amount (Z) to be written off annually
for profit and depreciation.
e — Annual expenses, constituting one year's net outlay.
g — First term of a geometric series.
m — Interval between intermittent yields in a many-aged
forest.
n — Period required to produce a crop of timber. Rotation.
Interval between yields produced by even-aged stands
of timber.
p — Standard rate of interest in forestry.
q — Ratio, or multiple, for a geometric series.
q% — Per cent of legitimate profit to be allowed in logging
and milling, or in logging alone, in stumpage ap-
praisals.
r — Annual rental, regarded either as income or outlay.
/ — Intermittent rental, due at regular intervals greater
than one year.
r% — Per cent of legitimate profit to be allowed in milling
alone, in stumpage appraisals.
s — Per cent of overrun per thousand board feet, log scale.
t — Number of payments expected in a temporary inter-
mittent rental.
242 APPENDIX
X — Rate of dividends or interest earned by an investment.
2 — Per cent of value to be written off annually for depre-
ciation in Formula Po.
A — Original capital investment in assets subject to depre-
ciation.
C — Cost of initial silvicultural and protective measures,
incurred in first year.
Cd, Ce, Cf — Cost of silvicultural and protective measures,
incurred in subsequent years, d, e and /.
D — Total amount to be written off for depreciation during
the life of an enterprise.
E — Expectation or capital value of annual expenses, e,
by Formula XII,
■' ■ o.op
"Fc — Total cost of forest property, including both land and
growing stock or timber, for the year a. For year n,
substitute "F^ or F^.
Fg — Sale value of forest property, both land and timber, in
the year n or when timber is mature.
"Fj — Expectation value of this sale value for the year a,
previous to the year n or year of sale.
F^ — Expectation value (capital value) of forest property,
including both land and timber. Applicable to both
even-aged and many-aged stands.
"F„ — Expectation value of forest property for year a pre-
vious to year n.
Gc — Cost of growing stock or standing timber.
°Gv — Expectation value of growing stock, or standing timber,
separate from land, for the year a previous to year n.
L — Total amount of loss or damages to forest property.
LC — Logging costs.
LD — Depreciation of logging investments.
MC — Milling costs.
MD — Depreciation of milling investments.
P — Profit or enterpriser's gain, remaining after paying
interest at p per cent on capital investment.
Q — Sum of terms in a geometric series.
APPENDIX
243
R — Expectation or capital value of the sum of payments
constituting a rental.
S — Sale value of lumber or of logs. Value of soil.
'S'c — Cost of soil and of permanent improvements.
S, — Sale value of soil.
S^ — Expectation or capital value of forest soil.
Tp, Tg, Tr — Net income from sale of thinnings in years p,
q and r.
V — Value of a single sum.
Vo — Value of sum at beginning of period.
Va — Future value in year a of the sum of items of income
and expense on a crop of timber.
F„ — Value of a single sum at end of a period of n years.
^r — Future value of the sum of payments constituting a
rental.
W — Final, wrecking or residual value of assets in logging
or milling, after writing ofT total depreciation.
X — Annual sum required to be written ofT for depreciation.
Y — Sale value, or appraised value, of timber stumpage.
F' — Sale value, or appraised value, of timber stumpage,
resulting from fire or other damage.
Ym — Stumpage value of 1000 board feet of manufactured
lumber, used as basis to determine Y.
Z — Annual sum which combines income or profit on in-
vested capital with depreciation, the sum constitut-
ing one of a series of equal annual payments.
summary of formul.e in forest valuation
Costs
Cost of a single even-aged stand of timber.
Index Art.
Lettf r
Gc=(C-\-Sc + E)i.op--(Sc-\-E) .... A 105
Gc=iC + Sc-\-E)i.op--\-C,{i.op-'')-\-Ce{i.op"-')
+ Q(i.o/>"-0 -Tp (i.o/)"-") - r,(i.o/>"-')
-Trii.op"-^ -(Sc-\-E) Ai 105
Cost of a forest, including timber and soil, for year a.
"F, = (C + S, -^ E)i.op'' - E Ao 105
244
APPENDIX
Cost of a normal many-aged forest.
^ (C-^Sc + E){i.oP" - i)
Uc = 7
o.op
Index Art.
Letter
— n {Sc + E). . A3 109
Values
Sale value of a single even-aged stand in year n, in-
cluding value of soil.
F,= Y-\-S, B 112
Expectation or capital value of above for year a, pre-
vious to year n.
ap ^F + 5. + E_^^
ap _ .
I. Op"-"
Bi 112
i.o/>"-"
Expectation or capital value of forest property in
the year n, previous to removal of crop.
Y -C
E. B2 112
F, = Y +
-(C + £). ...... C
l.o/>" —I
UTrii.op^-^-C-Cii.op'^-')
F^ = F-(C+£)-f l-Ce(i.or-)-Q(i.or-0 c,
I. op" — I
Expectation or capital value of forest property in
the year a, previous to year n.
(F - C) i.o/>°
114
114
"F,, = ^ rA.±:riL. _E
I. op" — I
y^j:j^^Jl_^Tr(l.OP") _^
I.O/?" i.op" I. op"
D 115
Cgd.OP") _Ce(l.OP") Cyjl.OP")
l^p^ I. Op"
I.op
E. Di 115
I.op" — I
.p = F + 5„ + £ _ ^ D2 116
i.op"-^
APPENDIX 245
Index Art.
Letter
Expectation or capital value of forest soil.
5„ = — ^'-^^^- (C + £) E 116
i.o/>" — I
lY-^T„{i.op"-^)-\-T,{i.op'^-")-\-Tr{i.op'^-')
S^ ^ l-C-C,(i.or-^)-C(i.o/>-')-C/i.or-/) _.^ , £)
I. op" — I
El 116
Soil rent = 5„ X o.op E2 116
Expectation or capital value of a many-aged forest
in year m, just subsequent to removal of crop.
F.= ^"^ -iC + E) F 117
I. op"' — I '
Expectation or capital value of a many-aged forest
in year a, previous to year m.
_ F + F. + £
Tv = — tl, Tl 117
Expectation or capital value of a many-aged forest
producing armual income.
/"„ = - - 7 1^2 117
o.op
Expectation or capital value of a many-aged forest
for irregular yields and periods.
Y—C Y — C Y — C
F.^-^ 1 2 E
I. op" - I
F3 118
Expectation or capital value of growing stock or
timber separate from soil, in year a, previous to
year n, for a single even-aged stand.
Y 4- ^ -\- F
°G,= •" ^^'•^^-(5, + £) G 119
246 APPENDIX
Index Art.
Letter
Expectation or capital value of growing stock or
timber separate from soil, in year a, previous to
year m, for a many-aged stand.
°G.= ^ + ^;+/-(5, + £) Gi 119
I. op
Profits
Profits in destructive lumbering, on timber and land,
for year n or at time of sale of timber.
p = 7 + 5, + £- (C + 5c + £;)i.o/?" . . . H 122
P = F + 5,-}-£ + rp (i.op^-^) + T, (i.op-^)
+ Tr (i.o/>"-0 -(C-\-Sc + E) I. op"
- C, {i.op--') - Ce ii.op"-") - Cf {i.op--^. Hi 122
Profits in destructive lumbering, on timber alone, for
year n.
P=Y -^Sc-\-E-{C + Sc + E)i.op\ . . . K 123
Profits in destructive lumbering, on timber alone, for
year a, previous to year n.
P = ^^^'~^^ -{C-\-S.-\-E) i.op\ . . . Ki 124
I .o/>"~"
F + 5. + £ , Tp , T^ T
P = ^ ' -- ' - + -^^^^ + -^^^ +
i.o/?"-" i.opp-" I. op"'" i.op"-"'
- (C + 5e + £) i.o/)" - C, {i.op'^-')
-Ceii.op"-') -Cf(i.op''-0 K2 124
Profits in continuous forest production, for year n.
P = F + 5, + £- (C + 5c + £)i.o/>". . . . L 125
Profits in continuous forest production, for year a,
previous to year «.
P = I_±j??L±_^_(C + 5o + £:)i.or • . • Li 126
i.op"~°
P = ''F,- "Fc. U 126
P = (5, - 5„) i.op" L4 126
Profits in continuous forest production for year o,
previous to origin of crop.
P = S,-Sc L3 127
APPENDIX 247
Index Art.
Letter
Interest Earned
Rate of interest earned on soil capital.
..„,,, '• + ^. + £-(c + £) ■or N 1.9
Rate of interest earned on soil and initial investments.
^^^;^y + S. + E-EU.or) N, .,,
Rate of interest earned on entire investment.
— £^|^ ^^ "9
Mean annual forest per cent.
c
X ^ ^X p N3 129
Current annual forest per cent.
.r = /^n+i - F„ - g^ ^^ -^^ J29
orx = (^"+i~^"~')ioo N6 129
Current annual forest per cent, for normal forest.
X =^ Xp Ne 129
re
Damages
Damages to mature timber.
L=Y -Y' O 140
Damages to young timber for year a, previous to
year n.
L = ^^^^ Oi 141
i.o/>"-"
Damages to timber and soil, for year a.
^^ Y-\-S„ + E _ ^^^ _^ £) + (c' - C). . . Oo 142
248 APPENDIX
Index Art.
Letter
Depreciation
Depreciation, Method A.
D (o.op)
X = 7 P 171;
Depreciation, Method B.
X -- = Pi 175
Depreciation, Method C.
s= 100(^1 -y/jj P2 175
Depreciation, Method D.
^^Ai^^otl^ p^ ^^^
Z = yl (0.0/?) + —(Hunter's formula). . . . P4 175
Geometric Series
Sum of rentals, increasing temporary series.
Sum of rentals, decreasing temporary series.
Q = sJl.:irl Q^ 80
I -q
Sum of rentals, increasing perpetual series.
Q = 00 Q3 80
Sum of rentals, decreasing perpetual series.
Q = —^— Q4 80
I -g
APPENDIX 249
Index Art.
Letter
Stumpage Values
Stumpagc appraisal on basis of manufactured lumber;
profits, a per cent of operating costs.
F„. =S-(LC-{- MC + D)- q% (LC + MC + D) R 177
F„ = S-{MC+MD+LC+LD) -r%{MC+MD)
-q%(LC + LD) Ri 177
Stumpage appraisal on basis of manufactured lumber;
profits, a per cent of sale value.
Ym= f ^- (LC + MC + D) R, 177
Stumpage appraisal on basis of manufactured lumber;
profits, a per cent of margin between operating costs
and sale value.
Ym = q7olS-(LC + MC-\-D)\ R3 177
Stumpage appraisal on basis of manufactured lumber;
reduction to log scale.
Y = Ymii.os) R4 179
TABLE VI
COMPOUND INTEREST TABLES
The period, n years, in left-hand column.
Column I. Formula I. — Future value of $1 at end of n years.
Column II. Formula II. — Present, expectation or capital value of $1 due in »
years.
Column III. Formula III. — Future value at end of 11 years of an annual rental
of $1 payable « times.
Column IV', Formula IV. — Present, expectation or capital value of an annual
rental of $1 payable n times.
2SO
APPENDIX
1
2
PER CENT
n years.
I.
II.
III.
IV.
1
1.0050
■ 99SO
I. 0000
-9950
2
I .0100
.9901
2.0050
1-9851
3
I.OI5I
.9851
3-0150
2.9702
4
1.0202
.9802
4 - 0301
3-9505
S
I -0253
• 9754
5-0503
4-9259
6
I . 0304
-9705
6.0755
5 - 8964
7
I -0355
-9657
7-1059
6.8621
8
I .0407
.9609
8.1414
7-8230
9
1.0459
9561
9.1821
8.7791
10
I. 05 I I
-9513
10.2280
9-7304
11
1.0564
.9466
11.2792
10.6770
12
I. 061 7
9419
12.3356
II .6189
13
1.0670
9372
13-3972
12.5562
14
1.0723
9326
14.4642
13.4887
15
1.0777
9279
15-5365
14.4166
16
1.0831
9233
16.6142
15-3399
17
1.0885
9187
17.6973
16.3586
18
I 0939
9141
18.7858
17-1728
19
1.0994
9096
19.8797
18.0824
20
I . 1049
9051
20.9791
1S.9874
21
I. I 104
9006
22.0840
19.8880
22
1. 1 160
8961
23.1944
20.7841
23
1.1216
8916
24.3104
21.6756
24
I . 1272
8872
25-4320
22.5629
25
I. 1328
8828
26.5591
23-4456
26
1.138s
8784
27.6919
24-3240
27
I . 1442
8740
28.8304
25.1980
28
I . 1499
8697
29-9745
26.0677
29
1.1556
8653
31.1244
26.9330
30
I . 1614
8610
32.2800
27.7941
31
I. 1672
8567
33-4414
28.6508
32
1-1730
852s
34 . 6086
29-5033
33
I. 1789
8482
35-7817
30-3515
34
1.1848
8440
36.9606
31-1955
35
I . 1907
8398
38.1454
32.0354
36
I . 1967
8356
39-3361
32.8710
37
I .2027
8315
40.5328
33-7025
38
I . 2087
8274
41-7354
34-5299
39
I. 2147
8232
42.9441
35-3531
40
1.2208
8191
44-1588
36.1722
41
I .2269
8151
45-3796
36.9873
42
1 . 2330
8110
46 . 6065
37-7983
43
1.2392
8070
47 - 8306
38.6053
44
I • 2454
8030
49.0788
39-4082
45
I. 2516
7990
50.3242
40.2072
46
1-2579
7950
51-5758
41 .0022
47
1.2642
7910
52-8337
41-7932
48
1-2705
7871
54-0978
42-5803
49
1.2768
7832
55-3683
43 3635
50
I . 2832
7793
56.6452
44.1428
65
1.3156
7601
63 . 1 200
47-9782
60
1.3488
7414
69.7600
51.7020
65
1.3829
7231
76.5800
55-2764
70
I. 4178
7053
83 - 5600
58-9364
75
1-4536
6879
90.7200
62.4745
80
1-4903
6710
98.0600
65-7988
85
1-5280
654s
105.6000
69.1099
90
1.566s
6383
113.3000
72-3268
95
I. 6061
6226
121.2200
75-4747
100
I . 6467
6073
129.3400
78-5449
105
1.6882
5923
137.6400
81.5306
100
I . 7309
5777
146.1800
84-4531
115
1.7746
5635
154.9200
87.2985
120
I. 8194
5496
163.8800
90.0736
APPENDIX
251
I PER CENT
H years.
1.
II.
III.
IV.
1 I
0100
.9901
I. 0000
.9901
i I
0201
.98o,{
2.0100
1.9704
S I
OJ03
.9706
3 0301
2.9410
4 I
0400
.9610
4.0604
3 9020
6 I
0510
• 9515
5.1010
4-8534
6 I
00 1 5
.9420
6.1520
5-7955
7 1
0721
.9327
7-2135
6.7282
8 I
0829
• 9235
8.2857
7 6517
9 I
ogj?
• 9143
9.368s
8.5660
10 I
104b
• 9053
10.4622
9 4713
11 I
1157
.8963
11.5668
10.3676
12 I
1268
.8874
12.6825
11-2551
IS I
1381
.8787
13.8093
12.1337
14 I
1495
.8700
14.9474
13 OOJ7
15 I
lOio
.8613
16.0969
13-8651
16 I
1726
.8528
17 2579
14.7179
17 I
1S43
■8444
18.4304
15.5622
18 I
igOi
.8360
19.6147
16.3983
19 I
2081
.8277
20.8109
17.2260
SO I
2202
.8195
22.0190
18.0456
SI I
2324
.8114
23.2392
18.8570
SS I
2447
.8034
24.4716
19.6604
SS I
2572
•7954
25.7163
20.4558
S4 I
2697
.7876
26.973s
21.2434
SS I
2824
■ 7798
28.2432
22.0232
S6 I
2Q53
.7720
29.5256
22.7952
S7 I
3082
.7644
30.8209
23 5596
28 I
3213
.7568
32.1291
24.3164
29 I
3345
■7493
33 4504
25.0658
30 I
3478
•7419
34 7849
25-8077
31 I
3613
•7346
36.1327
26.5423
32 I
3749
■7273
37-4941
27.2696
S3 I
3887
.7201
38.8690
27-9897
34 I
4026
•7130
40.2577
28.7027
35 I
4166
•7059
41.6603
29 . 4086
36 I
4308
.6989
43.0769
30-1075
37 I
4451
.6920
44.5076
30.7995
38 I
4595
.6852
459527
31.4847
39 I
4741
.6784
47.4123
32.1630
40 I
4889
.6717
48.8864
32.8347
41 I
SO38
.66so
50.3752
33.-4997
4S I
5188
,6584
5 1 - 8790
34-1581
43 I
5340
.6519
53-3978
34.8100
44 I
5493
• 6454
54-9318
35-4554
45 I
5648
.6391
56.4811
36-0945
46 I
5805
• 6327
58.0459
36-7272
47 I
5963
.6205
59-6263
37-3537
48 I
0122
.6203
61.2226
37-9740
49 I
6283
.6141
62.8348
38-5881
50 I
6446
.6080
64.4632
391961
55 I
7284
.5786
72.8400
42.1430
60 I
816O
■ 5505
81.6600
44 9521
66 I
9093
.5238
90.9300
47.6247
70 2
0066
.4983
100.6600
50.1644
76 2
1090
• 4742
110.9000
52.5841
80 2
2166
.4500
121 .6600
54-8858
86 2
3296
.4292
132.9600
57 0742
90 2
4485
.4084
144.8500
591750
96 2
5733
.3886
157-3300
61.1394
100 2
7046
.3697
170.4600
63.0259
106 2
8425
.3518
184.2500
64.8197
110 2
9875
.3347
198.7500
66.5272
116 ,
1 300
.3185
213.9900
68.1518
130 s
3001
• 3030
230.0100
69 . 6979
252
APPENDIX
If
PER CENT
tt years.
I.
II.
III.
IV.
1
I. 0150
.9852
I. 0000
.9852
2
1.0302
.9707
2.0150
1-9559
3
I 0457
-9563
3-0452
2.9122
4
I. 0614
.9422
4-0909
3-8544
5
I 0773
.9283
5-1523
4-7826
6
I 0934
• 9145
6.2290
5-6972
7
I . 1098
.9010
7-3230
6.5982
8
1.1265
8877
8-4328
7-4859
9
I -1434
8746
9-5593
8 -3605
10
1-1605
8617
10.9027
9-2222
11
I 1779
8489
11.8633
10. 07 1 1
12
I 1959
8364
13-0412
10.9075
13
1.2130
8240
14-2368
11-7315
14
I. 2318
8118
15-4504
12-5434
16
1.2502
7999
16.6821
13-3432
16
I . 2690
7880
17-9324
14-1313
17
I . 2880
7764
19.2014
14-9076
18
1-3073
7649
20.4894
15.6726
19
1.3270
7536
21.7967
16.4262
20
1.3469
7425
23-1237
17.1686
21
1-3671
7315
24-4705
17-9001
22
1.3876
7207
25-8376
18-6208
23
I . 4084
7100
27.2251
19-3309
24
1-4295
6995
28.6335
20 . 0304
26
1.4509
6892
30.0630
20.7196
26
1-4727
6790
31-5140
21.3986
27
1.4948
6690
32-9867
22.0676
28
1-5172
6591
34-4815
22.7267
29
I . 5400
6494
35-9987
23-3761
30
1-5631
6398
37-5387
24.0158
31
1.5865
6303
39-1018
24.6461
32
1.6103
6210
40 . 6883
25.2671
33
1-6345
6118
42.2986
25.8790
34
1.6590
6028
43-9331
26.4817
36
1-6839
5939
45-5921
27 0756
36
I -7091
5851
47-2760
27.6607
37
I - 7348
5764
48-9851
28.2371
38
I . 7608
5679
50.7199
28.8051
39
1.7872
5595
52.4807
29.3646
40
I. 8140
5513
54.2679
29.9158
41
1 .8412
5431
56.0819
30-4590
42
1.8688
5351
57-9231
30.9940
43
I . 8969
5272
59.7920
31-5212
44
1-9253
5194
61.6889
3 2 . 0406
46
1-9542
5117
63.6142
32.5523
46
1-9835
5042
65 . 5684
33-0565
47
2-0133
4967
67-5519
33-5532
48
2 -043s
4894
69.5652
34 0426
49
2.0741
4821
71.6087
34-5247
60
2.1052
4750
73-6828
34-9997
66
2.2679
4409
84.5296
37-2715
60
2-4432
4093
96.2147
39-3803
66
2.6320
3799
108.8000
41-3373
70
2-8355
3527
122.3640
43-1549
75
3-0546
3274
136.9670
44 - 8409
80
3 - 2907
3039
152.7110
46-4073
86
3 -5450
2821
169.6600
47 - 8603
90
3-8189
2618
187.9300
49 2099
96
4-I141
2431
207 . 6000
50.4618
100
4-4320
2256
228.8030
51.6247
106
4-7746
2094
251-6330
52-7036
110
5-1436
1944
276.2380
53 - 7055
116
5-S4II
1805
302.7330
54-6351
120
5-9693
1675
331-2880
55-4985
APPENDIX
253
2 PER CENT
n years.
I.
II.
III.
IV.
1
I.0200
.9804
I .0000
.9804
S
1.0404
.9612
2.0200
1 .9416
s
I . 06 1 2
• 9423
3 . 0604
2.8839
4
1.0824
.9238
4.1216
3.8077
6
I . 1041
.9056
5 2040
4 713s
6
1 . 1262
.8S80
0.3081
5.6014
7
I. 1487
.8706
7 4343
6.4720
8
1-1717
-8535
8.5830
7.3255
9
I. 1951
.8368
9 7546
8.1622
10
I. 2 190
.8203
10.9497
8.9826
11
I • 2434
-8043
12.1687
9.7868
12
1.2682
.7885
13.4121
10.5753
IS
I . 2936
-7730
14.6803
11.3484
14
1-3195
-7579
15 -9739
12. 1062
IS
1-3459
-7430
17 2934
1 2 . 8493
16
1.3728
-7284
18.6393
13.5777
17
1.4002
.7142
20.0121
14.2919
18
1.4282
.7002
21.4123
14.9920
19
1.4568
.6864
22.8406
15.678s
20
1-4859
.6730
24.2974
16.3514
21
1-5157
-6598
25 7833
17.0112
22
1.5460
.6468
27 . 2990
17.6580
S3
1-5769
-6342
28.8450
18.2922
24
I . 6084
.6217
30.4219
18.9139
26
I . 6406
.6095
32.0303
19.523s
26
1-6734
-5976
33 6709
20. 1210
27
I . 7069
-5859
35-3443
20.7069
28
I. 7410
-5744
37-0512
21 .2813
29
1-7758
■5631
38.7922
21.8444
SO
1.8114
-5521
40.5681
22.3965
SI
1.8476
■ 5412
42.3794
22.9377
S2
1.8845
■5306
44.2270
23,4683
S3
1.9222
-5202
4O. 1116
23.9886
34
I . 9607
.5100
48.0338
24.4986
S6
1.9999
.5000
49-9945
24.9986
36
2.0399
.4902
51-9944
25.4888
37
2 . 0807
• .4806
54.0343
25.969s
38
2.1223
.4712
56.1149
26.4406
39
2.1647
.4619
58.2372
26.9026
40
2 . 2080
-4529
60.4020
27.3555
41
2.2522
.4440
62.6100
27.799s
42
2.2972
-4353
64.8622
28.2348
43
2.3432
.4268
67-1595
28.6616
44
2.3901
.4184
69.5027
29.0800
46
2-4379
.4102
71.8927
29.4902
46
2.4866
.4022
74-3306
29 8923
47
2.5363
-3943
76.8172
30.2866
48
2.5871
-3865
79.3535
30.6731
49
2.6388
•3790
81 .9406
31.0521
60
2.6916
-3715
84.5794
31.4236
66
2.9717
-3365
98.586s
33.1748
60
3-2810
.3048
114.0520
34 ■ 7609
66
3-6225
.2760
131.1250
36.1973
70
3-9995
.2500
149.9780
37.4986
76
4-4158
.2265
170.7900
38.6763
80
4-8754
.2051
193.7720
39. 7445
86
5-3828
-1858
219.1400
40 . 7 11 I
90
5-9431
.1683
247.1570
41.5869
96
6.5617
•1524
278.0850
42.3800
100
7 • 2446
-1380
312.2320
43.0984
106
7-9987
.1250
349.9300
43-7489
110
8.8312
.1132
391.5590
44-3382
116
9.7503
.1026
437.5150
44.8719
130
10.7652
.0929
488.2580
45 3554
254
APPENDIX
2* PER CENT
n years.
