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. FOREST VALUATION,

VOLUME II

Michigan Manual of Forestry

FILIBERT ROTH

1916 )/

PUBLISHED BY THE AUTHOR
ANN ARBOR, MICHIGAN

Ni *

TABLE OF CONTENTS

FOREST VALUATION.

PAGE;

I. INTRODUCTION i

A. Literature I

B. Scope and Application 2

1 . General 2

2. Valuation and Statics 3

3. Application 4

C. History of Valuation 7

II. ARITHMETIC OF FOREST VALUATION 10

a. General 10

b. Prolongation, Discount and Rate n

c. Summation of Series 1 1

d. Present Value of Series 13

e. Series of Periodic Payments 14

f . Sum of Infinite Series 15

g. Change of Periodic to Yearly Payments 17

h. Table of Formulae 17

III. APPLICATION OF VALUATION 19

A. Timber Crop, its Nature and Value 19

B. Risk in Forestry . 22

C. Interest Rate in Forestry 24

D. Valuation of Land or Soil 29

a. Cost, Sale — Income Value 29

b. Cost and Sale — Value of Forest Land in United

States 31

c. Income Value of Land in Forestry 32

E. Valuation of Soil and Statics 36

a. Relation of Se and its Factors 36

b. Values of Factors of Se and Variation in these

Factors 38

1. The Final Yield or Yr 38

2. Thinnings 46

3. Cost of Reproduction, c 48

4. Current Expenses, e 51

5. Rotation, r 54

6. Interest Rate, p 55

333963

IV FOREST VALUATION

c. Actual Values of Se 56

d. Appreciation of Calculation of Se 57

e. Se of the Copice Woods '. . . . 60

f. Se in the Selection Forest. 60

F. Value of Stand or Growing Stock in Even-aged Stand. 60

a. Sale Value of Growing Stock 61

b. Cost Value of Growing Stock 61

c. Expectation Value of Growing Stock. . . . , 63

d. Which Value to Use 64

e. Value of Land and Growing Stock together 65

G. Value of Growing Stock of Regulated or Normal

Forest 65

a. The Regulated Forest 66

b. Expectation Value of Growing Stock of Regulated

Normal Forest 66

€. Cost Value of Growing Stock in Regulated or

Normal Forest 70

H. Value of Growing Stock in the All-aged Forest 70

a. In the Regulated Forest 70

b. In the Irregular Forest. . . 72

IV. RELATION OF CAPITAL AND INCOME: IN FORESTRY 73

a; Nature of Income and Profit in Forestry. . 73

b. Interest made by the Forest 75

1. Interest made by a Single Stand of Even-aged

Forest 75

a. During a Short Period 76

b. During an Entire Rotation 78

2. Rate of Interest made by a Regulated Forest 79

3. Rate of Interest made in Forestry when starting

with Bare Land as Capital 81

c. Comparison of Properties with Yearly and with Inter-

mittent or Periodic Income 82

V. ROTATION 85

a. Rotation for Largest Income 85

b. Rotation for Largest Net Rental or Highest Rate of

Interest 87

VI. VALUE OF STUMPAGE 89

A. Cost Value of Stumpage 89

B. Sale Value of Stumpage 90

C. Expectation Value of Stumpage 96

otf CONTENTS v

VII. DAMAGE IN TIMBER 98

a. Shade Tree 98

b. Young Plantation of Forest Trees 99

c. Older Plantations 99

d. Ordinary Stand in Wild Woods 99

e. Young Stands of Wild Woods 101

f. The Lumberman's Case 102

VIII. TAXATION otf FORESTS 105

a. Nature of Taxation 105

b. Assessment and Rate 105

c. Forest Tax Impersonal 108

d. Forest Taxation in Europe 108

e. Forest Taxation in the United States 112

f. Recent Reforms in Forest Taxation 114

g. Basis of New Tax Laws • 115

h. Future in Forest Taxation 119

IX. FIRE INSURANCE IN FORESTRY 122

X. RIGHT USE OF LAND 128

a. Nature of Land .- 128

b. Classification of Lands 128

c. Factors affecting the Use of Land 128

d. Use of Lands in the Old World 130

e. Land Conditions in the United States 131

f. Agricultural Use 131

g. Income from Land 133

1. Income from Farm Lands. . 135

2. Income from Forests 138

3. Income from Range 140

APPENDIX , 143

A. Normal Yield Tables 143

B. Tables for Prolongation and Discount 157

C. Suggestions for Problems for School use 167

FOREST VALUATION

I. INTRODUCTION

A. LITERATURE.

Endres, Dr. Max. Lehrbuch der Waldwertrechnung und
Forststatik, 2nd ed. 1911, published by Julius Springer, Berlin;
308 pp.

Dr. Endres is Professor of Forestry at the University of
Miinchen, and author of the great "Forst Politik," one of the most
instructive books in forestry literature. On pages 1-4 is given a full
list of the literature of the subject. In addition the literature and
historic facts of interest are added to all important points in the
treatise. An excellent set of tables of compound interest, etc., forms
the appendix. As Dr. Endres says (p. 2), "Scientific forest valuation
is based on the labors of Faustman, Pressler and Gustav Heyer,"
and so it is but natural that this excellent and most complete treatise
should follow the works of these three great men and represent
what is accepted today as correct and scientific in forest valuation.

Stoetzer, Dr. H. Waldwertrechnung und Forstliche Statik,
Frankfurt, 1894 ; 4th ed. 1908.

Dr. Stoetzer's work as author, teacher and administrator, and
also as editor of the great Handbuch, is well known. In Valuation
and Statics he has stood and stands today one of the foremost
authorities.

Martin, Dr. H. Die Forstliche Statik, Berlin, 1905, Julius
Springer, 361 pp.

Dr. Martin is Professor of Forestry at Tharandt, formerly at
Eberswalde, author of "Forsteinrichtung," a prolific writer, well
known teacher and recognized authority. This book is entirely de-
voted to Statics of Forestry; its position is defined in the sentence
(p. 22), "As to the system and contents of this book, the author
closely follows Hundeshagen." In his introduction, one of the most
interesting and instructive chapters ever published on Forest Valua-
tion and Statics, he discusses the historic development and points
out the fact that the useful study of Statics was opposed in practice

2*'. , FOREST VALUATION

chiefly because the writers clung too much to mathematics and
formulae. The chapter, ''Choice between agriculture and forestry
in the use of land," to which thirty-five per cent of the book is
devoted is one of the best discussions of this subject and particularly
interesting at the present time to students of forestry and economics
in the United States.

Schlich, Dr. W. Manual of Forestry, vol. Ill, 1895, 4th
ed. 1911.

A brief chapter, fifty-nine pages in the first edition, following
closely the treatment by German authors.

Schenck, Dr. C. A. Forest Finance, published by Dr. Schenck,
Biltmore, N. C., 1909.

Chapman, H. H. Forest Valuation, Wiley & Sons, New York,
1915; 310 pp.

Professor Chapman treats the subject from the American stand-
point, and adds a number of topics not ordinarily treated in this
connection, particularly, Appraisal of damages; Forest taxation;
Stumpage values ; Future values of forest products, and Risks.
Convenient tables of the various formulae, compound interest values
and logarithms form the appendix.

Fernow, Dr. B. E. Forest Economics and Forest History.

Dr. Fernow, now Professor of Forestry at Toronto University,
himself a student of Gustav Heyer, points out the historic develop-
ment and the application of Forest Valuation and Statics.

B. SCOPE AND APPLICATION OF FOREST
VALUATION AND STATICS.

i. General.

In Forestry, just as in farming and other lines of business,
nearly every transaction involves expense and income and demands
judgment of values. If a piece of land, the timber on the land, or
a piece of forest (land and timber together) is bought, sold, rented,
leased, or in any way contracted for, the first question concerns the
value of the property under consideration. If a forester plants an
acre of land to forest trees the owner wants to know what such
work should cost and if under the particular, conditions it may be
expected to pay. Since it may take the crop fifty or more years to
grow to useful size, the question as to whether it will pay or not
involves the future and the owner must of necessity have faith in
certain premises. He must believe that the trees will grow and

VALUATION AND STATICS 3

thrive on the particular site, that a certain amount of expense will
suffice to care for them, that they will reach a useful size in a cer-
tain time, and finally, that they will have a definite value when cut.
If he has no faith in any of these premises it is an inexcusable
"gamble" for him to plant the trees. But to have faith in business
premises is not peculiar to forestry ; a man buying a farm believes
that the land will produce certain crops, produce them in ten or
twenty years just as now, and that the crops have a certain value,
justifying his labor and expense. Some years a dry season, frost,
hail or insects destroy most of his crops, but in the long run he main-
tains a successful average.

2. Valuation and Statics.

When the buyer estimates and examines a stand of timber
which he intends to cut over at once, he merely determines the
value for immediate use and the work is one of simple forest
valuation.

When a lumberman buys a body of timber with a view of
supplying his business for the next twenty years, the case is less
simple. He has to reckon with the future and with many uncer-
tainties; the timber may be old and become defective before he is
ready to cut ; fire and insects may destroy ; certain railway develop-
ments which he expects may not take place ; the prices of timber may
not advance; taxes, interest, or other expense may eat up all the
expected profits. It is a case of nice judgment in which the differ-
ent factors and conditions are estimated, if possible, in money value
and balanced to arrive at a final result. It is a case of weighing
various conditions; weighing effort and expense against expected
results. It is no longer simple valuation, but complex valuation
with a heavy proportion of statics, of the science and art of weigh-
ing cause and effect in our case, costs and results.

When the owner of a piece of land decides to change from
farm crop to forest, he does so because he has weighed the advan-
tages and disadvantages of both lines and found that the forest
will pay better. This weighing is Forest Statics. The "pay better"
need not be in money at all.

When a forester decides to give up natural reproduction and
plant five year transplants of spruce, he does, or should do this only
after careful weighing or calculation. His calculation should show
clearly that he may expect a material gain by going to this greater
expense of planting. In making his calculation he- starts with the
cost of planting. This he knows from experience. He figures on

4 FOREST VALUATION

a more even stand, more rapid growth, earlier thinnings, more in-
come from thinning and on an earlier final cut, saving him several
years waiting, use of the land and interest on the value of the stand.
Aside from the planting, all seems guess work. But this is not the
case; he has the. experience of centuries, of thousands of men, of
many thousand acres of timber to guide him. He has faith in this
experience and decides to plant. His process of weighing possi-
bilities is Forest Statics. It computes extra costs and forecasts
extra results.

It is clear that Forest Valuation and Forest Statics are not
sharply separated, that in most cases of valuation more or less
statics is involved and for this reason the two are generally treated
together in forestry, just as in other forms of valuation.

In the above cases the lumberman or the forester might prefer
not to go through any tedious process of reasoning, analysis or
calculation, and simply "jump at" the conclusion that he could-pay
ten dollars per acre for the timber, or in the case of the forester
that he could better afford to plant than to go on with natural repro-
duction. No doubt much of this is done. Some gifted or lucky men
succeed, most men lose. The gifted man has his own short method
and his results are correct in proportion as he is clever. The aver-
age man can not and does not jump at conclusions or guess results
if he can avoid it. And it is to help the average man analyze a given
case, weigh the various factors and combine them in a scientific
and effective manner that modern forest valuation was developed.
The importance of this development in forestry is emphasized by
the fact that the forester commonly deals with large properties, not
his own, where it becomes necessary to place the case before the
owner or his agent in a perfectly clear and convincing form. At
such a time every item must be clearly stated in a form capable of
detailed discussion, the methods of analysis and calculation must
be explained and stand the test of examination and trial.

3. Application of Valuation and Statics.

As in every other business, so in forestry, the work of valua-
tion or the determination of cost or value of property (land, timber,
etc.,) or of operations (planting, thinning, protection, logging, etc.,)
follows every line of work and is always in evidence. For example
its application in a few of the most important branches of forest
business :

i. In purchase, sale and exchange of property, such as land
timber, or forest (land and timber together) the necessity of ascer-

APPU CATION Otf VALUATION 5

taining the value of the property bought or sold is evident. This
kind of work in the United States at the present time is very im-
portant and will be more important in the future than it has been
in the past. The mere cruise for merchantable timber will no longer
satisfy men buying and selling forest properties. To sell a forest
for the value of the merchantable stuff alone is equivalent to giving
away over half the value in many localities and this condition is
rapidly extending.

2. Holding of timber for future use is a common practice
among lumbermen. In buying for ten or twenty years it is neces-
sary to compute expenses, taxes, interest, protection, probable losses,
and it requires an estimate or forecast of the price which may be
obtained at the end of the period or at the time of cutting. Taxes
and interest together with other current expenses come every year
and accumulate with compound interest; the final value must be
discounted to the present time. There is a right way of doing this
and many wrong ways and some of our lumbermen in the Lake
Region and elsewhere are finding today that it is not always easy
to make a state tax commission see the right way of computing the
true value of a lot of stumpage which can not possibly be cut "before
ten or twenty years.

3. Timber contracts, leases, rights of way. etc., are common
and necessary. A long time contract for hemlock in a hemlock and
hardwood forest may become a very difficult and troublesome affair.
To draw up such a contract requires a forester's judgment; to settle
it equitably involves forest valuation and statics.

4. Damage in timber, usually trespass or fire, is very com-
mon. In the past it was impossible for the courts to administer
justice: these cases were among the most unsatisfactory; the evi-
dence was neither clear nor convincing, the methods of calculation
could not be explained, they were never agreed upon ; it was a battle
of unproved assertion backed by a pretence of experience and
authority. As a result the courts granted nothing beyond a simple
provable loss of material actually saleable at the time of destruction.
Since modern forest valuation has found its way into the woods
business this situation has been relieved very materially and the
courts are glad to be able to grant real justice based upon an orderly,
intelligent method of determining the values. In fact the applica-
tion of modern forest valuation in the United States had its first
tests in damage cases.

5. Taxation requires assessment of the true value of the
property. As long as it was a fight with local assessors the old

6 FOREST VALUATION

methods alone were effective. Since the state tax commission takes
a hand in the assessment it becomes necessary to apply forest valua-
tion to show that if hemlock is worth five dollars per M. feet on the
stump for immediate use that the stuff to be cut in ten years from
now is not worth five dollars unless it doubles in value during the
ten years, which it has not done in the last ten years and will not in
the next. Similarly in our efforts at tax reform. Several states,
notably Pennsylvania, New York, Massachusetts and Connecticut
have initiated change of laws regarding taxation of forest property.
In all cases a "yield tax" was introduced and the taxation of the
land was modified. But what is a reasonable tax on stumpage? Is
it ten per cent as in Pennsylvania, or six per cent as in Massachusetts
and what basis has either state for its estimate? Guessing and
juggling a few figures will not give any permanent, satisfactory
relief ; it will require modern forest valuation to supply a basis.

6. The right use of land is one of the most important economic
questions in two-thirds of the United States. Is it wise to try to farm
all lands in Michigan, New York and Pennsylvania ; should part be
devoted to forest and if so what part, in what amount; what will
be the economic result if these lands are used to raise timber; how
may we determine which of the two, forest or field should have
preference in a given case ? Booster oratory or decision by the man
in the office may deceive some people for a time but it will lead to
great losses in the end. Pennsylvania, the Lake Region and other
districts today have millions of acres of idle, unused lands entailing
a loss of millions of dollars. The chief obstacle to any improve-
ment in this situation is the land boomer and his friends who con-
tinue to convince the legislatures that all land is farm land. The loss
is great and has accumulated for years. Nothing but the application
of sound methods of valuation and the recognition of this valuation
by the legislatures will prepare for the remedy and change great
money loss to income for the people.

7. The Management of the forest is and must always be the
most important subject of forest valuation and statics. As stated
before, every time an acre of land is planted to trees the question
arises — does it pay — should a different kind of tree, cheaper plant
stock, cheaper methods of planting be used. Later on — does it pay
to thin, should the thinning be light or heavy, and how often can we
afford to thin in this stand. All along there is expense for protec-
tion— should it be cheap, less than five cents per acre, will it pay to
go as high as ten cents, is it better to use many men or depend on
outfit, etc. In the end comes the question — is it more profitable to

HISTORY OF VALUATION 7

cut the stuff at the age of fifty, eighty or a hundred years. These
and many other questions must be studied and answered for each
stand, for each neighborhood, not merely once but repeatedly because
the answer varies with the premises, with success of silviculture,
market, transportation, cost of logging, labor in general, and many
other conditions. It is evident that in management the. wrork of
valuation is largely a matter of weighing or statics, though a great
deal of simple valuation also enters. Every year dozens of stands
must be estimated and millions of feet of timber appraised as to
their proper stumpage value.

C. HISTORY.

Forest valuation is old. Timber was an object of traffic with
the ancients, and traffic is unthinkable without valuation or the
setting of a price on the object bought or sold. When timber was
shipped or rafted, forests sold or exchanged, or mortgaged as is
recorded as early as the days of Charlemagne, an important part of
the transaction was the determination of the value of the forest or
timber.

Even the more modern conception of forest valuation the com-
parison of the growing stock to a capital increasing at a certain per
cent, the influence of the rotation or long interval between planting
and harvest, and finally the application of an orderly mathematical
analysis to discover the proper rotation and to compare different
kinds of forest, beech, spruce, etc., date back one hundred and fifty
years and more.

According to Endres (p. 183) the Forest Order of the princi-
pality of Neuburg, Bavaria, of the year 1577 makes it clear that the
yield from the forest is in the nature of interest on a capital and
that the person in possession has no right to cut more than the
growth or proper yield, being entitled only to the interest.

As early as 1623 the English economist Culpepper explained
that the forest could not produce a large interest rate. In 1721
Reaumur pointed out that too long a rotation meant real money
loss, and in 1742 Buffon in his "Memoirs sur la culture des forets"
discussed the same subject and pointed out the accumulation of ex-
penses in growing a forest crop.

In 1764 the great von Zanthier, first to establish a "Meister-
schule" for foresters, used compound interest calculations in forest
valuation ; worked out a comparison for different rotations in
beech, a comparison of beech, spruce and oak in which all expenses

8 FOREST VALUATION

are prolonged to the end of the rotation. He also prepared the first
money yield tables. Endres says of these calculations that they
were satisfactory (zweckentsprechend) so that we have here a
perfectly up-to-date piece of valuation and statics one hundred and
fifty years old.

In 1765 a writer in Stahl's Forstmagazin discusses a proper
interest rate to use in forest valuation and brings up the same argu-
ments used to this day to show that the ordinary commercial rate,
then four per cent, was too high.

With the rapid development of forest regulation and literature
about the end of the eighteenth century came considerable discus-
sion of forest valuation, for it now became necessary to promulgate
regular instructions to guide the practicing forest officials. G. L.
Hartig, Cotta, Konig and Pfeil all busied themselves with this
subject. Konig in 1813 first expressed clearly the value of using
the net rental on the land which might be secured in forestry as
proper measure not only of the value of the land but of the success
of the operation in silviculture, protection and utilization.

In 1823 Hundeshagen first uses the term forest statics and
defines it as the ''art of measuring the productive forces and results
in forestry."

About the same time Konig in his "Forstmathematik" discusses
the profitableness of forestry and introduces the idea of the profit
of undertaking (unternehmergewinn) and that of the per cent at
which a given forest works. In 1849 Faustman, more or less inde-
pendently, worked out the expectation or income value of the soil,
first expressed by Konig, and gave to forest valuation this analysis
in a formula — Se— which has never been changed or even modified
materially since, and which is recognized as the most important
analysis in forest statics. He showed that this analysis is applicable
alike to forests cut over at intervals (intermittent) and to regulated
properties with yearly cut.

In 1858 Pressler began publishing his works "Rationelle Wald-
wirt" and "Waldan des hochsten Ertrags" which really form the
beginning of a new epoch in forest valuation.

In 1865 Gustav Heyer published the first complete treatise on
valuation and followed this up in 1871 by the first treatise on forest
statics. Lehr worked over the subject for the Handbuch in 1887,
and Kraft, in 1882, distinguished himself in his efforts to determine
correct methods of measuring the value-growth in the forest, in his
"Zuwachsrechnungen."

The practice, as usual, was reluctant to accept everything. Yield
tables and every kindred means of helping the forester to know the

HISTORY Otf VALUATION 9

volume and value of the stand and the growth in time found no
difficulty in adoption by the practice. But when it came to formulae
with compound interest and especially when these formulae seemed
to be wrong as soon as five per cent, the current interest rate, was
used and when they seemed to lead to wholesale reduction of rota-
tions, the practicing forester ceased to have faith and refused to
accept.

Common sense and experience showed the forester that it
required at least eighty years (in a given case) to grow marketable
sizes of spruce, that smaller stuff was drug on the market. When
Pressler's and Heyer's calculations and formulae demanded a "finan-
cial" rotation of fifty years it was clear to the forester that some-
thing was radically wrong and even good men like Borggreve, Urich,
Bose and Baur denounced the whole method.

Some discussion is still going on, but the truth is gradually
becoming evident to all, that all these calculations have nothing to
do with the raising of timber, that this is left to silviculture and
regulation as guided by growth on one hand and market on the
other, and that these calculations merely try to supply a correct
measure, a reasonable, orderly, acceptable analysis to show exactly
what forestry is doing and wrhat it can do in any given case. If
then the growth of timber is so slow that the crop increases only
at the rate of two per cent compound, there is no amount of calcula-
tion and no juggling of methods and figures which will change the
plain fact and only one question remains — will we keep on raising
timber or quit? If the timber is needed and the land will not grow
any other crops or do better it is quite certain that forestry will
continue regardless of the rate per cent which it makes on the
capital.

At the same time it is becoming evident to all that valuation
is necessary. As pointed out before, the owner wants to know what
is actually made, what the land is worth if used to raise timber,
whether expensive planting of transplants is actually better than
cheap natural reproduction, etc. And he is not willing to take the
forester's mere word for it, he wants to see by what method of
calculation and upon what premises the recommendation is based.

In the efforts of bringing correct forest valuation and statics
into the forest business the labors of Judeich, master of forest
regulation, stand out conspicuously. In his long and successful
career at the head of the Saxon forests, he not only recommended
but introduced everything of value into the practice and he may
well be regarded as the most powerful exponent of modern forest
statics and especially of the general usefulness of Se.

II. ARITHMETIC OF FOREST VALUATION

a. General.

