FOREST VAl UNIVERSITY OF B.C. LIBRARY HER U.B.C. LIBRARY 'M^ft^t^k ^Aumhbi Digitized by tine Internet Archive in 2010 witii funding from University of Britisii Columbia Library http://www.archive.org/details/forestvaluatioOOchap 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 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 University of British Colutnbia Library DUE DATE AGRICULTURE FORESTRY LIBRARY