I.
II.
III.
IV.
1
1.0250
•9756
I. 0000
.9756
2
1.0506
.9518
2.0250
1-9274
3
i.o76g
.9286
3-0756
2 . 8560
4
I . 1038
.9060
4-1525
3.7620
6
1.1314
.8839
5-2563
4.6458
6
I .1597
.8623
6-3877
5 -5081
7
I. 1887
-8413
7-5474
6-3494
8
I .2184
.8207
8.7361
7.1701
9
I . 2480
.8007
9-9545
7.9709
10
I. 2801
.7812
I I . 2034
8-7521
11
1.3121
.7621
12.4835
9-5142
12
1-3449
•7436
13-7956
10.2578
13
1.3785
•7254
15.1404
10.9832
14
I. 4130
.7077
16.5190
I I . 6909
IS
1.4483
.6905
17-9319
12.3814
16
1-4845
.6736
19.3802
13 0550
17
I. 5216
.6572
20.8647
13-7122
18
I -5597
.6412
22.3863
14-3534
19
I ■ 5987
•6255
23-9460
14.9789
20
1.6386
.6103
25-5447
15-5892
21
I .6706
•5954
27-1833
16.184s
22
1 .7216
.5809
28.8629
16.7654
23
I . 7646
.5667
30.5844
17-3321
24
I . 8087
■5529
32-3490
17-8850
26
1.8530
•5394
34-1578
18.4244
26
1.9003
.5262
36-0117
18.9506
27
1-9478
-5134
37.9120
19.4640
28
1.9965
.5009
39-8598
19.9649
29
2.0464
.4887
41-8563
20.453s
30
2.0976
.4767
43.9027
20.9303
31
2.1500
•4651
46 . 0003
21.3954
32
2 . 2038
-4538
48.1503
2 1 . 8492
33
2.2589
•4427
50.3540
22.2919
34
2.3153
■4319
52.6129
22.7238
36
2.3732
.4214
54-9282
23-1452
36
2.4325
.4111
57 3014
23 5563
37
2 . 4933
.4011
59-7339
23-9573
38
2.5557
■3913
62.2273
24.3486
39
2.6196
.3817
64.7830
24 7303
40
2.6851
•3724
67.4026
25 . 1028
41
2.7522
•3633
70.0876
25-4661
42
2.8210
-3545
72.8398
25.8206
43
2.8015
•3458
75.6608
26. 1664
44
2.9638
•3374
78.5523
26.5038
46
3-0379
.3292
81.5161
26.8330
46
3-II39
.3211
84-5540
27-1542
47
3-1917
• 3133
87 . 6679
27.467s
48
3-2715
■3057
90.8596
27.7732
49
3-35S3
.2982
94-1311
28.0714
60
3-4371
.2909
97-4843
28.3623
66
3-8888
•2571
11S-551
29.7140
60
4.3998
.2273
135-992
30.9087
66
4.9780
.2009
159.120
31-963
70
5-6321
•1775
185.284
32.898
76
6.3722
.1569
214.888
33 -64s
80
7 . 2096
.1387
248-383
34-452
86
8.1570
.1226
286.280
35-096
90
9.2289
.1084
329. 154
35-666
96
10.4416
.0958
377 664
36.171
100
11.8137
.0846
432^549
36.614
106
13.3661
.0748
494-644
37-007
110
15.1226
.0661
564-902
37-355
lie
17.1098
.0584
644.392
37 664
120
19-3581
•0517
734326
37 934
APPENDIX
255
.^ PER CENT
H years.
I.
II.
IH.
IV.
1
1.0300
.9709
I. 0000
.9700
a
I .0609
.9426
2.0300
I. 9135
3
1.0927
.9'5i
3 0909
2.8286
4
II2SS
.8885
4.1836
37171
s
I 1503
.8626
5. 3091
4-5797
6
I.IQ4I
•8375
6 . 4684
5417a
7
1.2299
.8131
7.6625
6 . 2303
8
I . 2668
.7894
8.8923
7.0197
9
I . 3048
.7664
10.1591
7.7861
10
1-3439
.7441
11.4639
8.S302
11
1.3842
•7224
12.8075
9-2526
12
1.4258
.7014
14. 1920
9 -9540
13
1.4685
.6810
15-6178
10.6350
14
1.5126
.6611
1 7 . 0863
I I. 2961
16 •
1.5580
.6419
18.5989
11-9379
16
1.6047
.6232
20.1569
12.5611
17
1.6528
.6050
21 .7616
13.1661
18
1.7024
■5874
23-4144
I3-7S3S
19
1-7535
•5703
25.1169
14-3238
20
I. 8061
•5537
26.8704
14-8775
21
1.8603
■ 5375
28.6765
15-4150
22
I .9161
■ 5219
30.5368
15-9369
23
1.9736
• 5067
32.4529
16.4436
24
2.0328
.4919
34-4265
16.9325
2S
2.0938
.4776
36-4593
17-4131
26
2.1566
.4637
38.5530
17.8768
27
2.2213
• 4502
40 . 7096
18.3270
28
2.2879
• 4371
42.9309
18.7641
29
2.3566
■ 4243
45 2189
19.1885
30
2.4273
.4120
47-5754
19.6004
31
2.5001
.4000
50.0027
20.0004
32
2.5751
.3883
52.5028
20.3888
33
2.6523
• 3770
550778
20.7658
34
2.7319
.3660
57-7302
21.1318
36
2.8139
• 3554
60.4621
21.4872
36
2.8983
• 3450
63-2759
21.8323
37
2.9852
• 3350
66.1742
22.1672
38
3.0748
• 3252
69.1594
22.4925
39
3.1670
• 3158
72.2342
22.8082
40
3.2620
.3066
75-4013
23 1148
41
3.3599
.2976
78.6633
23 4124
42
3 4607
.2890
82.0232
23.7014
43
3.5645
.2805
85-4839
23.9819
44
3.6715
.2724
89.0484
24-2543
45
3.7816
• 2644
92.7199
24-5187
46
3 8950
• 2567
96.5015
24-7754
47
4.0119
• 2493
100.3965
25-0247
48
4.1323
.2420
104 .4084
25 . 2667
49
4 2562
• 2350
108 . 5406
25 5017
60
4.3839
.2281
112. 7969
25.7298
66
5.0821
.1968
136.072
26.7744
60
5-8916
.1697
163-053
27-6756
66
6.8300
.1464
194-333
28.452
70
7.9178
.1263
230.594
29.123
76
9.1789
.1089
272.630
29 . 702
80
10.6409
.0940
321.363
30.201
86
12.3357
.0811
377-857
30.701
90
14-3005
.0699
443-349
31.002
96
16.5782
.0603
S19 273
31-323
100
19.2186
.0520
607.288
31-599
106
22.2797
.0449
709.323
31-838
110
25.8282
• 0387
827.608
32.043
116
29.9420
• 0334
964 • 733
32.220
120
34-7110
.0288
1123.70
32.373
256
APPENDIX
3I PER CENT
n years.
I.
II.
III.
IV.
1
I 0350
.9662
I. 0000
.9662
2
I .0712
.9335
2.0350
I - 8997
3
I . 1087
.9019
3.1062
2.8016
4
1-1475
.8714
4-2149
3-6731
S
I. 1877
.8420
5-3625
4-5151
6
1.2293
.8135
6.5502
5 3286
7
1.2723
.7860
7-7794
6.114s
8
I. 3168
.7594
9-0517
6 . 8740
9
1.3629
• 7337
10.3685
7.6077
10
I. 4106
.7089
II -7314
8.3166
11
1.4600
.6849
13-1420
9.0016
12
1.5111
.6618
14.6020
9 6633
13
I . 5640
• 6394
16.1130
10.3027
14
I. 6187
.6178
17.6770
10.9205
15
1.6753
.5969
19-2957
11-5174
16
I -7340
-5767
20.9710
12.0941
17
I • 7947
-5572
22.7050
12.6513
18
1-8575
• 5384
24.4997
13.1897
19
1.9225
.5202
26.3572
13 - 7098
20
1.9898
.5026
28.2797
14.2124
21
2.0594
-4856
30.2695
14 . 6980
22
2.1315
.4692
32.3289
151671
23
2 . 2061
-4533
34.4604
15.6204
24
2.2833
-4380
36.6665
16.0574
25
2.3632
■4231
38.9499
16.4815
26
2 . 4460
.4088
41-3131
16.8904
27
2.5316
■3950
43-7591
17.2854
28
2.6202
-3817
46 . 2906
17.6670
29
2.7119
.3687
48.9108
18.0358
30
2 . 8068
.3563
51.6227
18.3920
31
2.9050
.3442
54-4295
' 18.7363
32
3 - 0067
.3326
57-3345
19.0689
S3
31119
.3213
60.3412
19.3902
34
3.2209
.3105
63-4532
19.7007
36
3-3336
.3000
66.6740
20 . 0007
36
3-4503
.2898
70.0076
20 . 2905
37
3-5710
.2800
73-4579
20.5705
38
3 - 6960
.2706
77.0289
20.8411
39
3.8254
.2614
80.7249
21.1025
40
3-9593
.2526
84.5503
21.35^1
41
4.0978
.2440
88.5095
21.5991
42
4 2413
.2358
92.6074
21.8349
43
4-3897
.2278
96.8487
22.0627
44
4-5433
.2201
101.2383
22.2828
46
4-7024
.2127
105.7817
22.4955
46
4.8669
.2055
110.4840
22.7009
47
5 0373
.1985
115.3510
22.8994
48
5-2136
.1918
120.3883
23.0912
49
5-3961
.1853
125.6018
23.2766
60
5.5849
.1791
130.9979
23.4556
66
6.6331
.1508
160,947
24.2641
60
7.8781
.1269
196.517
24-9447
65
9-3567
.1069
238.763
25-5168
70
1 1. 1 1 28
.0900
288.938
26.0004
76
13.1986
.0758
348.531
26.4067
80
15-6757
.0638
419.307
26.7488
86
18.6179
•0537
503.368
27.0368
90
22. 1122
■ 0452
603 . 205
27.2793
96
26.2623
.0381
721.780
27.4798
100
31-1914
.0321
862.612
27-6554
106
37-0456
.0270
1029.874
27.8002
110
43-9986
.0227
1228.53
27.9221
116
52-2565
.0191
1464.471
28.0247
120
62.0643
.0161
1744.69
28. II II
APPENDIX
257
4 PER CENT
n years.
I.
II.
III.
IV.
1
I .0400
.9615
1 .0000
961 s
S
I. 0861
.9246
2.0400
I. 8861
s
1 . 1 249
.8890
3-I2I6
2 7751
4
I . i6qq
.8548
4-2465
3-6299
6
1.2J67
.8219
S-4163
4 4518
6
1.2653
-7903
6.6330
5.2421
7
1-3159
-7599
7.8983
6.0021
8
1.3686
7307
9-2142
6.7327
9
I 4233
.7026
10.5828
7-4353
10
1.4802
.6756
12.0061
8. 1109
11
I • 5395
.6496
13-4864
8.7605
12
1.6010
.6246
150258
9-3851
13
I . 665 1
.6006
16.6268
9.9856
14
1-7315
•5775
18.2919
10.5631
15
1.8009
-5553
20.0236
II. 1184
16
1.8730
-5339
21.8245
11.6523
17
1-9479
• 5134
23-6975
12.1657
18
2.0258
• 4936
25.6454
12.6593
19
2 . 1068
-4746
27.6712
13.1339
20
2.1911
-4564
29-7781
13-5903
21
2.2788
.4388
31-9692
14.0292
22
2.3699
.4220
34 - 2480
14 4511
23
2.4647
• 4057
36-6179
14.8568
24
2.5(133
■ 390I
39- 0826
15-2470
25
2.6658
-3751
41.6459
15.6221
26
2.7725
.3607
44-3117
15.9828
27
2.8834
.3468
47.0842
16.3296
28
2.9987
■ 3335
49-9676
16.6631
29
3.1187
-3207
52.9663
16.9837
30
3-2434
.3083
56.0849
17.2920
31
33731
.2965
59 3283
17-5885
32
3 ■ 5081
.2851
62.7015
17.8736
33
3.6484
.2741
66.2095
18.1476
34
3-7943
.2636
69.8579
18.4112
3S
3-9461
.2534
73.6522
18.6646
36
4- 1039
■2437
77.5983
18.9083
37
4.2681
•2343
81.7022
19.1426
38
4 4388
•2253
85 - 7903
19.3679
39
4.6164
.2166
90.4091
19-5845
40
4 . 8010
.2083
95-0255
19.7928
41
4-9931
.2003
99.8265
19.9931
42
5.1928
.1926
104.8200
20. 1856
43
5 4005
-1852
110.0124
20.3708
44
5-6165
.1780
115.4129
20.5488
46
5.8412
.1712
121.0294
20.7200
46
6.0748
.1646
126.8706
20.8847
47
6.3178
-1583
132.9454
21 .0429
48
6.570s
.1522
139.2632
21.1951
49
6.8333
.1463
145-8337
21.3415
50
7.1067
.1407
152.6671
21.4822
55
8.6464
•I157
191.159
22.1086
60
10.5196
-0951
237.991
22.6235
65
12.7987
.0781
294.967
23 . 0466
70
15-5716
.0642
364.290
23-3945
75
18.9453
.0528
448.642
23.6281
80
23.0498
-0434
551-245
23-9154
85
28 . 0436
•0357
676.090
24.1085
90
34-1193
.0293
827.983
24.2673
95
41-5114
.0241
1012.785
24-3977
100
50.5049
.0198
1237.622
24-5050
106
61 .4470
.0163
1511-175
24-5931
110
74-7597
•0134 •
1843.992
24 . 6656
116
90.9566
.0110
2248. 91S
24-7251
lao
110.663
.0090
2741-558
24.7741
258
APPENDIX
4| PER CENT
n years.
I.
II.
III.
IV.
1
I . 0450
.9569
I. 0000
.9569
2
1.0920
• 9157
2.0450
1.8727
3
1.1412
.8765
3 •1370
2 . 7490
4
1-1925
.8386
4.2782
3.587s
6
1.2462
.8022
5-4707
4.3900
6
1.3023
.7679
6.7169
5.1579
7
1.3609
.7348
8.0192
5-8927
8
I. 4221
.7032
9-3800
6-5959
9
I. 4861
.6729
10.8021
7 . 2688
10
I -5530
• 6439
12.2882
7-9125
11
1.6229
.6162
13 • 841 2
8.5289
12
1.6959
.4897
15-4640
9.1186
13
1.7722
■ 5643
17-1599
9.6829
14
I. 8519
.5400
18.9321
10.2229
16
1-9353
• 5167
20.7841
10.7395
16
2.0224
• 4945
22.7193
I I . 2340
17
2-I134
■ 4732
24.7417
11.7072
18
2 . 2085
.4528
26.8551
12.1600
19
2.3079
■ 4333
29.0634
12.5933
20
2.4117
.4146
3i^37i6
13.0079
21
2.5202
.3968
33 •7831
13-4047
22
2.6337
•3797
36.3034
13.7844
23
2.7522
-3634
38.9370
14.1478
24
2 . 8760
-3477
41.6892
14.495s
25
3-0054
.3327
44.5652
14.8282
26
3-1407
.3184
47.5706
15.1466
27
3.2820
•3047
50.7113
15.4513
28
34279
.2916
53-9933
15.7429
29
3 • 5840
•2790
57-4230
16.0219
30
3-7453
.2670
61.0071
16.2889
31
3-9139
•2555
64.7524
16.5444
32
4.0900
•2445
68.6662
16.7889
33
4.2740
• 2340
72.7562
17.0229
34
4 . 4664
• 2239
77 0303
17.2468
36
4.6673
.2143
81.4966
17.4610
36
4-8774
.2050
86.1640
17.6660
37
5.0969
.1962
91.0413
17.8622
38
5-3262
.1878
96.1382
18.0500
39
5-5659
.1797
loi .4644
18.2297
40
5.8164
.1719
107.0303
18.4016
41
6.0781
.1645
112. 8467
18.5661
42
6.3516
•1574
118.9248
18.723s
43
6.6374
• 1507
125.2764
18.8742
44
6.9361
.1442
131. 9138
19.0184
46
7.2482
.1380
138.8500
19-1563
46
7-5744
.1320
146.0982
19.2884
47
7-9153
.1263
153.6726
19.4147
48
8.2715
. 1209
161.5879
19.5356
49
8.6437
•I157
169.8594
19.6513
60
9-0326
.1107
178.5030
19.7620
65
11.2563
.0888
227.9180
20.2480
60
14.0274
• 0713
289.4980
20.6380
66
17.4807
-0572
366.2380
20.9509
70
21 .7841
-0459
461.8700
21.2021
76
27.1470
• 0368
581.2670
21 .4118
80
33-8301
.0296
729.5580
21.5653
86
42.1585
•0237
914.6330
21.6951
90
52-5371
.0190
1145.2700
21.7992
96
65.4708
•0153
1432.6840
21.8828
100
81.5885
.0123
1790.8600
21.9499
105
101.674
.0098
2237.2000
22.0036
110
126.704
.0079
2793.4300
22.0468
116
157-807
• 0063
3486 . 6000
22.0815
120
196.768
.0051
4350.4000
22.1093
APPENDIX
259
S PER CENT
n years.
I.
11.
III.
IV.
1
1.0500
•9524
I .0000
9524
S
i.iois
.9070
2.0500
1-8594
s
I. 1576
.8638
31525
2.7232
4
I-2ISS
.8227
4-3101
3.5460
S
1.2763
-7835
5-5256
4 329s
6
1.3401
.7462
6.8019
5.0757
7
I. 4071
.7107
8. 1420
5. 7864
8
1-4775
.6768
9-5491
6.4632
9
1.5513
.6446
11.0266
7.1078
10
1.0289
•6139
12.5779
7-7217
11
I. 7103
-5847
14.2068
8.3064
12
I. 7959
-5568
15.9171
8.8623
IS
1.8856
.5303
17.7130
9 3936
14
1.9799
.5051
19.5986
9 8986
16
2.0789
.4810
21.5786
10.3797
16
2.1829
-4581
23-6575
10.8378
17
2.2920
-4363
25-8404
11.2741
18
2 . 4066
.4155
28.1324
1 1 . 6896
19
2.5270
• 3957
30.5390
12.0853
20
2-6533
•3769
33.0660
12.4622
21
2 . 7860
• 3589
35-7193
12.8212
22
2 9253
.3418
38-5052
13 -1630
23
3-0715
.3256
41.4305
13-4886
24
3-2251
.3101
44.5020
13 - 7986
26
3.3864
.2953
47.7271
14.0939
26
3.5557
.2812
51-1135
14-3752
27
3-7335
.2678
54.6691
14.6430
28
3.9201
-2551
58.4026
14.8981
29
4.1161
.2429
62.3227
15-1411
30
4.3219
.2314
66.4388
15-3725
31
4-5380
.2204
70.7608
. 15-5928
32
4.7649
.2099
75.2988
15.8027
33
5-0032
.1999
80.0638
16.0025
34
5-2533
■1904
85.0670
16.1929
36
5-5160
.1813
90.3203
16.3742
36
5-7918
.1727
95 . 8363
16.5469
37
6.0814
.1644
lOI .6281
16.7113
38
6.3855
.1566
107.7095
16.8679
39
6 . 7048
.1491
114.0950
17.0170
40
7.0400
.1420
120.7998
17-1591
41
7-3920
• 1353
127.8398
17.2944
42
7.7616
.1288
135-2318
17.4232
43
8.1497
.1227
142.9933
17-5459
44
8-5572
.1169
151-1430
17.6628
46
8-9850
.1113
139.7002
17-7741
46
9-4343
.1060
168.6852
17-8801
47
9.9060
.1009
178.1194
17.9810
48
10.4013
.0961
188.0254
18.0772
49
10.9213
.0916
198.4267
18.1687
60
11.4674
.0872
209.3480
18.2559
66
14-6356
.0683
272.7130
18-6335
60
18.6792
.0535
353-5840
18.9293
66
23-8399
.0419
456.7980
19.1191
70
30.4264
.0329
588.5290
19-3427
76
38.8327
• 0257
756.6540
19.4849
80
49.5614
.0202
971.2290
19.5965
86
63 . 2544
.0158
1245.0880
19.6838
90
80.7304
.0124
1594. 6100
19 7523
96
103.035
• 0097
2040 . 7000
19-8058
100
131.501
.0076
2610.0300
19.8479
106
167.833
.0060
3336.6600
19.8808
110
214.202
.0047
4264.0300
19.9066
116
273.382
-0037
5447.6400
19.9268
120
348-912
.0029
6958.2400
19.9427
26o
APPENDIX
Sh PER CENT
« years.
I.
II.
III.
IV.
1
I -0550
-9479
I. 0000
-9479
2
I. I 130
-8985
2.0550
1-8463
3
1-1742
.8516
3.1680
2.6979
4
I . 2388
.8072
4-3423
3-5052
6
1.3070
-7651
5-5811
4-2703
6
1.3788
.7252
6.8881
4-9955
7
1-4547
.6854
8.2669
5-6830
8
I -5347
.6516
9.7216
6.3346
9
1.6191
.6176
11-2563
6.9522
10
I. 7081
-5854
12.8754
7-5376
11
I. 8021
-5549
14-5835
8.0925
12
I .goi2
.5260
16.3856
8.6185
13
2.0058
.4986
18.2868
9.1171
14
2.1161
• 4726
20.2926
9-5896
16
2.232s
.4479
22.4087
10.0376
16
2-3553
.4246
24.6411
10.4622
I"
2.4848
.4024
26.9964
10.8646
18
2.6215
-3815
29.4812
11.2461
19
2.7656
-3616
32.1027
11.6077
20
2.9178
-3427
34-8683
11.9504
21
3-0782
• 3249
37-7861
12.2752
22
3-2275
■ 3079
40 . 8643
12.5832
23
3.4262
.2919
44. I I 18
12.8750
24
3.6146
.2767
47-5380
13-1517
25
3-8134
.2622
51-1526
13-4139
26
4-0231
.2486
54.9660
13-6625
27
4 • 2444
-2356
58.9891
13-8981
28
4-4778
-2233
63 -2335
14.1214
29
4.7241
.2117
67.7114
14-3331
30
4.9840
.2006
71-4355
14-5337
31
5-2581
.1902
77-4194
14-7239
32
5-5473
.1803
82.6775
14.9042
33
S-8524
.1709
88.2248
15-0751
34
6.1742
.1620
94.0771
15-2370
36
6.S138
• 1535
100.2514
IS -3906
36
6.8721
-I4SS
106.7652
15-5361
37
7-2501
• 1379
113-6373
15-6740
38
7.6488
• 1307
120.8873
15.8047
39
8.0695
-1239
128.5361
15-9287
40
&-5133
-II7S
136.6056
16.0461
41
8.9815
-1113
145.1189
16.1575
42
9-4755
-1055
154.1005
16.2630
43
9 . 9967
.1000
163.5760
16.3630
44
10.5465
.0948
173-5727
16.4579
46
1 1. 1 266
.0899
184.1192
16.5477
46
11.7385
.0852
195-2457
16.6329
47
12.3841
.0807
206.9842
16.7137
48
13 0653
-0765
219.3684
16.7902
49
13-7838
.0725
232.4336
16.8628
60
14-5420
.0688
246.217s
16.9315
66
19.0046
.0526
327 3563
17-2251
60
24.8381
.0403
433-4200
17.4498
66
32.4623
.0308
572.0364
17.6216
70
43-4150
.0230
771.1818
17-7630
76
56.7414
.0176
1,013.4800
17.8614
80
72.4703
.0138
1,299.4600
17.9309
86
94-7152
.0106
1,703.9127
17.9898
90
123-7883
.0081
2,232.5145
18.0349
95
161.7855
.0062
2,923.3727
1 8 . 0694
100
211.4463
.0047
3,826.2963
18.0958
106
276.3503
.0036
5,006.3691
18.1160
110
361.2768
.0028
6,550.4873
18.1315
116
472.0413
.0021
8,564-3873
18.1433
120
616.9357
.0016
11,198.8309
18.1523
APPENDIX
2f)I
6 PER CENT
n years.
I.
II.
III.
IV.