A stand of timber fifty years old after planting may be worth
two hundred dollars per acre. If this stand is to remain and con-
tinue to grow until it is eighty years old, it is right for the owner
to ask — at what rate is the stand, now fifty years old, growing, what
per cent is this growth on the two hundred dollars which the stand
is now worth, etc.

Since the stand does not pay or give up any interest, the two
hundred dollars or the value of the fifty year old stand is evidently
like a capital out at interest, where the interest remains unpaid, but
is added to the capital every year. In other words, the stand of
timber grows like capital out at compound interest.

If the owner wishes to know what this stand has cost to pro-
duce or grow to the age of fifty years he adds up the various items,
cost of planting, care and taxes during the fifty years, and the rent
on the land. The ten dollars per acre spent in planting have been out
for fifty years without drawing any interest, they have grown, there-
fore, at compound interest for fifty years. The expense of taxes
and care comes every year, the sum paid out the first year has been
out for forty-nine years, the sum paid the second year has been out
forty-eight years, etc., for none of this interest has been paid.

If the owner wishes to forecast or estimate what this stand is
worth to him today if it is to continue to grow until it is eighty years
old, he must first decide that when eighty years old the stand will
bring, say, five hundred dollars per acre and then discount the five
hundred dollars to the present day, i. e., for thirty years.

From this it is evident that forest valuation works a good deal
with the arithmetic of interest, with discount and with the summa-
tion of series, usually geometric series, the geometrical progressions
of many writers.

The following are the more common forms of interest here.1

1The elementary treatment of these simple problems in literal arithmetic
has been fully justified by fifteen years experience in University teaching.
The student will do well not only to go over this ground very thoroughly,
work out all formulae on paper and repeat often, but also to speak aloud
the true meaning of each formula and learn to state, as in geometry, exactly
what each formula means.

DISCOUNT AND PROLONGATION I I

b. Discount, Prolongation and Rate.

If $75 is put out at 4% compound interest for eight years, the
capital and interest to be paid at the end of the period, the $75
capital grows as follows :

at the start, C0 = $75; at the end of

first year, Ct— 75 -f- interest for one year = 75 +75 (.04)

= 75 (i +.04)= 75 (1.04);
second year, C2 = 75 (1.04) -f- interest = 75 (1.04) (1.04)

= 75(1.04')!

third year, C3 = 75 (1.04*) (1.04) —75 (i.O43) ;
eighth year, C8 = 75 (i.O4T) (1.04) =75 (l.Qf);
or, in general, Cn=^C0 (i.opn) ;
that is: the final capital equals the initial capital multiplied by i.opn.

From the above : - - = C0 or, the initial capital equals the final
i.opn

capital divided by i.opn, or it is equal to the final capital discounted
for n years at p per cent.

Also : — = i.opn, or i.op" equals the final capital divided by the
Co

initial capital.

Since the numerical value of i.opn may be found in the table,
the value of p, or the interest rate is readily determined.

C0 (i.opn) signifies that the initial capital C0 is prolonged at p

per cent for n years. — signifies that the final capital Cn is dis-
i.opn

counted at p per cent, n years.2

c. Summation of Geometrical Seriez.

If the yearly expenses on a property are $500, and these con-
tinue for fifty years and money is worth 3%, what will these ex-
penses amount to? Evidently the first $500 is out at compound
interest for 49 years, the second for 48 years, etc., and it is desira-
ble to find a short way of computing these various amounts.

2 The word capital is used here in a rather loose way, perhaps, but not
more so than .in ordinary conversation, etc., and it is a very helpful term to
employ in these explanations.

12 FOKF.ST VALUATION

1. Fundamentally this series is:

sum, S = a -j- ar -j- ar2 + ar3 + ar4
and

Sr — ar + ar2 -f ar3 + ar4 + ar5

subtracting the upper from the lower,

Sr— S — ar5 — a
or

S(r-i)=a(r5-i)
when

0 a(r5-!)
: (r-i)

since 5 is the number of terms in the series, or n, and this form is
perfectly general, it may be written :

a (rn— i)

:77^7T

In this series a is the regular payment, and r is the ratio between

ar2
any two consecutive terms, as : ->=-•= r.

2. Applying this to the above case of a yearly or current ex-
pense of $500 at 3%.

sum, S = 500 (i-0349) + 500 (I.0348) + +500

S (1.03) = 500 (i.035°) + 500 (i.0349) -f etc + 500 (1.03)

here 1.03 is the ratio, i. e.,

5oo(i.Q349) ._
500 (I.0348) ~ r'°3
subtracting :

S (1.03—1) =5oo(i.o350— i)

SOP (I.0350— i)

(1.03 -i)

By looking up I.O350 in the tables (see Appendix), the compu-
tation becomes perfectly simple and requires little time.

3. Since this same process applies to any similar case it may
be written as a general formula :

a(i.opn— i)
1 d.op-i)

which may be expressed:

The sum of a series of payments a coming every year, contin-
ued for n years and compounded at p per cent.

PRESENT VALUE OF SERIES 13

Since this sum represents the value of all these payments at
the end of the period, it may be termed the end value of the series.3

500 (i.o350— i)

Query : Is the sum - - the same whether it begins

(1.03—1)

in 1902 or in 1925, whether it begins in ten years from now, or has
run for fifteen years?

d. Present Value of the Series.

A farmer or forester may be able to get $500 rent per year
from a certain property. He may wish to know the value of twenty
years rent of this property with a view to raising money or selling
the twenty years' rent.

i. The end value or sum of the twenty years' rent is found as
above and is expressed :

500(1.03"— i)

sum or end value =: -
1.03—1

But what is the value of this sum today?
Keeping in mind that

-i.opn
and that Cn is the above sum or end value of the series :

CM 500 (l.032° — • i)

present value, Co = — ^ = / - — N - i
1.03" (1.03—1) 1.03"

Expressed in words : The present value of a series of payments
of $500 coming every year, continued twenty years, compounded
at 3% and discounted at the same per cent, the first payment coming
a year from now, in general,

a (i.op" — i )

present value of series = -, - ^r-7 - ^
(i.op— i) (i.opn)

2. Assuming that the above series runs for twenty years and
suppose that it has already run for seven years, what is its present
value ? Evidently the owner is seven years to the good, he does not

8 The student will do well to write these formulae exactly as he has
learned to develop them. The temptation is to write, for instance,
a (i.opn — i

— . This is correct, but it loses the connection, the student for-
.op

gets how he came by it. In solving ordinary problems write out the general
formula and keep this before you. This will avoid many mistakes.

14 FOREST VALUATION

need to discount it for twenty years but only for twenty less seven
or thirteen, and the case may be written :

500 (I.0320— i)
present value = ^— — y—^

500 (i.Q320 — O i.Q37
(1.03—1) i.of

this latter having the advantage that it keeps the whole story clearly
before the student.

If in the above case the series does not begin until fifteen years
from today, evidently the discount to present time must be longer
by these fifteen years, and the case may be written :

500 (i.032°— i)

present value = — ; rr-p-

(1.03—1) I.03**1
or to make it more clear,

500 (i.Q329 — 1),

(1.03-1) (i.o320) (i.o315)

e. Series of Periodic Payments.

If a forest property can be cut over every fifteen years and at
•each return the cut nets $500 it may become of interest to determine
what the value of ten cuts of the forest is. Assuming that the
property has just been cut over so that the next cut comes in fifteen
years and the last cut in one hundred and fifty years, the end value
or the value of the sum of these cuts is :

i. End value or sum :

S = 500 (I.03150-15) + 500 (i.o3150-30) 500

S (i.o315) = 500 (i.o3150) + 500 (I.03150-15) 500 (i.o315)

(Note that the ratio here is I.O315.)
Subtracting :

S (i.o315— i)=5oo(i.o315c— i)
500 (i.Q3150— i)
(i.o315-i)

If in the above case we let fifteen years = t, and 10, the num-
ber of cuts = n, then 150 — nt, and we may write the general form :

a (i.opnt — i)
1 d.op4-!)

Note: The student will recognize these periodic cases by the
-exponent t in the denominator.

INFINITE; SKRIES . 15

Expressed in words : The end value or sum of a series of pay-
ments of $500 each coming every fifteen years continued for ten
payments compounded at 3% and the first payment to be made in
fifteen years. r^c-v^*—

Query : Will the above sum or end value be greater or smaller
if the first cut comes in five years instead of fifteen years?

2. Present value of the sum of a series of periodic payments.
The case is the same as under d — I and 2.

Present value is :

a (i.opDt— i)
(i.op* — i) i.opnt

and is modified according to the time when the series begins, or, in
the above case, when the first cut is made by writing it:

a (iopnt — i) ioptj*~-

(i.op1 — i) i.opnt
where x is the number of years before the first cut or payment.

.f. Sum of Infinite Series.

When a farmer buys a farm he really buys the yearly income
or rent of the farm for all time, at least there is no set limit. In
practice about fifty years' rent is worth as much as the farm, but
this fact does not alter the nature of the bargain.

i. Using the formula as developed under c — 2 and 3, and tak-
ing its present value as under d — i, present value:

a(i.opn— i)
(i.op — i) i.opn

and letting n infinity or oo the formula becomes:

a (i.op00 — i)
present value = (iQp_ j} ^ „

and since i.opcc — i -— i.opc/o : present value

a a

(i.op — -i) i.op00 ~~ i.op— i ~~ .op

If a is the rental per year or $500, and p = 5, then the present

500
value of all the rentals from this farm forever are worth - or

•05

$10,000, which simply means that the farm is worth $10,000 if it
brings a net income of $500 and the buyer is willing to take 5% on

1 6 FOREST VALUATION

his money. The $10,000 is the income value of the farm at 5%,
and is equal to the net income capitalized at 5%.

2. If the income is periodic, comes every fifteen years, as in
the case of the forest cut over every fifteen years, the foregoing is
modified as follows :

500 (1.03 °° 15— i)
present value =

500 (l,03

i.0315— i (1.03
500

or in general :

(i.op'-i)

where A is the periodic rent or money income at each cut in the
above case. If in the above case the first cut comes in six years
instead of fifteen the owner is fifteen less six or nine years to the
good and this may be expressed as follows : value of property :

500 1.03"
~(i.0315-i)

That is, the sum is prolonged at 3% for nine years, or in general,

A i.op1-*
-(i.op'-i)

where x is the number of years before the first payment is due.
Note: Care must be taken to see that the sum A is really the
sum in every case. To illustrate : A forest of 100 acres can be cut
over every 20 years for $50 worth of timber (stumpage value) per
acre. The yearly expenses for the 20 years sum up to $15 per acre
so that the net income A is 50-15 or $35. ]f now the first cut may
be made at once the value of this property is :

income value = $50 + M—I, and not ' ^ Q^ __ I

because the first income is larger by 15 than the established future
incomes.

OF FORMULAE; 17

g. Change of Periodic to Yearly Payment.

Where a forest property furnishes an income only every twenty
years it may be desirable to convert this periodic income into a year-
ly one. If this property, on account of the periodic income is worth,
or has a safe income value of :

$48000 48000

—2-^ = -g = $60,000

1.03 — i i. 80 — i

and the bank or trust company is willing to accept this as fact and
pay the owner a yearly interest on the full $60,000 at 3% ; the owner
of the forest would receive 0.03 X 60,000 = $1,800 per year.
This may also be stated as follows :

$48,000 _ 1800 .
I.03'-"0 — i ~ .03

or the yearly income,

_ $48,000 (0.03)

loOO — .YI

1-03 — i
In general then :

A a A (.op)

(i.op* — i) (.op)' i.op* — i

h. Table of Formulae.

As above developed.

No. FORMULA. MEANING OF FORMULA.

£ _ £ (I0nn) Prolongation of initial capital C0 for n years at

p per cent.

2 ro__ 'CQ Discount of final capital Cn for n years at p

i.opn per cent.

3. Cn _ n Final capital Cn divided by initial capital Co to
Co ~ find interest rate p.

ofTon11— T") Sum. or end value of a series of payments a

4. Cn = S = ( v ^- coming every year continued for n years com-

(i.op — i) pounded at p per cent.

Present value of a series of payments a com-
/ n_,>> ing every year continued for n years com-

5. Co = - —^ pounded at" p per cent and discounted _at the

(i.op — i) i. op same per cent, first payment to come in one

year from now.

1 8 FOREST VALUATION

a(iopnt j^ Rnd value or sum of a series of payments a

6. €n = S = ( ' t_ ' coming every t years continued for n pay-
ments compounded at p per cent.

Present value of a series of payments a com-

- P _ a(i.opp — i) ing every t years continued for n payments

(i.pp* — i) i.oput compounded at p per cent, discounted at same

per cent, the first payment to come in t years.

The same as No. 7 but with the first payment

g £ — a^I-°P" — *) i-Qpt~x coming in x years so that the sum must be
(i.op* — i) ioprt prolonged for t — x years. Where x is greater
than t this becomes a discount.

Income value of a property producing a net

income a every year computed by capitalizing

a the income a at p per cent; or the present

9. Co— value of a series of payments a coming every

year continued forever compounded and dis-.
counted at p per cent, the first payment to
come in one year from now.

Present value of a series of payments A com-
ing every t years continuing forever com-
^ pounded and discounted at p per cent, the

10. Co — -, 't first payment to come in t years from now.

This is also the income value of a property
furnishing a net income A every t years com-
puted at p per cent.

jj Co = — I-°P "x Same as No. 10 but with the first payment

(i.op* — i) coming in x years from now.

Changing a periodic rental A coming every

A (o.op) t years into a yearly rental a where the value

i. op1 — i of the property is computed by capitalizing the

income at p per cent.

III. APPLICATION OF VALUATION

A. TIMBER CROP, ITS NATURE AND VALUE.

Timber was not only important to man in the past, it was a
necessity, a basic condition to every reasonable development. With
the great progress in manufacture, extended use of iron and steel,
especially with the introduction of cement the importance of wood
seemed to decrease materially and it was commonly predicted that
wood had really ceased to be a necessity. But the actual facts, the
consumption per head, the great traffic, export and import of tim-
ber, the intimate relation even dependence of many of our industries
on a liberal use of wood and the unexpected rise in price of timber,
the world over, all flatly contradict the common assertions and
prophecy of the past years. (See Fernow, Economics.)

The people of Europe use more wood today than formerly and
pay higher prices.

The timber import into Great Britain more than doubled be-
tween 1850 and 1890 and is about seventy per cent greater now than
in 1890, having exceeded one hundred and twenty millions.

Germany, an exporter until 1860, is the second greatest timber
importer in the world and this in spite of intensive forestry. France
is a growing importer and is exceeded in its import by Italy.

In the United States the consumption per head has increased
from about three hundred and fifty feet b. m. of lumber in 1880 to
over four hundred feet in 1910, in spite of the fact that stumpage
and lumber have increased in price by about one hundred per cent.

Our railways have not been able to free themselves from the
wooden tie, the telegraph and telephone lines use wooden poles, as
much lumber goes into ship building now as previously, charcoal
iron is still a preferred product, pulp and paper industries demand
more wood every year and nearly every new invention, even to the
propeller of the aeroplane calls for wood.

In keeping with this increased demand for wood prices have
advanced for a century. While the price of rye, the stable bread-
stuff, in Prussia decreased by fifteen per cent, the price of timber
increased by fifty-five per cent, between 1860 and 1903, and while
the income from the field remained nearly stationary the income
from forest, state forest, during the same period increased by one
hundred and eighty per cent in Bavaria, one hundred and forty-

20 FOREST VALUATION

seven per cent in Prussia and by over one hundred per cent for all
Germany.

Generally the demand is for lumber or larger sizes, and not
merely cordwood or quickly grown small stuff. The demand also
is more for conifers than for hardwoods ; in the United States the
consumption of conifers to hardwoods being about three to one.

Larger sizes require longer time to grow so that a forester of
central Europe does not expect to cut his timber before it is eighty
years old, the average rotations for conifers staying close to one
hundred years.

The forests of the world are limited, the really useful ones
amount to about one acre for each human being. In the United
States we now have about five acres of woods per head of popula-
tion. The population increases and the forests decrease. Even
under present conditions the people of the United States are depend-
ent for the future on the growth of five acres per head. This growth
at present is practically nothing. Even if cared for, it would prob-
ably just suffice for the needs of the population as it is at present.

This means that the future will demand reduction in consump-
tion regardless of all human efforts. With this reduction will come
further advance in price. In many localities this reduction has al-
ready come, the supply of raw material for hundreds of mills is
gone and from the state of Michigan alone industries with over
sixty million dollars investment have disappeared in the past twenty
years. The whole Lake Region, New York, Pennsylvania, parts of
the South and parts of Canada share in this change. In many local-
ities over large areas the change has been from industrial prosperity
to utter desolation, so that towns have been deserted, railway lines
taken up or abandoned.

The forest crop has its peculiarities. Categorically stated :

1. The forest takes many years to grow.

2. It can use sand lands, cold, steep, rocky, even poorly drained
lands, and so utilize large areas not useful otherwise.

3. The forest improves the land, and protects it against ero-
sion.

4. It is a much more certain crop than the field crops.

5. It is more independent of man, reproduces and grows very
well without human effort wherever climate, chiefly moisture, is at
all congenial to tree growth.

6. It requires not merely land but involves large investment
in the growing stock.

IMPORTANCE; OF TIMBER 21

A forester with ten thousand acres of woods properly regulated
so that he can cut every year, would cut about one hundred acres of
ripe timber. The other ninety-nine hundred acres have timber from
one to ninety-nine years old and this body of growing stock is worth
about four or five times as much as the land on which it stands.

In farming there is very little of this kind of investment, the
orchard trees, bushes of smaller fruit and meadow grass resemble it.

7. The crop is not ripened in a week or even a year but may
be cut when it is thirty, fifty or a hundred years old.

8. In case of accident, fire, insects, etc., a large part of the
damaged timber can be used, providing there are means of getting
it out, and a ready market.

9. Timber after it is cut is not a perishable material like po-
tatoes, fruits, etc., but is improved by seasoning. A body of sawed
timber may make from three to five per cent on its value in this way.
This gives independence in holding.

10. Timber crop requires further manufacture, sawmill, plan-
ing mill, pulp, etc. It stimulates industries.

11. The forest furnishes more material for transportation per
acre than the farm. The latter about two hundred and fifty .pounds
per acre, the forest about one thousand pounds.

12. The forest requires little help, therefore making larger
net income.

13. From all ordinary and inferior lands the forest makes as
large a gross income as does ordinary farming at present prices.

14. To the rural people the forest is a necessity to preserve
sufficient independence with regard to fuel and building material.

15. The forest prevents erosion, agriculture leads to erosion.
The forest is the only large agency at the disposal of man to influ-
ence the flow of water in streams, safely, effectively and permanent-
ly. In mountainous countries where the forest, because of the to-
pography, covers seventy-five per cent of the land it is the greatest
factor in water distribution.

16. Forest influences evaporation and rainfall, protects, locally,
against drying wind. It encourages bird and insect life and tends
to maintain a biological equilibrium, helpful to man, especially in
agriculture.

17. The forest is the greatest and most important feature of
the beauty of the earth. Thinking man will never wish to do with-
out the forest wherever it can be made to grow.

22 FOREST VALUATION

B. RISK IN FORESTRY.

The following statement is made with an apology; it is not
made because there is any special risk in forestry, or that forestry
is less safe a business than farming or other industries. It is made
because there is a very strong prejudice in the United States and
because this prejudice is constantly being fostered and its arguments
repeated in legislatures, among timber owners and others, as an
excuse for not doing their simple duty to the country and the for-
ests they control. The people of central Europe do not discuss the
risks in forestry. They have practiced forestry for more than five
hundred years. But many of the people of the United States who
have never practiced forestry at all, who still prefer to let the native
forests burn up rather than make any kind of adequate effort at
protection, are fully convinced that forestry is not practicable be-
cause forest fires can not be stopped.

In speaking of risks, it is usually the fire danger which is in
the minds of the people. As is shown in detail in the chapter on
fire insurance in forestry, this danger is universally overrated. For
forty years the matter of forest fire insurance has been agitated'
abroad, but in spite of the fact that some good companies are ready
to take up this insurance at $1.80 per $T,OOO property, the forester
generally has not felt the need of insurance and at every meeting
where this is discussed it is pointed out that the actual losses from
fire, even in the pinery districts of North Germany do not amount
to more than one-tenth the amount of this premium so there is no
reason why large owners should spend their money in this direction.
The statistical reports of Baden and Wiirttemberg do not find it
necessary even to mention losses from fire, and Bavaria for years
staid below four cents on the thousand dollars worth of woods.

In the United States without any effort to prevent the fires and
with many people eager to get rid of the forest, burning the forest
intentionally, the losses from fire have been very great. The report
of the United States Commission of Conservation in 1909 gives the
estimated losses per year, since 1870, at about fifty million dollars
for saleable material. This is about ten cents per acre per year and
therefore not far from the premium rate now demanded by the Ger-
man insurance companies, so that it was as cheap to let the woods
burn as it would have been to insure them in up to date companies,
even if this could have been done. It is evident then that even in the
United States in spite of all neglect, lack of law and law enforce-
ment, in spite of land clearing, etc.. which made burning necessary,
the fire losses in the forest are relatively small. Had they been

RISK IN FORESTRY 23

spread over all forests evenly instead of being concentrated at cer-
tain points, there would not be the general fear of fire risk in for-
estry.

As a real menace to forestry insects and wood- destroying fungi
are much more serious. Even in the best cared for forests of Ger-
many, fungi, producing defects and decay in the timber, and even
killing young trees, are a constant trouble. But this is true of the
wild woods as it is of the cultivated forest and it is true of the farm
crop more than of the woods. One of the greatest tasks of the
United States Department of Agriculture and of all state experi-
ment stations is to find remedies for the many plant enemies of our
crops and fruits. Millions are spent every year by the farmer in
spraying, etc., and millions more are lost for lack of effective treat-
ment. The same is true with insects; scale, louse, moth, weevil,
chinch bug, wheat fly, and potato beetle have, and do cost many
millions every year. If the fly gets into wheat, the chinch bug into
the corn or the boll weevil into cotton the loss is often complete. An
attack of insects in timber, even if severe enough to kill, is only a
partial loss, all large stuff can be used, wherever forestry has become
a real business with means of utilization and a market. While the
German forester is much more concerned about insects and fungi
than about forest fires, it does not occur to anyone to think of these
difficulties as a risk sufficient to discourage forestry as a business.
Weber in the Handb-uch and Endres in his Forst Politik made no
effort to estimate these losses. Like those from fire in the United
States they are great both here and abroad but they even up as they
do in farming. To the small owner they are serious, in large hold-
ings they form a regular trouble to figure with. Endres (p. 95)
mentions the losses from wind, snow, ice and insects, (leaves out
fire) and says that in all computation of averages these losses are
inconspicuous — "Kommen nur wenig zum Ausdruck.''