1
i.oOoo
.9434
1. 0000
•9434
2
1.1230
.8900
2.0600
1.8334
3
I.I9IO
.8396
3.1836
2.6730
4
1.2025
.7921
43746
3.4651
6
1.3382
.7473
5.6371
4.2124
6
1.4185
.7050
6.9753
4.9173
7
I • 503O
.6051
8.3938
5.5824
8
I ■ 5938
.6274
9.8975
6 . 2098
9
1.689s
.5919
I I. 4913
6.8017
10
I . 7908
.5584
13.1808
7.3601
11
I . 8983
.5268
14.9716
7 . 8869
12
2.0122
.4970
10.8099
8.3838
13
2.1329
.4688
18.8821
8.8527
14
2.2609
• 4423
21 .0151
9.2950
IS
2.3966
.4173
23.2760
9.7122
16
2 . 5404
.3936
25.6725
10. 1059
17
2.6928
.3714
28.2129
10.4772
18
2 . 8543
• 3503
30.9057
10.8276
19
3.0256
.3305
33.7600
11.1581
ao
3.2071
.3118
36.7856
1 1 . 4699
21
3.3906
.2942
39.9927
11.7641
22
3.6035
.2775
43 3923
12.0416
33
3.8197
.2618
46.9958
12.3034
24
4.0489
.2470
50,8156
12.5504
2S
4.2919
• 2330
54.864s
12.7834
26
4 • 5494
.2198
59.1564
13.0032
27
4.8223
.2074
63 . 705 8
13.2105
28
5.1117
.1956
68.5281
13.4062
29
5.4184
.1846
73.6398
13.5907
30
5.7435
.1741
79.0582
13.7648
31
6.0881
.1643
84.8017
13.9291
32
6.4534
.1550
90.8898
14.0840
S3
6.8406
.1462
97.3432
14.2302
34
7.2510
■ 1379
104.1838
14.3681
36
7.6861
.1301
III. 4348
14.4982
36
8.1473
.1227
119. 1209
14.6210
37
8.6361
.1158
127.2681
14.7368
38
9.1543
.1092
135.9042
14.8460
39
9.703s
.1031
145.0585
14.9491
40
10.2857
.0972
154.7620
15.0463
41
10.9029
.0917
165.0477
151380
42
11.5570
.0865
175.9505
15.2245
43
12.2505
.0816
187.5076
IS 3062
44
12.9855
.0770
199.7580
15.3832
46
13.7646
.0727
212.7435
15.4558
46
14.5905 ■
.0685
226.5081
15 5244
47
15.4659
.0647
241.0985
IS 5890
48
16.3939
.0610
256.564s
15.6500
49
17.3775
■ 0575
272.9584
15.7076
60
18.4202
• 0543
290.3359
15.7619
66
24.6507
.0406
394.1783
15.9905
60
32.9883
■ 0303
533.1383
16. 1611
66
44.1458
.0226
719.0966
16.2891
70
59.0772
.0169
967.9533
16.3845
76
79.0587
.0126
1.300.9783
16.4558
80
105.7985
.0095
1,746.6416
16.5091
86
141.5287
.0071
2,343.0450
16.5489
90
189.4698
.0053
3,141.1633
16.5787
96
253.5538
.0039
4,209.2300
16.6009
100
339-3125
.0029
5,638.5416
16.6175
106
454.0770
.0022
7.SSI.2833
16.6299
110
607.6591
.0016
10,110.9850
16.6392
116
813.1867
.0012
13.536.44.SO
16.6461
120
1088.2280
.OOOQ
18,120.4667
16.6513
262
APPENDIX
7 PER CENT
n years.
I.
II.
III.
IV.
1
1.07CX)
• 9346
I .0000
.9328
2
I . 1449
.8736
2.0700
1.8043
3
1.2250
.8163
3.2142
2.6228
4
1.3108
.7629
4.4400
3.3857
6
1.4026
■ 7130
5.7514
4 . 0986
6
1.5007
.6663
7.3529
4.7657
7
1.6058
.6227
8.6542
5. 3886
8
I. 7182
.5820
10. 2600
5.9700
9
1.8385
• 5439
11.9786
6.5143
10
I. 9671
.5083
13.8159
7.0228
11
2 . 1049
• 4751
15.7843
7.4971
13
2.2522
.4440
17.8886
7.9414
13
2.4098
• 4150
20. 1400
8.3557
14
2.5785
.3878
22.5500
8.7442
16
2.7590
.3624
25.1286
9.1071
16
2.9522
.3387
27.8886
9.4457
17
3.1588
.3161
30.8400
9.7686
IS
3.3800
.2959
34.0000
10.0571
19
3.6165
.2765
37.3786
10.3343
20
3.8697
.2584
40.9528
10.5928
21
4.1406
•241S
44.8657
10.8343
22
4.4304
.2257
49.0057
I I . 0600
23
4 7405
.2109
S3. 4343
II. 2714
24
5.0724
.1971
55 3200
I I . 4685
26
5.4275
.1842
63 . 2500
11.6528
26
5.8075
.1722
68.6786
11.8242
27
6.2140
.1609
74.4857
11.9857
28
6 . 6490
.1504
80.7000
12.1357
29
7.1144
.1406
87.3346
12.2757
30
7.6124
-1314
94.4628
12.4071
31
8.1452
.1228
102.0742
12.5300
32
8.7154
.1147
110.2700
12.6457
33
93255
.1072
118.9500
12.7528
34
9.9783
. 1002
128.2618
12.8528
36
10.6768
.0937
138.2400
12.9457
36
II. 4241
.0875
148.9157
13.0343
37
12.2239
.0818
160.3414
13.1157
38
13.0795
.0765
172.5642
13.1914
39
13.9950
.0715
185.6428
13.2628
40
14.9747
.0668
199.6386
13.3300
41
16.0230
.0624
214.6143
13.3928
42
17.1446
.0583
230.6371
13.4514
43
18.3448
.0545
247.7828
13.5057
44
19.6290
.0509
266.1428
13.5571
46
2 1 . 0030
.0476
285.7571
13.6043
46
22.4332
.0445
306.1886
13.6485
47
24.0463
.0416
329.2328
13.6900
48
25.7888
.0387
354.1257
13.7314
49
27.5306
.0363
379.0086
13 7657
60
29.4577
.0339
406.5386
13.8000
66
41.3162
.0242
575.9458
13.9385
60
57.9482
.0173
813.5458
14.0371
66
81.2755
.0123
1,146.7928
14.1085
70
113.9929
.0088
1,614. 1844
14.1585
76
159.8823
.0062
2,141.1757
14.1959
80
224.2440
.0045
2,269.7471
14.2200
86
314.5138
.0032
3,160.6285
14.2385
90
441.1230
.0023
4,478.7682
14.2514
96
618.7000
.0016
6,287.4714
14.2614
100
867 . 7600
.0011
8,824.2857
14.2685
106
1 217.0812
.0008
12,382.2855
14.2728
110
1707.023s
.0006
17,372.5886
14.2757
116
2394.1978
.0004
24,371.7642
14.2785
120
3357.9923
.0003
34,188.5400
14.2800
APPENDIX
263
8 PER CENT
n years.
I.
II.
III.
I .0000
IV.
1
1.0800
-9259
.9250
a
I . 1664
.8573
2.0800
1.782s
s
I 2597
-7938
3 ■ 2463
2.5762
4
iit>o5
•7350
4-S062
3-3112
6
I . 46Q3
.6806
5-8366
3-9912
6
1.5869
• 6302
7 3362
4.6212
7
I. 7138
.5840
8.9225
5-1987
8
1.8509
-5403
10.6363
5-7450
9
1 9990
.5002
12-4875
6.2462
10
2.1589
.4632
14.4862
6.7087
11
2.3317
.4289
16.6463
7-1375
13
2.5182
.3971
18.9775
7 5350
IS
2.7196
.3676
21.4950
7 9037
14
2.9372
-340s
24.2150
8.2425
IS
31722
-3152
271525
8.5587
16
3 4200
.2919
30-3250
8.8513
17
3 7000
•2703
33-7500
9.1200
18
3 • 9960
.2502
37-4500
9-3712
19
4 3157
•2317
41.4463
9-6025
SO
4.6610
.2145
45-7625
9-8175
21
5 0339
.1987
50-4237
10.0150
S2
5 4366
.1839
55-4575
10.2000
as
5.8716
-1703
60. .8950
10.3700
24
6.3413
■1577
66.7663
10.5275
as
6.8486
.1460
73 1075
10.6737
as
7 3964
-1352
79.9800
10.8087
a7
7.9882
.1252
87.3525
10.9337
as
8.6272
-1159
95-3400
11 .0500
a9
9-3174
-1073
103-9675
11.1575
so
10.0629
-0994
113.2862
11.2562
SI
10.8678
.0920
123.3475
"•3487
sa
II-737I
.0S52
134-2138
11-4337
ss
12.6763
.0789
145-9537
11-5125
S4
13.6904
.0730
158.6300
11.5862
ss
14 7853
.0676
172.3163
11.6537
S6
15.9684
.0626
187.1050
II .7162
S7
1 7 . 2460
.0580
203.0750
11-7737
38
18.6249
-0537
220.3113
11.8275
S9
20.1159
.0497
238.9488
11-8775
40
21.7250
.0460
259.0625
11-9237
41
23 4630
.0426
280.7875
1 1 . 9662
42
25.3400
•0395
304.2500
1 2 . 0050
4S
27.3672
•0365
329.5900
12.0425
44
29 5567
•0338
356.9588
12.0762
4S
31.9213
-0313
386.5163
12.1075
46
344750
.0290
418.4375
12.1362
47
37.2330
.0269
452.9125
12.1625
48
40.2117
.0249
490.1463
12.1875
49
43 4207
.0230
530.2588
12.2112
60
46.9029
.0213
573 7863
12.2325
66
68.9160
-0145
848.9500
12.3175
60
loi . 2605
.0099
1,253-2563
12.3750
66
148.7849
.0067
1,847-3113
12.4150
70
218.6150
.0046
2,720.1875
12.4412
76
321.2177
.0031
4,002.7213
12.4600
80
471.9761
.0021
5,887.2013
12.4725
86
693.4888
.0014
8,656.1100
12.4812
90
1,018.9649
.0010
12,724.5613
12.4862
96
1,497 1993
.0007
18,702.4913
1 2 . 4900
100
2,199.8838
.0005
27,486.0475
12.492s
106
3,232.3656
.0003
40,392.0700
12.4950
110
4,749-4130
.0002
59,355.1625
12.4962
116
6,978.4677
.0001
87.218.3463
12-4975
120
10.253.6792
.0001
128,158.4900
1 2 . 4989
264
APPENDIX
10 PER CENT
n years.
I.
II.
III.
IV.
1
I. 1000
.9091
I. 0000
0.908
2
I . 2100
.8264
2.1000
1-735
3
I-33IO
.7513
3.3100
2.486
4
I. 4641
.6830
4.6410
3.169
6
1.610S
.6200
6. 1050
3.790
6
I. 7716
•564s
7.7160
4.354
7
1.9487
.5132
9.4870
4.867
8
2.1436
.4665
11.4360
5-334
9
2.3580
.4241
13.5800
5-758
10
2.5938
•385s
15.9380
6.144
11
2.8531
.3505
18.5310
6.494
12
3.138s
.3186
21.3850
6.813
13
3.4523
.2897
24.5230
7.102
14
3.7976
.2633
27.9760
7.366
15
4.1773
.2394
31.7730
7.605
16
4.5950
.2176
35 9500
7 823
17
5. 0545
.1978
40.5450
8.021
18
5 5600
.1799
45 . 6000
8.200
19
6. I 160
•1635
51.1600
8.364
20
6.7276
.i486
57.2760
8.513
21
7.4004
■1351
64 . 0040
8.648
22
8.1404
.1228
71.4040
8.771
23
8.9545
.1117
79.5450
8.882
24
9.8500
.1015
88.5000
8.984
25
10.8349
.0923
98.3490
9.076
26
II. 9184
.0839
109.1840
9.160
27
13. I 103
•0763
121. 1030
9.236
28
14.4213
.0693
134.2130
9.306
29
15-8634
.0630
148.6340
9-369
30
17.4498
•0573
164.4980
9.426
31
19.1948
.0521
181.9480
9.478
32
21.1143
.0474
201.1430
9-525
33
23.2257
.0431
222.2570
9-568
34
25.5483
.0391
245.4830
9.608
35
28.1032
■0356
271.0320
9-643
36
30.9135
.0324
299.1350
9 675
37
34.0049
.0294
330.0490
9-705
38
37.4054
.0273
364.0540
9.726
39
41.1460
• 0243
401.4600
9.756
40
45.2605
.0221
442 . 6050
9.778
41
49.7866
.0201
487 . 8660
9-798
42
54.7655
.0183
537.6550
9.816
43
60.2420
.0166
592.4200
9-833
44
66.2662
.0151
652.6620
9-848
45
72.8928
.0137
718.9280
9.862
46
80.1822
.0125
791.8220
• 9 . 874
47
88.2004
.0113
872.0040
9.886
48
97 0207
.0103
960.2070
9.896
49
106.7228
.0094
1,057.2280
9.905
60
117.3926
.0085
1)163.9260
9.914
66
189.0668
.0053
1,880.6680
9.946
60
304.4944
.0033
3,034.9440
9.966
66
490.3932
.0020
4,893.9320
9.979
70
789.7876
.0013
7,887.8760
9.986
76
1,271.9648
.0008
12,709.6480
9.991
80
2,048.5188
.0005
20,475.1880
9.994
86
3,299.1742
.0003
32,981.7420
9.996
90
5.313.3659
.0002
53,123.6590
9.997
96
8,557.2549
.0001
85,562.5490
9.998
100
13,781.6139
.00007
137,806.1390
9.9992
106
22,195.5102
.00005
221,945.1020
9.9994
110
35,746.1983
.00003
357,451.98,50
9.9996
116
57,569.8666
.00002
575,688.6660
9.9997
120
92,717.0213
.00001 1
927,160.2130
9.9998
TABLE Vn.— LOGARITHMS OF NUMBERS.
N.
0
X
a
3
4
5
6
7
8
9
Diff.
too
000000
0434
0868
1301
1734
2166
2598
3029
34t>t
3S91
''32
lOI
432 J
4751
51S1
5^
6038
6466
6894
7321
7748
8174
428
103
8600
9026
9451
9876 <
0300
►0724
•1147
•1570
•1993
•2415
424
103
012837
3259 3680 1
4100
4521
4940
53f«
5779
6197
6616
420
104
7033
021 1S9
7451
7868
8284
8700
91 16
9532
9947
♦0361
•0775
416
xos
1603
2016
2428
2841
3252
3664
4075
4486
4846
^'l
loS
5306
5715
6125
6533
»o6oo '
6942
7350
7757
8164
8571
•2619
8978
408
13
93S4
97^
►0195 "
'1004
»I408
•1812
•2216
•3021
404
033424
3S26
4227
462S
5029
5430
5830
6230
6629
7028
400
X09
7426
7825
8223
8620
9017
9414
981 1
•0207
•0602
•0998
397
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
434
43
87
130
174
217
260
304
347
391
434
433
43
87
130
173
217
260
303
346
390
433
43»
43
86
130
173
216
259
302
346
389
43a
431
43
86
129
172
216
259
302
345
388
431
430
43
86
129
172
215
258
301
344
387
430
429
43
86
III
172
215
257
300
343
386
St
428
43
86
171
214
257
300
342
3^5
427
43
85
128
171
214
256
299
342
384
437
%6
43
85
128
170
213
256
298
341
383
436
425
43
85
128
170
213
255
298
340
3^3
425
424
42
85
127
170
212
254
297
339
382
424
423
42
85
127
169
212
254
296
33^
381
423
422
42
84
127
211
253
295
338
380
42a
421
42
84
126
168
211
253
295
337
379
421
420
42
84
126
168
210
252
294
336
378
430
03
:ii
42
84
126
168
210
251
293
335
377
419
H
42
84
125
167
209
251
293
334
376
418
<
0.
417
42
83
125
167
250
292
334
375
^'l
416
42
83
125
166
250
291
333
374
416
415
42
83
125
166
208
249
291
332
374
415
J
414
41
83
124
166
207
248
290
331
373
414
<
413
41
83
124
165
207
248
=^
330
372
413
z
412
41
82
124
165
206
247
288
330
371
412
0
411
41
82
123
164
206
247
288
329
370
411
(1
410
41
82
123
164
205
246
287
328
369
410
X
409
41
82
123
164
205
245
286
327
368
Si
0
408
41
82
122
163
204
245
286
326
367
a,
407
41
81
122
163
204
244
285
326
366
407
0
406
41
81
122
162
203
244
284
325
365
406
405
41
81
122
162
203
243
284
324
365
405
404
40
81
121
162
202
242
283
323
364
404
403
40
81
121
161
202
242
282
322
363
403
402
40
80
121
161
201
241
281
322
362
403
401
40
80
120
160
201
241
281
321
361
401
400
40
80
120
160
200
240
280
320
360
400
398
40
80
120
160
200
239
279
319
359
lU
40
80
119
159
199
239
279
318
358
397
40
79
119
159
199
238
278
3«8
357
397
396
40
79
119
158
198
238
277
317
356
396
395
40
79
119
158
198
237
277
316
356
395
394
39
79
118
158
197
236
276
3>5
355
394
393
39
79
118
157
197
236
275
314
354
393
393
39
78
118
157
196
235
274
3>4
353
39a
391
39
78
117
156
196
235
274
313
352
39»
390
39
78
117
156
195
234
273
312
351
390
389
39
78
117
156
195
233
272
3"
350
iii
388
39
78
116
155
194
233
272
310
349
Diff.
I
2
3
4
1 ^
6
1 ^
8
9 Diff.
265
TABLE
VII.—
LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff
no
041393
1787
2182
2576
2969
3362
3755
4148
4540
4932
393
III
5323
^n
6105
6495
6885
7275
7664
8053
8442
8830
390
1X3
9218
9606
9993
♦0380
*0766
*ii53
*I538
♦1924
♦2309
♦2694
386
"3
053078
'^^^i
3846
4230
4613
4996
5378
5760
6142
6524
383
114
6905
7286
7666
8046
8426
8805
9185
9563
9942
*0320
379
"5
060698
1075
1452
1829
2206
2582
2958
3333
3709
4083
376
116
4458
4832
5206
5580
5953
6326
6699
7071
7443
7815
373
"7
8186
8557
8928
9298
9668
♦0038
*0407
*0776
*ii45
*I5I4
370
X18
071882
2250
2617
2985
3352
3718
4085
4451
4816
5182
366
119
5547
5912
6276
6640
7004
7368
7731
8094
8457
8819
363
120
0791S1
9543
9904
*0266
♦0626
■"=0987
*I347
*I707
*2o67
*2426
360
121
082785
3144
3503
3861
4219
4576
4934
5291
5647
6004
357
122
6360
6716
7071
7426
7781
8136
8490
8845
9198
9552
355
123
9905
*0258
*o6ii
♦0963
*I3I5
*l667
*20l8
♦2370
*272I
*307X
352
124
093422
3772
4122
4471
4820
5169
5518
5866
6215
6562
349
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
387
39
77
116
155
194
232
271
310
348
387
386
39
77
116
154
193
232
270
347
386
afs
39
77
116
154
193
231
270
308
347
385
384
38
77
"5
154
192
230
269
307
346
384
383
3f
77
115
153
192
230
26S
306
345
383
382
38
76
"5
153
191
229
267
306
344
382
38'
3^
76
114
152
191
229
267
305
343
381
380
38
76
114
152
190
228
266
304
342
380
379
3f
76
114
152
190
227
265
303
341
379
378
38
76
"3
151
189
227
265
302
340
378
377
38
75
113
151
189
226
264
302
339
377
376
38
75
"3
150
188
226
263
301
338
376
375
38
75
113
150
188
225
263
300
338
375
CO
H
374
37
75
112
150
187
224
262
299
337
374
373
37
75
112
149
187
224
261
298
336
373
<
372
37
74
112
149
186
223
260
298
335
37a
0,
371
37
74
III
148
186
223
260
297
334
371
370
37
74
III
148
185
222
259
296
333
370
<
z
0
3^
37
74
III
148
185
221
258
295
332
369
368
37
74
no
147
184
221
258
294
331
368
367
37
73
no
147
184
220
257
294
330
367
366
37
73
no
146
183
220
256
293
329
366
H
365
37
73
no
146
183
219
256
292
329
365
0
b
0
364
36
73
109
146
182
218
255
29X
328
364
363
3^
73
109
145
182
218
254
290
327
363
362
3f
72
109
145
181
217
253
290
326
362
OS
361
36
72
108
144
181
217
253
289
325
361
0.
360
36
72
108
144
180
2X6
252
288
324
360
359
36
72
108
144
180
215
251
287
323
359
358
3f
72
107
143
179
215
251
286
322
358
357
36
71
107
143
179
214
250
286
321
357
356
3^
71
107
142
178
214
249
285
320
356
355
36
71
107
142
178
213
249
284
320
355
354
35
71
106
142
177
212
248
2S3
319
354
353
35
71
106
141
177
212
247
282
318
353
353
35
70
106
141
176
211
246
282
317
35a
351
35
70
105
140
176
211
246
28 X
3X6
351
350
35
70
105
140
175
2X0
245
280
315
350
349
35
70
105
140
175
209
244
279
314
349
348
35
70
104
139
174
l^
244
278
313
348
347
35
69
104
139
174
243
27a
312
347
Diff.
I
2
3
4
5
6
7
8
9
Diff.
266
TABLE VU— LOGARITHMS OP NUMBERS.
N.
0
I
3
3
4
5
6
7
8
9 iDlflf.
096910
7257
7604
7951
H298
8644
8990
9335
9681
•0026 1 346 I
10037 1
07 '5
1059
1403
4828
1747
2091
2434
2777
3n9
6531
3462
6871
343
137
ia8
3804
4146
44S7
§'^
55"o
8903
5851
6191
341
7210
7549
7888
8227
8565
9241
9579
9916
*o253
338
"9
I 10590
0926
1263
1599
1934
2270
2605
2940
327s
3609
335
130
"3943
4277
461 1
4944
5278
5611
8926
5943
6276
6608
^6940 1 333 1
131
7271
7603
7934
8265
8595
9256
9586
2871
99'5
3198
•0245
330
132
120574
0903
4178
1 231
1560
1888
2216
'^
3525
328
133
3>*52
4504
4830
5156
5481
8722
6131
6456
6781
325
134
7105
7429
7753
8076
8399
9045
2260
9368
9690
•0012
323
IP
130334
0655
0977
1298
1619
1939
2580
2900
3219
321
3539
3858
4177
4496
7671
4814
5'33
§551
5769
6086
6403
3«8
137
6721
7037
7354
7987
8303
8618
8934
9249
9564
316
138
9879
*oi94
•0508
•0822
♦1136
*I450
•1763
•2076
•2389
•2702
314
139
1430 I 5
3327
3639
3951
4263
4574
4885
5196
5507
5818
311
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
347
35
69
104
139
174
208
243
278
312
347
346
35
69
104
138
173
208
242
277
311
346
345
35
69
104
'3|
173
207
242
276
3"
345
344
34
69
103
138
172
206
241
275
310
344
343
34
69
103
137
172
206
240
274
309
343
34a
34
68
103
137
171
205
239
274
308
342
341
34
68
102
136
171
205
239
273
307
341
3140
34
68
102
136
170
204
238
272
306
340
ill
34
68
102
136
170
203
237
271
305
IP
34
68
101
135
169
203
237
270
304
337
34
67
lOI
135
169
202
236
270
303
337
336
34
f7
lOI
134
168
202
235
269
302
336
09
335
34
^7
lOI
134
168
201
235
268
302
335
(-■
334
33
67
100
134
167
200
234
267
301
334
OS
333
33
^l
100
133
167
200
233
266
300
333
<
332
33
66
100
133
166
199
232
266
299
33a
0.
331
33
66
99
132
166
199
232
265
■ 298
331
<
330
33
66
99
132
165
198
231
264
297
330
329
33
66
99
132
165
197
230
263
296
329
z
328
33
66
98
131
164
197
230
262
295
328
0
327
33
65
98
131
164
196
229
262
294
327
326
33
65
98
130
163
196
228
261
293
326
325
33
^5
98
130
163
195
228
260
293
325
0
324
32
65
97
130
162
194
227
259
292
324
0.
323
32
65
97
129
162
194
226
*5!
291
323
0
322
32
64
97
129
161
193
225
258
290
323
K
321
32
64
96
128
161
193
225
257
289
331
0.
320
32
64
96
128
160
192
224
256
288
330
31Q
318
32
64
96
128
160
191
223
255
287
319
318
32
64
95
127
159
191
223
254
286
317
32
63
95
127
159
190
222
254
285
317
316
32
63
95
126
158
221
253
284
316
315
32
63
95
126
158
221
252
284
315
3»4
31
63
94
126
157
188
220
251
283
314
313
31
63
94
125
157
188
219
250
282
313
313
31
62
94
125
156
187
218
250
281
313
311
31
62
93
124
156
'^7
218
249
280
3"
3x0
31
62
93
124
155
186
217
248
279
310
^
31
62
93
124
155
185
216
247
278
13
.31
62
92
123
154
185
216
246
277
307
31
61
92
123
154
184
215
246
276
307
Diff.
I
2
3
4
5
6
7
8
9 Diffj
267
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
309
140
I46I28
6438
6748
7058
7367
7676
7985
8294
8603
891 1
141
9^^2
9527
9835
*0142
*0449
*0756
*io63
*i37o
*i676
*I9S2
307
142
152288
2594
2900
3205
3510
3S15
4120
4424
4728
5032
305
143
5336
5640
5943
6246
6549
6S52
7154
7457
7759
8061
3°3
144
8362
8664
8965
9266
9567
9868
*oi68
♦0469
*0769
*lo68
301
145
16136S
1667
1967
2266
2564
2S63
3161
3460
3758
4055
299
146
4353
4650
4947
5244
5541
5838
6134
6430
6726
7022
297
"•2
7317
7613
7908
8203
8497
8792
9086
9380
9674
9968
295
148
170262
0555
0848
II4I
1434
1726
2019
2311
2603
2895
293
149
31S6
3478
3769
4060
4351
4641
4932
5222
5512
5802
291
150
I 7609 I
6381
6670
6959
7248
7536
7825
8113
8401
86S9
289
151
8977
9264
9552
9839
*OI26
*04i3
*o699
♦0986
♦1272
*I558
287
152
181844
2129
Z415
2700
2985
3270
3555
3839
4123
4407
285
153
4691
4975
5259
5542
5825
6108
6391
6674
6956
7239
283
154
7521
7803
8084
8366
S647
8928
9209
9490
9771
*005i
281
155
190332
0612
0892
II7I
I45I
1730
2010
2289
2567
2S46
279
156
3125
3403
3681
3959
4237
4514
4792
5069
5346
5623
278
^57
5900
6176
6453
6729
7005
7281
7556
7832
8107
83S2
276
158
8657
8932
9206
9481
9755
*0029
*0303
*0577
*oS50
*II24
274
159
201397
1670
1943
2216
2488
2761
3033
3305
3577
384S
272
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
306
31
61
92
122
153
184
214
245
275
306
305
31
61
92
122
153
'^3
214
244
275
305
304
30
61
91
122
152
182
213
243
274
304
303
30
61
91
121
152
182
212
242
273
303
302
30
60
91
121
151
181
211
242
272
302
301
30
60
90
120
151
181
211
241
271
301
300
30
60
90
120
150
180
210
240
270
300
299
30
60
90
120
150
179
209
239
269
299
298
30
60
&9
119
149
179
209
238
268
298
297
30
59
89
119
149
178
208
238
267
297
296
30
59
89
118
148
178
207
237
266
296
295
30
59
89
118
148
177
207
236
266
295
K
294
29
59
88
118
147
176
206
235
265
294
<
293
29
59
88
117
147
176
205
234
264
293
a.
292
29
5^
88
117
146
175
204
234
263
292
<
291
29
58
87
116
146
175
204
233
262
291
290
29
58
87
116
145
174
203
232
261
290
z
289
29
58
87
116
145
173
202
231
260
289
0
288
29
58
86
"5
144
173
202
230
259
288
H
""ll
29
57
86
115
144
172
201
230
258
287
Bi
286
29
57
86
114
143
172
200
229
257
286
0
'=5
29
57
86
114
143
171
200
228
257
285
Oi
284
28
57
85
114
142
170
199
227
256
284
0
283
28
57
85
113
142
170
198
226
255
283
0.
282
28
56
85
"3
141
169
197
226
254
282
281
28
56
84
112
141
169
197
225
253
281
280
28
56
84
112
140
168
196
224
252
2 So
279
28
56
84
112
140
167
195
223
251
279
278
28
56
83
III
139
167
195
222
250
278
277
28
55
83
III
139
166
194
222
249
277
276
28
55
83
no
138
166
193
221
248
276
275
28
55
83
no
138
165
193
220
24S
275
274
27
55
82
no
137
164
192
219
247
274
273
27
55
82
109
137
164
191
218
246
273
272
27
54
82
136
163
190
21S
245
272
—
271
27
54
81
108
136
163
190
217
244
271
Diff.
Diff.
I
2
3
4
5
6
7
8
9
268
TABLE VIl.— LOGARITHMS OF NUMBERS.
N.
0
X
a
3
4
5
6
7
8
9
Diff.
x6o
304130
6836
439 «
4663 4934 5204
5475
5746
8441
6016
6286
6556
371
i6i
7096
73b.5 7634 7904
'^'73
8710
8979
9247
369
x6a
9515
313188
9783 *0O5l 1*0319 *o,s86 ;
•0'\S3
•1121
•1388
•>654
•1921
'^
163
2454
2720
29-S6
3252
35 1«
3783
4049
43>4
4579
266
164
4$44
5'°9
5373
8010
5638
8273
5902
6i66
6430
6694
6957
7221
264
i6s
3174S4
7747
8536
879S
9060
9323
9585
2196
9846
262
166
330108
0370
0631 0892 1
"53
1414
1675
•936
2456
361
X67
3716 3976 i 3236 1 3496 1
3755
4015
4274
4533
4792
5051
259
168
5309
78S7
556.S 5826 ' 6084 1
6342
6600
6858
7115
7372
7630
258
169
8144
8400 8657 1
8913
9170
9426
96S2
9938
•0193
256
170
230449
0704
0960
1215
1470
1724
1979
2234
2488
2742
255
171
2996
3250
3504
3757
401 1
4264
6789
4517
4770
5023
5276
253
17a
5528
57'' I
6033
6285
6537
7041
7292
7544
7795
252
173
8046
8297
8548
8799
9049
9299
9550
9800
•0050
•0300
250
»74
340549 0799
1048
1297
1546
J 795
2044
2293
2541
2790
249
»75
243038
3286
3534
6006
3782
4030
4277
4525
4772
5019
5266
248
176
55'3
5759
6252
6499
6745
9198
6991
7^F
7482
*'^'a
246
177
7973
8219
8464
8709
8954
9443
9687
9932
♦0176
245
«78
250420
0664
0908
1151
1395
1638
188 1
2125
2368
2610
243
179
2853
3096 3338
3580
3822
4064
4306
4548
4790
5031
242
N.
Diff.
I
2 3
4
5
6
7
8
9
Diff.
973
27
54
82
109
136
163
190
218
245
373
371
27
54
81
108
136
163
190
217
244
371
370
27
54
81
108
135
162
189
216
243
370
369
27
54
8i
108
135
161
188
225
242
36l
368
27
54
80
107
134
l6l
188
214
241
367
27
53
80
107
134
160
'?!
214
240
367
366
27
53
80
106
133
160
186
213
239
366
965
27
53
80
106
133
159
186
212
239
265
364
36
53
79
106
132
158
^^5
211
238
364
OQ
363
26
53
79
105
132
158
184
210
^^I
263
H
363
26
52
79
105
131
157
183
210
236
363
X
36x
26
52
78
. 104
13J
157
183
209
235
361
<
360
26
52
78
■ 104
130
156
182
208
234
360
ou
359
26
52
78
104
130
155
181
207
233
359
-)
358
26
52
77
103
129
155
181
206
232
358
<
957
26
51
77
103
129
154
180
206
231
257
Z
356
26
51
77
102
128
154
179
205
230
356
0
255
26
51
77
102
128
153
179
204
230
255
H
254
25
51
76
102
127
152
178
203
229
254
OS
253 ^ 25
51
76
lOI
127
152
177
202
228
253
0
353
25
50
76
lOI
126
151
176
202
227
253
0
OS
251
25
50
75
100
126
151
176
201
226
251
350
25
50
75
100
125
150
175
200
225
350
0.
349
25
50
75
100
125
149
174
199
224
349
348
248
25
50
74
99
124
149
174
198
223
347
25
49
74
124
148
173
198
222
347
346
25
49
74
98
123
148
172
'S
221
346
24s
25
49
74
98
123
147
172
196
221
245
244
24
49
73
98
122
146
171
195
220
244
343
24
49
■73
97
122
146
170
194
219
343
34a
24
48
73
97
121
145
169
194
218
343
341
24
48
72
9!
121
145
\^
193
217
241
340
24 48
72
96
120
144
192
216
340
Did.
Diff. 1 '^ 1 ^
3
4
5
6
'
8
9
269
TABLE VII.— I^OGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
i8o
255273
5514
5755
5996
5?37
6477
6718
6958
7198
7439
241
i8i
7679
7918
8158
8398
8637
8877
91 16
9355
9594
9833
239
183
260071
0310
0548
0787
1025
1263
1501
1739
1976
2214
238
'^3
2451
2688
2925
3162
3399
3636
3873
4109
4346
4582
237
184
4.8 1 8
5054
5290
5525
5761
5996
6232
6467
6702
6937
235
'?§
267172
7406
7641
7875
8110
8344
8578
8812
9046
9279
234
186
9513
9746
9980
*02I3
♦0446
*o679
♦0912
*ii44
*i377
♦1609
233
187
271842
2074
2306
2538
2770
3001
3233
3464
3696
3927
232
188
4158
4389
4620
4850
5081
5311
5542
5772
6002
6232
230
l8g
6462
6692
6921
7I5I
7380
7609
7838
8067
8296
8525
229
igo
278754
8982
921 1
9439
9667
9895
*0I23
*035i
*0578
*o8o6
228
igi
281033
1261
1488
1715
1942
2169
2396
2622
2849
3075
227
192
3301
3527
3753
3979
4205
4431
4656
4882
5107
5332
226
193
5557
5782
6007
6232
6456
6681
6905
7130
7354
7578
225
194
7802
8026
8249
8473
8696
8920
9143
9366
9589
9812
223
195
290035
0257
0480
0702
0925
"47
1369
1591
1813
2034
222
ig6
2256
247S
2699
2920
3141
3363
3584
3804
4025
4246
221
197
4466
4687
4907
5127
5347
5567
5787
6007
6226
6446
220
ig8
6665
6884
7104
7323
7542
7761
7979
8198
8416
8635
219
199
8853
9071
9289
9507
9725
9943
*oi6i
*0378
*0595
*o8i3
218
200
301030
1247
1464
168 1
1898
2114
2331
2547
2764
2980
217
20I
3196
3412
3628
3844
4059
4275
4491
4706
4921
5136
216
202
5351
5566
5781
5996
6211
6425
6639
6854
7068
7282
215
203
7496
7710
7924
8137
8351
8564
8778
8991
9204
9417
213
204
9630
9843
*oo56
*0268
*048i
♦0693
*09o6
*iii8
*i330
*I542
212
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
239
24
48
72
96
120
143
167
191
215
239
238
24
48
71
95
119
143
167
190
214
238
237
24
47
7t
95
119
142
166
190
213
237
236
24
47
71
94
118
142
165
189
212
236
235
24
47
71
94
118
141
165
188
212
235
234
23
47
70
94
117
140
164
187
211
234
233
23
47
70
93
117
140
163
186
210
233
CO
H
<
232
23
46
70
93
116
139
162
186
209
233
231
23
46
69
92
116
139
162
185
208
231
230
23
46
69
92
115
138
161
184
207
230
dn
229
23
46
69
92
"5
137
160
183
206
239
>J
228
23
46
68
91
114
137
160
182
205
328
7
407S
6180
4289
4499
47«o
6.S09
4920
5'30
5340
5551
5700
210
ao7
5970
8063
6390
6599
7018
7227
7436
7646
7854
209
303
8272
84S1
86S9
8898
9106
9314
9522
9730
9938
20S
aog
320146
0354
0562
0769
0977
1 184
139'
1598
1805
2012
207
3IO
322219
2426
2633
2839
3046
3252
3458
3665
3871
4077
206
ail
42S2
6336
44SS
4694
6745
4899
5105
53>o
5516
5721
5926
6131
205
aia
f>54l
6950
7155
7359
9398
7563
7767
7972
8176
204
313
83S0
8583
8787
8991
9194
9601
9805
*ooo8
*02II
203
314
3304 '4
0617
0819
1022
1225
1427
1630
1832
2034
2236
202
316
332(38
2640
2842
3044
3246
3447
3649
3850
4051
4253
202
4454
4655
^
5057
5257
5458
5658
5859
6059
6260
201
317
6460
6660
7060
7260
7459
7659
7858
8058
82 S7
200
3I8
8456
8656
8855
9054
9253
9451
9650
9849
*oo47
♦0246
199
319
340444
0642
0S41
1039
1237
1435
1632
1830
2028
2225
198
330
342423
2620
28,7
3014
3212
3409
3606
3802
3999
4196
'^i
331
4392
4589
47^5
4981
5178
5374
5570
5766
5962
6157
196
333
6353
6549
6744
'>939
7135
7330
7525
7720
79' 5
81 10
195
333
8305
8500
8694
8SS9
9083
9278
9472
9666
9860
*oo.S4
194
334
350248
0442
06^6
0829
1023
1216
1410
1603
1796
19S9
193
335
352183
2375
2568
2761
2954
3'47
3339
3532
3724
3916
>93
336
4108
4301
4493
4685
4876
5068
5260
5452
5643
5834
192
337
6026
6217
6408
6599
6790
6981
7172
7363
7554
7744
191
338
7935
8.25
8316
8506
8696
8886
9076
9266
9456
9646
ITg
339
9835
♦0025
*02I5
♦0404
*0593
♦0783
*0972
*ii6i
*I350
*i539
330
361728
1917
2105
2294
2482
2671
2859
3048
3236
3424
188
331
3612
3800
39SS
4176
4363
4551
4739
4926
5113
5301
188
333
5488
5675
5862
6049
6236
6423
6610
6796
f^^
7169
187
333
7356
7542
7729
7915
8101
8287
8473
8659
8845
9030
186
234
9216
9401
95S7
9772
9958
*oi43
♦0328
♦0513
•0698
♦0883
185
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
313
21
42
64
85
106
127
148
170
191
313
311
21
42
63
84
106
127
148
169
190
311
3IO
21
42
63
84
105
126
147
168
189
3 10
2og
21
42
63
84
105
125
146
167
188
308
208
21
42
62
83
104
125
146
166
^ll
to
H
Oi
<
207
21
41
62
83
104
124
145
166
186
307
306
21
41
62
82
103
124
144
165
'^5
306
305
21
41
62
82
103
123
144
164
'f5
305
cu
304
20
41
61
82
102
122
143
163
184
304
<
z
0
303
303
20
20
41
40
61
61
81
81
102
lOI
122
121
142
141
162
162
'?3
182
303
303
301
20
40
60
80
lOI
121
141
161
181
30I
200
20
40
60
80
100
120
140
160
180
200
H
199
20
40
60
80
100
"9
139
159
179
199
Oi
198
20
40
59
79
99
119
139
'5^
178
198
0
197
20
39
59
79
118
138
158
177
'^
a.
196
20
39
59
78
98
118
137
'57
176
196
0
195
20
39
59
78
98
"7
137
156
176
195
0.
194
19
39
58
78
97
116
136
155
175
194
193
'9
39
58
77
97
116
135
154
174
193
192
19
38
58
77
96
"5
134
154
173
193
igi
19
38
57
76
96
115
134
153
172
191
190
19
38
57
76
95
114
133
152
171
190
189
19
38
57
76
95
"3
132
151
170
\U
188
19
38
56
75
94
"3
132
150
169
Diff.
I
2
3
4
5
1 ^
7
8
9
Diff.
271
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
235
371068
1253
1437
1622
1806
1991
2175
2360
2544
2728
1S4
236
2912
3096
3280
3464
3647
3831
4015
4198
4382
4565
1S4
237
4748
4932
5115
5298
5481
5664
5846
6029
6212
6394
183
238
6577
6759
6942
7124
7306
7488
7670
7852
8034
8216
182
239
S398
8580
8761
8943
9124
9306
9487
9668
9849
*0030
181
240
3802 I I
0392
0573
0754
0934
1115
1296
1476
1656
1837
181
241
2017
2197
2377
2557
2737
2917
3097
3277
3456
3636
180
242
3SI5
3995
4174
4353
4533
4712
4891
5070
5249
5428
179
243
5606
5785
5964
6142
6321
6499
6677
6856
7034
7212
178
244
7390
7568
7746
7923
8ioi
8279
8456
8634
881 1
89S9
178
245
389166
9343
9520
9698
9875
*oo5i
*0228
"0405
*0582
*0739
177
246
390935
1112
1288
1464
164 1
1817
1993
2169
2345
2521
176
247
2697
2873
3048
3224
3400
3575
3751
3926
4101
4277
176
248
4452
4627
4802
4977
5152
5326
5501
5676
5850
6025
175
249
6199
6374
6548
6722
6896
7071
7245
7419
7592
7766
174
250
397940
8114
8287
8461
8634
8808
8981
9154
9328
9501
173
251
9674
9847
*O02O
*0I92
*0365
*o538
*o7ii
*o883
*I056
*I22S
173
252
40I40I
1573
1745
1917
20S9
2261
2433
2605
2777
2949
172
253
3I2I
3292
3464
3635
3807
3978
4149
4320
4492
4663
171
254
4834
5005
5176
5346
•5517
56S8
5858
6029
6199
6370
171
255
406540
6710
6881
7051
7221
7391
7561
7731
7901
8070
170
256
8240
8410
8579
8749
8918
90S7
9257
9426
9595
9764
169
257
9933
*0I02
*027I
♦0440
*o6o9
*0777
*0946
*iii4
*I2S3
*i45i
169
258
41 1620
1788
1956
2124
2293
2461
2629
2796
2964
3132
168
259
3300
3467
3635
3803
3970
4137
4305
4472
4639
4806
167
260
414973
5140
5307
5474
5641
5808
5974
6141
6308
6474
167
261
6641
6807
6973
7139
7306
7472
7638
7804
7970
8135
166
262
8301
8467
8633
8798
8964
9129
9295
9460
9625
9791
165
263
9956
*OI2I
*0286
*045i
*o6i6
*078i
*0945
*IIIO
*I275
*I439
165
264
421604
1768
1933
2097
2261
2426
2590
2754
2918
3082
164
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
187
19
37
5^
75
94
112
131
150
168
187
186
19
37
56
74
93
112
130
149
167
186
^fs
19
37
56
74
93
III
130
148
167
18s
184
18
37
55
74
92
no
129
147
166
184
183
18
37
55
73
92
no
128
146
165
183
09
182
18
36
55
73
91
109
127
146
164
182
H
181
18
36
54
72
91
109
127
145
163
181
(^
180
18
36
54
72
90
108
126
144
162
180
<
179
18
36
54
72
90
107
125
143
161
179
178
18
36
53
71
89
107
125
142
160
178
hJ
177
18
35
53
71
89
106
124
142
159
177
<
176
18
35
53
70
88
106
123
141
158
176
z
175
18
35
53
70
88
105
123
140
158
175
0
174
17
35
52
70
87
104
122
139
'57
174
H
173
17
35
52
69
87
104
121
138
156
173
Oi
172
17
34
52
69
86
103
120
138
155
172
0
171
17
34
51
68
86
103
120
137
154
171
0
170
17
34
51
68
85
102
119
136
153
170
169
17
34
51
68
85
101
118
135
152
169
OU
168
17
34
50
67
84
lOI
118
134
151
168
'!2
17
33
50
67
84
100
117
134
150
167
166
17
33
50
66
83
100
116
133
149
166
165
17
33
50
66
83
99
116
132
149
165
164
16
33
49
66
82
98
"5
131
148
164
Diff.
I
2
3
4
5
6
7
8
9
Diff.
272
TADLK VII.— LOGARITHMS OP NUMBERS.
'
N.
0
X a
3
4
5
6
7
8
9
Diff.
164
lU
423246
3410 3574
3737
3901
4065
4228
4392
6023
7648
4555
61S6
4718
4882
5045
5208
5371
6999
5534
5697
5860
6349
i'>3
1%
651 1
6674
6836
7161
8783
♦0398
7324
8944
7486
7811
7973
162
8135
8297
8459
8621
9106
9268
9429
9591
162
369
9752
99>4
*oo75
♦0236
*0559
•0720
•0881
•1042
•1203
161
ayo
431364
1525
1685
1846
2007
2167
2328
24S8
2649
2809
161
271
2909
3 •3°
3290
3450
3610
3770
3930
4090
5«>85
4249
4409
160
373
4569
6163
4729
4888
5048
5207
53^-7
5526
5844
6004
159
373
6322
6481
6640
83^
6957
7116
8701
7275
4,859
7433
7592
159
274
7751
7909
8067
8226
8542
9017
9175
158
375
439333
9491
9648
9806
9964
*OI22
*0279
•0437
♦0594
•0752
158
376
440909
1066
1224
1381
J538
•695
1852
2009
2166
23-3
157
377
2480
2637
2793
2950
3106
3263
3419
3576
3732
38S9
'^I
378
4045
4201
4357
4513
4669
4825
4981
5137
5293
5449
156
379
5604
5760
5915
6071
6226
6382
6537
6692
6848
7003
155
38o
447158
7313
7468
7623
7778
7933
8088
8242
8397
8552
155
38x
8706
8861
9015
9170
9324
9478
9633
9787
9941
*oo95
154
383
450249
0403
0557
0711
0865
lOiS
1 172
1326
1479
1633
154
383
1786
1940
2093
2247
2400
2553
2706
28S9
3012
3165
153
384
3318
3471
3624
3777
3930
4082
4235
4387
4540
4692
153
a85
4997
5150
5302
5454
5606
5758
59 '0
6062
6214
152
386
6518
6670
6821
6973
7125
7276
7428
7579
7731
152
287
7882
8033
8184
8336
8487
8638
8789
8940
9091
9242
151
388
9392
9543
1048
9694
9845
9995
♦0146
*0296
*0447
*o597
•0748
151
389
46S98
1198
1348
1499
1649
1799
1948
2098
2248
150
390
462398
2548
2697
2847
2997
3146
3296
3445
3594
3744
150
391
3893
4042
4191
4340
4490
4639
4788
4936
50S5
5234
149
393
53S3
5532
5680
5829
5977
6126
6274
6423
6571
6719
149
393
6868
7016
7164
7312
7460
7608
7756
7904
8052
8200
148
394
8347
8495
8643
8790
8938
9085
9233
9380
9527
9675
148
ags
469822
9969
*oii6
♦0263
•0410
*0557
*o704
*o85i
♦0998
*II45
147
396
471292
1438
1585
1732
1878
2025
2171
2318
2464
2610
146
397
2756
2903
3049
3195
3341
3487
3633
3779
3925
4071
146
398
4216
4362
4508
4653
4799
4944
5090
5235
5381
5526
146
399
5671
5816
5962
6107
6252
6397
6542
6687
6832
6976
145
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
164
164
16
33
49
66
82
98
"5
131
148
163
16
33
49
65
82
98
114
130
147
163
163
16
32
49
65
81
97
"3
130
146
163
161
16
32
48
64
81
97
"3
129
145
161
CO
160
16
32
48
64
80
96
112
128
144
160
159
16
32
48
64
80
95
III
127
143
isi
<
J58
16
32
47
63
79
95
III
126
142
PU
157
16
31
47
f3
79
94
110
126
141
'57
J
156
16
31
47
62
78
94
109
125
140
156
<
155
16
31
47
62
78
93
109
124
140
155
z
154
15
31
46
62
77
92
108
123
139
154
0
153
15
31
46
61
77
92
107
122
138
153
0
15a
15 30
46
61
76
91
106
122
137
15a
151
15
30
45
60
76
91
106
121
136
151
ISO
15
30
45
60
75
90
105
120
135
150
a.
0
Oi
a,
149
148
15
30
45
60
75
89
104
119
134
149
15
30
44
59
74
II
104
118
133
148
147
15
29
44
P
74
103
118
132
147
146
15
29
44
73
88
102
"?
131
146
145
15
29
44
58
73
fz
102
116
131
M5
144
14
29
43
58
72
86
10 1
"5
130
144
143
14
29
43
57
72
86
100
114
129
J43
Diff.