As regards the growth and reproduction of the crop itself which
expresses more properly the certainty or success in crop production,
the forest far excels the farm crop. From Michigan to the Gulf,
the forest was practically unbroken, there were no large "burns"
or other gaps. Nature had reproduced one crop after another, the
crops had grown to old age, died and given way to new crops.
Windstorms, insects and fungi had collected their toll but the forest
was there and asked no help. In the most intensive forestry in Ger-
many less than twenty per cent of the expenses are devoted to plant-
ing, etc., to protection and care of the crop, about fifty per cent is
spent in harvesting. Where the forest has not been abused and
where the climate is good the new crop comes in without any help

24 FOREST VALUATION

or delay, and even where planting is justified by better returns, this
planting makes rarely more than ten per cent of the total expenses
on a forestry property. The growth of the forest is quite secure, a
dry season may produce less wood, but the next season makes up
for it and the harvest of the year does not show the effects at all.
Frost, hail, extremes of cold and heat, etc., all affect the forest, but
only in a small degree and the cut of the year remains unchanged.
Insects may partly defoliate a stand of oak and hurt it quite severe-
ly ; but if the stand recovers, as is usually the case, the man who har-
vests this stand will never know the difference and the effects of the
injury are hardly felt or known by the business.

In farming the time of ripening is a critical period ; a few days
of dry weather, dry hot winds, a hail storm, rain, etc., may largely
destroy the season's yield. Nothing of this kind exists in forestry.
If a sixty-year-old stand is not growing well, if fungi have started
their work and the stand begins to be defective it is cut and used
and another put in its place.

In a twenty-year average farming over large areas must be
content with about sixty per cent full or normal crop, even in the
great staples, wheat, corn, etc., while forestry, where properly prac-
ticed at all, produces over seventy per cent of a full crop. In fruit
farming it is doubtful if the average crop is twenty per cent of a
regular full crop.

From this sketch it is evident that the risk in forestry is small,
smaller than in farming and much smaller than in most city business.
It is this very security which has distinguished the state forests and
forests of other large owners and which has made the forest the
valuable and desirable property it is. Where the forest is neglected,
stocked with poor species and handled by poor methods, coppice in
France, for instance, and where mismanagement has left unmade
suitable improvements, it is only natural that the value of the prop-
erty is small, in keeping with low income. But even in these cases
it is not risk but low income, due to neglect, which is the fault.

C. THE INTEREST RATE IN FORESTRY.

a. General.

When a farmer who paid $6,000 for a loo-acre farm finds that
for 10 years back he averaged $300 net income per year for his crops
he naturally asks — what per cent is this on my investment? If he is
satisfied with the 5% which it made he will be satisfied with farm

INTEREST RATE 25

business, if he feels that he ought to make 10% on his money he
will want to sell out.

In this case it is a matter of experience and fact, with $300 in-
come 5% is what the farm made on $6,000 cost price. If now a man
wishes to buy this farm and is shown that the farm made $300 net
income per year he may say : the farm is good for $300 per year,
is a safe property, I may as well put my money into this farm as
keep it in the bank at three per cent. To him the income value of the

$300

farm is: - - or $10,000 and he may be. satisfied to pay this price.
0.03

To another man who values his money at 6% the farm is worth
only half this amount. In this case the three per cent or six per cent
are set by the man who wishes to buy the farm and judges its value
by the income it makes and a per cent which he determines himself.

In forestry, too, these two fundamental cases of determining
interest rate occur and very commonly are both present in the same
calculation.

If a planted stand of pine sixty years old is ready to cut and
worth $300 per acre the owner may want to know what per cent
was made on the investment. He knows that it cost $10 to plant,
that the land cost $20 per acre and that it cost 60 cents per acre each
year to take care of the forest and pay taxes. The ten dollars for
planting have been out at compound interest for fifty-nine years,
and the question arises — at what per cent? Evidently it is for the
man to choose this per cent. When the calculation is finished and
he finds that all expenses for the sixty years amount to $180 per
acre he can find the net income and real value of his business.

The calculation of what interest rate a stand of timber actually
makes or has made is comparatively simple and there is little dis-
agreement as to method. But what per cent to assume or set in
calculations of forest valuation is quite a different question, and the
opinions often differ and have differed since valuation began.

To choose a high rate, such as the current rate of interest paid
by business men and farmers gives the calculation a business-like
air and seems practical. But even the reasonable rate of five per cent
will seem to prove most forestry a failure or lead to a demand for
absurdly low rotations, etc. To choose a low rate, say two or three
per cent, is unpopular, seems to discredit forestry, sounds theoretic
and unpractical.

But the choice must be made, forest valuation is impossible
without it. The man who puts money into land and timber for for-

26 FOREST VALUATION

estry must have some reasonable calculation to show what he ex-
pects of the business. Tax commissions and legislatures will not
change their methods unless shown convincing facts as argument.
It is self-evident that the assumed interest rate and all calculations
based on this rate have nothing at all to do with the growth of the
timber and all these calculations can possibly do is to give a reason-
able measure of what actually takes place and compare forestry as
a business with other kinds of business. The question is — is there
a reasonable and acceptable basis for interest rate to set in forestry?

b. Interest rates paid and made.

In the United States today the ordinary loan pays about 5%,
timberland owners and many industrials pay 6% and over, the far-
mer pays about 6 % in the east and north, larger per cents in the
south and west, so that it was reported in 1912 that the farmer of
the United States borrows about 6,000 million dollars at an average
rate of 8%. Large railroad companies, etc., pay four or five per
cent. Cities and states pay about four per cent on their bonds, the
United States Government can borrow at from two to two and a
half per cent, and the savings banks with their enormous deposits -
pay generally three per cent, while millions of dollars are deposited
in banks and draw no interest.

In Germany mortgages pay about four or four and a half per
cent, bonds about 3.4% to 3.8%.

Interest rates are higher in new and undeveloped countries, the
West pays higher than the East.

In the fourteenth century the common rate in Germany was ten
per cent, it sank to five per cent by the sixteenth century. After
the Napoleonic wars it went up to eight per cent, then it sank to
three per cent by 1870, rose again to five and then declined to present
rates.

2. The fact that a man pays six per cent on his mortgage is
no indication that the man makes six per cent in his business, what-
ever that may be. This seems self-evident, and yet it is the most
common fallacy in connection with this discussion to assume that
because a certain per cent is paid by the men of a certain industry
when in need of money this rate is also made or approximated by
the industry.

a. Since agriculture in the broad sense really includes forest-
ry, it is fair to use farm business as a criterion and see what farm
business pays. The data for the following analysis are taken from
circular I32-A, 1913, of the United States Department of Agricul-
ture, and based on the Census of 1910.

INTEREST ON FARM 27

The average farm of the United States has 138 acres and is
valued at $6,443, including stock and implements.

The total or gross income is $980, leaving off cents, of which
$860 is the value of the crop, including stuff fed.

In the summary on page four of circular 132, the data are ar-
ranged as follows :

"Total gross income .$980

Total expenses 340

Net farm income 640

Interest on investment 5% 322

Labor income, including unpaid family labor and all
the farm furnishes toward the family living except
milk and cream. Does not include income from
outside sources, and the amount paid for live stock

bought must be deducted from this sum" 318

"Interest on mortgage, $1,715 at 6% $102

Available for live stock and for family living $537"

These same data may be arranged as follows, where it is as-
sumed that the farmer and his family should receive for their labor
at least the wages of one- farm laborer without board, since they
board themselves, and that it takes $50 per year to replace teams
and other live stock.

Gross income per year $980

Expenses :

Labor $102

Fertilizer 18

Feed 47

To maintain buildings 49

To maintain implements 39

Taxes, at 0.6% 38

Miscellaneous .' 44

Salary of farmer and family 360

Replacement of live stock 50 $750

Net income . $230

This $230 is three and a half per cent on the $6,443 capital.
If the $102 interest on the mortgage is deducted there remains only
two per cent interest actually made by the average farm of the
United States in 1910.

28 FOREST VALUATION

Since the average farmer with his family can not be engaged
at less than $500 per year and usually demand part or all the gro-
ceries for the household paid by the employer it is evident that the
above three and a half per cent is too high and it is doubtful if two
per cent is actually made.

This fully agrees with the findings of Cornell Agricultural Col-
lege and with bulletin 41, United States Department of Agriculture,
1914, which shows that the interest made on selected farms in Indi-
ana, Illinois and Iowa in 1911 was about three and a half per cent
and in cash rent system less than three per cent. It is evident that
many farmers make no interest at all and do not even make the com-
mon farm hand wages.

Whether this fact is explained by saying that farm products
are sold too cheaply or that cost of production is too high is imma-
terial, the fact remains that the rate actually made by the most im-
portant industry of the country and the industry most closely re-
lated to forestry is less than three per cent. In Germany farming
paid about two per cent, in some provinces only one and a half, in
1899.

b. What other kinds of business actually make is little known
and much disguised. If the losses and gains of our stores, factories,
railways, etc., could be known, and if the natural wealth, timber,
coal, etc., could be deducted and also the entrepreneur's risk and
effort, if these could be ascertained, it is doubtful if the business of
the country really makes one and a half per cent, even in good times
like 1900-1910.

Generally it is a fact that the current rate paid by the farmer
is not made by the farm, it is equally certain that as an average it
is not made by other business. To employ or set the current rate as
measure, then, would discourage most of our ordinary industries.

c. What rates a good forest business makes is well illustrated
by the state forests of Saxony where the rate actually made has been
2.3 to 2.6% for over forty years. Since a great deal of forest prop-
erty is assessed on a basis of income and an assumed rate of inter-
est this interest rate in Germany frequently is an argument in circle.

d. Germany today uses an interest rate of 3% or less, in Baden
2^, in all calculations of values of land, timber or forest.

e. In adopting an interest rate in forest valuation we have the
choice and say :

I. Adopt a rate which the ordinary forest business can make,
which encourages the improvements and methods necessary for a
secure paying enterprise. The best measure and basis is the farm
business.

VALUATION OF LAND 29

2. Adopt a rate which the business can not make, which tends
to abandonment of land and great loss, which even under good con-
ditions discourages all improvements and all better but more ex-
pensive methods.

Germany, Switzerland and Denmark have, unconsciously chosen
the first, France and England the second, England has no forests,
France little and mostly poor forests. See also Professor Kirkland's
article on the influence of the interest rate on timber production.
Washington University Forestry Club Annual, 1915.

D. VALUATION OF LAND OR SOIL.

Generally, land is valuable in proportion as it produces rent.
A city lot is valuable owing to its location, a field or forest land is
valuable owing to the crop it can produce. The value of the crop is
the measure of the value of the land. But even in the simplest case
the matter is more or less complicated. The value of the crop does
not depend only on the kind and amount of the crop, but also on the
market and transportation and so on the location of field or forest.

Again the same field may be used to raise wheat, corn, hay or
timber and for each crop the same field may have a very different
value. In farming, nature demands a change of crop and it is im-
possible or at least unprofitable to raise wheat on the same area
continuously. Generally the crop making the largest income is most
trying to the land and succeeds only on good land and at reasonable
intervals. Some crops, like tobacco, are very exhausting, while oth-
ers like clover and timber tend to improve the land.

a. Cost value, sale — and income — or expectation — value.

1. If a man bought a tract of land ten years ago for five thou-
sand dollars and if the income from this land has paid expenses and
interest it is evident that this tract today costs him the original five
thousand. Generally however, the case is complicated, the income
has been irregular, greater or less than expenses and interest, and
so the cost value of a piece of land is not as clear or easily com-
puted as it would seem.

2. The sale or market value of land seems to require no ex-
planation. It is determined by sales actually made in the district,
by supply and demand. It is interesting to see what conditions are
most important in determining this sale value. The conditions may
be divided as follows :

30 FOREST VALUATION

a. Conditions affecting the Income:

1. Conditions which are part of the property itself; area and
shape of the property, soil, topography, water supplies and drain-
age, improvements.

2. Conditions which are not part of the property, or which
extend beyond the property : climate, market, facilities for trans-
portation, labor, taxation, character and business of the surround-
ing people, and demand for properties.

b. Conditions not affecting the income but important from the
standpoint of sentiment :

Beauty of the property and surroundings, social conditions,
church, school, etc., family ties, habits, love of sport, "land hunger,"
etc.

With farmlands it is often more the second group of conditions,
(b) which set the price, so that generally, the world over, farm lands
are rated and paid for at a price higher than is warranted by income.
But even in forestry it is frequently this second set of conditions
which are decisive so that the majority of large estates held as for-
est parks today in the United States are held more for love of
scenery or sport than as properties for income.

The sale value fluctuates greatly with demand for land and is
easily affected by "booms." It is an old experience in the United
States to see a few land dealers, by means of shrewd advertising,
succeed in a few sales at high prices. Whether always bona fide or
not, such sales tend to raise the price of land for the entire district,
in spite of the fact that there is no justification for this advance in
larger crops or better prices.

2. The income value of the land, or expectation value de-
pends on the crop, rent or income which the land produces and the
interest rate which is assumed or is set by the individual making the
valuation. As indicated before :

net income

= income value,

o.op

wrhere p is the interest rate assumed and where the income is a
yearly one as in farming.

The income itself depends on the conditions enumerated under
sale value and the ability of the owner.

The interest rate usuall varies with:

a. Outside conditions :

Money market, location of property (old country as against
newly settled districts), good and bad times, etc.

COST- VALUE; OF LAND 31

b. Conditions of property and business itself:
Size of property, term of investment, regularity of income,
safety of property and income.

b. Cost-value and sale-value of land or soil in forest
properties in the United States.

Aside from the sales of small woodlots, etc., it is generally
true that the land itself is not considered in sales of timber. In the
past and even at the present time it is the common practice in buy-
ing and selling timberlands to estimate the merchantable timber or
the stuff now ready for ax and market and to set a price only on
this marketable material leaving out of consideration both the land
and the growing stock smaller than merchantable. In many cases
even part of the large timber is considered non-merchantable and
is not paid for. For instance, balsam, cedar and oak in California,
hemlock and balsam in the northwest, Douglas fir and balsam in the
northern Rockies, hardwoods in the northeast, gum and other .hard-
woods in the south.

Generally, then, the cost value and the sale value of forest lands
in the real forest districts of the United States is practically nothing.
In the Great Lakes Region millions of acres were simply abandoned
by the lumbermen after the timber had been cut and allowed to re-
vert for non-payment of taxes. Of late these lands are turned over
to some land company, often the same men, to sell to settlers. In
the south millions of acres of cutover lands can be bought at less
than three dollars per acre though there is a remnant of tree growth
usually worth the price paid for the land. Michigan and Wisconsin
and Ontario have sold millions of acres in the last twenty years at
prices generally not over one dollar per acre and in these cases, too,
the land was bought more for the remnants of timber than the" land
itself.

New York bought over one and one-half million acres of land,
over seventy-five per cent covered with timber, at about three dol-
lars and sixty cents ; Pennsylvania bought about a million acres at
two dollars and twenty-seven cents ; Pisgah forest of eighty thous-
and acres was bought in 1914 at five dollars for land and timber
and over thirty thousand acres in the White Mountains were bought
at about four and a half dollars an acre, though in both cases nu-
merous old abandoned farms were included, and the remaining tim-
ber is worth the price paid. In 1915 a tract of over thirty-six thous-
and acres in North Carolina was bought at one dollar and ninety
cents an acre for land and timber.

32 FOREST VALUATION

c. INCOME VALUE OF LAND OR SOIL IN FORESTRY.

Expectation value of soil or Se.

When a man buys land to raise timber and does this as a matter
of business and not merely sentiment, for sport or summer home,
etc., the case is one of investment and he values the land in propor-
tion as it produces an income or crop. In business the income, here
net income, which can be made from the land by raising a particu-
lar crop, timber, is the only reliable measure of value.

To the man who is in the business of raising the crop, whether
farm crop or timber, this net income per acre is not only the correct
measure of the value of the land but it is also a measure of the work
or operation of raising the crop. A good farmer or forester who
selects the right kinds of crop, best suited to the soil and climate,
cares for the land, sows, tends and harvests well, gets a larger net
income than a less competent man. Any mistake or neglect reduces
the income and with this the income value of the soil or land.

In this way the income value of the land becomes a measure of
the value of land and the effectiveness of its management.

i. General method of calculation for Se.

In the case of farm property where the income from each acre
is a yearly one, the income value of a given acre of land is the net
income capitalized. If an acre of land on a ten-year average can
produce $10 net income and money is rated at 3% the income value

of this acre of land is or $33^3^

0.03

Where an acre of land is planted to pine and the pine requires
eighty years to grow to acceptable size, the income from this acre
comes not yearly but every eighty years- It is a periodic income or
rental which is assumed as in the case of a farm to come forever.

The present value of these net incomes, coming every eighty
years is the value, of the acre of land. If the timber is worth $400
and it has cost $175 to raise it; the net income is $225 and the pres-
ent value of all these net incomes, coming every eighty years,

Se = (i. op1— i) == (i.o3S(t— i) = (10.64—1) =

which means that this particular acre of land is worth $23.40 when
used to raise pine where this is allowed to grow to the age of eighty

INCOME-VAIAJE) OF I.AND 33

years, where the expenses are $175 during the eighty years, and
where the final crop is worth $400 and money is rated at 3%. That
the value of this acre may change if a different kind of timber is
raised or if the pine is cut at sixty years, or expenses are lower or
higher, or if a different rate of interest is set, is evident. It is clear
too, that if the man pays $23.40 per acre for this land and uses it
as outlined above, he makes three per cent on his investment and
no more. This Se then, is rather the maximum price which he can
actually pay.

It is evident, also, that these same considerations hold in case
of a piece of farmland. The same acre of land produces a larger
income with sugar beets or potatoes than with wheat and more with
wheat than hay, so that the same acre has different income value in
different years owing to change in crops, yield, expenses, etc. Yet
this income value is considered the safest measure of value and
forms the basis of all farm valuation and assessment.

2. The usual case of Se.

a. Premises :

Area, 40 acres ; method, clear cut. and plant.

Rotation r, 80 years ; interest rate p, 3%.

Cost of planting c, $6 per acre.

Yearly expenses, taxes and care, e, twenty-five cents per acre.

Yield of timber eighty years old, or Yr, 30 M ft. at $10, $300
per acre.

Thinning when stand is 20 years old, T20, just pays expenses,
hence no income.

Thinning when stand is 40 years old, T4o, yields 5 cords at $3
or $15 per acre.

Thinning when stand is 60 years old, T60, yields 10 cords at
$4.50 or $45 per acre.

b. Gross 'income per acre at end .of rotation :

Final yield or cut 80 years old, Yr $300

Thinning when 20 years old, Tzo o

Thinning when 40 years old, T4O,
$15, with interest for 80-40 years

or $15(1. 0340) 50.40

Thinning when 60 years old, T6o,

$45 with interest for 80-60 years

or $45(1.03") 81

Total $43140

34 FOREST VALUATION

c. Total expenses per acre at end of rotation.

Cost of planting, c, $6 with interest

for eighty years or 6 (i.O3s<)) ...... $ 63.84

Care, protection, and taxes, e, 0.25,
coming every year with interest.

Total expense .................. $144.09

d. The net income per acre at end of rotation:

$431.40
144.09

$287.31 per acre.

This net income of $287.31 per acre may be and is expected to
come every 80 or r years and the value of all these net incomes or
the value of the acre of land producing them is :

value of land per acre, Se 2*7-3i — = $2980

(i.o;f— i)

value of 40 acres : $1,192.

In the above simple case it is assumed that the plantation suc-
ceeds and that it does not require any filling in or cultivation, etc.
If such work has to be done it is charged exactly like the plantation
itself. Similarly, if there are more thinnings as there would be
where intensive work is justified and also where there are other in-
comes, such as grazing, turpentine, etc., these incomes are credited
and prolonged exactly like the thinnings in the above simple case.

It is evident from the above that this analysis is clear and logi-
cal that it resembles computations made in other lines of business,
requires only ordinary interest arithmetic and that there is no neces-
sity for putting it into a formula which often seems to hinder rather
than help.

Nevertheless it is convenient and makes the matter much clearer
and easier to discuss, and to understand the relation and influence
of the various factors if it is arranged in a concise formula, and the
usual arrangement follows closely the above sample case :

e. Formula of Se :

f Tc(.I.OPr-c)_c(l.Opr)—

- ...

be = _ . _ (lop — i )

(i.opp— i)

where Yr is the stumpage value of one acre of timber r years old :

FORMULA FOR SD 35

Ta the stumpage value of the thinnings from one acre a

years old, etc. ;

c the cost of planting, or otherwise reproducing, one acre. ;
e the regular yearly expenses of tax and care for one acre

of land;
r the rotation ;
p the interest rate employed or assumed;

Se the expectation or income value of one acre of land or
soil.*

(i.opr— i)
In the above formula the term^ - - may also be writ-

(i.op— i)

e e

ten - - ( i .opr — i ) — E ( i .opr — i ) where E = — = e

(i.op— i) .op

capitalized so that E is a sum of money which will bear a yearly in-
terest e at p per cent and therefore, if put out at interest will ''take
care" of the regular yearly expenses e.

The formula then may also be written :

Yr4-Ta(i.opr-a)) + ...... etc. — cd.opr)— E(i.opr— i)

which may be and usually is simplified into :

Yr + Ta(i.opr-")-f ...... etc. — c(iopr)

(i.op'-i)

* It is of great help to the student to use these terms or symbols con-
sistently and use no more terms than are actually necessary. To use Y and
Yr interchangeably or use Yr for one acre and for a given area of many acres.
etc.. soon confuses even able students. Where new cases come up, especially
cases which are not really standard, but exceptional, it is much better to write
out fully what each part means and use the full analysis, as in the above
sample case, rather than try to force it into a formula.
* This fprmula is written by Emdres as follows :

which means exactly the same but changes the order for c so that it confuses
the beginner and the general student. As stated before, the average student
will ftfrd it helpful to stay closely with the simple forms and write them out
in full so that the formula shows clearly just how it was derived.