1 Diff.
X 1 2
1 3
1 ^
1 3
6
7
8
9
273
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
145
300
4771 21
7266
741 1
7555
7700
7844
7989
8133
8278
8422
301
8566
8711
8855
8999
9143
9287
9431
9575
9719
9863
144
302
480007
0151
0294
0438
0582
0725
0869
1012
1 156
1299
144
303
1443
1586
1729
1872
2016
2159
2302
2445
2588
2731
143
304
2874
3016
3159
3302
3445
3587
3730
3872
4015
4157
143
305
484300
4442
4585
4727
4869
501 1
5153
5295
5437
5579
142
306
5721
5863
6005
6147
6289
6430
6572
6714
6855
6997
142
307
7138
7280
7421
7563
7704
7845
7986
8127
8269
8410
141
308
8551
8692
8833
8974
9114
9255
9396
9537
9677
9818
141
309
9958
*0O99
*o239
*038o
*O520
*o66i
*o8oi
*094i
*io8i
*I222
140
310
491362
1502
1642
1782
1922
2062
2201
2341
2481
2621
140
311
2760
2900
3040
3179
3319
3458
3597
3737
3876
4015
139
312
4155
4294
4433
4572
47"
4850
4989
5128
5267
5406
139
313
5544
5683
5822
5960
6099
6238
6376
6515
6653
6791
139
3M
6930
7068
7206
7344
7483
7621
7759
7897
8035
8173
138
315
4983 n
8448
8586
8724
8862
8999
9137
9275
^9412
9550
138
316
9687
9824
9962
*0099
*0236
*0374
*05ii
*o648
*0785
♦0922
137
317
501059
1196
1333
1470
1607
1744
1880
2017
2154
2291
137
318
2427
2564
2700
2837
2973
3109
3246
3382
3518
3655
136
319
3791
3927
4063
4199
4335
4471
4607
4743
4878
5014
136
320
505150
5286
5421
5557
5693
5828
5964
6099
6234
6370
136
321
6505
6640
6776
691 1
7046
7181
7316
7451
7586
7721
135
322
7856
7991
8126
8260
8395
8530
8664
8799
8934
9068
135
323
9203
9337
947 r
9606
9740
9874
*ooo9
*oi43
*0277
*04ii
134
324
510545
0679
0813
0947
1081
1215
1349
1482
1616
1750
134
325
51 1883
2017
2151
2284
2418
2551
2684
2818
2951
3084
133
326
3218
3351
3484
3617
3750
3883
4016
4149
4282
4415
133
327
4548
4681
4813
4946
5079
5211
5344
5476
5609
5741
133
328
5874
6006
6139
6271
6403
6535
6668
6800
6932
7064
132
329
7196
7328
7460
7592
7724
7855
7987
81 19
8251
8382
132
330
518514
8646
8777
S909
9040
9171
9303
9434
9566
9697
131
331
9828
9959
*0090
*022I
*0353
*0484
*o6i5
*0745
♦0876
*I007
131
332
521 138
1269
1400
1530
1661
1792
1922
2053
2183
2314
131
333
2444
2575
2705
2835
2966
3096
3226
3356
3486
3616
130
334
3746
3876
4006
4136
4266
4396
4526
4656
fo5
4915
130
335
525045
5174
5304
5434
5563
5693
5822
5951
6081
6210
129
336
6339
6469
6598
6727
6856
6985
7114
7243
7372
7501
129
337
7630
7759
7888
8016
8145
8274
8402
8531
8660
8788
129
338
8917
9045
9174
9302
9430
9559
9687
9815
9943
*0072
1 28
339
530200
0328
0456
0584
0712
0840
0968
1096
1223
1351
128
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
142
142
14
28
43
57
71
fs
99
114
128
CO
141
14
28
42
56
71
85
99
113
127
141
H
140
14
28
42
56
70
84
98
112
126
140
<;
139
14
28
42
56
70
83
97
III
125
139
&
138
14
28
41
55
69
83
97
110
124
138
<
Z
0
137
14
27
41
55
69
82
96
no
123
137
136
14
27
41
54
68
82
95
109
122
136
135
14
27
41
54
68
81
95
108
122
135
134
13
27
40
54
67
80
94
107
121
J34
133
13
27
40
53
67
80
93
106
120
133
H
132
13
26
40
53
66
79
92
106
119
13a
0
0.
131
13
26
39
52
66
92
105
118
131
130
13
26
39
52
65
78
91
104
117
130
0
129
13
26
39
52
65
77
90
103
116
;^i
Oi
128
13
26
38
51
64
77
90
102
115
cu
127
13
25
38
51
64
76
89
102
114
127
Diff.
Diff.
I
2
3
4
5
6
7
8
9
274
TABLE VII.— LOGARITHMS OP NUMBERS.
1
N.
0
I
a
3
4
5
6
7
8
9
Uiff.
340
531479
1607
1734
1862
1990
2117
2245
35>8
2372
3645
2500
2627
128
341
4020
2882
3009
3136
3264
339«
3772
3899
127
34a
4153
42S0
4407
4534
4661
4787
4914
5041
5'67
127
343
5294
5421
5547
5674
5800
5927
6053
6i8>
6306
6432
126
344
<^55S
6685
6S11
6937
7063
8322
V^l
73'5
744'
Z5^7
7'>93
126
345
537«i9
7945
8071
8197
8574
8699
^8825
8951
126
346
9076
9202
9327
9452
9578
9703
9829
99A
•0079
♦0204
125
347
540329
0455
0580
0705
0830
0955
1080
1205
1330
1454
125
348
1579
1704
1829
»953
2078
2203
2327
""1^1
2576
2701
«25
349
2S25
2950
3074
3199
3323
3447
3571
3696
3820
3944
124
350
544068
4192
4316
4440
4564
4688
4812
6049
4936
5060
5183
124
35X
5307
5431
5555
5678
5802
5925
6172
6296
6419
124
35a
6543
6666
6789
6913
7036
7159
7282
8512
7405
7529
7652
123
353
7775
7S98
8021
8144
8267
8389
8635
8758
8S81
J 23
354
9003
550228
9126
9249
9371
9494
9616
9739
9861
9984
*oio6
123
355
035"
0473
0595
0717
0S40
0962
1084
1206
1328
122
356
1450
1572
1694
1816
1938
2060
2181
2303
2425
2547
122
357
2668
2790
291 1
3033
3155
3276
3398
3519
3640
3762
121
358
3883
4004
4126
4247
4368
4489
4610
4731
4852
4973
121
359
5094
5215
5336
5457
5578
5699
5820
5940
6061
61S2
121
360
556303
6423
6544
6664
6785
6905
7025
7146
7267
7387
120
361
7507
7627
7748
7868
7988
8108
8228
8349
8469
8589
120
362
8709
8829
8948
9068
9188
9308
9428
9548
9667
9787
120
363
9907
*0026
♦0146
♦0265
*0385
♦0504
*c624
*0743
♦0863
♦0982
119
364
561 lOI
I22I
1340
1459
1578
1698
1817
1936
2055
2174
119
365
562293
2412
2531
2650
2769
2887
3006
3125
3244
3362
119
366
34S1
3600
3718
3837
3955
4074
4192
43"
4429
4548
119
367
4666
47S4
4903
5021
5139
5257
5376
5494
5612
5730
118
368
5848
5966
6084
6202
6320
6437
6555
6673
6791
6909
118
369
7026
7144
7262
7379
7497
7614
7732
7849
7967
8084
118
370
568202
8319
8436
8554
8671
8788
8905
9023
9140
9257
117
371
9374
9491
9608
9725
9842
9959
♦0076
*oi93
♦0309
♦0426
117
37a
570543
0660
0776
0893
lOIO
1 126
1243
1359
1476
1592
117
373
1709
1S25
1942
2058
2174
2291
2407
2523
2639
2755
116
374
2872
2988
3104
3220
3336
3452
3568
3684
3800
3915
116
375
574031
4147
4263
4379
4494
4610
4726
4841
4957
5072
116
376
5188
5303
5419
5534
5650
5765
5880
5996
6111
6226
U5
377
6341
6457
6572
6687
6S02
6917
7032
7147
7262
7377
115
378
7492
7607
7722
7836
7951
8066
8181
8295
8410
8525
115
379
8639
8754
8868
8983
9097
9212
9326
9441
9555
9669
114
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
128
13
26
38
51
64
77
90
102
"5
laS
127
13
25
38
51
64
76
89
102
114
127
126
13
25
38
50
63
76
88
101
"3
126
"5
13
25
38
50
^3
75
88
100
113
las
<
ia4
12
25
37
50
62
74
87
99
112
124
^
ia3
12
25
37
49
62
74
86
9f
III
123
laa
12
24
37
49
61
73
!5
98
no
133
O4
lai
12
24
36
48
6i
73
85
97
109
131
s
120
12
24
36
48
60
72
84
96
108
Z20
Jx'i
12
24
36
48
60
71
f3
95
^°1
111
12
24
35
47
59
71
l^
94
106
"7
12
23
35
47
59
70
82
94
105
117
116
12
23
35
46
58
70
81
93
104
116
Diff.
I
2
3
4
5
6
7
8
9
Diff.
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
380
5797S4
9898
*00I2
*OI26
♦0241
*0355
♦0469
*0583
♦0697
*o8ii
114
3^'
5S0925
1039
1153
1267
1381
1495
1608
1722
1836
1950
114
382
2063
2177
2291
2404
2Sl8
2631
2745
2858
2972
3085
114
383
3199
3312
3426
3539
3652
3765
3879
3992
4105
4218
113
384
4331
4444
4557
4670
4783
4896
5009
5122
5235
5348
'■3
385
585461
5574
5686
5799
5912
6024
6137
6250
6362
6475
"3
386
65S7
6700
6812
6925
7037
7149
7262
7374
7486
7599
112
387
7711
7823
7935
8047
8160
8272
8384
S496
8608
8720
1X2
388
S832
8944
9056
9167
9279
9391
9503
9615
9726
9838
112
389
9950
*oo6i
*oi73
♦0284
♦0396
*0507
*o6i9
*0730
*o842
*o953
112
390
591065
1 176
1287
1399
1510
1621
1732
1843
1955
2066
III
391
2177
228S
2399
2510
2621
2732
2843
2954
3064
3175
III
392
3286
3397
3508
3618
3729
3840
3950
4061
4171
4282
III
393
4393
4503
4614
4724
4S34
4945
5055
5165
5276
5386
110
394
5496
s6o6
5717
5827
5937
6047
6157
6267
6377
6487
no
395
596597
6707
6817
6927
7037
7146
7256
7366
7476
75S6
no
396
7695
7805
7914
8024
8134
8243
8353
8462
8572
868 1
no
397
8791
8900
9009
9119
9228
9337
9446
9556
9665
9774
109
398
98S3
9992
*OIOI
*02I0
*03i9
*042S
*0537
♦0646
*o755
*oS64
109
399
600973
1082
1191
1299
1408
1517
1625
1734
1843
195 1
109
400
602060
2169
2277
23S6
2494
2603
2711
2819
2928
3036
108
401
3'44
3253
3361
3469
3577
3686
3794
3902
4010
4118
108
402
4226
4334
4442
4550
4658
4766
4874
4982
5089
5197
108
403
5305
5413
5521
5628
5736
5844
5951
6059
6166
6274
108
404
6381
6489
6596
6704
681 1
6919
7026
7133
7241
7348
107
405
607455
7562
7669
7777
7884
7991
8098
8205
8312
8419
107
406
S526
S633
8740
8847
8954
9061
9167
9274
9381
94S8
107
407
9594
9701
9808
9914
*002I
*OI28
*0234
*034i
*0447
*0554
107
408
610660
0767
0873
0079
1086
1 192
1298
1405
1511
1617
106
409
1723
1S29
1936
2042
214S
2254
2360
2466
2572
2678
106
410
6127S4
2S90
2996
3102
3207
3313
3419
3525
3630
3736
106
411
3842
3947
4053
4159
4264
4370
4475
4581
4686
4792
106
412
4897
5003
510S
5213
5319
5424
5529
5634
5740
5845
105
413
5950
6055
6160
6265
6370
6476
6581
6686
6790
6895
105
414
7000
7105
7210
7315
7420
7525
7629
7734
7839
7943
105
415
61804S
8 1 53
8257
8362
8466
8571
8676
8780
8884
8989
105
416
9093
9198
9302
9406
9511
9615
9719
9824
9928
*0032
104
t'7
620136
0240
0344
0448
0552
0656
0760
0864
0968
1072
104
418
1176
12S0
1384
148S
1592
1695
1799
1903
2007
2IIO
104
419
2214
2318
2421
2525
2628
2732
2835
2939
3042
3146
104
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
"5
12
23
35
46
58
69
81
92
104
"5
114
11
23
34
46
57
68
80
91
103
114
Vi
"3
11
23
34
45
57
68
79
90
102
"3
<
0,
112
11
22
34
45
5^
67
78
90
101
113
III
II
22
33
44
56
67
78
89
100
III
IIO
"
22
33
44
55
66
77
88
99
IIO
log
II
22
33
44
55
65
76
87
98
ISi
0
0!.
108
II
22
32
43
54
65
76
86
97
107
II
21
32
43
54
64
75
86
96
107
106
II
21
32
42
53
64
74
^5
95
106
105
II
21
32
42
53
^3
74
84
95
105
104
10
21
31
42
52
62
73
!3
94
104
103
10
21
31
41
52
62
72
82
93
103
Diff.
'
2
3
4
5
6
7
8
9
Diff.
276
TABLE VII.-LOGARITHMS OP NUMBERS.
N.
0
I
a
3
4
5
6
7
8
9
Dlff.
4ao
623249
3353
3456
3559
3663
3766
3869
3973
4076
4179
103
421
42S2
4385
4488
4591
4«>95
4798
4901
5004
6032
5107
6135
5210
6238
7263
82S7
103
4aa
53>2
54>5
n:i
5021
6648
5724
6751
5827
6956
»03
433
6340
6443
7463
6853
7058
8082
7161
81S5
103
434
7306
7571
8593
7673
8695
7775
8797
7878
8900
7980
102
SI
62S3S9
8491
9002
9104
9206
9308
102
9410
95" 2
9613
9715
9817
99«9
•0021
*OI23
•0224
•0326
102
437
630428
0530
0631
0733
0835
0936
1038
1139
1241
1342
102
438
1444
J 545
1647
1748
1849
1951
2052
2153
2255
2356
lOI
439
2457
2559
2bbo
2761
2Sb2
2963
S064
3165
3266
3367
lOI
430
633468
3569
3670
3771
3872
3973
4074
4175
4276
4376
lOI
431
4477
457S
4679
4779
4S80
4981
5182
5283
6287
5383
63S.8
lOI
43a
54S4
5584
5685
66S8
5785
5886
5986
6087
6187
100
433
64S8
65S8
6789
68S9
6989
7089
7189
7290
8290
7390
8389
100
434
7490
638489
ip9
7690
7790
7S90
'^
8090
8190
100
S?
8689
8789
8888
9088
9188
.92S7
9387
100
9486
9586
9686
9785
9885
9984
♦0084
•0183
♦0283
•0382
99
437
640481
0581
06S0
0779
0879
0978
1077
"77
1276
1375
99
438
1474
1573
1672
1771
1S71
1970
2069
2168
2267
2366
99
439
2465
2563
2662
2761
2860
2959
3058
3156
3255
3354
99
440
643453
3551
3650
3749
3847
3946
4044
4143
4242
4340
98
441
4439
4537
4636
4734
4S32
4931
5029
5127
5226
5324
98
443
5422
5521
5619
5717
5815
5913
6oti
61 10
6208
6306
98
443
6404
6502
6600
6698
6796
6894
6992
7089
71S7
8165
72S5
98
444
7383
74S1
7579
8555
7676
7774
7872
7969
8067
82t>2
98
445
648360
8458
8653
8750
8848
8945
9043
9140
9237
97
446
9335
9432
9530
9627
9724
9821
9919
0890
*ooi6
*oii3
*02I0
97
447
65030S
0405
0502
0599
0696
0793
09S7
10S4
IlSl
97
448
1278
1375
1472
1569
253^
1666
1762
'fs?
1956
2053
2150
97
449
2246
2343
2440
2633
2730
2826
2923
3019
31 16
97
450
653213
3309
3405
3502
3598
3695
3791
3888
3984
4080
96
451
4177
4273
4369
4465
4562
4658
4754
4850
4946
5042
96
453
5138
5235
5331
5427
5523 5619
5715
5810
5906
6002
96
453
6098
6194
6290
6386
64S2
6577
6673
6769
6S64
6960
96
454
7056
7152
7247
7343
7438
7534
7629
7725
7820
7916
96
^
65801 I
8107
8202
8298
8393
8488
8584
8679
8774
8870
95
456
896^
9060
9155
9250
9346
9441
9536
9631
9726
9821
95
^57
66^5
*OOII
*o:o6
*020I
♦0296
♦0391
•0486
♦0581
♦0676
•0771
95
458
0960
1055
1150
1245
1339
1434
1529
1&23
I718
95
459
1813
1907
2002
2096-
2191
2380
2475
2569
2663
95
460
662758
2852
2947
3041
3135
3230
3324
341S
3512
3607
94
461
370I
3795
3889
3983
4078
4172
4266
4360
4454
4548
94
46a
4642
4736
4830
4924
5018
5112
5206
5299
5393
5487
94
463
5581
5675
5769
5862
5956
6050
6143
6237
6331
6424
94
464
6518
6612
6705
6799
6892
6986
7079
7173
7266
7360
94
N.
DifF. I
2
3 4 5
6
7
8
9
Diff.
09
104
10
21 1 31
42 1 52
62
73
83
94
104
103
10
21
31
41
52
62
72
82
93
103
oi
I03
10
20
31
41
51
61
71
82
92
102
<
lOI
10
20
30
40
51
61
71
81
91
lOI
a.
100
10
20
30
40
50
60
70
80
90
100
cu
99
10
20
30
40
50
59
69
7?
89
P
0
98 10
20
29
39
49
59
78
88
OS
97 10
19
29
39
49
58
68
78
87
97
0.
96 10
19
29
38
48
58
67
77
86
96
95 ! 10
19
29
38
48
57
67
76
86
95
Diff.
I
2 1 3 4 5
6
7
8
9
Diff.
277
TAl
3LE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
465
667453
7546
7640
7733
7826
7920
8013
8106
8199
8293
93
466
83S6
8479
8572
8665
8759
8852
8945
9038
9131
9224
93
^Po
. 9317
9410
9503
9596
9689
9782
9875
*oo6o
*oi53
93
468
670246
0339
0431
0524
0617
0710
0802
0895
0988
loSo
93
469
1 173
1265
1358
145 1
1543
1636
1728
182 1
1913
2005
93
470
672098
2190
2283
2375
2467
2560
2652
2744
2836
2929
92
471
3021
3113
3205
3297
3390
34S2
3574
3666
3758
3850
92
472
3942
4034
4126
4218
4310
4402
4494
45S6
4677
4769
92
473
4861
4953
5045
5137
5228
5320
54'2
5503
5595
56S7
92
474
^ 5778
5870
5962
6053
6145
6236
6328
6419
651 1
6602
92
475
676694
67S5
6876
6968
7059
7151
7242
7333
Itlt
7516
91
476
7607
7698
7789
7881
7972
8063
8154
8245
8427
91
477
8518
8609
8700
8791
8S82
8973
9064
9155
9246
9337
91
478
.o9428
9519
9610
9700
9791
9S82
9973
*oo63
*oi54
*0245
91
479
680336
0426
0517
0607
0698
07S9
0879
0970
1060
1151
91
480
681 24 I
1332
1422
1513
1603
1693
1784
1874
1964
2055
90
481
2145
2235
2326
2416
2506
2596
2686
2777
2867
2957
90
482
3047
3137
3227
3317
3407
3497
3587
3677
3767
3857
90
483
3947
4037
4127
4217
4307
4396
44 86
4576
4666
4756
90
484
^4845
4935
5025
5114
5204
5294
5383
5473
5563
5652
485
685742
5831
5921
6010
6100
6189
6279
6368
6458
6547
89
486
6636
6726
6815
6904
6994
7083
7172
7261
7351
7440
89
487
7529
7618
7707
7796
7SS6
7975
8064
8153
8242
8331
89
488
8420
8509
8598
8687
8776
8865
8953
9042
9131
9220
89
489
9309
9398
9486
9575
9664
9753
9841
9930
*ooi9
*oio7
89
490
690106
0285
0373
0462
0550
0639
0728
0816
0905
0993
89
491
1081
1 170
1258
1347
1435
1524
1612
1700
1789
1877
88
492
1965
2053
2142
2230
2318
2406
2494
2583
2671
2759
88
493
2S47
2935
3023
3111
3199
3287
3375
3463
3551
3639
88
494
, 3727
3815
3903
3991
4078
4166
4254
4342
4430
4517
88
495
694605
4693
4781
4868
4956
5044
5131
5219
5307
5394
88
496
5482
5569
5657
5744
5832
5919
6007
6094
6182
6269
87
497
6356
6444
6531
6618
6706
t>793
6880
6968
7055
7142
87
498
7229
73'7
7404
7491
7578
7665
7752
7839
7926
8014
87
499
8101
8188
8275
8362
8449
S535
8622
8709
8796
8883
87
500
698970
9057
9144
9231
9317
9404
9491
9578
9664
9751
87
501
9838
9924
*OOII
♦0098
*oi84
*027I
*035S
*0444
*053i
*o6i7
87
502
700704
0790
0877
0963
1050
1136
1222
1309
1395
1482
86
503
1568
1654
174 1
1827
1913
1999
2086
2172
2258
2344
86
504
2431
2517
2603
2689
2775
2861
2947
3033
3119
3205
86
505
703291
3377
3463
3549
3635
3721
3807
3893
3979
4065
86
506
4151
4236
4322
4408
4494
4579
4665
4751
4837
4922
86
5°2
5008
5094
5179
5265
5350
5436
5522
5607
5693
5778
86
508
5864
5949
6035
6120
6206
6291
6376
6462
6547
6632
85
509
6718
6803
6888
6974
7059
7144
7229
7315
7400
7485
85
N.
CO
Diff.
I
2
3
4
5
6
7
8
9
Diff.
94
9
19
28
33
47
56
66
75
85
94
93
9
19
28
37
47
56
65
74
84
93
oi
92
9
18
28
37
46
55
64
74
83
92
<
91
9
18
27
36
46
55
64
73
82
91
0.
90
9
18
27
36
45
54
63
72
81
90
0.'
0
U
9
9
18
18
'I
36
35
45
44
53
53
62
62
71
70
80
79
si
Oi
87
9
17
26
35
44
52
61
70
78
87
cu
86
9
17
26
34
43
52
60
69
77
86
85
9
17
26
34
43
51
60
68
77
85 1
Diff.
I
2
3
4
5
6
7
8
9
Diff.
278
TABLE vn.— LOGARITHMS OF NUMBERS.
N.
0
I
a
3
4
5
6
7
8
9
Diff.
85
510
5"
707570
8421
g^
7740
8591
7826
8676
791 1
8761
&
8081
8931
8166
9015
8251
9100
8336
9'85
5"
9270
9355
9440
9524
960Q
0456
9694
9779
9863
9948
♦0033
85
513
7IOII7
0202
0287
0371
0540
0625
0710
0794
0H79
85
514
0963
1048
1 132
1217
1301
1385
1470
1554
1639
2566
84
5»6
7IIS07
1892
'g^t
2060
2144
3229
2313
2397
2481
84
2650
2734
28:8
2902
2986
3070
3154
3238
3323
3407
84
5*2
3491
3575
3659
3742
3826
3910
3994
4078
4162
4246
84
5>8
4330
4414
4497
4581
4665
4749
4833
4916
5000
5084
84
519
5'67
5251
5335
5418
5502
55S6
5669
5753
5836
5920
84
sao
716003
6S38
60S7
6170
6254
6337
6421
6504
6588
6671
6754
7S87
83
531
6921
7004
7088
8003
^
7338
7421
7504
83
52a
7671
S502
m^
I^
7920
8169
8253
8336
8419
83
S»3
S5S5
8751
8834
8917
9000
9083
9165
9248
83
S»4
933'
94>4
9497
95S0
9663
9745
9828
991 1
9994
•0077
83
535
720159
0242
0325
0407
0490
0573
0655
0738
0821
0903
83
526
09S6
1068
1151
1233
1316
1398
1481
1563
1646
1728
82
527
iSii
1^3
1975
2798
2058
2140
2222
2305
2387
2469
2552
82
538
2634
2716
2881
2963
3045
3127
3209
3291
3374
82
529
3456
3538
3620
3702
3784
3866
3948
4030
4112
4194
82
530
724276
4358
4440
4522
4604
4685
4767
4849
4931
5013
82
531
5095
5>76
5258
5340
5422
5503
5585
5667
5748
5830
82
53a
59" 2
5993
6075
6156
^238
6320
6401
6483
6564
6646
82
533
6727
6S09
6S90
6972
7053
7134
7216
7297
7379
7460
81
534
7541
7623
7704
7785
7866
7948
8029
81 10
8191
8273
81
535
72S354
8435
8516
8597
8678
8759
8841
8922
9003
9084
81
536
9165
9246
9327
9408
9489
9570
9651
9732
9813
9893
81
537
9974
*oo55
♦0136
*02I7
*0298
*0378
•0459
•0540
*062I
♦0702
81
538
7307^2
0S63
0944
1024
1105
1186
1266
1347
1428
1508
81
539
15S9
1669
1750
1830
191 1
1991
2072
2152
2233
2313
81
540
732394
2474
2555
2635
2715
2796
2876
2956
3037
3"7
80
541
3197
3278
3358
3438
3518
3598
3679
3759
3839
3919
80
54a
3999
4079
4160
4240
4320
4400
4480
4560
4640
4720
80
543
4800
4880
4960
5040
5120
5200
5279
5359
5439
6237
551.9
80
544
5599
5679
5759
5S38
5918
599S
6078
6157
6317
80
545
736397
6476
6556
6635
6715
6795
6874
6954
7034
7113
80
546
7193
7272
7352
7431
75"
7590
7670
7749
7829
7908
79
^l
79S7
8067
8146
8225
8305
8384
8463
8543
8622
8701
79
548
8781
8860
8939
9018
9097
9177
9256
9335
9414
9493
79
549
9572
9651
9731
9810
•9S89
9968
•0047
»0I26
*0205
*0284
79
550
740363
0442
0521
0600
0678
0757
0836
0915
0994
1073
79
551
1152
1230
1309
1388
1467
1546
1624
1703
1782
i860
79
552
1939
2018
2096
2175
2254
2332
241 1
2489
2568
2647
79
553
2725
2S04
2882 2961
3039
3118
3196
3275
3353
343 «
78
554
3510
35S8
3667 3745
3823
3902
3980
4058
4136
4215
78
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
CO
H
86 i 9 17
26
34
43
52
60
,
77
86
ei
P
9
J7
26
34
43
51
60
68
77
85
<
!<
8
17
25
34
42
50
59
67
76
84
0.
!3
8
'Z
25
33
42
50
58
66
75
83
83
8
16
25
33
41
49
57
66
74
83
&
0
OS
81
80
8
8
16
16
24
24
32
32
41
40
49
48
51
56
64
73
72
81
80
0.
79
8
16
24
32
40
47
55
63
71
79
Diff. I
2 3
4
5
6
7
«
9
Diff.
279
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
555
0
I
2
3
4
5
6
7
8
9
Diff.
744293
4371
4449
4528
4606
4684
4762
4840
4919
4997
78
556
5075
5153
5231
5309
5387
5465
5543
5621
5699
5777
78
557
5S55
5933
601 1
60S9
6167
6245
6323
6401
6479
6556
78
558
6634
6712
6790
6868
6945
7023
7101
7179
7256
7334
78
559
7412
7489
7567
7645
7722
7800
7878
7955
8033
8110
78
560
748188
8266
8343
8421
8498
8576
8653
8731
8808
8885
77
561
8963
9040
9n8
9195
9272
9350
9427
9504
9582
9659
77
562
9736
9S14
9S91
9968
*oo45
*OI23
*020O
*0277
*0354
*043i
77
563
75050S
05S6
0663
0740
0817
0894
0971
1048
1125
1202
77
564
1279
1356
1433
1510
1587
1664
174 1
1818
1895
1972
77
565
752048
2125
2202
2279
2356
2433
2509
2586
2663
2740
77
566
2816
2893
2970
3047
3123
3200
3277
3353
3430
3506
77
567
3583
3660
3736
3813
3S89
3966
4042
4119
4195
4272
77
568
4348
4425
4501
4578
4654
4730
4807
4883
4960
5036
76
569
5112
51S9
5265
5341
5417
5494
5570
5646
5722
5799
76
570
755875
5951
6027
6103
6180
6256
6332
6408
6484
6560
76
571
6636
6712
67S8
6S64
6940
7016
7092
7168
7244
7320
76
572
7396
7472
754S
7624
7700
7775
7851
7927
8003
8079
76
573
8155
8230
8306
83S2
8458
8533
8609
8685
8761
8836
76
574
8912
8988
9063
9139
9214
9290
9366
9441
9517
9592
76
575
759668
9743
9S19
9S94
9970
*oo45
*OI2I
♦0196
♦0272
*0347
75
576
760422
0498
0573
0649
0724
0799
OS75
0950
1025
IIOI
75
577
1176
1251
1326
1402
1477
1552
1627
1702
1778
1853
75
578
1928
2003
2078
2153
2228
2303
2378
2453
2529
2604
75
579
2679
2754
2S29
2904
2978
3053
3128
3203
3278
3353
75
580
763428
3503
3578
3653
3727
3802
3877
3952
4027
4101
75
5^'
4176
4251
4326
4400
4475
4550
4624
4699
4774
4848
75
5?^
4923
4998
5072
5147
5221
5296
5370
5445
5520
5594
75
5^3
5669
5743
5818
5S92
5966
6041
6115
6190
6264
6338
74
584
6413
6487
6562
6636
6710
67S5
6859
6933
7007
7082
74
5^5
767156
7230
7304
7379
7453
7527
7601
7675
7749
7823
74
586
7898
7972
8046
8120
8194
8268
8342
8416
8490
8564
74
5^2
8638
8712
87S6
8S60
8934
9008
9082
9156
9230
9303
74
588
9377
9451
9525
9599
9673
9746
9820
9S94
9968
♦0042
74
589
7701 15
0189
0263
0336
0410
04S4
0557
0631
0705
0778
74
590
770852
0926
0999
1073
1 146
1220
1293
1367
1440
1514
74
591
1587
166 1
1734
1S08
iSSi
1955
2028
2102
2175
2248
73
59s
2322
2395
2468
2542
2615
2688
2762
2835
2908
2981
73
593
3°55
3128
3201
3274
3348
3421
3494
3567
3640
3713
73
594
3786
3S60
3933
4006
4079
4152
4225
4298
4371
4444
73
595
774517
4590
4663
4736
4809
48S2
4955
5028
5100
5173
73
596
5246
5319
5392
5465
5538
5610
5683
5756
5829
5902
73
597
5974
6047
6120
6193
6265
6338
641 1
6483
6556
6629
73
598
6701
6774
6846
6919
6992
7064
7137.
7209
7282
7354
73
599
7427
7499
7572
7644
7717
7789
7862
7934
8006
8079
72
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
78
8
16
23
31
39
47
55
62
70
78
V,
77
8
15
23
31
39
46
54
62
69
77
<
76
8
15
23
30
38
46
53
61
68
76
0.
75
8
15
23
30
38
45
53
60
68
75
d
0.
74
7
15
22
30
37
44
52
59
67
74
73
7
15
22
29
37
44
51
58
66
73
7a
7
14
22
29
36
43
50
58
65
73
Diff.
Diff.
I
2
3
4
5
6
7
8
9
280
TABLB VII.— LOGARITHMS OP NUMBERS.
N. i
0 I
a
3
4
5
6
7
8
9
Diff.
7a
600
778«5>
8224
8296
8368
8441
9103
8513
9236
8585
9308
8658
8730
880a (
601
8874
8947
9019
9091
9380
^9452
9524
72
60a
9596
9669
9741
9813
9885
9957
•0029
•0101
•0173
•0245
72
603
7S0317
0389
0461
0533
obos
0677
0749
0821
0893
0965
72
6<4
J037
1109
1181
1253
1324
1396
1468
1540
1612
1684
72
^
7S1755
1827
1S99
1971
2042
2114
2186
2258
2329
2401
72
2473
2544
2616
26S8
2759
2831
2902
2974
3046
3117
72
607
3"^9
3260
3332
3403
3475
3546
3618
36.'<9
37«'i
3'<32
7"
608
3904
3975
4046
4118
4189
4261
4332
4403
4475
4546
71
609
4617
40S9
47tjo
483'
4902
4974
5045
5116
5'87
5259
71
610
785330
5401
5472
5543
5615
56S6
5757
f^l
5899
5970
6680
71
611
t)04i
6112
61S3
6254
6325
6396
6467
6538
6609
71
6ia
6751
6822
6893
6964
7035
7106
7>77
7248
7319
7390
71
613
7460
7531
7602
7673
7744
7815
8522
7885
S593
i2§^
8027
8098
71
614
8168
8239
8310
8381
8451
8663
8734
8804
7'
615
616
788875
8946
9016
9087
'^l
9228
9299
9369
9440
9510
71
9S8i
9651
9722
9792
9933
•0004
•0074
•0144
5
70
617
7902S5
0988
0356
0426
0496
0567
0637
0707
0778
0S4.S
0918
70
618
1059
1129
1199
1269
1340
1410
1480
1550
1(320
70
6ig
1691
I76I
1S31
1901
197 1
2041
2111
2181
2252
2322
70
6ao
792392
2462
2532
2602
2672
2742
2812
2882
2952
3022
70
631
3092
3162
3231
3301
3371
3441
35"
3581
3651
3721
70
633
3790
3S60
3930
4000 1 4070
4139
4209
4279
4349
4418
70
633
4488
4558
4627
4697 4767
4836
4906
4976
5045
5115
70
634
5185
5254
5324
5463
5532
5602
5672
5741
5811
1°
635
795880
5949
6019
6088
6158
6227
6297
6366
6436
6505
^
6a6
6574
6644
6713
6782
6852
6921
6990
7060
7129
7198
S
637
7268
7337
7406
7475
7545
8236
7614
76S3
7752
7S21
7890
69
638
7960
8029
8098
8167
f3°5
8374
8443
8513
8582
S
63g
8651
8720
8789
8858
8927
8996
9065
9134
9203
9272
69
630
799341
9409
9478
9547
9616
9685
9754
9823
9892
9961
^
^
631
S00029
oogS
0167
0236
0305
0373
0442
051 1
0580
0648
63a
0717
07S6
0854
0923
0992
1061
1129
1198
1266
1335
69
633
1404
1472
1541
1609
1678
1747
1S15
18S4
J952
2021
6
634
20S9
2158
2226
2295
2363
2432
2500
2568
2637
^705
68
635
802774
2842
2910
2979
3047
3116
^l^
3252
3321
3389
68
68
636
3457
3525
3594
3662
3730
3798
3867
3935
4003
4071
637
4>39
4208
4276
4344
4412
44S0
4548
4616
46S5
4753
68
638
4821
48S9
4957
5025
5093
5161
5229
5297
5365
5433
68
639
5501
5569
5637
5705
5773
5S41
5908
5976
6044
6112
63
640
806180
6248
6316
6384
6451
6519
6587
6655
6723
6790
68
68
641
6858
6926
6994
7061
7129
7197
7264
P^o
7400
7467
64a
7535
7603
7670
7738
7806
7873
7941
8008
8076
8143
68
6^3
8211
8279
8346
8414
8481
8549
8616
8684
8751
8818
P
tl
644
8886
8953
9021
9088
9156
9223
9290
9358
*^^§
9492
645
809560
9627
9694
9762
9829
9896
9964
*003l
♦0098
♦0165
67
67
646
810233
0300
0367
0434
0501
0569
0636
0703
0770
0837
1508
647
0904
1642
1039
1106
1173
1240
1307
1374
144 1
648
1575
1709
1776 1843
1910
1977
2044
2111
2178
f7
67
649
2245
2312
2379
2445 2512
2579
2646
2713
2780
2847
N.
1 Diff. I
2
3
4
5
6
7
8
9
Diff.
73
09
i 73
1 *5
22
29
37
44
51
5|
66
H
7a
14
22 1 29
36
43
50
58
65
73
0<
7«
14
21
28
36
43
50
51
64
7X
70
14
21
28
35
42
49
56
63
70
a,
U
14
14
21
20
28
27
35
34
41
41
48
' 55
54
62
61
Diff.
j Diff. I
2
3 4
1 5
6
7
8
9
281
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
67
650
SI29I3
29S0
3047
3114
3181
3247
3314
3381
3448
3514
65t
35«i
3648
3714
3781
3848
3914
3981
4048
4114
41S1
67
652
4248
4314
4381
4447
4514
4581
4b47
4714
47S0
4S47
67
653
4913
4980
5046
5113
5'79
5246
5312
5378
5445
5511
66
654
5578
5644
571 1
5777
5843
5910
5976
6042
6109
6175
66
655
816241
6308
6374
6440
6506
6573
6639
6705
6771
6838
66
656
6904
6970
7036
7102
7169
7235
7301
7367
7433
7499
66
657
7565
7631
7698
7764
7830
7S96
7962
8028
8094
8160
66
658
8226
8292
8358
8424
8490
8556
8622
8688
8754
8820
66
659
8S85
8951
9017
9083
9149
9215
9281
9346
9412
9473
66
660
819544
9610
9676
9741
9S07
9873
9939
*ooo4
*oo7o
*oi36
66
661
820201
0267
0333
0399
0464
0530
0595
0661
0727
0792
66
662
0858
0924
0989
1055
1 1 20
1186
1251
13 1 7
1382
1448
66
663
1514
1579
1645
1710
1775
1841
1906
1972
2037
2103
65
664
2i68
2233
2299
2364
2430
2495
2560
2626
2691
2756
65
665
822822
2887
2952
3018
3083
3148
3213
3279
3344
3409
65
666
3474
3539
3605
3670
3735
3800
3865
3930
3996
4061
65
667
4126
4191
4256
4321
4386
4451
4516
4581
4646
47n
65
668
4776
4841
4906
4971
5036
5101
5166
5231
5296
5361
65
66g
5426
5491
5556
5621
5686
5751
5815
5880
5945
6010
65
670
826075
6140
6204
6269
6334
6399
6464
6528
6593
6658
65
671
6723
6787
6852
6917
6981
7046
7ni
7175
7240
7305
65
672
7369
7434
7499
7563
7628
7692
7757
7821
7886
7951
65
673
8015
80S0
8144
8209
8273
8338
8402
8467
8531
8595
64
674
8660
8724
8789
8853
8918
8982
9046
9111
9175
9239
64
675
829304
9368
9432
9497
9561
9625
9690
9754
9818
98S2
64
676
9947
*0OII
*oo75
*oi39
*0204
*o268
*0332
♦0396
♦0460
♦0525
64
677
8305S9
0653
0717
0781
0845
0909
0973
1037
1102
1 166
64
678
1230
1294
1358
1422
I4S6
1550
1614
1678
1742
1806
64
679
1870
1934
1998
2062
2126
2189
2253
2317
2381
2445
64
680
832509
2573
2637
2700
2764
2828
2892
2956
3020
3083
64
681
3147
321 1
3275
3338
3402
3466
3530
3593
3657
3721
64
682
3784
3848
3912
3975
4039
4103
4166
4230
4294
4357
64
^^3
4421
4484
4548
4611
4675
4739
4802
4S66
4929
4993
64
684
5056
5120
51S3
5247
5310
5373
5437
5500
5564
5627
63
685
835691
5754
5817
5S81
5944
6007
6071
6134
6197
6261
63
686
6324
6387
6451
6514
6577
6641
6704
6767
6830
6894
63
687
6957
7020
7083
7146
7210
7273
7336
7399
7462
7525
63
688
7588
7652
7715
7778
7841
7904
7967
8030
8093
8156
63
68g
8219
8282
8345
8408
8471
8534
8597
8660
8723
8786
63
690
838S49
8912
8975
9038
9101
9164
9227
9289
9352
9415
63
691
0^478
9541
9604
9667
9729
9792
9855
9918
99S1
*oo43
63
692
840106
0169
0232
0294
0357
0420
04S2
0545
060S
0671
63
693
0733
0796
0S59
0921
0984
1046
1 109
1172
1234
1297
63
694
1359
1422
1485
1547
1610
1672
1735
1797
i860
1922
63
69s
841985
2047
2II0
2172
2235
2297
2-^60
2422
2484
2547
62
696
2609
2672
2734
2796
2859
2921
29S3
3046
3108
3170
62
f97
3233
3295
3357
3420
3482
3544
3606
3669
3731
3793
62
698
3855
3918
3980
4042
4104
4166
4229
4291
4353
4415
62
699
4477
4539
4601
4664
4726
4788
4850
4912
4974
5036
62
N.
DiflF.
X
2
3
4
5
6
7
8
9
Diff.
67
CO
67
7
13
20
27
34
40
47
54
60
hi
66
7
13
20
26
33
40
46
53
59
66
65
7
13
20
26
33
39
46
52
59
65
6
64
6
13
19
26
32
38
45
51
58
64
0.
63
6
13
19
25
32
38
44
50
57
63
63
6
12
19
25
31
37
43
50
56
62
Diff.
Diff.
I
2
3
4
5
6
7
8
9
282
TABLE vn— LOGARITHMS OF NUMBERS.
1
N.
0
I
a
3
4
5
6
7
8
9
Diff.
62
700
845098
5160
5222
5284
5346
5408
6028
5470
5532
6151
IIT,
5656
6275
701
5718
5780
5842
64t)i
5904
5966
6090
62
70a
6337
6399
6523
6585
6646
6708
6770
6832
6894
62
703
6955
7017
7079
7141
7202
7264
7326
7388
8004
7449
8ob6
7511
8128
62
7ii
3t>87
3741
3795
3S49
3904
395S
4012
4066
4120
54
80a
4«74
4229
4283
4337
4391
4445
4499
4553
4607
4661
54
803
4716
4770
4824
4878
4932
49S6
5040
5094
5148
5202
54
8°4
5256
5;5>o
5364
5418
5472
5526
55f>o
5634
5688
574*
54
1^
905796
6335
5904
0443
5958
6497
6012
6551
6066
6604
6119
665S
6>73
6712
6227
6766
6281
6820
54
54
807
6874
6927
6981
7035
70S9
7M3
7ig6
7250
7304
7358
54
808
809
741 1
7949
74b5
8002
Wst
7573
8110
7626
8163
76.S0
8217
7734
8270
77S7
8324
7841
8378
8431
54
54
810
90S485
8539
8592
8646
8699
8753
8S07
8S60
8914
8967
54
811
9021
9074
9128
91S1
9235
92S9
9342
9396
9449
9503
54
8l3
9556
9610
9663
9716
9770
9823
9877
9930
9984
♦0037
53
8x3
910091
0144
0197
0251
0304
0358
0S91
04U
0464
0518
0571
53
814
0624
0678
0731
0784
0838
0944
0998
1051
1 104
53
815
816
911 158
i2n
1264
1317
137 1
1424
1477
1530
15%
2116
1637
53
1690
1743
1797
1850
1903
1956
2009
2063
2169
53
817
2222
2275
2328
23S1
2435
2488
2541
2594
2647
2700
53
8x8
2753
2S06
2S59
2913
2966
3019
3072
3' 25
3178
3231
53
819
3284
3337
3390
3443
3496
3549
3602
3655
3708
3761
53
820
913814
3867
3920
3973
4026
4070
4132
4184
4237
4290
53
831
4343
4396
4449
4502
4555
4608
4660
4713
4766
4819
53
833
4872
4925
4977
5030
5083
5136
51S9
5241
5294
5347
53
833
5400
5453
59S0
5505
5558
561 1
5664
5716
5769
5822
5875
53
834
5927
6033
6085
6138
6191
6243
6296
6349
6401
53
835
916454
6507
6559
6612
6664
6717
6770
6822
6875
6927
53
836
6980
7033
7085
7138
7190
7243
7295
7348
7400
7453
53
837
7506
7558
761 1
7663
7716
7768
7820
7S73
7925
7978
52
838
8030
8083
8135
8188
8240
8293
8345
8397
8450
8502
52
839
8555
8607
8659
8712
8764
8816
8869
8921
8973
9026
52
830
919078
9130
9183
9706
9235
9287
9340
9392
9444
9496
9549
52
831
9601
9653
9758
9810
9862
99J4
9967
*ooi9
*007i
52
833
920123
0176
0228
0280
0332
0384
0436
0489
0541
0593
52
833
0645
0697
0749
0801
0853
0906
0958
lOIO
1062
1 1 14
52
834
1 166
1218
1270
1322
1374
1426
1478
1530
1582
1634
" 52
921686
1738
1790
1842
1894
1946
1998
2050
2102
2154
52
836
2206
2258
2310
2362
2414
2466
2518
2570
2622
2674
52
837
2725
2777
2829
2881
2933
2985
3037
30S9
3140
3192
52
838
3244
3296
3348
3399
3451
3503
3555
3607
3658
3710
52
839
3762
3814
3865
3917
3969
4021
4072
4124
4176
4228
52
840
924279
4331
4383
4434
4486
4538
45S9
4641
4693
4744
52
841
4796
4848
4899
4951
5003
5054
5106
5157
5209
5261
52
843
5312
5364
5415
5467
5518
5570
5621
5673
5725
5776
52
843
5828
5879
5931
5982
6034
6085
6137
6188
6240
6291
51
844
6342
6394
6445
6497
6548
6600
6651
6702
6754
6805
51
845
926S57
6908 1 6959
701 1
7062
71U
73^5
7216
7268
7319
51
846
7370
7&3
7422
7473
7524
7576 , 7627
7678
7730
7781
7832
51
847
7935
8037
8088 8140
8191
8242
f^3
5^5
51
848
8396
8447
8498
8549
8601 8652
8703
S754
8805
8857
51
849
890S
8959
9010
9061
9112 9163
9215
9266
9317
9368
51
N.
Diff.
I
2
3
4 5
6
7
8
9
Diff.
03
55 1 6 ; 11 ; 17 1 22 28
33
39
44
50
55
CU
54
5 11 16 1 22 27
32
38
43
49
54
53
5 11 16 1 21 27
32
37
42
48
53
06
0.
5a
5 } 10 16 21 26
I'll
31
36
42
47
5a
iHff.
X ^ 3 j 4
5
6
7
i 8
9
Diff.
285
TABLE VII.— LOGARITHMS OF NUMBERS.
1
N.
0
I
2
3
4
5
6
7
8
9
i
Diff.
850
929419
9470
9521
9572
9623
9674
..9725
9776
9827
9879
51
^5'
9930
9981
♦0032
*oo83
*oi34
*oi85
♦0236
*0287
*0338
♦0389
51
852
930440
0491
0542
0592
0643
0694
0745
0796
0847
0898
51
853
0949
1000
105 1
1102
"53
1204
1254
1305
1356
1407
51
854
1458
1509
1560
1610
1661
1712
1763
1814
1865
I9'5
51
855
931966
2017
2068
2118
2169
2220
2271
2322
2372
2423
51
856
2474
2524
2575
2626
2677
2727
2778
2829
2879
2930
51
857
2981
3031
3082
3133
3183
3234
3285
3335
3386
3437
51
858
3487
3538
3589
3639
3690
3740
3791
3841
3892
3943
51
859
3993
4044
4094
4145
4195
4246
4296
4347
4397
4448
51
860
934498
4549
4599
4650
4700
4751
4801
4852
4902
4953
50
861
5003
5054
5104
5154
5205
5255
5306
5356
5406
5457
50
862
5507
5558
5608
5658
5709
5759
5809
5860
5910
5960
50
863
601 1
606 1
6111
6162
6212
6262
6313
6363
6413
6463
50
864
6514
6564
6614
6665
6715
6765
6815
6865
6916
6966
50
865
937016
7066
7117
7167
7217
7267
7317
7367
7418
7468
50
866
7518
7568
7618
7668
7718
7769
7819
7869
7919
7969
50
867
8019
8069
8119
8169
8219
8269
8320
8370
8420
8470
50
868
8520
8570
8620
8670
8720
8770
8820
8870
8920
8970
50
86g
9020
9070
9120
9170
9220
9270
9320
9369
9419
9469
50
870
939519
9569
9619
9669
9719
9769
9819
9869
9918
9968
50
871
940018
006S
0118
0168
0218
0267
0317
0367
0417
0467
50
872
0516
0566
0616
0666
0716
0765
081S
0865
0915
0964
50
873
1014
1064
1114
1 163
1213
1263
1313
1362
1412
1462
50
874
1511
156 1
1611
1660
1710
1760
1809
1859
1909
1958
50
875
942008
2058
2107
2157
2207
2256
2306
2355
2405
2455
50
876
2504
2554
2603
2653
2702
2752
2801
2851
2901
2950
50
877
3000
3049
3099
3148
3198
3247
3297
3346
3396
3445
49
878
3495
3544
3593
3643
3692
3742
3791
3841
3890
3939
49
879
3989
4038
40S8
4137
41S6
4236
4285
4335
4384
4433
49
880
944483
4532
4581
4631
4680
4729
4779
4828
4877
4927
49
881
4976
5025
5074
5124
5.173
5222
5272
5321
5370
5419
49
882
5469
5518
5567
5616
5665
5715
5764
5813
5862
5912
49
!?3
5961
6010
6059 6108
6157
6207
6256
6305
6354
6403
49
884
6452
6501
6551
6600
6649
6698
6747
6796
6845
6894
49
885
946943
6992
7041
7090
7140
71S9
7238
7287
7336
7385
49
886
7434
7483
7532
7581
7630
7679
7728
7777
7826
7875
49
III
7924
7973
8022
8070
8119
8168
8217
8266
8315
8364
49
888
8413
8462
8511
8560
8609
8657
8706
8755
8804
8853
49
889
8902
8951
8999
9048
9097
9146
9195
9244
9292
9341
49
890
949390
9439
9488
9536
9585
9634
9683
9731
9780
9829
49
891
9878
9926
9975
*0O24
*oo73
*0I2I
*oi70
*02I9
♦0267
*03i6
49
892
950365
0414
0462
05II
0560
0608
0657
0706
0754
0S03
49
893
0851
0900
0949
0997
1046
1095
1 143
II92
1240
1289
49
894
1338
1386
1435
I4S3
1532
1580
1629
1677
1726
1775
49
^1
951823
1872
1920
1969
2017
2066
2114
2163
2211
2260
48
896
2308
2356
2405
2453
2502
2550
2599
2647
2696
2744
48
^l
2792
2S41
28S9
2938
2986
3034
3083
3I3I
3180
3228
48
898
3276
3325
3373
3421
3470
3518
3566
3615
3663
371 1
48
899
3760
3808
3856
3905
3953
4001
4049
4098
4146
4194
48
N.