36 FOREST VALUATION

E. VALUE OF SOIL AND STATICS.

Just as in farming, so in forestry, the net income is larger on
good land and with good management than on poor land or with
less efficient work. vSince the income value of the land is the net
income capitalized at an arbitrary, accepted per cent this income
value serves as a measure of land and management. With the ex-
penses constant, or what may be assumed the same, with the same
kind and quality of management, the income and with this the in-
come value increases only with the quality of the soil ; the better the
land the greater its income value. Similarly, on the same acre of
land the income and with this the income value of the land increases
with the efficiency or quality and correctness of the work and man-
agement.

It is interesting to see how the income value of the soil differs
with change in the various factors, what these several factors de-
pend upon, and how they vary under ordinary conditions.

a. Relation of Se and its Factors.

1. Increase of the final cut, Yr, increases the income and
therefore the value of the land. Since Yr is the value of one acre
of timber r years old it is evident that everything which increases
this Yr, such as good planting, right thinning, good prices, cheap
logging, etc. also increases the net income and income value.

2. Thinnings not only increase the total income but as they
come long before the final cut can be made, twenty to sixty years in
ordinary cases, they help to bear expenses which are piling up at
compound interest.

A good thinning practice raises the quality of the final cut and
so increases Yr; a very severe thinning practice may cut down the
Yr in volume and if too early also in quality.

3. Cheap planting or small c means small expenses, for every
dollar spent, even at three per cent, becomes nineteen dollars in a
hundred year rotation. But if cheap planting means poor planting
it may lead to a poor stand, reduce the income from thinnings and
cut down the final cut or Yr. A large c, therefore may mean larger
income. From the formula it is clear that whenever c (i.opr) is
larger than Yr + Ta (i.opr'a), etc., the term becomes negative, a
condition which applies to practically all young stands.

4. The current yearly expenses for taxes, protection, etc., ac-
cumulate with compound interest and reduce the income. They are

FACTORS OF SE 37

generally small in forestry and their importance in the business is
easily overrated.

Where cheap protection means unreliable protection, the kind
that fails in danger season, the saving in current expenses is the
proverbial penny wisdom. As appears from the formula, the capital-
ized expenses E affect the income or the income value of the soil
uniformly; they are constant regardless of rotation and so do not
cause the maximum of income value to come either earlier or later.

A glance at the formula shows that whenever E is greater than

Ta(i.opr-a) etc.— c(i.opr)

(i.opr— i)

the business is carried on at a loss and the income value of the soil
becomes negative.

5. The rotation, r, affects the value of the crop and in this
way the net income and income value. In spruce, pine, maple, etc.,
a five or ten year rotation would mean a final cut of mere brush of
practically no value. Even a twenty year rotation would in most
cases not even pay for the plantation. For these short rotations
then, Se is negative regardless of quality of land or management.
In the above cases the business would just about pay expenses at a
thirty year rotation ; the income value would continue to increase and
reach a maximum at about eighty years. After that the expenses,
planting and current expenses, together with the discount would
grow faster than the timber and Se would decrease, in spite of the
fact that the final cut would be larger at one hundred years than
at eighty years.

The following figures for spruce site III (Endres, p. 275) illus-
trate this : At three per cent Se is :

Age, or rotation years 30 40 50 60 70 80 go 100 no 120
Income value of land
per acre, Se ..... $ —14 13 38 53 59 59 56 51 46 41

which shows that even in the German forest and at three per cent
a rotation of thirty years leads to loss and negative value of Se of
$14 per acre ; that Se increases with increase in rotation up to sev-
enty years, declines after eighty years and reaches a value of $41
with a 1 20 year rotation.

6. The interest rate, p, which is assumed in these calculations
greatly affects the results. If in the sample case outlined above the

3§ FOREST VALUATION

interest rate of five per cent is set instead of three, the Se of $29.80
changes to a negative quantity ; i. e., the same land and management
which gives to the land an income value of $29.80 per acre becomes
a losing business to the man who values his money at five per cent.
The same is illustrated by the following figures for spruce, site II
(Endres, p. 274). The income value of the land, Se, with an 80
year rotation is at

3 % $105 per acre

2l/2% 173 per acre

2 % 285 per acre

b. Values of the Factors of Se, and Variation in these Fac-
tors under different conditions.

i. The final cut, Yr, depends on the growth to produce the
crop and on market to pay for it.

a. Both site and species affect the final cut. These possible
variations are laid down in the yield tables for different species at
least so far as volume and size or quality are concerned. In the
more modern tables and for the settled conditions of the Old World
they are commonly worked out for money values or made into mon-
ey yield tables. The yield tables giving size and volume of timber
per acre have been a matter of experience and growth. Even for
the different districts of central. Europe they are being improved
continually and will be modified further with better methods of sil-
viculture, added experience and more accurate and extended statis-
tics. Nevertheless, for central Europe they are good now, quite the
best we have ; they are more reliable than farm yield tables and far
surpass in safety the forecasting of ordinary business enterprises.
In all new forest districts including the United States, data for yield
tables are gradually accumulating. Asa beginning the practice takes
what it finds in the wild woods and the assumption is that what
nature has produced unaided will be produced again on the same
land and by the same species. Since the wild. woods generally do
not produce as much timber nor as good a quality, for ordinary
rotations, the figures of yield and growth are conservative. This
is doubly true of money yield tables. In fact money yield tables for
most parts of the United States where they are based on present
stumpage prices are conservative to the point of uselessness, as is
clearly shown by comparing present stumpage prices with those of
twenty-five years ago.

VARIATION IN YR

b. The influence of site or quality of land, including climate,
etc., is very great. Endres, (p. 94) using Lorey, Weise and Baur's
tables gives the following figures for the one hundred-year-old stand
of timber fullv stocked :

Yield per acre.

Relative figures or per cent for different sites.

On site I
Cubic feet.

III

Pine

9200

100

Spruce

16000

100

White fir ...

17200

100

—

Beech

. 10400

100

Since this classification itself is really based on arbitrary but
generally accepted figures for the volume of timber per acre at a
given age it may be said that the above figures are an argument in
a circle. But the important fact is that in actual practice the forester
deals with lands on which the yield at one hundred years differs as
above. The figures clearly show therefore, the great influence of
the site on the same kind of timber. That the influence of site is
just as great in the United States as in central Europe is certain;
the western yellow pine in the Black Hills makes a two or three log
tree and yields about five or ten thousand feet per acre, while in
parts of California and Oregon it is a six to eight log tree yielding
forty thousand feet and over.

The influence of site on the money value of the final cut, the
Yr of the calculation, is even greater than on the volume, since the
quality and price are largely matters of size and good land produces
larger timber in the same time. Schwappach in his tables of 1902
gives the following for spruce, one hundred years old : Volume of
site I per acre is 13800 cubic feet, its value $2,085 ; putting the val-
ues for site I equal to 100, the relative figures for the different sites
are:

Sites I II III IV

Volume 100 "85 65 50

Value per acre 100 75 54 36

so that site IV produces half as much timber in volume, but only a
little over one-third in value. In pine the average price per 100

4° FOREST VALUATION

cubic feet of timber in the stand 120 years old, in Prussia is given
by Schwappach (pine, 1908, p. 144) as follows:

Site I $12.00 per 100 cubic feet

Site II 1 1.20 per 100 cubic feet

Site III 9.10 per 100 cubic feet

'Site IV 8.25 per TOO cubic feet

Site V 6.60 per 100 cubic feet

These figures well illustrate the effect of site on size, quality, and
price of the material.

The final cut in practice and for large areas involving a variety
of sites is best illustrated by the cut in the German state forests.
According to Endres' Forst Politik, p. 96, in the year 1900 the cut
for the state forests was set as follows : cubic feet of stuff three
inches and over, per acre of forest area :

Baden 73 cubic feet

Wiittemberg 71 cubic feet

Saxony 70 cubic feet

Bavaria 60 cubic feet

Prussia 43 cubic feet

Which means about sixty or sixty-five per cent of what the
yield table calls for, on a basis of site III and the usual rotations.
Since this condition is rapidly changing owing to the conservative
cutting in the past, the later figures for Wurttemberg are interest-
ing.

In the three years 1906-1908, the cut of the state forests aver-
aged one hundred and three cubic feet per acre of woods. Of this
about one-third is hardwoods, mostly beech. Using beech with one
hundred and twenty year rotation and spruce with ninety year rota-
tion, and assuming on an average forty per cent of area site II, and
sixty per cent site III (very nearly the actual condition as reported
by Graner) the cut according to Schwappach's tables should be one
hundred and forty cubic feet to be full or normal. Being one hun-
dred and three cubic feet it is seventy-three per cent of normal, or
in other words, the practice today in Wurttemberg is seventy-
three per cent efficient, or successful. Since the cut is increasing
in all states it is clear why the state forest authorities of Bavaria in
their late instructions consider seventy-five or eighty per cent a pos-
sible goal.

VARIATION IN YR 41

c. The value of the final cut, Yr is greater for spruce than for
pine, greater for pine than beech, etc. The following German fig-
ures for site II, age one hundred years, ilnstrate this :

Spruce $1563 per acre

Pine 627 per acre

Oak 377 per acre

Beech 347 per acre

While this comparison is not quite fair, since oak does not really
develop quality until after one hundred years, yet it bears out the
general experience that the hardwoods do not make the values like
conifers, and that tolerant conifers produce more value per acre than
intolerants. When it is remembered that the land producing pine is
generally poor sand, while oak land is good loam or clay, commonly
fair agricultural land, the above comparison is even more impressive.

d. The final cut depends on the methods of silviculture. A
slow, long drawn out, natural restocking of the land wastes time
and can not possibly produce the same volume and value of Yr which
a good prompt reproduction does. Defective or imperfect cover at
time of reproduction wastes space and leads to irregular stands
where some trees have too much, others too little room and light.
Very dense natural reproduction leads to dense stands, great com-
petition, and if no thinning is practicable, leads to great loss of
material by death and decay, loss of growth, and, besides producing
less healthy and safe conditions, it leads to smaller timber, small
volume and value of Yr.

A good planting practice assures prompt reproduction, proper
spacing, healthy growth, safe conditions, and with these, larger and
better timber and larger Yr. A saving of five years in the rotation
or what amounts to the same, a Yr five years better in size, volume
and value may be secured by good planting.

Mixed stands have often been claimed to produce a larger cut
per acre. The proof has never been furnished ; the practice abroad
does not believe it, the pure stand is gaining and not losing ground.
Mayr was right in pointing out the poorer development of crown
and waste of space on the line of contact between different species
such as beech and spruce, etc.

Clear cutting methods save in logging and so increase Yr. On
good ground with proper improvements, roads, etc., the skidding
is saved and buyers haul directly from the area. In parts of Ger-
many this item alone offsets the cost of planting. Methods like the
coppice produce small, cheap stuff, often difficult to market. The

42 FOREST VALUATION

general experience of France with its non-paying coppice woods
on relatively valuable sites clearly proves this.

The regular timber forest with rotations over sixty years alone
makes a satisfactory Yr.

e. Up to reasonable limits the final cut varies almost directly
with the length of the rotation. German experience indicates that
for pine, spruce, fir and beech a one hundred and forty year rotation
produces as high a Yr as is likely to be produced by any. higher rota-
tion. The difficulty of keeping the stand intact and growing is
very great and generally demands the cut before one hundred and
forty.

While the effects of the methods of treatment, silviculture, on
Yr are quite well understood and fully recognized, their estimate in
dollars and cents is not easy. This is especially true of the effects
of thinning, and it is one of the important tasks of the forest ex-
periment stations today, to gather reliable data based on careful ex-
periment. Schwappach has made an effort to estimate the effects
of thinnings in beech and spruce, and to a less extent in pine, but
these efforts are still tentative. That a full and clear appreciation
of these facts really constitutes the most important part of a for-
ester's judgment regarding his business, is self-evident.

f . The market with its prices and grading determines the value
of the crop when once it is produced. In the United States the
market is irregular, uncertain and localized ; it is excellent in New
York, Boston, Chicago, etc., but poor in the forest districts. Most
of the timber has to be transported over long distances and the price
at the mill and in the forest is low as a result. Cypress goes from
the Gulf to the northern states and east ; red fir, sugar pine and red-
wood are railroaded clear across the continent.

A good telephone pole or a 1,000 feet of good pine retail for
as much money in the towns of southern Michigan, Ohio or Indiana
as they do in Germany. But an enormous supply of merchantable
or mature stuff ready for the ax encourages destructive competi-
tion among manufacturers so that while good quality pine is retailed
in Michigan as high as one hundred dollars per thousand feet it may
be sold by the manufacturer in California or Oregon for less than
cost of production, leaving no Yr at all for the stand in the forest.

These conditions are rapidly changing and the value of the stand
in the United States as in Germany will be determined largely by
the cost of growing the timber.

As it is, the stumpage price or unit price of Yr has increased
rapidly being now more than one hundred per cent greater than
twenty-five years ago.

STUM PAGE; IN EUROPE

In Europe timber prices have increased for one hundred years
past, they have practically doubled between 1830 and 1890, but have
remained rather constant since that time.

The following figures from Endre's Forst Politik, p. 120, will
illustrate changes in price of timber sold from state forests in Ger-
many.

Average price in dollars per 100 cubic feet solid, paid in the
state forests .of:

Average
for the •
years

Prussia
All wood
$ per 100 c. ft.

Bavaria
All wood
$ per loo c. ft.

Baden
All wood
$per looc. ft

Saxony
Only wood
3" and over
$ per loo c. ft.

1830-39

2.50

....

4.60

1840-49

3.00

....

5-70

1850-59

3.20

3-50

4.10

6.40

1860-69

3-80

4.10

6.50

7-90

1870-79

4.40

5.20

7.90

9.20

1880-89

4.40

5-oo

6.40

9.30

1890-99

4.90

5.8o

7.60

10. 2O

1900

6 . fio

7.00

8.70

11.80

These prices were paid for the timber cut or cut and piled, in
part at least, skidded to the road, i. e., in the form in which the tim-
ber is usually sold by the authorities. Log timber is usually sold full
length, cordwood is piled in the usual way.

Prices for pine in eastern Prussia in sound clean sticks contain-
ing thirty-five cubic feet or more according to Schwappach, 1908,
p. 143, are $13 to $1540 per TOO cubic feet solid, or about $16 to $19
per thousand feet b.m. actual stumpage. For spruce, Schwappach
gives the folowtng prices:

Logs class I $20.40 per M. feet bm. stumpage

Logs class IT 19.20 per M. feet bm. stumpage

Logs class III iS.Soper Mk feet bm. stumpage

For oak in Prussian state forests the same author gives prices
as follow for logs cut and skidded :

Logs over 24 inch diameter $42 per 100 cubic feet or $53 per M. feet bm.
Logs 20-24 inch diameter 35 per 100 cubic feet or 44 per M. feet bm.

Logs 16-20 inch diameter 28 per 100 cubic feet or 35 per M. feet bm.

Logs 12-16 inch diameter 17 per 100 cubic feet or 22 per M. feet bm.

For beech saw timber Schwappach uses the average price of $7
per 100 cubic feet or $8.90 per M feet stumpage for north Germany

FOREST VALUATION

and $2.10 to $4.90 per 100 cubic feet solid for cordwood and small
timber, also on the stump.

Average prices for log timber cut and usually peeled and
skidded, i. e., ready to haul from the woods, in the state forests of
Wurttemberg were as follows :

Oak

Conifers

$per 100 c.ft.

$ per M. ft. bm.

$ per 100 c.ft.

$ per M. ft. bm.

1880-84
1885-89
1890-94
1895-99

17.70
17.40
24.00
24.60

22.25
23.00
30.00
30.75

9.00
9.50
10.50

12.80

11.50
ii.6o
13.20
16.00

g. The cost of exploitation and transportation are intimately
associated with market and greatly affect the value of the final cut.
In the United States the cost of getting the timber cut, skidded and
hauled to the railway, landing, etc., has not changed very much in
spite of the great variety of conditions under which the work must
be done. A cost of from four to six dollars per M feet of logs
would probably include seventy-five per cent of all operations. Nor
has this cost changed materially in the last twenty years. Generally
the employment of machinery and the utter disregard for the safe-
ty and condition of the forest have enabled forest utilization to keep
down the expenses of logging or immediate exploitation.

Timber exploitation in Europe works with cheaper labor, less
equipment and less efficiency. In districts with good and ample
road systems it is cheaper than the work in the United States, in all
difficult situations and whenever it works over long distances as is
the rule in the United States, it is not cheaper and often eats up the
larger part of the value of the cut.

The cost of exploitation, (Werbung's Kosten), for all timber
in the state forests was as follows in 1900:

Prussia $0.98 per 100 cubic feet, or about $1.25 per M. feet bm.

Saxony 1.26 per 100 cubic feet, or about 1.55 per M. <feet bm.

Wurttemberg 1.33 per 100 cubic feet, or about 1.65 per M. feet bm.

But these figures are not readily comparable to logging costs
in the United States. The stuff includes cordwood, poles, ties, mine-
props, etc. Moreover the material is commonly not skidded, and
even if skidded, it is so only for a very short distance, generally less
than two hundred yards.

TRANSPORTATION AND YR 45

The logging costs in the German states have increased in keep-
ing with better wages ; this increase is over fifty per cent since 1870
and the increase continues. Usually the costs vary but little from
year to year and so may be estimated very closely. Transportation
of logs to mill and of timber and .lumber to markets affects Yr very
seriously everywhere. In the United States the transportation of
logs to mill formerly meant long drives, costly improvements, much
loss by "sinkers" and a great deal of risk. Today it involves costly
railway construction where the one cut must pay for all improve-
ment in this way subtracting heavily from the value of the standing
material.

Transportation to market in the United States is normally long
distance haul. The average haul in the United States for cypress
and southern pine may be assumed to be over six hundred miles be-
tween mill and customer ; for western timber over fifteen hundred
miles, and even for Lake states' stuff over three hundred miles, and
this practically all by rail.

In Europe too the influence of transportation costs on the price
of timber is evident in spite of shorter railway haul and more exten-
sive use of waterways. The same kind of timber in east Prussia
and Poland sells for fifty to one hundred per cent less than it does
in the industrial Rhine districts.

The influence of a good system of roads is well illustrated in the
Black Forest, while the utter lack of roads in parts of the Alps pre-
vents many villages from having any material income from the for-
est properties.

h. The volume, quality and value of the final cut depends on
the care and protection of the stand and the presence or absence of
injurious agencies like storm, fire, insects, fungi, drought, snow,
sleet, etc.

On every large property some of these enemies are at work at
different times and it is the rare exception that a stand of timber
passes through its entire life of one hundred years or more without
suffering more, or less injury. Fungi and insects are always present
and need only suitable conditions to multiply into regular epidemics.
Often these enemies are assisted through the mistakes of the for-
ester in selecting the wrong species for the site in question, by keep-
ing too dense a stand, etc. It is due to these enemies and injurious
conditions that most stands of timber, especially intolerants, "break,"
or open up long before the end of the rotation and often compel
earlier cutting or underplanting, and on poor sites, adoption of
shorter rotation.

FORKST VALUATION

Much of the trouble, particularly from fire, can be averted by
proper protection and much can be done by prompt and frequent
thinning and underplanting of older stands on poor, sandy sites.
For this reason a saving in current expenses or in caring for the
stand may prove false economy by reducing the final cut.

2. Thinnings. The incomes from thinnings are set down in
most modern yield tables for the important species and the several
sites and have of late been expressed as money tables. These tables
for thinnings are not as fully developed as the tables for the final
yield because of the great difference in the practice of thinnings.
Different practicing foresters still disagree within rather wide limits
in their views regarding the proper degree of thinning. In addi-
tion the market, income, labor, etc., may enable one forester to thin
early and often and compel another to postpone thinnings, and to
come only at long intervals. Modern practice in good intensive
work expects a thinning every ten years and in young stands of oak
on good sites five years is considered a long interval.

Like the final cut, Yr, the thinnings vary in volume and value
income with species, site and practice.

a. For a stand one hundred years old, on site I, as per Schwap-
pach, the sum of all thinnings taken out during the life of the stand
and the volume and value of the main stand one hundred years old
are as follows for wood of all sizes per acre :

Main stand 100 years old

Thinnings taken out
during life of stand

Volume cu. ft.

$ per acre

Volume cu. ft.

$per acre

Pine
Spruce . . .
Oak

6550
11500
6150
9200

627
2028
798
43i

6100
10800
7800

5720

363
450
535
193

Beech ...

Arranging these values of thinnings as per cents of the volume
and value of the final cut gives the following interesting compari-

son

Thinnings expressed as per cent of main stand or final
cut of stand one hundred years old, site I
In volume

Oak 126%

Pine 94%

Spruce 94%

Beech 62%

In value
67%

57%

22%

45%

VALUE; OF THINNINGS

In oak and pine thinning out of a large, volume is necessary, in
spruce and beech it is not necessary but it is possible and desirable.
The smaler value of thinnings is due to inferior quality, is most
conspicuous in spruce and least in beech where even the final cut is
largely firewood. The tendency at present is for heavier thinnings
and a larger return from this source. In pine (Schwappach, p. 5)
the thinnings in 1889 made about thirty-five per cent of the total
growth while in 1908 they made about fifty per cent and the same
change is apparent in the treatment of other species.

The influence of site on thinnings is ilustrated in the following
figures for the stand of pine one hundred and twenty years old :

Main or final cut,

Sum of thinnings during

120 years old.

life of stand.

Volume cu. ft.

$ per acre

Volume cu. ft.

$ per acre

Site I

6860

774

7540

505

Site II

5640

600

6650

365

Site III

4550

368

5340

284

Site IV

3620

268

3940

203

Site V

2760

153

2800

136

From the foregoing figures it is apparent that site greatly af-
fects the volume and value of thinnings and also that the difference
for different sites corresponds closely to that of the final stand.

b. The influence of the method of treatment or silviculture
extends beyond the mere practice of thinning itself. A dense repro-
duction like good stands of natural reproduction, or dense seeding
and planting, call for early thinning. In many localities even in
central Europe such a thinning is made at a loss. Thinnings of oak
ten years old from usual seeding, also thinnings of beech and even
pine and spruce, come under this description. Here the method, if
artificial, by wider spacing may save money in seeds and plants and
again save the expense of early thinnings, besides producing larger
material in the same period of time.