Diff..
I
2
3
4
5
6
7
8
9
Diff.
51
CO
H
a.
51
5
10
15
20
26
31
36
41
46
50
5
10
15
20
25
30
35
40
45
50
a.
49
5
10
15
20
25
29
34
39
44
49
48
5
10
14
19
24
29
34
38
43
48
Diff.
I
2 3 4
5
6
7
8
9
Diff.
286
TABLE vn.— LOGARITHMS OP NUMBERS.
N.
0
Z
a
3
4
5
6
7
8
9
Diff.
48
900
954243
4291
4339
4387
4435
4484
4532
4580
4628
4677
901
4725
4773
4821
4869
4918
4966
5014
5062
51 10
5'58
48
90a
5207
5255
5303
5351
5399
5447
5495
5543
5592
5640
6120
48
903
5688
6i68
5736
5784
5832
5880
6361
5928
5976
6457
6024
6072
48
904
6216
6265
63'3
6409
6505
6553
6601
48
^
956649
7128
6697
6745
6793
6840
68H8
6936
6984
7032
7080
48
7176
7224
7272
7320
7368
7416
7464
75'2
7559
48
907
7607
8086
7655
7703
7751
7799
7847
7H94
7942
7990
8468
8038
48
908
8134
8181
8229
8277
8325
8373
8421
8516
48
909
8564
8612
8659
8707
8755
8803
8850
8898
8946
8994
48
910
959041
9089
9137
9185
9232
9280
9328
9375
9423
9471
48
9"
9518
9566
9614
9661
9709
9757
9804
9«52
9900
9947
48
gu
,9995
•0042
♦0090
♦0138
♦0185
*0233
*0280
*0328
♦0376
♦0423
48
913
960471
0518
0566
0613
0661
0709
0756
0804
0851
0899
48
9M
0946
0994
104 1
1089
1136
1 184
1658
1 231
1279
1326
1374
48
"'5
gio
961421
1469
1516
1563
1611
1706
1753
1801
1848
47
1895
1943
1990
2038
2085
2132
2180
2227
2275
2322
47
917
2569
2843
3310
2417
2464
251 1
2559
2606
2653
2701
2748
2795
47
918
2890
2937
2985
3032
3079
3126
3174
3221
3268
47
919
3363
3410
3457
3504
3552
3599
3646
3693
3741
47
gao
963788
3835
3882
3929
3977
4024
4071
4118
4165
4212
47
gai
4260
4307
4354
4401
4448
4495
4542
4590
4637
4684
47
gaa
4731
4778
4825
4872
4919
4966
5013
5061
5108
5155
47
933
5202
5249
5296
5343
5390
5437
.5484
5531
5578
5625
47
934
5672
5719
5766
5S13
5860
5907
5954
6001
6048
6095
47
935
966142
6189
6236
6283
6329
6376
6423
6470
6517
6564
47
ga6
6611
6658
6705
6752
6799
6S45
6892
6939
6986
7033
47
937
7080
7127
7173
7220
7267
73'4
7361
7408
7454
7501
47
938
ml
7595
7642
7688
7735
7782
7829
7875
7922
7969
47
gag
8062
8109
8156
8203
8249
8296
8343
8390
8436
47
930
9684S3
8530
8576
8623
8670
8716
8763
8810
8856
8903
47
931
8950
8996
9043
9090
9136
9183
9229
9276
9323
9369
47
93a
9416
9463
9509
9556
9602
9649
9695
9742
9789
9835
47
933
9882
9928
9975
*002I
*oo68
*oii4
*oi6i
*0207
*0254
*0300
47
934
970347
0393
0440
0486
0533
0579
0626
0672
0719
0765
46
935
970812
0858
0904
0951
0997
1044
1090
II37
1183
1229
46
936
1276
1322
1369
I415
1461
1508
1554
1601
1647
1693
46
937
1740
1786
1832
1879
1925
197 1
2018
2064
2110
2157
46
938
2203
2249
2295
2342
2388
2434
2481
2527
2573
2619
46
939
2666
2712
2758
2804
2851
2897
2943
2989
3035
3082
46
940
973128
3636
3220
3266
3313
3359
3405
3451
3497
3543
46
941
3590
36S2
3728
3774
3820
3S66
3913
3959
4005
46
94a
4051
4097
4143
41S9
4235
4281
43-;7
4374
4420
4466
46
943
4512
4558
4604
4650
4696
4742
4788
4834
4880
4926
46
944
4972
5018
5064
5IIO
5156
5202
5248
5294
5340
5386
46
945
975432
5478
5524
5570
5616
5662
5707
5753
5799
5845
46
946
5891
5937
5983
6029
6075
6l2I
6167
6212
625S
6304
46
947
6350
6396
6442
6488
6533
6579
6625
6671
6717
6763
46
948
6808
6854
6900
6946
6992
7037
7083
7129
7175
7220
46
949
7266
7312
7358
7403
7449
7495
7541
7586
7632
7678
46
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
m
^2
5
10
15
20
25
■29
34
39
44
0.
48
5
10
14
19
24
29
34
38
43
•
47
5
9
14
19
24
28
33
38
42
*l
0.
46
5
9
14
18
23
38
32
37
41
46
Diff.
I
2
3
4
5
6
7
8
9
Diff.
287
TABLE VII.— LOGARITHMS OF NUMBERS.
N.
0
I
2
3
4
5
6
7
8
9
Diff.
950
977724
7769
7815
7861
7906
7952
7998
8043
8089
8135
46
951
81S1
8226
8272
8317
8363
8409
8454
8500
8546
8591
46
952
8637
8683
8728
8774
8819
8S65
891 1
8956
9002
9047
46
953
9093
9138
9184
9230
9275
9321
9366
9412
9457
9503
46
954
9548
9594
9639
9685
9730
9776
9821
9867
9912
9958
46
955
9S0003
0049 0094
0140
0185
0231
0276
0322
0367
0412
45
956
0458
0503
0549
0594
0640
0685
0730
0776
0821
0867
45
957
0912
0957
1003
1048
1093
"39
1184
1229
1275
1320
45
958
1366
1411
1456
1501
1547
1592
1637
1683
1728
1773
45
959
1819
1864
1909
1954
2000
2045
2090
2135
2l8l
2226
45
960
982271
2316
2362
2407
2452
2497
2543
2588
2633
2678
45
961
2723
2769
2814
2859
2904
2949
2994
3040
3085
3130
45
962
3175
3220
3265
3310
3356
3401
3446
3491
3536
3581
45
963
.3626
3671
3716
3762
3807
3852
3897
3942
3987
4032
45
964
4077
4122
4167
4212
4257
4302
4347
4392
4437
4482
45
965
984527
4572
4617
4662
4707
4752
4797
4842
4887
4932
45
966
4977
5022
5067
5II2
5157
5202
5247
5292
5337
5382
45
967
5426
5471
5516
5561
5606
5651
5696
5741
5786
5830
45
968
5875
5920
5965
6010
6055
6100
6144
6189
6234
6279
45
969
6324
6369
6413
6458
6503
6548
6593
6637
6682
6727
45
970
986772
6817
6861
6906
6951
6996
7040
7085
7130
7175
45
971
7219
7264
7309
7353
7398
7443
7488
7532
7577
7622
45
972
7666
7711
7756
78CX)
7845
7890
7934
7979
8024
8068
45
973
8113
8157
8202
8247
8291
8336
8381
8425
8470
8514
45
974
8559
8604
8648
8693
8737
8782
8826
8871
8916
8960
45
975
989005
9049
9094
9138
9183
9227
9272
9316
9361
9405
45
976
9450
9494
9539
9583
9628
9672
9717
9761
9806
9850
44
977
9895
9939
9983
*0028
♦0072
*oii7
*oi6i
*0206
♦0250
*0294
44
978
990339
0383
0428
0472
0516
0561
0605
0650
0694
0738
44
979
0783
0827
0871
09i'6
0960
icx)4
1049
1093
"37
1182
44
980
991226
1270
1315
1359
1403
1448
1492
1536
1580
1625
44
981
1669
1713
1758
1802
1846
1890
'935
1979
2023
2067
44
982
2111
2156
2200
2244
22S8
2333
2377
2421
2465
2509
44
983
2554
2598
2642
2686
2730
2774
2S19
2863
2907
2951
44
984
2995
3039
3083
3127
3172
3216
3260
3304
3348
3392
44
9^f
993436
3480
3524
3568
3613
3657
3701
3745
3789
3833
44
986
3877 3921
3965
4009
4053
4097
4141
4185
4229
4273
44
987
4317
4361
4405
4449
4493
4537
4581
4625
4669
4713
44
988
4757
4801
4845
4889
4933
4977
5021
5065
5108
5152
44
989
5196
5240
5284
5328
5372
5416
5460
5504
5547
5591
44
990
995635
5679
5723
5767
581 1
5854
5898
5942
5986
6030
44
991
6074
6117
6161
6205
6249
6293
6337
6380
6424
6468
44
992
6512
6555
6599
6643
6687
6731
6774
6818
6862
6906
44
993
6949
6993
7037
7080
7124
7168
7212
7255
7299
7343
44
994
7386
7430
7474
7517
7561
7605
7648
7692
7736
7779
44
995
997823
7S67
7910
7954
7998
8041
8085
8129
8172
8216
44
996
8259
8303
8347
8390
8434
8477
8521
8564
8608
8652
44
997
8695
8739
8782
8826
8869
8913
8956
9000
9043
9087
44
998
9131
9174
9218
9261
9305
9348
9392
9435
9479
9522
44
999
9565
9609
9652
9696
9739
9783
9826
9870
9913
9957
43
N.
Diff.
I
2
3
4
5
6
7
8
9
Diff.
46
5
9
H
18
23
28
32
37
41
46
a,
45
5 i 9
14
18
23
27
32
36
41
45
44
4 1 9
13
18
22
26
31
35
40
44
a.
43
4 9
13
17
22
26
30
34
39
43
Diff.
I
2
3
4
5
6
7
8
9
Diff.
TABLB VII.— LOGARITHMS OP NUMBERS.
N.
0
I
a
3
4
5
6
7
8
9
Diff.
xooo
000000
0043
0087
0130
0174
0217
0260
0304
0347
039'
43
lOOI
0434
0477
0521
0564
0608
0651
0694
0738
0781
0824
43
looa
0Hb8
0911
0954
0998
1041
1084
1128
U71
1214
1258
43
X003
1301
1344
1388
1431
1474
1517
1561
1604
2036
2468
1647
Ibgo
43
1004
xooo
002166
1777
2209
1820
2252
1863
2296
1907
2339
iir.
1993
2425
2080
2512
2123
2555
43
43
2598
2641
2684
2727
2771
2814
2857
3288
2900
2943
43
X007
3029
3073
3116
3159
3202
3245
3676
3331
3374
3417
43
X008
3461
3504
3547
3590
3633
3719
3762
3805
3848
43
xoog
3891
3934
3977
4020
4063
4106
4149
4192
4235
4278
43
lOIO
004321
4364
4407
4450
4493
4536
4579
4622
4665
4708
43
XOII
4751
4794
4837
4880
4923
4966
5000
5438
5052
5095
5138
43
xoia
5181
5223
5266
5309
6166
5352
5395
5481
5524
5507
43
X013
S
5652
5695
5781
5824
5S67
633I
5952
5995
43
X014
6o8i
6124
6209
6680
6295
63S0
6423
43
xoij
X016
006466
6509
6552
6594
6637
6723
6765
6808
6851
43
6S94
6936
6979
7022
7065
7107
7150
7 '93
7236
7278
43
X017
7321
7364
7406
7449
7492
7534 7577
7620
7662
7705
43
1018
7748
7790
8217
7833
7876
7918
7961
8004
8046
8089
8132
43
loig
8174
8259
8302
8345
8387
8430
8472
8515
8558
43
X03O
008600
8643
8685
8728
8770
8813
8856
8898
8941
8983
43
xoai
9026
9068
9111
9153
9196
9238
9281
9323
9366
9408
42
xoaa
9451
9493
9536
9578
9621
9663
9706
9748
9791
9S33
42
1033
9876
9918
9961
*ooo3
*0045
»oo88
♦0130
*oi73
*02I5
*0258
42
X034
010300
0342
0385
0809
0427
0470
0512
0554
0597
0639
0681
42
xoas
010724
0766
0851
0893
0936
0978
1020
1063
i486
1 105
42
X036
1 147
1190
1232
1274
1317
1359
140 1
1444
1528
42
xoa7
1570
1613
1655
1697
1740
1782
1824
1866
1909
1951
42
xoaS
1993
2035
2078
2120
2162
2204
2247
2289
2331
2373
42
loag
2415
2458
2500
2542
2584
2626
2669
2711
2753
2795
42
X030
012837
2879
2922
2964
3006
3048
3090
3132
3174
3217
42
1031
3259
3301
3343
3385
3427
3469
35"
3553
3596
3638
42
1033
3680
3722
3764
3806
3848
3890
3932
3974
4016
4058
42
1033
4100
4142
4184
4226
4268
4310
4353
4395
4437
4479"
4898
42
1034
4521
4563
4605
4647
4689
4730
4772
4814
4856
42
1035
014940
4982
5024
5066
5108
5150
5192
5234
5276
5318
42
1036
5360
5402
5444
5485
5527
5569
561 1
5653
5695
5737
42
1037
5779
5821
5863
5904
5946
5988
6030
6072
6114
6156
42
1038
6197
6239
6281
6323
6365
6407
6448
6490
6532
6574
42
1039
6616
6657
6699
6741
6783
6824
6866
6908
6950
6992
42
1040
017033
7075
7117
7159
7200
7242
7284
7326
7367
7409
42
1041
7451
7492
7534
7576
7618
7659
7701
7743
7784
7826
42
X043
7868
7909
7951
7993
8034
8076
8118
8159
8201
8243
42
X043
8284
8326
8368
8409
8451
8492
8534
8576
8617
8659
42
X044
8700
8742
8784
8825
8867
8908
8950
8992
9033
9075
42
1045
019116
9158
9199
9241
9282
9324
9366
9407
9449
9490
42
1046
9532
9573
9615
9656
9698
9739
9781
9822
9864
9905
41
1047
9947
9988
*oo30
♦0071
*oii3
*oi54
*oi95
*0237
*0278
♦0320
41
X048
020361
0403
0444
04S6
0527
0568
0610
0651
0693
0734
41
1049
0775
0817
0858
0900
0941
0982
1024
1065
1 107
1 148
41
1050
021189
1231
1272
1313
1355
1396
1437
1479
1520
1561
41
N.
Diff.
I
2
9
3
4
5
6
7
8
,9
Diff.
.
CO
44
4
13
18
22
26
31
35
40
44
CU
43
4
9
13
17
22
26
30
34
32
43
0.
43
4
8
13
^l
21
25
29
34
38
43
41
4
8
12
16
21
25
29
33
37
41
Diff.
I
2
3
4
5
6
7
8
9
Diff.
289
INDEX
Article Pace
Accessibility of standing timber, definition of 176 178
Account, general outlay and income, in forestry 131 118
profit and loss, in forestry 131 118
trading and profit and loss, in forestry 131 1 18
Accounts, capital 20 11
capital, in forestry 131 118
cost 26 16
cost, in forestry 92 70
economic, forms of, in forestry 132 1 19
outlay and income 21 12
profit and loss 21 12
proprietary 19 11
proprietary, in forestry 91 69
specific 19 II
specific, in forestry, forms for 131 1 1 7
valuation 54 35
valuation, versus specific accounts 19 11
valuation, in forestry • 110 85
Accumulations of compound interest, effect of rate of interest upon ... 51 30
Additions to capital 73 49
Administration expenses 100 75
.Esthetic values 147 138
Age, economic 145 137
Agricultural land, expectation value of 237 230
sale value of 238 230
soils, definition of 226 226
value, timber as an 239 230
versus forest values of land 236 229
Agriculture versus forestry as a source of livelihood 232 227
All-aged stand, taxes paid upon 168 148
Amortization, definition of 173 173
Annual profits 40 2^
Anticipation of continuous profits 126 107
Anticipated profits on young timber 124 106
Application of methods of computing depreciation in lumbering 178 185
Appraisal in lumbering 120 102
of damages, principles underlying 133 1 20
timber left after logging 107 83
value 60 38
291
292 INDEX
Article Page
Appraisals, field 213 2t6
of stumpage, price basis in 172 1 70
value 171 169
stumpage, reports 224 222
stumpage, increasing future values as basis of 195 206
principle underlying 18 10
Appraised value 17 10
effect of capital value upon 70 45
Assets, appreciation of 73 50
in balance sheet 73 46
re-valuation of 73 48
valuation accounts for 19 11
Average logging costs, the basis of stumpage appraisals 175 179
Balance sheet 73 48
economic, in forestry 132 119
in forestry 131 117
problem of the 73 46
specific, in forestry 120 100
Bark-boring beetles 202 211
Basis for profits in lumbering, investment 178 184
of comparison of agricultural with forest values of land 236 229
damages, expectation or capital value 139 129
sale value 138 128
stunipage appraisals, increasing future values as 195 206
value of forests, income as Ill 85
Bonds, timber, interest on, as a carrying charge 181 192
on standing timber 96 72
Boxes and crates, use of wood for 189 199
Brown-tail moth 202 211
Brush burning, cost of 100 74
Building, use of wood for 189 199
Business investments, rate of interest for 47 28
of forest production, the 90 68
venture 28 17
Cancellation of classification of lands for forest taxation 166 164
of cost of land from sale of timber 107 83
Capital 12 6
additions to 73 49
deductions from 73 49
definition of 12 7
working 24 15
account, nature of 20 12
accounts 20 11
in forestry 131 1 18
and income, distinction in timber property 166 145
expenditures, in forestry 93 71
INDEX 293
Article Page
Capital, invested in forest production, earning ijower of 129 iii
investment, stumpage as a 176 180
returns on 31 18
stock 28 17
value, a basis of damages 139 1 29
detinition of 62 39
effect of rate of interest on 66 42
effect u[)on ai)praised value 70 45
sale value 69 44
independence of past outlay or cost 68 44
of forest soil 116 92
future sums 77 54
perpetual rentals 86 02
temporary annual rentals 81 58
intermittent rentals 83 60
time element in 65 42
uncertainty of 67 43
values, intlation of . . 71 45
Capitalist, function of the 13 7
Capitalization, regulation of 72 46
Capitalized expenses, as additions to capital 73 50
income value, definition of 62 40
rental value, definition of 62 40
value, definition of 62 39
Carrying charge, interest as a 36 22
charges versus profits on stumpage , . , . 181 igi
Chestnut bark disease 203 211
Classification of costs in forest production 104 76
land 235 229
land, national forest policy in 166 164
lands, cancellation of, in forest taxation 250 238
Clear lumber 184 196
Cleared land versus stump land 240 2^ i
Clearing stump lands, cost of 241 232
Climate, agricultural 228 226
Climatic injuries as a physical risk 204 211
Closeness of utilization 186 197
as affecting timber estimates 217 219
Combined capital tax and income tax 163 154
Commutation tax on forest property, Massachusetts 166 163
Comparison of agricultural and forest values of land 236 229
agriculture with forestry as a source of livelihood 232 227
bare forest soil with agricultural soil 248 237
costs, profits and stumpage value by overturn methods, diagram III 177 1 84
results of simple and compound interest 49 28
taxes on different forests, Table 11 158 148
forest rent versus soil rent 161 151
total forest values Vvith value of agricultural soil 249 237
294 INDEX
Article Page
1 20
4
Compensation, in damages 133
Competition, efifect of 7
Compound interest, definition of 16 8
comparison of results with simple interest 49 28
uses of 16 9
Computation of taxes under general property tax 164 157
Connecticut, taxation of forests in 166 161
Constitutional provisions of general property tax 166 165
Continuous forest production, profits from 125 107
value of forest property for 113 88
profits, anticipation of 126 107
Contractors' profits in logging 177 182
Contracts, long term, revision of stumpage values in 196 207
to provide against damages 140 132
Control of risks, insurance 209 213
private measures 211 214
public measures 210 213
Conversion of intermittent into annual rentals. 88 65
Correction factor in timber estimating 222 221
Cost accounts 26 16
in forestry 92 70
and value, essential difference between 58 37
as a basis of value 56 35
interest as a 36 20
of assets, addition of annual deficit to 73 48
brush burning 100 74
clearing stump lands 241 232
growing timber, calculation of 105 77
investments in standing timber 106 79
labor, in lumbering 190 201
many-aged forests • 108 83
milling 174 177
producing a normal forest 109 84
raw material, stumpage as a 176 181
re-establishing protective cover, as basis of damages 146 138
replacement, as basis of damages 137 126
restoration, in damages 133 121
slash disposal 100 74
transportation, elements in 98 73
past. Independence of capital value and 68 44
Costs, formula; for 243
future, effect on value 10 5
of forestry compared with destructive lumbering 107 81
logging 175 178
in forest production, classification of 104 76
specific 25 16
Cruisers, timber 218 219
Current annual forest per cent 129 114
INDEX 295
Akticle Page
Damage by fire, character of 136 1 22
to forest soil 143 135
forest property, elements of 133 122
immature timber, partial loss 141 132
total loss .' 142 133
many-aged stands 146 137
merchantable timber 140 131
single trees 144 136
soil, expressed in extra initial costs 142 134
watersheds 146 137
Damages, basis of; cost of replacement 137 126
expectation or capital value, a basis of 139 129
formula? for 247
increased future prices not a basis of 139 130
principles underhnng appraisal of 133 1 20
punitive 147 139
rate of interest as afifecting 139 131
sale value a basis of 138 1 28
Deductions from capital 73 49
Deferred profits 41 23
Definition of symbols 241
Defoliating insects 202 2 1 r
Demand 6 2
Depreciation as a cost of milling 174 177
a deduction from capital 73 49
an expense in logging > 175 179
definition of 173 173
formulse for 247
fund 173 173
Himter's formula 173 175
methods of reckoning 173 1 74
necessity for, in accounting 20 11
Destructive lumbering, costs of, compared with forestry 107 81
profits in 122 105
value of forest property for 112 86
Deterioration of merchantable timber, damages due to 140 132
standing timber 185 196
Determination of legitimate profits in lumbering 177 181
Diagram I, periods required for Si to multiply 51 31
II, method of balancing future costs and income 115 93
III, comparison of stumpage values, by overturn methods. ........ 177 184
Diaporthe parasitica 203 211
Difference between cost and value, essential 58 37
Discount 15 8
factor, definition of 74 53
Discrimination against forest values in land classification 246 236
in favor of forest values in land classification 247 236
Diseases, fungous 203 211
296 INDEX
Article Page
Disposition of income 30 17
Distinction between capital and income in timber property 156 145
Dividends, interest versus 32 18
Douglas fir, deterioration of, in Washington State 185 196
Doyle log rule 179 187
Doyle-Scribner log rule 179 187
Earning power of capital invested in forest production 129 iii
an investment 121 105
Economic accounts, forms of, in forestry 132 119
age of a stand 145 137
balance sheet, in forestry 132 119
comparison, in accounting 73 52
factors, in classification of soil as agricultural 231 227
forecast, in forestry 120 loi
opportunity 27 16
per cent earned on forest investments 129 112
profits 120 104
Efifect of capital value upon appraised value 70 45
sale value 69 44
deferred income upon rate of interest 48 28
general property tax on forest production 165 158
present condition of forest upon choice of methods of taxation. . . . 158 147
rate of interest upon accumulations of compound interest 51 30
interest upon capital value 66 42
risks on the business of forest production 212 214
substitutes on wood prices ; 189 198
taxes on property values 153 143
Effort or outlay 6 3
Elements of damage to forest property 134 122
value for forest land 243 233
Enterpriser, definition of term 39 23
Enterpriser's profit or gain 39 23
Entrepreneur, definition of term 39 23
Equality of taxation 153 143
Errors in methods of timber estimating 219 220
Estimation of standing timber 216 218
Even-aged forest, value for any j-ear 115 90
for any year, formula 116 95
just previous to cutting 114 89
stand, taxe^ paid upon 158 148
Exchange 29 17
Expectation value, a basis of damages 139 1 29
definition of 62 39
of agricultural soil 237 230
forest soil 116 92
future series 77 54
perpetual rentals 86 62
INDEX 297
Abti'lf. Pace
Expectation value, of temiwrary annual rentals 81 5°
intermittent rentals 83 Oo
Expenses, future, appraisal of "* 4^
included in outlay and income accounts 21 12
mvestments versus **' •>
or temporary outlay in forestry ^* 7'
versus value ^S
Exploitation of land purchasers *** ^^9
Factors affecting future value of forest products 182 195
determining stumpage prices 1'" '"7
Federal income tax law, with reference to cost accounts for parcels of
land 181 193
Field appraisals, scope of 213 216
methods of timber estimating *18 219
Final income, definition of °1 ^°
Financial risks ^^^ ^'^
definition of ^^^ '°^
Finished products, prices of 8 4
Fire as a moral risk *"'
physical risk 200 209
killed limber, damages for 1*" '-3'
lines, cost of ^^^ '5
public measures for control of *1" ^^^
T- . 200 20Q
Fire-rcsistance m trees ^
Forced sales ' • ^°
Forecast, economic, in forestry 120 101
or prospectus, in accounting '^ 5 1
Forest of 50 acres, taxes paid upon 1°8 148
investments, rate of interest on "2 32
land bare of timber, taxation of 1^^ ^^^
tax J60 X50
per cent, current annual 1^^ ^ '"*
1 .. 129 114
mean annual ^
production, classification of costs in 1"* 7"
continuous, profits from 120 107
value of forest property for 113 88
earning power of capital invested in 1*9 1 1 1
effect of general property tax upon 1^° ^5°
risks upon 212 214
, vT • 90 68
versus lumbenng
products, changes in prices of 188 ^97
future value of ^^2 195
property
, elements of damage to 1^*
122
sale value of 245 235
tax 159 ^49
tax reform for ^^^ ^^°
value, for destructive lumbering 112 86
298 INDEX
' Article Page
Forest rent, theory of 166 146
versus soil rent, comparison of taxes on 161 151
soil, damage to . 143 135
value of 116 92
young timber as part of value of 244 234
Forest statics, definition of 120 100
taxation in Connecticut 166 161
Massachusetts 166 161
Pennsylvania 166 161
problem of interest in 157 146
valuation, summary of formulae in 243
values, discrimination against, in land classification 246 236
in favor of, in land classification . . . ". 247 236
utilization, business of 90 68
versus agricultural values of land 236 229
Forestry, interest rates in, compared with other investments 53 33
versus agriculture as a source of livelihood 232 227
Forms for specific accounts in forestry 131 117
economic accounts in forestry 132 119
Formulae for costs 243
damages 247
depreciation 247
geometric series 248
geometric series, discussion of 80 57
interest earned 246
profits 246
stumpage values 248
values 244
in forest valuation, summary 243
of compound interest, summary 240
Fumes, as a physical risk 206 212
Fungous diseases, as a physical risk 203 211
Future crops of trees, as a measure of damage to soil 143 135
expenses, appraisal of 64 41
in taxation 162 152
income as a basis of value 61 38
operating costs, effect on stumpage values 190 201
prices and values, uncertainty of 63 41
as a basis of damages 139 130
supply of timber, as a local factor in stumpage appraisals 193 204
transportation facilities, in stumpage appraisals 191 202
value of forest products 182 195
temporary annual rentals 79 56
intermittent rentals 82 59
or cost of single sums 76 53
values, increasing, as basis of stumpage appraisals 196 206
INDEX 299
Article Pace
Gauging of risks 199 209
General oulla>- and income account in forestry 131 1 18
price changes as affecting stumpage values 187 igfj
property tax, the 154 144
effect of, upon forest production 166 158
on forest property 164 155
Geometric series, formula for 248
formulae for, discussion of 80 57
Grades of lumber, prices for, as basis of stumpage appraisals 172 1 7 1
Grading logs 223 222
Grass, intlammability 200 2 10
Growing stock, even-aged, value of 119 98
many-aged, value of 119 99
Growth in volume of stand 183 195
Gypsy moth 202 2 1 1
Hardwood litter, inflammability 200 210
Hazard, in risks, definition of 199 209
Humus or duff, inflammability 200 210
Hunter's formula for depreciation and interest 173 176
Immature timber, partial loss, damages 141 132
total loss, damages 142 133
Improvement in quality of products 184 196
Improvements, permanent investment in 96 73
Income 26 16
accounts, outlay and 21 12
as the basis of value of forests Ill 85
disposition of 30 17
future, as a basis of value 61 38
interest as 37 22
or products tax 162 152
potential 73 48
secondar>-, from forests Ill 86
tax, combined with capital tax 163 154
law, federal, with relation to cost accounts by parcels 181 193
on 150 141
timber lands . 162 152
value, capitalized, definition of 62 40
definition of 62 40
versus profits 42 24
Increase in stumpage value, rate of 194 204
Increased future prices not a basis of damages 139 130
Increasing future values as basis of stumpage appraisals 195 206
Independence of capital value and past outlay or cost 68 44
Industries and markets, local, effect on stumpage appraisals 192 203
Inflation of capital values 71 45
Influence of personality on the rate of interest 44 26
300 INDEX
Article Page
Influences determining the rate of interest 43 26
Injurious fumes, as a physical risii 205 212
Insects, as a physical risk 202 211
Installation, period of, in business 23 14
Insurance on timber 209 213
Intention to grow timber, influence in appraising damages to young
timber 138 129
Interest .• 14 7
as a cost 36 20
as distinguishing income from enterprisers' profits 42 25
as income 37 22
cannot be deducted from income; federal income tax 162 153
charges, as an expense 103 76
compound 16 8
definition of 14 8
earned, formulte for . . 246
not a cost in determining legitimate profit in lumbering 178 185
on bonds, as a carrying charge 181 192
problem of, the 35 20
in forest taxation 157 146
rate of, the 38 22
rate of, for business investments 47 28
rates in forestry, comparison with other investments 53 ;i^
rates paid by savings banks 53 2,3
simple 16 9
versus dividends 32 18
versus value 57 35
Inventory, definition of 55 35
Investments, business, rate of interest in 47 28
forest, rate of interest in 52 32
in lumbering, status of, resembling forest production 120 103
or permanent outlay in forestry 93 71
other than forestry, comparison of interest rates with forestry 53 33
versus expenses 22 13
Investment basis for profits in lumbering 178 184
in standing timber, total cost of 106 79
seed trees 107 82
total 24 14
Irregular income, value of many-aged forests producing 118 97
Labor, cost of, in lumbering 190 201
Land, agricultural versus forest values of 236 229
classification 235 229
national forest policy in 250 238
investment in 95 71
prices for 9 5
purchasers, exploitation of 234 229
tax, forest 160 150
INDEX 301
Article Page
Landscape gardening as basis for appraising damages 147 139
Larch s;uvfly 202 211
Legitimate profits in lumbering — overturn method 177 181
versus speculative value 67 43
Liabilities, in balance sheet 73 46
Liability, in risks, definition of 199 209
Life insurance, interest rates in 53 33
Limitation of opportunity 50 29
Loans 14 8
Local factors in stumpagc appraisals; industries and markets 192 203
stumpage appraisals; future supply of timber 193 204
stumpage appraisals; future transportation facilities 191 202
revenue, maintenance of, in forest taxation 166 161
Logarithms, use of 78 55
Log grades 223 222
markets 172 1 70
rules 216 218
Logging, definition of 90 68
Logging chance, definition of 213 216
costs and profit 175 1 78
effect on fire hazard 200 210
Logs, price of, as basis of stumpage appraisal 172 170
Long term contracts, revision of stumpage values in 196 207
Loss in value of entire property, a basis of damages 138 128
of income in damages 133 121
Lumbering, destructive, costs of, compared with forestry 107 81
status of investment in, resembling forest production 120 103
versus forest production 90 68
Maintenance of local revenue, in forest taxation 166 161
Many-aged forests, cost of 108 83
producing irregular income, value of 118 97
regular income, value of 117 96
.stands, damage to 145 137
Map, reconnaissance 214 217
Marketing of wind-thrown timber 201 211
Markets, local, effect on stumpage appraisals 192 203
Massachusetts, taxation of forests in 166 161
Mean annual forest per cent 129 1 14
Merchantable timber, definition of 167 166
damages to 140 131
taxation of 166 162
Methods of taxation, effect of present condition of forest upon 158 147
timber estimating, field 218 219
Mill prices, as a basis of stumpage appraisals 172 171
Mill run prices, in stumpage appraisals 172 172
Milling, definition of 90 68
costs and profits 174 177
302 INDEX
Article Page
Mixed stands, stumpage value for different species in 180 i88
Money, definition of 2 i
fluctuating values of, as affecting rate of interest 46 27
Monopoly, effect of, upon prices and values 7 4
Moral risks, fire 207 212
trespass 206 212
National forest policy, in land classification 260 238
forests, cost of replacement as basis of damages, on 137 126
Natural resources, value of 9 5
Nature of risks in forestry 198 208
Non-agricultural soils, definition of 232 228
Normal forest, cost of producing a 109 84
definition of 109 84
profit in forestry 107 82
Operating costs, future, effect on stumpage values 190 201
Opportunity, economic 27 16
limitation of 60 29
Outlay 6 3
classification of, in accounts 21 13
permanent, in forestry 93 71
past, independence of capital value 68 44
purpose of 20 11
temporary, in forestry 94 71
and income accounts 21 12
account, general, in forestry 131 118
relation in time between 23 14
Overhead charges 26 16
distribution of, in lumbering mixed stands 180 188
Overturn methods of appraising profits in lumbering 177 181
Overrun 179 187
Ownership _ 7 3
Paper pulp, use of wood for 189 200
Parcels, cost accounts by, versus entire operation 181 193
Partial loss, immature timber, damages 141 132
Past outlay or cost, independence of capital value 68 44
Penalty, taxes paid on cancellation of classification 166 164
Pennsylvania, taxation of forests in 166 i6r
Per cent, current annual forest 129 114
economic, on forest investments 129 112
of slope for agricultural soil 227 226
values taken by taxation, Table II 168 149
mean annual forest 129 114
Period of installation 23 14
Permanent improvements and equipment, investment in 97 73
outlay in forestry 93 71
IXDHX 303
Article Pace
Perpetual ronlals, explanation of meaning 86 64
present, expectation or capital value of 86 62
Personal factors in determination of agricultural soil 230 227
Personality, influence of, upon rate of interest 44 26
Philosophy of accounts, by Charles E. Sprague 73 52
Physical risks, delinition of 198 197
' fire 200 209
fungous diseases 203 2 1 1
insects 202 2 1 1
wind 201 210
separation of timber from soil 133 122
Pine needles, inflammability 200 210
Potential income 73 48
Present condition of forest, effect upon methods of taxation 158 147
value of future sums 77 54
perpetual rentals 86 62
temporary annual rentals 81 58
intermittent rentals 83 60
Price basis in appraisals 172 1 70
changes in forest products 188 197
general price changes affecting stumpage values 187 197
levels, changes in prices of forest products 188 197
Prices, definition 3 2
for grades of lumber, as basis of stumpage appraisals 172 171
future, and values, uncertainty of 63 41
of finished products 8 4
raw materials and natural resources 9 5
stumpage 169 167
factors determining 170 167
Principles underlying appraisal of damages 133 120
Private measures for control of fire risks 211 214
versus public forestry, profits in 130 115
Problem of the balance sheet 73 46
interest, the 35 20
in forest taxation 157 140
taxation for timber lands 155 145
Products, improvement in quality of 184 196
tax 162 1 5 2
Profit and loss account, form for 73 50
in forestry 131 1 iS
accounts 21 12
enterpriser's 39 2^
in lumbering, investment basis of 178 1S4
Profits as a per cent of logging and milling costs 177 182
margin between sale value of lumber, and costs 177 184
sale value of lumber 177 183
annual 40 23
anticipated, on young timber 124 106
304 INDEX
Article Page
Profits, continuous, anticipation of 126 107
deferred 41 23
definition of 33 19
economic 33 19
expressed as a ratio of income to capital 128 1 10
expressed in soil values 127 108
formulae for 246
from continuous forest production 125 107
in private versus public forestry 130 115
destructive lumbering 122 105
logging 176 179
lumbering, overturn methods 177 181
milling 174 177
income versus 42 24
of logging contractors 177 182
the undertaking, the 39 23
on a stand of timber 123 106
rate of interest in its relation to 121 104
versus carrying charges on stumpage 181 191
wages versus 34 19
Property, definition of 1 i
tax, forest 159 149
general 164 144
general, forest taxes under 164 155
on value of , 161 142
taxable value of 162 143
values, effect of taxes on 163 143
Proprietary accounts 19 n
in forestry 91 69
Proprietorship in balance sheet 73 46
Prospectus or forecast in accounting 73 51
Protection, expenses for 100 74
Protective values, damage to 146 137
Proximate damages 133 121
Pubhc measures for control of risks 210 213
policy in regulating private forestry 130 1 16
versus private forestry, profits in 130 115
Punitive damages 147 139
Purchasers of land, exploitation of 234 229
Quality of agricultural soil 226 226
products, improvement in 184 196
timber, estimation of 223 222
Railroad assets, valuation of, during construction 67 36
ties, use of wood for 189 200
Rate of increase in stumpage value 194 204
interest, the 38 22
INDKX 305
Abhcle Pace
Rate of interest, as affecting damages 139 131
earned 121 105
etTect of, upon capital value 66 42
deferred income upon 48 28
upon accumulations of comix)und interest. .. . 51 30
in forest investments 51 32
forestry, versus risks 197 208
its relation to profits 121 104
influences determining the 43 26
Rates of interest, in forestry, comparison with other investments 63 ^^
Ratio of income or earnings, to investments 89 66
to capital, profits expressed as! 128 1 10
Raw materials, prices of •g 5
material, stumpage as a cost of 176 i8i
Reciprocal values in forestry and agriculture 251 239
ReconnaisBance, definition of 55 35
map 214 217
Reform, tax, for forest property 166 160
Regulation of capitalization 72 46
pri\ate forestry by public measures 130 117
Relative importance of profits in private versus public forestry 130 115
Relation of rate of interest to profits 121 104
Rental value, definition of 62 40
Rentals, definition of 75 53
Replacement, cost of, basis of damages 137 1 26
Reports, stumpage appraisals 224 222
Resistance of trees to wind 201 2 10
Results of simple and compound interest, comparison of 49 28
Returns on capital 31 18
Re-valuation of assets 73 48
Revenue from which to meet taxes, sources of 149 141
Revision of stumpage values in long term contracts 196 207
Risk and expense as affecting rate of interest 45 27
Risks, control of — insurance 209 213
effect on the business of forest production 212 2x4
financial 208 2 1 2
definition of 198 208
gauging of 199 209
in forestry, nature of 198 208
logging 175 179
moral — trespass 206 212
— fire 207 212
physical, definition of 198 208
— fire 200 209
— fungous diseases 203 2 1 r
— injurious fumes 205 212
— insects 202 2 1 1
— wind 201 210
306 INDEX
Article Page
Risks, public measures for control of 210 213
versus rale of interest in forestry 197 208
Roads and transportation systems, investment in 98 7,3
Salaries versus profits 34 19
Sale value 17 9
as a basis of damages 138 1 28
value 59 37
efifect of capital value upon 69 44
of agricultural land 238 230
forest property 245 235
forests * Ill 86
stump lands 242 232
stumpage 167 166
Sales, forced 17 10
Savings banks, interest rates paid by 53 33
Scenery, value of 147 139
Scientific taxation, combined capital tax and income tax 154 163
forest land tax 160 150
property tax 159 149
income or products tax 162 152
Scope of field appraisals of timber stumpage 213 216
Sedgwick on damages 133 121
Sentimental value in damages 133 121
Separation of timber from soil, physical 135 122
value of timber from value of soil 136 123
Services or labor versus investments 22 13
Shingles, use of 189 199
Silvicultural operations, cost of 99 74
Simple interest 16 9
comparison of results with compound interest 49 28
Single trees, damage to 144 136
Slash disposal, cost of 100 74
Slope, per cent, for agricultural soil 227 226
Soils, agricultural, definition of 225 226
Soil, damage to 143 135
expectation value of 116 92
quality of 226 226
rent 116 95
as a cost of growing timber 136 124
deduction from damages 136 125
theory of 156 145
versus forest rent, comparison of taxes on 161 151
values, profits expressed in 127 108
Sources of revenue from which to meet taxes 149 141
Specific accounts 19 11
in forestry, forms for 131 117
balance sheet in forestry 120 100
iNDi:x J07
Articlk I' ace
Specific accounts, costs 25 i(>
Speculative value 67 43
Spra^ue, Charles K., philosophy of accounts 73 52
Stand, growth in volume of 183 195
improvement in quality of products 184 196
Standard log rules 216 21Q
of value 2 i
Standing timber, deterioration of 185 iy6
estimation of 215 218
investment in 96 72
State forester, power, in enforcing tax laws 166 164
Strip methods of timber estimating 219 220
Stump lands, cost of clearing 241 232
sale value of 242 2^2
land versus cleared land 240 231
Stumpage, carrjnng charges on, versus profits 181 191
appraisals, future local supply of timber as affecting 193 204
local industries and markets 193 204
reports 224 222
as a capital investment 176 180
cost of raw material 176 181
prices 169 167
factors determining 170 167
sale value of 168 166
value, appraisal of 171 169
rate of increase in 194 204
values, definition of 167 166
for different species in mixed stands 180 188
formuke for 248
revision of, in long term contracts 196 207
Substitutes, effect of, on wood prices 189 198
Summar\- of elements of value for forest land 243 233
formulcT in forest valuation 243
of compound interest : 240
Symbols, definition of 241
Table I — Comparison of Results of Simple and Compound Interest. . . 51 30
Table II — Comparison of Results of Taxation of Capital Values 158 148
Table III — Comparison of Sale Value with Expectation Value of
Even-aged Stand 164 156
Table IV — Periods within which Property Tax on Timber Becomes
Equivalent to Tax on Soil Value 165 159
Table V — Rate of Annual Increase in Value of Stumpage 194 205
Table VI — Compound Interest Tables 249
Table VII — Logarithms of Numbers 265
Tax, general property 154 144
on income 160 141
reform for forest property 166 160
308 INDEX
Article Page
Tax on value of property 151 142
Taxable value of property 152 143
Taxation for timber lands, problem of 155 145
of forest land bare of timber 166 161
bearing merchantable timber 166 162
property in Massachusetts 166 163
Pennsylvania 166 i6r
per cent of values taken by, for forest property 158 149
scientific, combined capital tax and income tax 163 154
forest property tax 159 149
land tax 160 150
income or products tax 162 152
Taxes as an expense 103 76
based on value, not on cost 161 151
comparison for forests of different age classes, Table II 158 148
of, on basis of forest rent versus soil rent 161 151
sources of revenue from which to meet 149 141
under general property tax 164 155
Telephone installation, cost of 100 75
Temporary annual rentals, future value of 79 56
present, expectation or capital value of 81 58
intermittent rentals, future value of 82 59
present, expectation or capital value of 83 60
outlay in forestry 94 71
Theory of forest rent 156 146
soil rent 156 145
Timber as an agricultural value 239 230
bonds, security for 96 72
cost of investments in 106 79
deterioration of 185 196
estimates, closeness of utilization as affecting 217 219
estimating, correction factors 222 221
errors in methods 219 220
field methods of 218 219
quality of timber 223 222
reports 224 222
strip methods 219 220
use of forest types in 221 221
estimation of 215 218
immature, partial loss, damages 141 132
total loss, damages 142 133
lands, problem of taxation for 155 145
merchantable, definition of 167 166
damage to 140 131
reconnaissance; the map 214 217
rights 96 72
separate from land, value of 119 98
standing, investment in 96 72
INDEX 309
ASTICLK I'AGK
Time, as a factor controlling stumpage prices 170 1O9
element in capital value 64 42
of, in values 11 6
relation in, between outlay and income 23 14
Total costs, calculation of, in growing timber 106 77
investment includes working capital 24 15
loss, immature timber, damages 142 133
Trading and profit and loss account in forestry 131 1 18
Transportation costs, effect on stumpage prices 170 169
efTect of methods, ujwn logging costs 176 178
facilities, future, as a local factor in stumpage appraisals 190 202
systems and roads, investments in 98 73
Trees, damage to 144 136
Trespass, damage as result of 140 131
as a moral risk 206 2 1 2
Types, forest, in timber estimating 221 221
Uncertainty of capital value 67 43
Undertaking, profits of the 39 23
Use of logarithms 78 55
Uses of wood 189 199
Utilization, closeness of 186 197
as aflecting timber estimates 217 219
Valuation accounts 19 i r
versus specific accounts 64 35
in forestry 110 85
of railroad assets during period of construction 67 36
Value, appraisal of 60 38
appraised 18 10
capital, definition of 62 39
uncertainty of 67 43
capitalized income, definition of 62 40
rental, definition of 62 40
cost as a basis of 66 35
essential difference between cost and 68 37
expectation, definition of 62 39
expenses and interest versus 67 35
future income as a basis of 61 38
income, definition of 62 40
of even-aged forest for any year 115 90
finished products 4 2
a forest of even age just previous to cutting 114 89
forests, income as basis of Ill 85
forest land, elements of 243 233
property for continuous forest production 113 88
destructive lumbering 112 86
soil 116 92
3IO INDEX
Article Page
Value of growing stock, even-aged 119 98
man3--aged 119 99
many-aged forests producing irregular income 118 97
regular income ". 117 96
money 2 i
fluctuating, as affecting rate of interest 46 27
property, tax on 151 142
scenery 147 139
soil, separation from value of timber 136 1 23
timber separate from land 119 98
young timber as part of the value of forest soil 244 234
rental, definition of 62 40
sale 17 9
as a basis of 59 37
speculative 67 43
standard of 2 i
stumpage, definition of . 167 166
appraisal of 171 169
taxable 152 143
time element in capital 64 42
Values 4 2
aesthetic 147 138
formula? for 244
effect of taxes on 153 143
future, uncertainty of 63 41
in forestry and agriculture, reciprocal 251 239
of stumpage for different species in mixed stands 180 188
Volume growth of stand 183 195
Wages versus profits 34 19
Water supply, dependence of agriculture on 229 227
Watersheds, damage to 146 137
Wealth 1 I
Wilful trespass, principle of damages in 140 131
Wind, as a physical risk 201 2 ro
Withdrawal of capital 73 49
Wood prices, effect of substitutes on 189 198
Wood, uses 189 199
Woodlot, effect on sale value of farm 138 128
Woodpeckers 202 211
Woodworking industries, effect on local stumpage values 192 203
Working capital 24 15
Yields per acre, basis of damages 139 130
Young timber, anticipated profits on 124 106
value of, as part of the value of forest soil 244 234
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