The mixed forest, especially mixture of hardwoods and con-
ifers, introduces disadvantages as well as advantages, with the for-
mer still prevailing. Thinnings of mixed stands require more judg-
ment and care and generally increase the difficulty of selling the
material. In hardwoods like ash, hickory, maple, where small sec-
ond growth stuff is valuable the mixture may prove an advantage.
As stated before, the greatest differences in the income from thin-
nings rest with the thinning practice itself. Fifty and more years

48 FOREST VALUATION

ago many foresters still believed in the dense stand, removed only
dead and dying trees. This did practically nothing to stimulate the
growth of the stand, either in volume or quality, and did not relieve
the stand of the struggle between individual trees. This method
furnished very little of value in thinnings and tended to produce
smaller timber for the final cut.

As indicated by Schwappach's tables the modern practice is
now taking out as much volume in thinnings as is expected in the
final cut and the tendency is for further increase. With a closer
utilization and better prices for small stuff it seems a possibility to
increase the income from thinnings and in pine, oak and many hard-
woods, make it approach closely the money value of the final cut.

3. The cost of reproduction, c of the formula, varies with site
species and methods and is greatly affected by enemies, fungi, in-
sects, rodents, also by season, storm, frost, or conditions which may
not be classed, ordinarily, with site. From a business point of view,
as expressed in the income value of the land, it is not enough that
reproduction may be accomplished but it is necessary that a new
stand be established with certainty and safety, and in reasonable
time. Generally natural reproduction is considered cheaper than
planting. In many cases this is true. But if a stand of beech is
opened in the shelterwood plan and has perhaps a growth of less
than one per cent in value with only about one-half cover it is poor
economy to wait ten years and more, as has actually been done even
of late years, for natural re-seeding. In some cases where this was
observed in 1910 the land readily produces from four to seven dol-
lars worth of timber per acre and year so that the expense of ten
years waiting would plant up the area several times.

a. Artificial reproduction.

Schwappach in his tables for pine uses ten dollars per acre as
cost of planting on site I and V, the best and poorest lands. For
sites II to IV he uses eight dollars per acre. The higher price for
site I is due to the troublesome weeds and brush which come into
clear cut areas on good land and usually require extra work to keep
down.

Endres, "Valuation," uses twelve dollars per acre and Schwap-
pach ten for all sites in spruce, for white fir Endres uses ten dollars
but evidently he has in mind that much of this is reproduced nat-
urally. For pine Endres follows Schwappach and uses ten dollars,
but does so for site III as well as I. For beech, where again arti-
ficial and natural reproduction are both employed and figures for
costs are mixed, he uses five dollars per acre. Reproduction of oak

COST OF ARTIFICIAL, REPRODUCTION 49

in Germany is rather costly since a great deal of protective work,
fencing, etc., must be done to prevent damage from game. Yet in
oak, as in beech the cost varies from almost nothing in good natural
reproduction to expensive planting of large transplants. The great-
er part of oak is started artificially by very dense seeding. Schwap-
pach therefore puts reproduction costs in oak at fifteen dollars per
acre.

For the state forests of Wiirttemberg, nearly five hundred
thousand acres, with sixty-nine per cent conifers and forty per cent
occupied by beech and white fir where natural reproduction prevails,
the official costs of reproduction include : drainage, seeding, whether
in the open or to assist natural reproduction, planting of all kinds
as well as maintenance of nurseries and purchase of seeds and
plants. But it does not include the extra expenses in logging due
to methods of natural reproduction, an item which would require
estimate from one piece of work to the next and so far is never
introduced in forest statistics. The following is taken from Graner,
for 1908:

Total expense for reproduction $129,000, or 26 cents per acre
of forest, of this total there was for (round numbers) :

1. Ditching $ noo

2. Seeding, new, I'SQ acres, corrections 40 acres, cost per acre
$10.30, total 2000

3. Planting, new plantations 4430 acres, corrections 1130, cost

per acre $10.03, cost per 1000 plants set out, $3.30, total 55800

4. (Maintenance of nurseries, 500 acres 49100

Cost of restocking lands or reproduction forms only seven
per cent of all expenses as against 12 per cent spent for roads in
1908.

The high cost of seeding is due to the large proportion of oak.
In the pineries of Prussia reproduction by artificial seeding has been
revived by Splettstosser and the cost in some cases is less than a
dollar and a half an acre. But in dry years this method fails and the
cost of successful reproduction by seeding is still uncertain and
greater than is usually assumed.

For the state forests of Prussia reproduction costs in 1900
were about twenty-seven cents per acre of forest. These expenses
have increased from about nine cents in 1870.

In the Saxony state forests the average costs for restocking
were about twenty cents per acre of forest, including ditching work,
having approximately doubled since 1870.

50 FORKST VALUATION

In the United States the cost of planting and seeding is very
variable. In the eastern states for conifers and most native hard-
woods it may be figured approximately :

Cost of raising plants: three year seedlings — $i per 1,000; four
year transplants, or 2-2 plants, $3 per 1,000; to set out either coni-
fers or hardwoods about $4 per i,ooa Since 1,060 per acre is quite
sufficient, the cost per acre is $5 to $7. To this must be added thirty
to fifty per cent for mishaps, bringing the cost per acre to $7 — $10,
or about the same as the cost in Europe, where, however, much
denser planting is practiced. For oak and beech about two to five
bushels of seed per acre is used. With acorns at a dollar and a
half, a common price, the seeding costs about $10 or $12 per acre.
These figures vary with site, labor, cost of seed, etc., and will
be high wherever conditions are adverse to forest growth and call
for extra effort. The experience of the United States Forest Ser-
vice though the most extensive in this country can not well be used
here, since the conditions under which most of this work has been
done so far are very difficult, particularly as regards site, accessi-
bility, cost of labor, and, in many lacalities, the work of seeding
suffered excessively through rodents, which make this method al-
most useless. Experience in district i, Montana, etc., indicates that
even here the cost of "effective" or successful planting is now close
to $11 per acre, and that much planting is done at about $7 per
acre, and seeding at about $2.50 per acre in conifers. But it should
be added here that seeding has generally been a failure in these
western forests and is largely abandoned.
b. Natural reproduction.

The cost of natural reproduction is assumed to be zero. This
is not true in most cases. If natural reproduction is slow it wastes
valuable time, years of rent are lost. If it produces a stand in
which a portion of the trees are of poor species and not wanted and
this condition requires the cutting out of material at a loss, this
expense may very well be charged to the form of reproduction. And
even where the natural reproduction is perfect as to species and time,
but produces dense thickets of stuff which cause extra expense by
early thinning or involve years of struggle and consequent loss of
growth, the method is certainly not without cost to the owner of the
forest. Unfortunately statistics on these points are still too im-
perfect to base general statements on. The universal adoption of
clear cutting and planting in pine and spruce in German and other
forests is the best wholesale evidence that natural reproduction in-
volves expense, or, what is the same thing, that artificial reproduc-

COST OF NATURAL REPRODUCTION 51

tion saves money. Similarly, when the best Danish foresters find
it to their advantage to spend fifteen or twenty dollars in tilling,
liming and artificial seeding to assist so-called natural reproduction,
we have here artificial seeding and the old stand is useful only as
shelter.

In good coppice on good. sites the expense of cleaning out use-
less sprouts and useless species is small and if need be can be neg-
lected. But such saving is poor business on excellent site which
should produce from ten to twelve dollars worth of good material
per acre and year.

In selection forest of our ordinary hardwoods natural repro-
duction is quite certain, fairly prompt, but often made up of the less
desirable species and either means a loss in the yield or an expense
for cutting out this material.

In situations where a dry climate, lack of seed, etc., prevent
prompt reproduction, the waste by having a part of the land unused
for years may be a very considerable expense, as pointed out above.

In nearly all cases, except coppice, natural reproduction in-
creases the cost of logging. In many cases in central Europe today
this amounts to more than twice the cost of planting and should be
charged to reproduction and not deducted from the final yield as is
always done.

In remote mountainous districts where the cold climate retards
growth and the site at best produces but a small yield, lodge pole,
Engelman spruce, tamarack in swamp, jack pine, etc., the cost of
artificial reproduction may not be warranted except perhaps as a
starter on burned over districts, and here the natural reproduction
in spite of its loss in time and rent may still be the only economical
method. And even on better sites in our unsettled districts, western
yellow pine, etc., with enormous masses of excellent but unsalable
material, natural reproduction may be indicated. But to leave large
areas of these better sites entirely bare for many years would be a
mistake. This is recognized so that even now planting is being
started in many localities.

4. Current expenses, e, usually consist of administration and
protection, improvements and taxes.

a. Taxes are beyond the control of the owner ; they are known
and remain fairly constant for large rural properties for many
years. In the United States under ordinary settled conditions rural
property pays about six or eight dollars on the thousand dollars
worth of property or about twelve dollars on a two-thirds valuation.

52 FOREST VALUATION

This will no doubt remain so whether forest taxation continues on
the present plan or changes to a yield tax or single tax, for in the
end the income or the income value of the forest determines the
ability of the owner to pay.

b. Administration and protection are usually given together in
recent statistics. Endres, "Valuation" p. 38, quotes the following
for the state forests of Germany: Prussia, Bavaria and Alsace-
Lorain about seventy cents per acre ; Baden eighty-six cents, Wurt-
temberg one dollar and five cents and Saxony one dollar and thirty-
five cents per acre. Usually about sixty per cent of this goes for
administration proper and the rest for protection. Since so much
of the under-forester's or ranger's time is spent in work where pro-
tection and supervision is combined it is impracticable to separate
the two. It is doubtful, however, if protection proper is done for
less than twenty cents per acre in any of these state forests. Ac-
cording to Schwappach, the larger private estates in south Germany
spend about forty-five or sixty-five cents per acre and year for ad-
ministration" and protection.

In the United States there are no satisfactory, comparable fig-
ures on this point. The total appropriation for the care of approx-
imately one hundred and sixty million acres of national forests is
only about five million dollars or three cents per acre., a figure which
can not be considered here for it does not even indicate a reasonable
interest in the property. Of this three cents it is assumed that about
two cents an acre are devoted to administration and protection. But
everything is new ; a large amount of labor is absolutely necessary
to survey, locate, map and describe or record things, to enable any
administration to be carried on at all, and in addition much work is
necessary to attend to the orderly disposition of timber, grazing, etc.,
so that it is doubtful if much more than one cent an acre is actually
devoted to protection and supervision.

It is difficult, as yet, to estimate what will constitute a satisfac-
factory figure for administration and protection in our extensive
enterprises. Recent experience would indicate that protection of
the kind that will really protect can not be furnished under ten cents
an acre ; about half this sum should be allowed for administration
if the property is to be properly regulated, inspected and its busi-
ness recorded. Undue economy in either direction is costly.

c. Improvements in forest properties consist chiefly in roads
and besides these in buildings for foresters and rangers, and in tele-
phone lines. Occasionally special improvements like chutes, flumes,
etc., are provided, but they may well be charged to exploitation and
deducted from the gross yield.

CURRENT EXPENSES 53

For the most part improvements are developed gradually and
the expense for improvement is fitted to the income, and may there-
fore remain fairly constant for a long term of years. In the state
forests of Europe the construction and maintenance of roads is
usually the only item quoted in the reports. In the state forests
of Wiirttemberg road work in the five years ending 1908, averaged
about forty cents per acre of forest and of this twenty-four cents
was for maintenance. Ever since 1875 tne roads have received over
twenty-five cents per acre and year, and while new construction will
become less in time the item of roads will always amount to over
thirty cents per acre and year.

In the United States there is as yet little experience in this mat-
ter outside the United States Forest Service and as stated, the Ser-
vice has had too little support to do more than make a beginning.

On a good forest property with satisfactory market, etc., a
suitable road system is a necessity and it is reasonable to suppose
that this will cost here what it does abroad.

Combining the factors of current expenses for our conditions
the following estimate will suit a large part of our forests :

Taxes 15 cents per acre

Protection 10 cents per acre

Administration 5 cents per acre

Improvements 10 cents per acre

Total 40 cents per acre

This should be regarded rather as minimum than average for good,
intensive work.

That these expenses must be suited to the income or the value
of the crop which any tract can produce is evident. From the for-
mula it is apparent that: Yr -f- Ta (i.opr"a) must be greater than
c (i.opr) +E (i.opr— i).

If we take the value of the thinnings, prolonged, to be equal
to one half Yr or the final cut, and use ten dollars for planting and
forty cents for current expenses, eighty years as rotation and figure
with three per cent, then the final cut must be worth more than one
hundred and seventy-five dollars to produce any rent on the land.
In jack pine, tamarack, or high mountain timber where the final cut
can not be expected to be worth over fifty dollars and in the moun-
tain forest requires perhaps one hundred and fifty years to grow,

FOREST VALUATION

it is evident that planting should be avoided and the current expenses
cut to one half or less of the above estimate.

5. The rotation is largey a matter of species, site and market
and also of treatment. The first condition is to produce material
which can be sold at fair price and in large quantities. Generally,
then, the market determines the size and quality while site, species
and method determine the time required to produce the demanded
size and quality.

In central Europe oak requires over one hundred and fifty years,
pine saw timber and beech over one hundred and twenty, while
spruce and balsam are now commonly cut at about one hundred
years.

The following figures of age, class, conditions for the timber
forests of all Germany are instructive in this connection :

Area in 1,000 acres of different age classes in 1900.

Over

100

80-100

60-80

40-60

20-40

to 20

bare

years.

Oak

244

147

181

208

250

272

Beech

792

823

937

816

657

5ii

• 29

Pine

975

H33

1801

2859

3319

3383

Spruce

403

548

875

1191

1517

White fir

150

118

120

108

122

116

Larch

o-3

1.6

—

From a financial standpoint the temptation is to set a rotation
producing the largest Se or largest interest rate on the business.

For spruce in Saxony state forests according to Schulze, the
following is true with present prices :

Rotation 50-60 years, rate .made 5 %

60-70 3-7%

70-80 3.2%

80-90 2.6%

90-100 2.2%

But if a rotation of fifty to sixty years was attempted on all
Saxon state forest lands the price of smaller sizes would drop and
the result would be a failure. Again, for large areas of poor sites,
IV and V, such a rotation would not produce marketable stuff at all.

INFLUENCE; OF INTEREST RATE 55

In fact, according to the same author, a rotation of fifty-five
or sixty-five years is most profitable, even with present prices, on
only eleven per cent of all forests, while the rest require, owing to
slower growth, rotations of over sixty-five and as high as one hun-
dred.

With better machinery, manufacture of pulp and extensive use
of timber in mining, etc., the use of smaller sizes has been increased.
In conifers timber ten to fourteen inches d.b.h. with bark can be
sold at good price and in largest quantities. In addition the modern
practice of thinning gives more space to each tree, stimulates growth
and so produces these sizes in shorter time. Accordingly, there is
a tendency toward shorter rotations in all timber except oak, where
satisfactory quality requires trees over eighteen inches d.b.h. In
the United States the timber industries are rapidly adapting them-
selves to the use of smaller sizes so that, locally, at least, as small
stuff is sawed and worked up as in Europe. In the handling of de-
fective stuff the United States methods far excell those of the old
world. It is reasonable, therefore, to assume that the conditions de-
termining the rotation will be the same here as abroad. With warm-
er climate and better growth, shorter rotations such as fifty years
even for saw timber are anticipated, established or accepted in legis-
lation, in Massachusetts and Connecticut. In loblolly pine, hard-
woods in river bottoms, etc., no doubt this will apply, but in all cases
the quality of "grain," fine or broad rings, will also be considered
by the market and may call for denser stands and longer time.

6. The interest rate, p, has been discussed before. Its effect
on calculation of the income value of the land and of the success of
the forest business is very great. The interest rate actually made
in the foresj business in the state forests of Germany varies from
two to three per cent on the sale value of the property. An interest
rate of five per cent will probably prove ninety per cent of European
forestry a failure. In the United States at present and for some
time to come the unsettled conditions of values in timber and tim-
ber lands will make it possible to acquire lands at prices which will
assure higher rates. In time the real value of land and timber will
approach the true income value and the interest rate made in the
business will be normal just as it is in agriculture and other lines of
business. To make these calculations reasonable, comparable and
useful it would be well if a uniform rate could be adopted and since
three per cent has been used extensively in European works it com-
mends itself for adoption here.

FOREST VALUATION

c. Actual values of Se.

The following figures are taken from Endres' Valuation, and
Schwappach's Tables of Growth. The interest rate is three per cent.

Income or expectation value of land per acre for different spe-
cies and rotations.

Spruce

White fir

Pine

Beech

Rotation

on sites

sites

on sites

years

III

dollars per acre

—14

— 10

—30

—19

100

—5

—4

139

134

159

156

166

105

156

v 13

161

105

145

151

130

100

138

114

126

— 2

1 20

117

—4

For white oak in Germany two per cent, the values are as fol-
lows for Se:

Rotation, years

Site I

Site II

Site III

IOO

$262

$131

$56

1 20

272

133

140

260

134

•60

IOO

236

124

180

215

200

201

101

The above figures are based on normal yield tables of Schwap-
pach for spruce, pine and oak, Eichorn, 1902, for white fir, and
Grundner, 1904, for beech. They asume cost of reproduction twelve
dollars per acre for spruce, ten for fir and pine, five for beech and
fifteen for oak. The current expenses are taken at ninety cents per
acre and year for all but oak where sixty cents is used. Since the
above values are based on normal yield tables, assuming full and sat-
isfactory stands, the values require reduction in practice by at least

APPRECIATION OF SE) 57

the amount by which the practice now fails to keep the forest in
fully stocked good growing condition. This for the state forests of
WKirttemberg would be less than thirty per cent, and for most state
forests would vary from thirty to forty per cent.

An examination of values for Se at three and two per cent re-
veals the interesting fact that the maximum for Se comes too early
at three per cent, and of course still earlier at higher rates, for a
safe technical rotation which works for the sizes most demanded
by the present market. On a basis of two per cent the maximum
Se and the best technical rotation fairly coincide for all species ex-
cept oak where even two per cent brings maximum Se too early by
at least forty years. This seems to indicate clearly that the true
value growth of the forest is about two per cent for pine and spruce
and below two per cent or about one and one-half for white oak in
the German forest and present conditions of market.

On the other hand a two per cent rate makes forest lands gen-
erally more valuable than farm lands of far better quality for all
species except oak. In oak even a two per cent rate gives to the land
no higher value than the same land would have for farming.

d. Appreciation of the calculation of the income value of
the land.

According to Endres, von Zanthiers articles in Stahl's Forst-
magazin, 1764, may be considered the earliest satisfactory efforts to
develop money yield tables and a calculation by which different
methods may be compared.

The first calculation of the income value of the soil was pub-
lished by Konig in his Anleitnng zur Holztaxation, 1813. His for-
mula agrees with the present except that he used c in place of

c(i.opr)

The formula as now used was first developed by Faustman in
1849 m tne Allgemeine I'orst und fagdseitung, under the title Wald-
bodenrentenformel, formula of soil rent in forest.

The formula has been and is still being attacked in spite of the
fact that the basis for the calculation, final cut and thinnings, cost
of planting and current expenses are well known, the values, yield
tables, etc., constantly used, and universally accepted as the best
there is, and as being as reliable as any similar compilations in other

58 FOREST VALUATION

lines of business. The calculation itself as a simple problem in arith-
metic is no longer discussed.

Usually the criticism is one of the three following :

a. Forest'valuation, in Germany, does not ordinarily start with
bare land but with a forest business fairly regulated for a long time.
There is no .deed of any compound interest calculation. This argu-
ment seems convincing but is not true. In modern forest practice,
excepting selection forest, every acre of forest is cut once in each
rotation. Whether this is done in clear cutting in a single year or
in shelterwood in several years, the land is cleared of the old timber
and a new stand is started. To start this stand and care for it dur-
ing eighty or a hundred years costs money and when the stand is ripe,
the question is : what has it cost to produce ? Since the money spent
in planting, protection, administration, taxes, etc., has not paid any
interest it is proper that this interest be compounded yearly and
charged to the cost of producing the stand exactly as is done in the
above calculation for Se.

b. The second criticism is that the values for final yield and
thinnings are useless, since timber prices advance so rapidly that
they may double and more during one rotation. This argument is
valid but it does not affect the case at all. If a man examines two
farms with a view to buying, he is apt to judge on a basis of present
prices and if one farm produces thirty bushels of corn per acre and
the other fifty bushels he will consider that the latter is worth more
than the former. And he will be right regardless of any change in
the price of corn. Exactly the same thing is true in forestry. If
Faustman applied his calculation to two tracts of forestland sixty
years ago and found one of them worth twice as much as the other
the important point in his calculation is still valid in spite of the fact
that timber has doubled in value during this time. And even the ab-
solute value was, for his purpose, entirely right, for no one. is willing
to buy a farm or forest on the assumption that in one hundred years
the crops will be worth double the price. Occasionally there are
cases where an advance in price is practically certain and may well
be introduced even in calculation of the business. For instance a
plantation of pine set out today in the eastern United States may
take eighty years to mature and will then certainly not be sold at
present stumpage prices. But even in such a case it is not necessary
or desirable to assume uncertain advances in prices and most men
would prefer to estimate the value of their enterprise on the basis of
present prices, using, no doubt, maximum rather than average fig-
ures.

CRITICISM OF S3 59

c. The third criticism is that the calculation is a failure as soon
as "reasonable'' or "current" rates of interest are employed. This
point has been discussed under "Rates of interest." As pointed
out, current rates of interest are normally far above what large in-,
dustries and business actually make. On the basis of six per cent
farming in the United States is a losing business, though the farmer
pays this as a current rate. The forests and their growth depend
on natural laws and have nothing to do with interest rates. The
only use of an interest rate in the study of these forests and their^
growth is to serve as a measure. We can use five per cent and have
all values of Se negative and still secure a very good comparison
between dififerentjracts of land, between differe"nt species and meth-
ods of treatment. But these negative values while making possible
this comparison will give a distorted picture of things ; they will tell
the_ triith and yetjpislead. The absolute values will be correct so
far as the five per cent basis goes but they will show a good safe
business bringing in millions and giving paying employment to
thousands as being a losing enterprise.

This same criticism was amplified by pointing out that this form
of calculation on a basis of ordinary interest rates would lead to a
ridiculous and disastrous shortening of rotation. In part this was
provoked by enthusiasts in mathematics who actually argued for
such shortening of rotation. That shorter rotations were needed
most authorities agreed but rotations of forty or fifty years in spruce,
etc., were evidently wrong and the practitioner saw this. The mis-
take was one of judgment in establishing the value, of timber. As
stated under rotation, the maximum Se for Saxon spruce with pres-
ent prices would come at about fifty years. At present the great
body of timber offered to the market is larger than is produced in
fifty years and the prices of the smaller, less useful stuff are pur-
posely kept up by not offering too much of this kind of material.
If the Saxon state forest should go to a fifty year rotation this
small stuff would at once become a drug on the market and what
seemed profitable would prove a loss.

But this merely proves that in deciding on the proper rotation
and consequent final yield, it is necessary to use some judgment and
consider the demands of the market.

Good material, clean stuff, fourteen inches in spruce, etc., need
not fear depression in prices. Its market is practically unlimited in
central Europe and therefore the rotation is set to produce this ma-
terial.

The calculation of the income value of the land devoted to for-
est is not mere formula, in fact the formula may well be dispensed

60 FOREST VALUATION

with, it is an analysis of value such as is used in other lines of bus-
iness. The estimate of value or the assessment of every farm in-
volves this same analysis and the only difference lies in the time eie-
ment, a peculiarity of the forest business.

Just as the forester uses yield tables, expenses of starting the
crop, caring for this crop, taxes, improvements, etc., so the farmer
has accepted standard figures for costs of plowing, seeding, culti-
vating, his "stock figures" or yield tables, and finally his average
prices which guide him in setting a value on the land, on different
crops and methods.

e. The Se in coppice woods.

Since in ordinary coppice the crop is cut clean and the ground
cleared there is a temptation to use the calculation for Se without
any allowance and put cost of reproduction equal to zero. This is
not correct for a piece of coppice woods recently cut is not bare land,
but bare land plus living stumps. These stumps are the equivalent
of a good plantation safely established and so have value.

f. The Se in the selection forest.

Here the crop is never entirely removed. Where the forest has
been in use for a long time and satisfactory records of growth have
been established the stumpage value of the material removed during
one rotation and properly prolonged may be substituted for Yr -j-
5 Ta (i.opr'a) in the usual calculation.

In most cases it is simpler to estimate the Yr, etc., from the
size, quality and growth of the timber found upon the land at any
time and make up a new case,

F. VALUE OF STAND OF TIMBER OR THE GROWING
STOCK IN THE EVEN-AGED STAND.

A stand of white pine now fifty years old may be sold without
the land to a man who intends cutting the timber at once. In a
neighborhood in New Hampshire where many such stands are cat
every year, this kind of a stand will have a fairly definite market-
or sale value.

Stands of white pine in this same vicinity but less than thirty
years old would probably have no ready market and there would be
no established or accepted sale value, while there would be leady
sale value for any stand over fifty years old. Under ordinary con-
ditions stands not yet ready for use. non-merchantable or immature,

VALUE) OF GROWING STOCK 6 1

have no regular sale value and this is true even of stands abroad,
for the sale of such stands is not sufficiently common, even there.

The same stand may be sold to a man who wants to keep it
until it is seventy years old and of better size and quality. He would
have considerable expense holding the stand ; interest on the money
he has to pay for the stand, rent to the owner of the land , care and
protection for twenty years and taxes for this period. To determine
what he could pay for the stand he would assume a certain value
wThich the stand is expected to have at seventy years, deduct all ex-
penses and find what he may expect to get at the end of twenty
years when the stand is cut. He would discount this to present date
and get the present value of the stand on the basis of his expecta-
tions. This would be the expectation value of the stand.

The owner who wishes to sell the stand would set the price
first of all by the amount which it has cost to produce the stand, by
the cost value of the stand. This cost value of an even-aged, plant-
ed stand he can determine exactly as the farmer finds the cost of
producing an acre of corn. He charges the expense of planting, the
rent on the land, taxes and care. But unlike the farmer he has to
charge and compound these sums for the whole fifty years or the
age of the stand.

Any stand of timber regardless of age or size has the usual
three values, cost, sale and expectation, with the sale value rather
indefinite for non-merchantable stands.

a. Sale value of growing stock.

Since this is largely a matter of stumpage of marketable stuff
either for immediate use or to hold for future use, and since in the
United States this is important chiefly in connection with our wild
woods, it is discussed under stumpage value in chapter VI.

b. Cost value of growing stock.

The usual case for an even-aged stand of timber is as follows :
i. Area. of stand, 80 acres; age, m, 45 years, interest rate, p,

2%. \p-V.

Premises per acre :

Cost value of land, Sc, $5, therefore rent Sc (.op) is ten cents.

Cost of planting, c, $8.

Current expenses yearly, e, 50 cents.

Income from thinnings :

Thinning at age of 20 years, Ta, costs $3, negative income,
30 Tb, just paid for cutting,

40 Tc, 5 cords of wood worth $10.

62 FORKST VALUATTON

2. Expenses incurred to produce the stand or grow it to the
age of 45 years :

Cost of planting prolonged, c (i.opm),

or 8 (i.024"') $ 19.40

Current yearly expenses e with intere'st.

e(iQpm— i =E( m_o where E= _e_
i. op — i .op

'y\l „
and yearly rent of land with interest,

rent0'0""-0 »Si(i.op--i),

i. op— i

simplifying (E-fS>c) (i.op™ — i) or

(25 + 5) (i.0245— i) $ 43. 13

Thinning at age of 20 years, cost with interest.

Ta(i.op'"-a) = 3(i-0225) 4-92

Total expenses per acre $ 67.45

3. Income per acre obtained from the stand during the 45
years,

Thinning at 30 (just paid expense) $ o

Thinning at 40, $10 with interest for five years 11.04

Total income $11.04

4. Net cost per acre:

$67.45 — $11. 04 = $56.41

and cost value of the stand of 80 acres, $4,5.12.

5. This calculation is usually expressed in a formula as fol-
lows :

mGc — c(i.opin)-f- (Sc + E) (i.op111— i>^(Ta(i.opm--a)+Tb etc.)

when Ta is made at a loss or is a negative quantity, — Ta, is de-
ducted from costs as — ( — Ta) as in the sample case above.

In the formula ™Gc means : the cost value of one acre of the
growing stock, m years old.

6. The above case fully illustrates the usual calculation. If
natural reproduction replaces planting, c may be zero. Similarly,
if there are expenses of clearing the land, as on a burn, of cultivat-
ing the plantation, of filling fail places, etc., these expenses are
charged and prolonged exactly as planting, c.

EXPECTATION VALUE OF STAND 63

7. In the above case the cost value Sc of the land was used.
In most cases it is but natural that this should be so. But where
the cost value is practically zero, quite common where the land and
timber were bought together and only the merchantable timber con-
sidered in the price, the cost value is misleading, the land may read-
ily be worth five or ten dollars an acre and so have an accepted sale
value.

In such cases the sale value, Ss, is used. Occasionally the land
has neither cost nor sale value which could be agreed upon, for in-
stance, state and national lands, remote mountain or non-agricultural
land. Here the temptation is to ignore the value of the land entirely.
This is wrong since any land which can and does, or actually has
produced a crop of timber having value, has value itself. Incon-
sistency here is liable to lead to trouble for sooner or later the value
of these very lands may come in question. In such cases, the Se
properly based and discounted should be substituted as S. ~ /a^l

To employ Se without deductions is hardly advisable since Se
is rather the maximum value of the land for the particular purpose
and to employ a maximum price in these calculations is hardly safe
or satisfactory.

c. Expectation value of growing stock.

Ordinary case: Spruce, clear cut, and plant; rotation, ninety
years; area, eighty acres; age of stand, forty-five years, p, two per
cent.

1. Premises per acre:

Land value Sc $20

Yearly current expense e 0.50

Final yield, Yr, stumpage value, 40 M. feet at $10 or. ... 400

Thinning at 50 years, stumpage 30

Thinning at 70 years, stumpage , 60

2. Gross income per acre at end of rotation :

Final yield '. $400

Thinning at 50 and interest for 40 years 66

Thinning at 70 and interest for 20 years 89

Total $555

3. Expenses per acre to end of rotation :

Rent of land and current expenses treated as in case of cost
value,

(SC + E) (l.0pr-m-l)=r- (20 + 25) (I.0245— 1)....$64.

64 FOREST VALUATION

4. Net income per acre at end of rotation or net value of the
stand then, $555 — $64 or $491.

5. Present value of the stand on basis of expected income :
Final value discounted to date, or

I.02

Value of the stand on 80 acres — $16.160.

6. This calculation may be put in a general formula :

mG _YT-4-Ta(i.opr-a)4-Tb(i.opr-b) etc.— (Sc + E) (i.opr-m— i)

i.opr-m

where mGe means the expectation value of one acre of growing
stock, m years old.

7. It is evident that proper allowances must be made in esti-
mating future incomes, i.e., that these values must be reasonably
conservative. It also appears that if, in the above case, $202 per
acre is paid and the values are secured as per estimate, the buyer
does not make anything over and above his two per cent on all in-
vestment. Evidently then, the full expectation value is the maxi-
mum which can be paid for the stand.

Where risks of injury from fire, etc., are great, such risks are
allowed for in the calculation by proper deduction from the values
of the final yield and thinnings.

d. Which value to use.

In selling and buying a house the owner first considers the cost
value or what the property cost him. The buyer cares little or noth-
ing about this cost value but considers the market or sale value or
else the value which he may make on the property. So in the valua-
tion of the stand of timber. The buyer does not care whether the
cost of planting was high or low, and how much expense the owner
had in care, protection, taxes, etc., he merely cares about the values
which he can make out of the timber, the sale or expectation value.

This situation is complicated by the uncertainties of a living
crop. Commonly the age and condition of the stand decide. If a
stand of pine ten years old is injured or destroyed the question
almost naturally is — what did it cost to reproduce or grow it, what
will it cost to replace the stand, i. e., what is the cost value?

In older stands it is the sale value which determines. But in
many cases, especially in new districts, as in the far west, it often
happens that even a fine, mature stand of timber has no sale value

Otf STOCK IN NORMAL, FOREST 65

at all, but is certain to have a value as soon as a certain railway is
finished. Similarly a stand of lodge pole may be nearly mature and
yet be a few inches below the marketable size ; here evidently the
stand has a future value or expectation value, though neither sale
value nor an accepted cost value exist.

In the courts the sale value has always been accepted. Of late,
since these matters have been more carefully considered and the
evidence has been sufficient and clear, both cost and expectation
value have been admitted. For young stands, less than half rota-
tion, the cost value or cost of replacing is the more satisfactory.

e. Value of land and growing stock, together, i, e., value of
forest with even age stands.

This is merely a matter of addition of the values of land and
timber. In adding, the question arises as to the use of cost, sale or
expectation value of both land and timber. As stated before, this
depends on the viewpoint of the person making the valuation. The
owner of a tract of timber is apt to use cost values for both land
and timber, the buyer will use sale values as far as possible. If the
stand is young, he too is apt to employ cost value for the stand, but
is quite certain to use the sale value of the land, for it would be use-
less to employ cost values where this is zero or at least uncertain.
Both buyer and seller should work out the expectation value to get
a fair measure and check on all sale value estimates. Since the
growing stock is expected to pay rent on the land, the value of the
land is not changed by the fact that the stand must remain for twen-
ty or more years on the land before removal and so prevents use of
the land for other purposes.

G. VALUE OF THE GROWING STOCK OF A REGU-
LATED OR NORMAL FOREST.

When the State of Michigan starts out to establish a million
acres of state forest it must determine: how much capital is to be
tied up in this property and how much of it in land and how much
in perishable growing stock or trees of all ages from the seedling to
mature timber. The same is true of any owner or buyer who con-
siders selling, buying or developing a real forest business. The im-
portance of the growing stock in such a business is great since it
usually makes from sixty to eighty per cent of the entire value of
the property.

66 FORF,ST VALUATION

a. The regulated or normal forest.

1. Premises: Area, 16,000 acres.

Method, clear cut, and plant, even age stands.
Rotation, 80 years.

Thinnings every 10 years, beginning when the stand is ten years
old, the last at seventy years.

2. Condition of forest in spring just after planting:
Two hundred acres just planted, growing stock o years old.
Two hundred acres growing stock I year old, etc.

Two hundred acres 79 years old, or r-i years old.

3. Yearly work, expense and income on this forest:
Two hundred acres are cut. income 200 x Yr.

Fourteen hundred acres thinned, income T10 (200), T20 (200),
T30 (200), etc.

Two hundred acres are planted, 200 x c.

Sixteen thousand acres protected and cared for in road building
and other improvements, taxes paid, cost 16,000 x e.

Sixteen thousand acres growing stock pay rent of land 16,000
x Sc (.op).

4. A proper sample of this regulated forest would contain 80
acres, one acre just planted, one acre with one year old stuff, one
acre two years old, etc. to one acre 79 years old, taken from the
oldest stands. Whatever is true as to the average value of this
sample of eighty acres applies to the whole forest of 16,000 acres
so that if the growing stock on the sample eighty acres is worth
fifty dolars an acre on the average, the growing stock on the 16,000
is worth fifty dollars an acre average.

b. Expectation value of the growing stock of the regulated
or normal forest.

For sake of simplicity the rotation is assumed to be only ten
years so that the sample of the regulated forest contains ten acres.
Diagram, Fig. I, illustrates this lo-acre sample and indicates the
present value of yields, Yr, and thinnings, which are to be obtained.

The yearly work and expense and income on this lo-acre sam-
ple are:

One acre cut, income Yr.

One acre thinned, when stand is 4 years old, income T4.

One acre planted, costs c.

Ten acres protected, cared for, taxes paid, expenses 10 x e.
Ten acres of growing stock pay rent on the 10 acres of land, cost
ipXSc(.op).

IN NORMAI,

2. Adding the values of the growing stock of the 10 acres
gives the value of the growing stock for the entire sample of 10
acres and dividing this sum gives the average value per acre for the
sample, and also of the regulated forest.

T-\

Jalue

dalive o^
oxve o.

\ \\

T-5

\x\xv\\\as ex

T-b

T-l

X-8

T-\0

\.op'°

Fig. i. Diagram representing 10 acres (r acres), a sample of a forest regulated on a
year rotation, indicating the age of the growing stock on each acre; the present value of
e final yield (Fr) from each, and the present value of the thinnings expected from each
.re. Since Yr on the acre of 7 year old stuff is to be cut in 3 years, its final value, or
umpage value is discounted for 3 years. On the several acres 4, or more years old, no
rther thinning is to be expecte^, but the stand 3 years old will furnish a thinning next
jar, and hence the value of this is discounted for one year, etc.

Since the general formula for expectation value of growing
stock reads:

mGe = Yr + Ta(i.opr-a) — (Sc -I- E) (i.opr-m— i)
i.opr-m

the value of the several acres beginning with the oldest stand may
be written :

op _Yr-f o— (Sc + E) (i.opr-9— i)

°Ge=:

i.opr

NOTE: — The thinning from this acre has been taken •and no. further
thinning is expected.

68 FOREST VALUATION

«Ge = Yr-f-o — (Sc-f E) (i.opr-8-i)

sOe __ Yr + T4(i.op'--4) — (Sc 4- E) (i.opr-3— i »
i. op1"-3

and °Ge =

Yr + T4(l-°Pr~4)— (S'C 4- E) (i.opr-°— i)*

To get a common denominator for S Ta, treat in this manner :

Ta(l.0pa— i) I.ppr-a __ Ta(l.Opr-a) (i.ppa— .T)

I0pa(i.op— I v I.Opr-a ' I.0pr(l.0p— I

adding we have :

q.(r-i?C (Yr + E + Sc) (l.Opr— l)+Ta(l.Opr-a) (i.opa-i) _ (

(I.0pr) (l.Op— I)

as the expectation value of the growing stock on the ten-acre, or r
acre sample. Dividing this by r the average value of the growing
stock per acre is obtained and the formula reads:

°-(r-1)Ge average per acre =

(Yr + E+Sc) (l.0pr— - 1)+ Ta(l.opr-a) (l.ppa— i]

r(i.opr) (i.op-i)

3. To illustrate: Assume an area 16,000; clear cut, and plant,
P, 2%.

Rotation, 80 years.

Premises per acre : final yield or Yr, stumpage value per acre,
$400.

Thinning at 20 years, no income.

Thinning at 40 years, $10 stumpage.

Thinning at 60 years, $20 stumpage. •

1.50

Current expenses $1.50, hence E = -- , or $75. •

.02

Cost value of land, Sc, $10.

*For the class it is helpful to write these out as follows:

Yr Ta(i.opr-a) _ QSc 4- E) i.opr-m

~ i.opr-m i.opr-m i.opr-m i.ppr

this makes addition of SYr, 2Ta, etc., much easier and clearer.

THE SIMPLE: FORMULA 69

The average value per acre of the growing stock on this forest

is:

(400 + 75 + 10) (1.02s0— I ) +10(1.02**) (l.024°— l)+20(l.02a>) (I.0260— I)

80(I.02S°) (1.02— I)

-(75+io)
— 253 — 85 = $168 per acre, or about $2,688,000 for the property.

This case closely resembles a fair case in spruce in Germany,
site II, except that the cost value of the land is taken rather low.
The calculation indicates that the growth produced by this growing
stock will pay two per cent on the capital invested in the property
and composed of $160,000 for land and $2,688,000 in growing stock.

4. Simplifying the above formula by substituting Se, or its
value for Sc, results as follows and gives a very useful form:

sinceSe = Yr + Ta(i.opr-a)— c( i.opr)— £( i.opr— i)
(i.opi— i)

Se (i.opr — i) may replace Sc (i.opr — i) in the above for-
mula as follows :

--e per acre =
Yr(i.opr— i)4-E(i.opr— i).f Yr + Ta(i.opr-a)— c(i.opr)— E(i.opr—

r( i.opi-) (i.op— i)

) Ci.0pa— i)

T(l.Opr) (I.op-l)

which simplifies into :

Yr + Ta— c Yr + Ta — c — re

E--Se -Se

In this last form the formula clearly shows the work, expense
and income of the r acre sample, of the regulated forest. The yearly
income is Yr and Ta; the yearly expenses are c and re, the differ-
ence is the net income from the r acres. This net income divided by
r is the net income per acre, and this capitalized gives the income
value of the forest, i. e., land and timber together, so that the value
of the growing stock is this income value of property minus the
value of the land.

Using the premises set before and putting c = $io and replac-
ing Sc with Se at $28 we have :

400 +10 4- 20 —TO —120 Q ^

Value of growing stock per acre— — g, Q^ — —20 = ^159.

In this particular case the result, $159, compares closely enough
with $ 1 68 as obtained by the ordinary formula. In any case it is

70 FOREST VALUATION

necessary to keep in mind that this simple formula depends on sub-
stituting Se for other values of soil, Sc or Ss.

c. Cost value of the growing stock of a regulated forest.

In this case the value of the growing stock of the ten-acre sam-
ple is obtained by adding the values of the ten acres, writing the
value of each by the general formula as developed before :

mGc — c(i.opm) + (E + Sc) (i.op171— i)— Ta(i.opm-a)

where again m is the age of any one stand.
i. This leads to the formula:

per acre=

2. To illustrate: forest of 16,000 acres, clear cut, and plant;
rotation, 80 years ; p, 2% ; premises per acre :

Cost value of land, $10.
Cost of planting, $10.
Current expense, $1.50, hence E, $75.
Thinning at 20 years, no income.
Thinning at 40 years, $10.
Thinning at 60 years, $20.
Then the average cost value of growing stock per acre :

(10 + 7=; + 10) (l.02S° — i) — IO(I.024° — l) — •2O(l.O22° — i) ,

80(1.02-1) -(75 + io)= $131

and for 16,000 acres about $2,096,000.

3. Simplification of this formula by substituting Se(i.opr — i)
for Sc(i.opr — i) results in the same form found for Q-^-^Ge so
that:

when Se is employed as the value of the land in place of Sc, or Ss.

H. VALUE OF THE GROWING STOCK IN THE ALL-
AGED OR MANY-AGED FOREST.

Two cases arise : the regulated and the irregular forest.

a. The stand is truly all-aged and regular as in the case of a
well managed selection forest. Here old and young are in proper
proportion, all age classes are represented and occupy equal areas.
The difference between the growing stock of this forest and that
of a forest of even aged stands is merely in the distribution of old

Y-\IYUE OI- ALL-AGED STAND 7 1

and young on the ground. Theoretically at least, the following
holds : if the rotation is 120 years, the area 3,600 acres, the period
of return 20 years, so that each year 180 acres are cut over, each

rotation

one of the 180 acre lots contains six age classes, - — , and on

return

the 3,600 acres all age classes, from I — 120 year old stuff, are repre-
sented, provided reproduction is secured promptly, as is here as-
sumed. On each i8o-acre lot the trees of the six age classes would
occupy the same amount of ground, 30 acres, not in separated areas,
but mixed, so that every acre would have old. young and middle aged
stuff, i. e., trees of all six age classes. If this forest were cut over
every ten years, each lot would have twelve age classes, and if cut
over every year every lot should contain every age class from one
to one hundred and twenty years old.

The work, expenses and income from this regulated forest of
many-aged stands would be similar to that on the regulated forest
of even aged stands. Every year there is :

a. A cut of 180 acres, (but not clear cut), which takes:

1. The mature, I2o-year-old stuff, theoretically occupying 30
acres, but scattered all over the 180 acres.

2. Thinnings, and stuff cut to improve the woods on the 180
acres, really from 150 acres.

b. The entire 3,600 acres are protected and cared for in im-
provements, etc., and have taxes paid on them.

c. The growing stock must pay rent on the 3,600 acres of land.
To illustrate the computation: The yearly income is the stuff

cut from the 180 acres, or 30 Yr +150 acres thinnings, say, $10,000;
the expenses $5,500 per year; net income $4,500 per year; cap-
italizing this at 3% gives the forest an income value or expectation

4500
value of - — or $150,000 for land and timber together.

•03

To find the value of the growing stock on this forest the value
of the land is deducted. This value of the land may be cost value
or sale value or expectation value, according to the object of the cal-
culation or viewpoint of the person making this valuation. If the
land cost $10 per acre and this value appears satisfactory to use,
the growing stock on this forest is worth $114,000, or about $31.60
per acre, on the basis of the yearly income it can produce and is ex-
pected to produce.

72 FOREST VALUATION

b. The irregular forest of many-aged stands requires a val-
uation from stand to stand and no general calculation can apply.
Such a forest can not possibly yield a uniform income, steadily until
it is changed by systematic, regulation. In our wild woods the fol-
lowing three forms or conditions are common :

1. The stand is generally mature, the merchantable timber
makes up seventy-five per cent and more of all growing stock. Such
stands have little value beyond that of the merchantable timber, for
usually the rest is stunted and is injured during the removal of the
old stuff. This, then, is a case of stumpage values.

2. The stand is largely middle age stuff, which may be ex-
pected to be merchantable in a certain number of years, as seen by
growth studies. Here it is simply a case of mGe, as developed
before.

3. The stand is mostly young stuff, such as reproduction on
burns, windfall, etc. In these cases the cost value, mGc, should pre-
vail. Where such reproduction comes in with open, mature, or over
mature stands, the area of the young stand is estimated; its cost
value and the stumpage value of the old stuff are determined sep-
arately.

IV. RELATION OF CAPITAL AND
INCOME IN FORESTRY

A. NATURE OF INCOME AND PROFIT IN FORESTRY.

i. General notion of profit.

a. If an article for a store is bought at one dollar and sold at a
dollar and a quarter there is twenty-five cents profit, or the profit is

25%.

b. If a house, bought at $1,000, is sold within two months at
$1,200, the profit is $200, or 20%.

c. An office building in a small town cost $150,000, there is
little demand for this and the income after paying taxes, running
expenses and upkeep is about $3,000 per year. There is this net in-
come but no one considers the building a profitable one. To the
contrary it is well known as a "losing proposition." Savings banks
and the best commercial papers would pay twice this income. In
figuring the loss it is asumed that the capital of $150,000 should
have been invested at 4%, the income therfore, $6,000, that the
yearly loss is $3,000,, or 2% on the money; and if the building had
to be sold this would mean a total loss of $75,000. We have income
here but certainly no profit.

d. A house is bought at $i>ooo and current rate of interest
is 5%, the true net income from this house is $80 per year. Evident-
ly the new owner makes 8% on his money and the house nets him
3% more than the current interest rate. In this case there is a
profit, even though the owner does not sell, and this profit is 3% and
not 8%. In this way the net income from the house divides itself
into two parts, a reasonable regular income on the capital invested,
i. e., the 5% on the $1,000, and a 3% profit.

Since on this point authors vary, some putting the net income
as synonymous or at least interchangeable with profit, the position
taken in these discussions is here stated.

e. A farm is bought at $5,000, the new owner borrows $2,000
additional at 5% as a working capital to buy teams, tools, etc. He
produces a net income of $700 or 10% on all the money put into the
enterprise. He pays his creditor $100 yearly interest and retains
$600. This $600 makes 12% on the farmer's own money so that he
has his regular 5% income and 7% profit in this business. But even

74 FOREST VALUATION

here there is a doubt as to whether part of this seven per cent profit
is not a personal matter.

These few cases suffice to show that the matter of profit is not
as simple as it seems ; a great variety of combinations necessarily
arise, there may be profit even though there is no sale of property,
and also there are various viewpoints possible.

f . A man buys a house for $5,000, he borrows the entire sum,
giving the house as security. In one month he sells the house at
$7,500, and returns teh cash with a few dollars interest. The profit
is practically $2,500 and is not made on any real investment on his
part. It is usually stated that his credit is used, etc., but in many
cases this is not true at all ; the capitalist does not trust the man but
considers the house good for the money.

It is neither ordinary profit nor wages but a special form of
profit paying him for his enterprise, shrewdness or more often his
good luck, exactly as in gambling.

2. Profit from income producing properties.

a. In case under i, c, a house is bought at $1,000, the interest
rate is 5%, the net income $80 or 8% on the money invested, the
yearly profit is $30 or 3%. The cost value of the house, He is $1,000,

income value He is - - or $1,600, the total profit is $1,600 — $1,000
•05

or $600 and may be stated as He — He.

b. A forest property is bought at $250,000, it produces $10,000
per year or 4% on the investment, net income. Whether this would
be regarded a profitable investment or not depends on the purchaser,
chances for investment, the current rate of interest, etc. In central
Europe it would be considered an excellent property, in the United
States at present, it would be considered poor, in the west, barely
paying in the middle states, fair in the east. Any one who could
easily get five per cent on his money would not buy this property,
and would certainly not speak of a profit in this case.

Assume now that the property yields $20,000 per year or 8%,
then the case is similar to that of the house, i. e.,
Cost value of forest, $250,000.

20,000

Income value or 400,000.

•05

WHAT IS PROFIT 75

The yearly profit is $20,000 — $12,500 or $7,500, or expressed
in per cent it is 8% — 5% or 3% ; and expressed as a total it is
$400,000 — $250,000 or $150.000 which may be stated as:

profit = Fe — Fc.

That the same reasoning applies to land which is to be used for
forest is evident and leads to the statement : Profit = Se — Sc.

3. Profit from a forest not producing regular yearly income.

Usual case: A tract of 40 acres of timber is bought at $5,000, the
owner is not ready to cut the timber, it is not to be sold, or else no
offer is made ; in many cases of this kind in the more remote districts,
it might be impossible at times to get a buyer even at half the real
value of the timber; there is neither loss nor profit here actually es-
tablished until the timber is cut or some sale is made. As a fore-
cast, however, it may be possible and worth while to work out an
expectation value in the manner outlined before, and then the prob-
able or expected profit is equal to the expectation value of this 40
acres minus the cost value, in this case $5,000.

From the foregoing illustration, it is evident that the term profit
is clear and that it is consistently employed in the ordinary store, and
in ordinary sale of property. But when employed in connection
with the regular income from a house, farm or forest, factory, etc.,
it is not clear, being confused, commonly, with gross, or net incomes
and largely loses its usefulness.

B. INTEREST MADE BY THE FOREST.

In forestry the question frequently comes up — what rate of in-
terest is made by the growth of timber on a given tract. Three
cases may be distinguished :

a. The growth of a single stand such as a 4O-acre stand of
even aged timber.

b. The growth of a regulated forest, or more precisely, of a
working section with perfect age class conditions.

c. The growth of timber which may be produced on an area
of land which is bare to start with.

i. The interest made by a single even aged stand of timber.

Here the usual case considers the growth for only a short period,
say 10 years, but frequently, however, it demands the interest made
by the growth for an entire rotation.

76 FOREST VALUATION

a. Interest made by the growth of a stand during a short
period or part of a rotation: If the cost value of the land is $10
per acre and the cost value of the stand, now 30 years old, is $80,
then the amount invested in this enterprise is $90 per acre. Evi-
dently the only increase in value of this piece of forest is due to the
growth of the timber. If the growth in volume, quality and mar-
ket price amounts to $20 in 5 years then this $20 represents the in-
terest for 5 years on the $90 invested, and approximately the rate of

20 X

interest is: — —or 4.4%. While this calculation is a fair ap-
5X90

proximation it requires modification for larger enterprises, and bet-
ter analysis. The following illustrates the usual modification.

Area, 40 acres ; stand, even aged 50 years old at beginning of
period, and 55 at end; p, 2% ; land, $10 per acre; yearly expenses,

e, $i per acre; therfore — - or E is $50; the value of the stand at

.02

Cn
50 years is $250 and at 55 is $300. The reasoning then is : i.opn = — .

The initial capital, Co, is made up of stand at 50 years, land, and E,
the final capital, Cn, of stand at 55, plus land and E, and we may
set:

Y53 4- S -f E $300 4-io 4- 50

i. op = ' = ^ - • - f-*- — 1.16 and hence p = 3%.

Y°° 4- S -j- E $250 -f 10 4- 50

This per cent made by the current growth of the stand may be term-
ed "forest per cent," or Pf, and is the "Weiser" per cent of the Ger-
man authors.

The formula as written bv Endres is :

AH-B4-V
or in our terms,

/„ lYx+n 4- S -I- E

" = ""(>/ Y. + SI-E -

which readily changes into the above simple form.

This form of analysis was used by Pressler and Heyer over
fifty years ago. It is useful in determinig whether a given stand
should be cut or left standing, the usual assumption is that if the

FOREST PER CENT 77

per cent drops below 3% or whatever per cent may reasonably be
demanded by the owner, the stand is no longer worth holding.

While the calculation is quite simple the actual determination
in the woods is not easy and is never more than an estimate rein-
forced by measuring the outer rings of a few trees.

From these measurements the Pv or growth in volume in per
cent is determined by Schneider's formula; the per cent growth in
quality is estimated on a basis of diameter at beginning and end of
the period, and the per cent increase in market price is a figure
worked out for several years in any given district. Having this, the
growth of the stand is expressed in per cent for the three lines and
Pressler conceived the idea of simply using these as follows : assum-

Ym
ing the actual growth in value per year is : (Pv + Pq + Ps)

and that this growth is made on a capital Ym -f- Se.

100

Then pf = (pv -f- pq ~j-ps) IOQ (Ym+ Se) = ^pv ~^ P<1 ~'r ps^ Ym -Tse

To illustrate : If the stand is worth $250 and land $10 per acre
and

pv=i.;
pq=I

ps— I

or 3-'i%.

Since this method or inquiry is usually applied only to older
stands where the value of the timber is very large as compared with

the value of the land, the value of may be put = I and for

Ym + Se

ordinary purposes, therf ore, it is quite sufficient to state :

Pf = Pv + Pq + Ps ; in the above case pf = 1.3 + I + I = 3.3%, a

very convenient form.

In the United States where at present the value of timber is
usually by M. ft. b.m. on rather uniform price per M. feet, the case
of working out the data for pf may take the following form :

Assume stand of pine, pure, even aged, 80 years old; volume
table exists for species and district ; from borings or felling the
diameter growth of the timber is ascertained, the stand is calipered

7 8 FOREST VALUATION

and volume known ; stumpage $10 per M. feet ; assume that the stand
now, 80 years old, contains 250 M. feet. Value of this 250 X 10 =
$2,500.

From growth study it appears that the stand 10 years ago con-
tained 200 M. feet, valued at $2,000. Then the growth in value, be-
side increase in market price, is $500 in 10 years. Expressed as per
cent:

I.OPx10= — = 1.25 Px= 2.3%.

This px or 2.3% includes both the growth in volume and the
growth in quality as it finds expression in our present day practice
of scaling timber so that we may state: 2.3% — px = Pv + pq, and
this requires merely the addition of ps or the growth in market price
to state the total growth in value.

b. Rate of interest made by the growth of an even aged stand
during the entire rotation, i. e., from the time of planting to time
of cutting.

Here again it is convenient to apply the fundamental form of
reasoning that

r Cr Capital or values at end of rotation

Co ~~ Capital or values at 'beginning

The initial capital Co is made up of : land, Sc ; cost of planting, c,
or the value of young growth ; capital E, to take care of the stand,
pay taxes, protection, etc.

While this capital, E, is not really on hand, the results are the
same, the owner must provide from some source, an amount equal
to the interest on E at p per cent. At the end, or time of cutting
the final capital, Cr, into which Co has grown, is made up of : land,
Sc; capital for expenses, E, stand of ripe timber, Yr, and the state-
ment becomes :

r_ stand + land + expense capital _ Yr + Sc + E

~ land + expense capital + cost of planting c + Sc + E

Concrete case: Land $15 per acre, p — 2%, e = $i, hence E

I. 00

_ = $50 ; Yr, $400 ; c, $12 ; r, 80 years ; then :

465 ,.

= TT = 6.04

12 + 15 + 50 77
and from tables : pf = 2.3%.

FOREST PER CENT 79

The above formula may also be written :

p= ic

which is nothing more than the old form of the Weiser per cent,
where the period includes the entire rotation, c the cost of planting
represents the value of the stand just planted or at the beginning,
and Yr is the value of the stand at the end of the period.

Whether the value of the land is taken at cost, sale or expecta-
tion value is optional. Certainly the introduction of Se means the
use of a maximum which is not to be recommended. Since the val-
ues of land are apt to change very decidedly during a period of
eighty years it is not only permissible but even proper to set a higher
value for S in the numerator, i. e., in the final capital, than in the
denominator or initial capital.

In some recent publications the formula is written in a modified
form as :

Yr 4- S — Ex i.opr— T

i.opr= 0 , „ — and Ei is equivalent to e

I. op— i

or merely the end value of all expenses during this one rotation com-
pounded at ordinary interest rate, the assumption being that money
is borrowed (actually or not) at ordinary rates for this purpose of
paying taxes, protection, etc. It is evident that this, as well as many
other forms, is possible and that some uniformity in the use of the
letters and writing of these formulae will greatly help all concerned.
Where thinnings are made, and this must be assumed as the
normal condition in forestry, the above formula is incomplete and
must be modified to take care of the receipts from thinnings. This
may be done as follows :

2. Rate of interest made by a regulated forest, or one pro-
ducing a regular yearly income.

Since the yearly net income is in the nature of interest on the
capital invested in the forest and since this income is known, it is
necessary only to determine the value of the property, stand, and
land. But as this may be cost, sale, or expectation value of either
land or stand, a variety of conditions are possible.

Where the forest has been purchased in recent time, where the
income so far received has paid all expenses including an acceptable
rate of interest, and where the management has prevented any de-

80 FOREST VALUATION

terioration of the forest, the cost price is evidently the capital in
vested, and the rate of interest made by this forest is :

yearly net income

X loo

,
co&t value of forest

If the man bought the forest at $250,000 and receives $10,000 per
year net income, he evidently makes 4%.

If this same man paid $250,000 ten years ago and has "put
back" $50,000 to develop a better road system then evidently the for-
est costs him more nearly $300.000 and the $10,000 income is about
3% on the cost value of the property. Similarly, if instead of get-
ting $10,000 net income he has saved with a view to improving the
growing stock on the property and has secured only $5,000 per year
net income, the $5,000 reduction of cut is an investment and in-
creases the cost value.

Again, the forest may be part of an old estate or it may have
been bought twenty years ago at a "bargain" so that the present
cost value is not clear and certainly not equal to the present sale
value of the property. In this case the income is not referred to the
cost value but to the sale value.

With properties which are not common objects of sale like state
forests, national forests, etc., the value of the property itself is
based on the very income made from it together with an assumed
interest rate. The forest producing $10,000 per year net income
would be valued by capitalizing the $10,000 at, say, 3%, and the

10,000

capital value would be --- or $333,000.

-03

If this capitalization is now accepted it may serve as a measure
to find the forest per cent for future years. For the present, how-
ever, this value of the forest must be regarded as arbitrary, for it
would have been just as fair to use two or four as the per cent of
capitalization, and for the present, therefore, the per cent or interest
rate which this forest makes can not be determined for lack of ac-
ceptable basis, the value of the property on which the $10,000 were
made.

In determining the rate of interest made by any property pro-
ducing regular yearly income there enters the notion or custom of
"watering stock." In the above case, for instance, the owner would
at once set a much higher sale value in place of the 250,000 cost
value and in this way bring down not the income but the apparent
rate of interest. Practicallv all state forests of Germany never cost

INTEREST ON LAND 8 1

the states any money, they were simply taken charge of by the gov-
ernments, paid their way and all improvements to the present day.
And yet their value is set so high that the splendid net income- bare-
ly makes 3%, in most cases not that. The strange part is that this
high value is not a fictitious one but a very real thing and that these
properties could readily be sold at these high prices.

We have the same situation in the case of farm properties in
Europe as well as in our country.

3. Rate of interest made in a forestry enterprise starting
with bare land.

Under this head come the ordinary plantations, where no forest
exists, where the bare land is considered as the real capital, where
the money for planting, etc., is or may be borrowed at the interest
rate used in the calculation. In this case then :

_ yearly income X ioo _ yearly income X ioo a X ioo

capital " cost value of land Sc

Since the income here is not a yearly one but a periodic one,
every r years, the value of the equivalent yearly income may be
found by the formula :

A .(

The periodic income is :

A = Yr + Ta(i.opr-a)— - C(i.opr) — E(i.opr— i)

and the above calculation for yearly income is then:
(Yr -j- Ta(i.opr'a) — C(i.opr) — 'E(i.opr — i) .op ^

_ a X ioo Se .op X ioo _ Se .

To illustrate :

If the land costs $10 per acre, the accepted rate, p, is 3%, and
the forest enterprise is such that it pays 3% on $30, i. e., makes the
land worth $30, then evidently the man makes on his cost value of
land on the $10, not 3% but 9%, or, as per formula :

P* = — X 3 or 9.
10

This is an interesting statement and has value especially in the
United States where cost values of forest lands are still very low.

82 FOREST VALUATION

To illustrate : Cut over lands in the southern states may be bought
at $2 per acre. The Se even on a very conservative basis is $20
per acre. To a company financially able to hold and develop such
lands as forest properties the enterprise would make :

P* = — 3 = 30 % on the cost value of the land.
2

It should be noted that p in this case should be the p employed in
calculation of Se, and also that the px, the 30% in the above case,
is the interest made only on the cost value of the land, on Sc, and
that the other parts of the investment, costs of planting, taxes, pro-
tection, etc., produce simply p the accepted rate of interest, usually
3% in these studies.

C. COMPARISON OF PROPERTIES WITH YEARLY
AND WITH INTERMITTENT INCOME.

The great advantage of having any kind of business in a condi-
tion of producing approximately equal and yearly incomes is quite
evident. Ordinarily an enterprise is not considered a business at
all until it does produce a yearly income at least balancing expenses.
In most cases it is difficult to interest and enlist financial support or
purchasers unless there is an assured yearly return at least equal to a
conservative rate of interest, except in cases where a body of nat-
ural wealth is in view, as in standing timber, coal veins, etc., or else
in cases of great possibilities or probabilities where the element of
lottery or gamble enters. Financial concerns under public control
are generally forbidden to lend on securities of this kind. The reg-
ular yearly income has been, therefore, one of the aims in forest
business and forms one of the principal tasks of forest regulation.
Merely to emphasize and illustrate this fact the following concrete
case is here considered.

Assume two properties of 1,000 acres each; rotation 80 years;
p, 3%; Yr, $400; Sc, $10; average growth of ripe stuff per acre,
one cord per year, value per cord, $4; cost of planting, c, $10 ; cur-
rent expenses, e, $i per acre. Thinnings left out for sake of sim-
plicity.

AND INTERMITTENT

Comparison of yearly and intermittent working.

Property with yearly
cut and yearly income.

Property with a cut
and income every 80
years.

1. Growing stock at
beginning.

2. Growth of ripe stuff
during the 80 years.

3. Growing stock at
end of 80 years.

4. Value of property
at beginning.

5. Income during the
80 years.

6. Income at 80, i. e.,
in last year.

7- Condition at end of
first twenty years :

40,000 cords.
80,000 cords.
40,000 cords.

$10,000 for land and
about $60,000 for grow-
ing stock.

$320,000 plus interest.

$4,000.

Has Earned:
Per year :

Income : 4000.
Expenses :

Rent 335-

Tax and care 1000.

Planting 125.

Total expense 1460.
Net income per year,

$2540.
Net income for 20 years

(i.03M— i)
2540 — — or about

i .01 — i
$67,700.

None.

80,000 cords.

$10,000 for land noth-
ing for 'growing stock;
might enter plantation.

None, thinnings not
considered.

$320,000.

In Debt :

Expenses per year :
Rent 33-5.

Tax and care 1000.
Total I335-

For 20 years' expenses :
(I.0329— i)

1335 - or

1.03—1
$35,6oo.

For planting 10,000.
Plus interest or

1 0,000 ( i .0320 ) — 1 8,000.
Total expenses for 20
years :
$53,600.

This simple case of a comparatively small property brings out
the great disadvantages of the intermittent working of a forest prop-
erty. The man who owns 1,000 acres of land and sees before him

84 FOREST VALUATION

the piling up of over $50,000 expenses in only one-fourth of the ro-
tation is not very much encouraged to go into the forest business.
It also illustrates why in common sense and fairness the owner of
such a property is not able to pay taxes like the owner of a regu-
lated forest who has a net income every year. It also illustrates the
fairness, in fact the necessity, of deferring the taxes to the time
when the timber is cut and an income secured, such taxes to stand
as a lien against the property.*

* Read : "The Need of Working Plans on National Forests and the
Policies Which Should be Embodied in Them," by Professor Burt P. Kirk-
land, in Proceedings of the Society of American Foresters, Oct. 1915. This
article shows clearly the necessity of working for a sustained yearly cut in
the forests, and the principles laid down in this article apply in all real forestry
work the world over.

V. ROTATION

In planning a forest business it becomes necessary to decide
upon a rotation. To do this is one of the most important tasks of
forest regulation and requires a most careful consideration of all
conditions and factors concerned. Among these the most impor-
tant are the market, site, species and treatment.

The market sets its requirements as to species, size and quality
which must be raised, and it is useless to discuss rotations which fail
to raise timber of the required size. Site, species, and treatment,
particularly practice of planting and thinning decide the length of
time in which the desired size and quality of timber can be raised.
Being largely a weighing of conditions and factors, the setting of
the rotation is primarily a problem in statics and perhaps the most
important task of statics in forestry.

In so far as the conditions and results require expression in
dollars and cents, the basis for the study of a proper rotation is sup-
plied by forest valuation. In any ordinary forest business the aim
is to keep the forest and land in best possible condition and at the
same time make the largest income.

Assuming the silvicultural conditions cared for, the best rota-
tion is the one furnishing the best income for the longest time.

There are two distinct ways of judging this income:

1. We may demand the largest net income per acre of estab-
lished forest;

2. We may wish to secure the largest per cent on the money
invested in the forest or the largest net rental on the soil, the max-
imum Se.

These two viewpoints have for many years divided the foresters
of central Europe into two schools, the division still exists and prom-
ises to continue for a long time.

a. Rotation for largest net income per acre of forest.

The assumption here is that we start with a forest and not
merely bare land ; that this forest is more or less regulated and able
to produce a yearly income. All of these conditions actually apply
to the majority of forest properties of central Europe.

The following case illustrates the calculation:

Area of forest, 16,000 acres; rotation, 80 years; age classes
fairly regular. From this forest we can select an 80 acres sample

ST VALUATION

with stands of all ages from 1-80 years. From this sample we
would get each year :

One acre of ripe stuff to cut or Yr,

Several acres of thinnings, or 3Tq,

And we should have expenses of one acre to plant, or c, and
80 acres to pay taxes, protection, etc., or re, which may be put into
the following form :
average net income per acre =

or according to the following table for spruce site II, for a rotation
of

583+ 71 — 12 — 54

60 years = $ 9.80

980 + 232 — 12 — 72

80 years = $14.10

Spruce site II, Germany, Endres, after Schwappach, gross in-
come, expenses, net income and Se for different rotations from 30
to 1 20 years for use in formula. Average net income per acre

Gross Income.

Expenses.

Net Income.

Yr or

2Tq

m Total

current

Total

on basis

Rotation
Years.

final
cut
per

sum of
thin-
nings

income
from r
acres

plant-
ing of

expense
tax, pro-
tection

expense
forr
acres

from
r acres
of

\verage
per

of 3%
rental
value

acre

from r

one

etc., for

normal

acre.

one acre

r years

acres.

normal

acre.

r acres

normal

forest.

bare

old.

forest.

e$o.9o

forest.

land

1. 00

203

210

163

4.00

371

402

354

6.90

583

654

588

9.80

786

137

.923

848

12.10

105

980

232

1212

1129

14^10

105

1123

35i

1474

1382

15-30

100

1222

488

I7IO

102

1609

16.00

I28l

683

1919

III

1808

16.40

120

I2Q6

791

2087

108

1 2O

1967

16.30

FINANCIAL ROTATION 87

From the foregoing table it appears that the average net in-
come with spruce site II and present prices, is but $1.60 per acre
for a rotation of thirty years, rises rapidly and steadily to $15.30
for a ninety year rotation and passes a maximum of $16.40 at a rota-
tion of about no years.

b. Rotation for largest net rental on land, maximum Se,
and with this of highest per .cent interest on the investment. See
also chapter on Se. The assumption is that the bare land is the
real capital and that by using it to raise timber this land is made to
pay a rental and the object is to decide upon a rotation which will
secure the highest net rental per acre, i. e., the highest Se.

That a forest producing the largest Se also pays the largest rate
of interest or p is evident from a previous study into p where it is
shown that :

px = — p, the rate of p on Sc.
Sc

Since Sc or the cost value of the land is fixed arid p is the accepted
rate of interest which is also fixed, it is evident that px increases
directly with Se. This calculation applies to every stand or every
acre in the forest and therfore to the entire property.

Generally longer rotation means larger and better timber, larger
growing stock, larger capital, larger net income per acre of property.
As seen from the table for spruce} site II, and from discussion of
Se it means a larger Se and better rate of interest. But this reaches
a maximum after which the Se and with it the rate of interest made
by the forest decreases. Formerly unduly long rotations and large
timber were the rule and in most forest districts there was no regard
to the relation of this rotation with the capital invested and the in-
come secured. It was against this kind of luxury in forest manage-
ment that Pressler and Heyer raised their voices and used the math-
ematics1 of forest valuation and statics. And it was the fundamen-
tal formula for Se first developed by Faustman which served to
make clear the mistakes of very long rotations. At first the current
rates of interest, four and five per cent, were employed. But as
seen from discussion of Se these higher rates not only reduce Se
but bring the maximum Se very early and so suggest or demand
too short rotations. That there must be a limit to shortening of
rotation and that good marketable timber must be raised regardless
of any formulae was evident to every good practitioner. Unneces-
sary stress on mathematical formulae on the one side and common
sense with an aversion for formulae, especially for bringing in com-

88 FdREST VALUATION

pound interest discussions into the business of raising timber, on
the other, have prevented the two schools from coming together.

Of late there is a better understanding, it is evident to all that
the forest must produce good marketable stuff, and that if the for-
est can not make more than 3% in doing this, there is little use of
introducing 5% in the formulae. On the other hand it is clear that
the planting of small saplings at $50 per acre and holding old stands
which have not earned i% for a quarter of a century are mistakes
to be avoided.

With an interest rate of 2%, the rotation of highest Se, the
financial rotation coincides closely with the technical rotation or
that producing the timber most in demand and now in actual use.

A few figures may serve to illustrate this :

Ordinary rotations for regular timber forest in central Europe
run about as follows :

Pine and spruce 80 to 100 years

Balsam and beech TOO to 120 years

Oak 150 to 200 years

For spruce in Germany as seen from the tables under discussion
of Se, the maximum Se, and therfore pf, for site I-IV, on a basis
of 2% comes at 70-80 years, at a 3% basis in 60-70 years.

For pine in Germany on sites I-IV, on a basis of 2% as well as
3% the maximum Se comes at 60-70 years.

For balsam in Germany according to Lorey, maximum Se for
sites II-III on a basis of 2l/2% comes at loo-no years, which ac-
cording to Lorey is also the preferable age from the standpoint of
silviculture.

For oak in Germany, according to Schwappach, a rate of 2%
puts the maximum Se at 120-130 years, but here the modern tech-
nical requirements demand a rotation of 160 or over.

For beech in Germany the maximum Se on 2% basis for sites
I-IV comes at about 80 years, a rotation which does not produce
satisfactory saw timber and similar goods.

Poor sites such as poor sands in the pinery of north Germany
are unable with any rotation to make a 3% income under the ordi-
nary conditions of German management, and barely work out 2%
for land and costs. That the rotation can be shortened by planting
good transplants and by an energetic practice of thinning is evi-
dent. In addition, the modern means of manufacture have made it
possible to use smaller sizes and so work toward shorter rotations
in the forest.

VI. VALUE OF STUMPAGE

Under present conditions in the United States timber is gen-
erally bought and sold as standing timber or on the stump, and
usually goes with the land, so that in most cases it is really a sale
of the forest, i. e., land together with the entire growing stock and
not merely a sale of the timber.

In these ordinary sales of timber or forest, the price paid is
determined merely by the value of the merchantable timber and the
rest of the growing stock as well as the land is left out of consid-
eration, thrown into the bargain. Of late, especially on the national
forests larger sales have been made where the value of the merchant-
able timber alone was concerned.

In some cases, timber, whether forest or timber alone, is bought
for immediate use or cutting, in other cases the timber is bought
years ahead with a view of supplying a regular lumber or timber
business, or else just for speculation, when it has to be held for
years before any return is secured from the money invested. In this
way a great variety of cases arise, each having its own peculiar con-
ditions as to time, location, market, cost of exploitation, etc.

But all of these cases have a few fundamental conditions in
common and these only can here be considered.

Timber, here only merchantable timber, like other property has
three forms of value : cost, sale, and expectation value.

A. Cost value of stumpage.

1. Where timber is raised the cost value of the merchantable
timber can be determined in the ways before described. But gen-
erally the time between planting and harvest is so long, that this
cost value is rarely considered, and mature timber even in central
Europe is estimated by sale, rather than cost value. But it is well
to keep in mind that with present prices of timber from twelve to
twenty dollars per M. feet b.m. and cut into logs for spruce and
pine, the per cent made in the forest business is generally three per
cent or less, so that present prices may be regarded as cost prices
with three per cent and no profit, in spite of the fact that forestry
pays a larger net rent per acre than farming.

2. Where timber is bought for immediate use, as is much of
the timber purchased on national forests, etc., the price paid is the
cost value.

90 FOREST VALUATION

But where timber was bought years ago, in advance of cutting.
the present cost value involves : price paid ; interest, compound, us-
ually 5-6% in the United States ; taxes with compound interest ; care
of property, of late some money for fire protection, with interest;
losses by fire, theft, insects, windfall, etc.

Part of these losses is made up by growth, but in most cases
it is not safe to figure on any material growth. On large areas the
growth is usually balanced by decay, on smaller areas, the decay or
lass may far outrun growth, as in timber infested by insects, etc. In
these cases only a detailed examination determines the true status.
Leaving out this very uncertain element of losses by fire, etc., the
cost value results in a case approximately like the following :

Area, 2,000 acres; price paid 10 years ago, $40,000;

Present value of this 40,000 (i.o510) =$65,160;

Taxes at i%% on half cost price, $300 per year;

Care of property by some local agent, lawyer, etc., together with
expenses of fire control and occasional visit by cruiser, etc., $200
per year. These two items with interest :

(300 -f- 200) — — = $6,200,

1.05—1

Total cost, $71,360, or nearly double the original cost price.

This explains a common phrase among timber owners in the
United States — that the value of a property must double every ten
years if there is to be no loss.

B. Sale value of stumpage.

This may be considered under two heads :

The ordinary market price of stumpage as determined by actual
sales.

The stumpage value for immediate use as determined by an an-
alysis of the various factors entering into, or affecting this value.

i. The ordinary market price of stumpage should approxi-
mate : value of lumber at mill — cost of logging and milling, where
a proper profit, etc., forms part of costs.

But so far the market price of stumpage has not been deter-
mined in this way. Probably more than ninety per cent of all stump-
age bought during the past twenty-five years was paid at prices quite
independent of the prices of lumber and cost of logging, and deter-
mined chiefly by the activity of large buyers. A number of causes
contributed to this peculiar condition. Large quantities, thousands
of acres of fine stumpage were secured without pay from the United

STUMPAGK AND DISCOUNT gi

States government under the homestead act, large areas were alien-
ated at the nominal price of two dollars and a half per acre under
the Timber and Stone act and by Commutation of homesteads, large
areas were given as land grants to railways, etc. Several of our
states, Florida, Oregon, Idaho, New Mexico and others sold lands,
given them by the government under various acts, at prices in no
way graded by the price of lumber. Even our lake states sold tim-
ber at give-away prices. In this way Michigan sold il/2 million
acres of land in the ten years ending 1910, at prices usually below
two dollars per acre and most of it below a dollar and a quarter,
and most of this land was bought for the timber. Large areas of
timberlands have been held by small owners, or owners financially
unable to exploit and market the materia.1 and in many cases, a lack
of market, transportation facilities, etc., prevented the owners from
doing anything with the timber. Aside from these personal factors
there has always been the great balance of demand and supply. Even

» today with more than fifty years cut in sight, of timber already ma-
tured, it is useless to estimate the value on a basis of immediate ex-
ploitation and present prices.

To illustrate : assuming prices of lumber, mill run, to stay at
about $15 per M. feet, and cost of logging and milling to average
$10 per M. feet. ' Then the true value of stumpage should be $5
per M. feet average.

But this is not true. The first year's cut is worth the $5, but
the second, third, etc. year's cut is not worth it. The stumpage cut
in the .tenth, twentieth or thirtieth year, at five per cent discount is

5.00 5.00 5.00

worth only - — , - — , - — , or $3.10, $1.89 and $1.15 per M. feet.
1.62 2.65 4.32

»In keeping with these peculiar and unsettled conditions of stumpage
prices stumpage of pine in Minnesota brought $12 while in the
same year millions of better stumpage was bought in Oregon for
less than $i per M. feet.

The man in Minnesota could use it at once and make money,
the man in Oregon bought it to hold and he had to hold, and may
lose money at it.

Stumpage prices today vary not only for species but vary with
locality, with market, railway facilities, habit of the people of the
district, etc. Average figures for stumpage have little value, they
vary chiefly between $3 and $7, go as high as $20 and as low as $i,
and generally make from 10 to 30% of the value of the lumber at
the mill.

FOREST VALUATION

In central Europe most of the timber is cut, or cut and skidded
to the road and sold not really as stumpage but as logs ready for
hauling. Here the prices have gradually settled to a fairly exact
condition, the value of the logs depending on mill or market value,
and cost of transportation.

The prices vary little from year to year, have risen steadily for
many years, about doubled, in Germany in the last sixty years. The
timber is bought at auction, the bids usually naming a per cent of
the price set by the forest office.

In pine and spruce the timber is classified by the cubic contents
of the stem, i. e., the number of cubic feet per stem. The following
figures illustrate :

Spruce, logs cut full length, ready to haul:

Stem Class:

Contents :

Price per c. ft.

Price M. ft. bm.

Class I

100 c. ft. or over

14 cts. per c. ft.

$20

Class II

70-100 c. ft.

13 cts. per c. ft.

$19

Class III

35- 70 c. ft.

ii cts. per c. ft.

$17

Class IV

18- 35 c. ft.

10 cts. per c. ft.

$15

Pine, stems cut full length, ready to haul :

Stem Class:

Contents :

Price per c. ft.

Price M. ft. bm.

Class I

70 c. ft. or over

15 cts.

$22

Class II

35-70 c. ft.

13 cts.

$19

Class III

18-35 c. ft.

9 cts

$13

Class IV

below 18 c. ft.

7 cts.

$10

Cordwood : 4 cts. solid, or $3.60 per cord.

White oak, classification by middle diameter of stem:

Stem Class :

Middle Diameter :

Price per c. ft.

Price M. ft. bm.

Class I

24 inches and over

42 cts.

$60

Class II

20-24

35 cts.

$50

Class III

16-20

28 cts.

$40

Class IV

12-16

17 cts.

$20

Class V

under 12

10 cts.

$10

VALUE; OF STUM PAGE:

Beech usually sells at 4-7 cents per cubic foot and most of it,
even clear logs 12 inches diameter and better go as cordwood. This
cordwood is commonly sold from $3~$4 per cord.

Table of size and value of average tree, all for site I :

Age

Pine.

Spruce

Oak

Beech

Diam. "

Value

Dbh. "

Value

Dbh. "

Value

Dbh. "

Value

9-5

$1.10

9.0

2-35

0.85

•55

2.90

12.6

4-5<>

10.8

1.30

100

4-50

15-8

8.30

9.80

2.25

120

6.80

18.4

11.40

22.50

3-25

140

17.2

9.60

21.5

16.8

4.20

160

180

24-5

200

The above prices are for straight, well-cleaned, sound timber.
They clearly indicate that prices in parts of the United States are
rapidly approaching and in many cases have fully reached those
paid in the forests of south Germany and other European countries.
In fact it is doubtful if the same grade of large stems could be
bought for the same prices in Ohio or Indiana and several other
states.

2. Sale value of stumpage, determined by consideration of
the various factors. Here the calculation attempts to show :

price of lumber at mill ;

cost of logging and milling ;

the assumption being that the stumpage price should be the dif-
ference between these two, i. e., if the lumber is worth $15 and it
costs $10 to log and mill then the stumpage should be $5.

a. Price of lumber at mill.

Where the lumber is sold "mill run" this value is easily obtained
providing the sale of the lumber is bona fide and under normal con-
ditions.

Where lumber is graded at mill and sold by grades to various
dealers, attempts are made to get at the true average price by learn-
ing the per cent each grade makes of the cut and the price of each
grade.

In some cases this is quite simple, in most it is not. Any change
in the quality of the timber in the woods affects the per cent of

94 FOREST VALUATION

grades. Where several species are logged together such as hemlock,
maple and beech, etc., the proportion as well as the quality vary
from one tract to another.

To use the general prices of the district and agree on some pro-
portion of kinds and grades is usually as far as the analysis can go.

b. Cost of milling.

This also involves various considerations differing radically for
different cases. In one case the logs go to an established mill, the
particular body of timber is only one of several- or many which are
cut at this mill. The large mills along, or at the mouths of the
rivers in Michigan and Wisconsin are of this order. In this case
the cost of milling is quite simple, there is a regular market value
of this milling toll which is fairly well established.

In other cases the mill is established to cut the particular body
of timber and no more, it must be torn down and moved away, is
largely a loss and with it also a number of other buildings, quarters
for men, boarding houses, office, store, shops, etc. In such a case
the cost of milling involves :

1. Labor, material and repairs;

2. Depreciation of all buildings and machinery;

3. Interest, taxes, insurance, supervision and profits.
Generally the direct cost of labor and materials is fairly well

known, varies within narrow limits, mostly between $1.50 and $3
per M. feet b.m.

The depreciation of mill and machinery and buildings may be
treated as follows :

Mill and buildings may be assumed to last throughout the job,
the different machines may and may not need separate treatment.
Suppose the amount of stumpage sufficient to furnish 10 years cut-
ting. Let the mill and other buildings, including those machines
which are fairly certain to last the ten years be worth $150,000 and
let the interest rate be 5%. Then this outfit together with interest
costs at the end of the ten years :

150,000 (i.O510) — the wrecking value of the outfit.

If the latter is $10,000, then the end value is 240,000 — 10,000
or $230,000.

Usually we desire to know what yearly sum will take care of
this $230,000 and from this derive the cost of the depreciation per
M. feet of lumber. To get this we may set for the above case:

(i.o510— i)

yearly cost of depreciation = X and X = $230,000, and

1.05—1
from this X = $18,400.

COST OF DUMBER 95

If the yearly cut is 20 million the depreciation is 92 cents per
M. feet. It should be noted that this 92 cents pays for this part of
the outfit including all interests.

c. The cost of logging.

Logging is a very simple kind of business but the conditions
under which it is done are variable and many, and tend to complicate
matters. Size and quantity of timber per acre, mixture of species,
mixture of large and small stuff, distances, topography, surface,
rocks, brush, swamp, weather, snow, etc., all exert their influence.
The men are scattered over a large area and not easily supervised.
Where the timber is large as in the Pacific coast country or located
in swamps as cypress so that heavy machinery must be employed
the matter is made still more difficult.

Nevertheless the cost of logging like milling varies within nar-
row limits, the good parts of the job making up for the bad. Us-
ually it may be said that the cost of logging varies from 4 to 6 dol-
lars per M. feet b.m., rarely going below 4, occasionally going up
to 8 in mountain country. For eastern United States it runs per M.
feet logs about as follows :

Felling and cutting into logs $ .75

Skidding and swamping i .25

Hauling to landing or railway 1 .50

Railway haul or drive I . oo

Overhead charges of supervision replacement of equip-
ment, teams, camps, roads 1 .50

$6.00

In these items the profit is included with each item.
For large timber on the Pacific coast :

Felling and cutting into logs $ .60

Yarding and loading 1 .00

Hauling to mill i . 50

Booming, scaling, etc 40

Direct costs $3-5o

Depreciation of machinery and wire cables on basis of
the time they last and how many millions they
handle, also railway track and rolling stock, etc $2.00

Taxes, insurance, interest on money invested, super-
vision and profit i . 50

$7.00

96 FOREST VALUATION

Usually logging is cheaper in the Great Lakes country and
South than in East and West. But these general average figures
are little more than guide marks, each job has its own peculiarities
and it is not easy to standardize where considerations are so varia-
ble and where the human element is so very important.

Logging as done in the United States is the work of a transition
period, many of the methods will disappear, simpler methods under
more uniform conditions will take their place. When that time
comes the cost of logging in the United States as is now the case
in many of the forest districts of Europe, may be predicted within
very close limits.

Where the sale of stumpage involves large amounts of timber,
requiring ten or more years to remove, though cutting begins at
once, the case of sale value grades into the expectation value, and
demands special consideration. On the national forests large bodies
of timber are sold, the timber is paid for as it is cut, the buyer does
not really own the stumpage, he takes no risks in case of fire or other
injury, except so far as the injury affects his camps, equipment and
the use of his outfit or investments. In this case he not only can
pay full stumpage value as calculated above but can pay higher
prices for stumpage as the prices of lumber increase. For this rea-
son provision is made in these contracts to review or re-arrange the
price scale at fixed intervals or on a particular scale.

C. Expectation value of stumpage.

Leaving out the question of timberland speculation there still
arise many cases where this value is involved. In buying a large
lumber business, mill, railway equipment and body of timber, the
first question is: what is the timber worth? Suppose the concern
has four hundred million feet or twenty years' supply of stumpage,
the present value of stumpage for immediate use being five dollars
per M. feet. Evidently it would be a mistake to pay for the four
hundred million at the rate of five dollars per M. feet unless the
buyer is very certain that the increase in value of lumber warrants
this. How much increase would this mean?

If he pays $5 per M. feet, or 2 million dollars for the 400 mil-
lion feet, and if money is worth 5%. then this sum grows to 2 mil-
lion X (J-OS20) °r $5>3OO>OO° m round numbers. The lumber val-
ues do not rise year by year but rise by groups of years usually, and
with this rises the value of stumpage. Assume that the stumpage
stays at $5 for the first 10 years and then rises to a constant figure
for the second TO years, how much must this be? About $13 per
'M. feet

EXPECTATION VALUE OF STUMPAGE 97

If he pays $5 and stumpage does not rise he loses upwards of
two million dollars in the twenty years. What can he pay if he
expects stumpage to stay at $5? About $3.10 per M. feet.

In these calculations no attention is paid to expenses, taxes, pro-
tection, etc., which the owner has to incur in holding these forest
lands. The way of computing these was indicated under cost value
of stumpage and in other connections.

From what has been said about stumpage valuation it is evi-
dent that in most cases it is a matter of business judgment and inti-
mate knowledge of conditions which guides the investor. This
knowledge is largely one of forest utilization. The methods of cal-
culation or arrangement of data present nothing new but follow the
general lines of forest valuation.

The traffic in stumpage as it has existed in the United States
up to the present time will be modified in time and take more and
more the form of timber sale now in use on the national forests and
in the more settled districts change to the form of timber disposal
now in use in central Europe. Good silviculture will press steadily
for full control of the timber cutting.

VII. DAMAGES IN TIMBER

Here belong a great variety of cases, from gas injury of shade
trees in the town to the burning of large bodies of timber by fires
started by a railway locomotive. And it' is not merely the cases
where someone is liable or supposed to be so, but the numberless
additional cases where it is part of the forest business to ascertain
damages done by fire, storm, insects, etc.

Normally, the damage is only to the live, growing trees, but at
times there is added damage, since it may cost considerable sums
to put the land in shape for a new crop. Commonly these cases are
complicated. A fire running through a stand of hardwoods may kill
half the trees and leave the rest in an injured condition so that a
few survive staying alive for twenty years, while most of them die
during the first five years. In such cases it is anything but easy to
determine the exact facts, or condition.

Such cases are usually complicated still further by the fact that
parts or all of the timber could be used if cut at once, but that various
circumstances prevent the owner from cutting, so it may be several
years before he gets to all of the lands burned over and in this way
loses nearly all of the timber. How far conditions compel him and
how far he is at fault himself is usually impossible to ascertain accu-
rately.

Only a few sample cases may be considered here :

a. The shade tree in town.

A tree forty years old, satisfactory in every way, is destroyed
by a gas leak. What is the true value destroyed ? The owner guid-
ed by his feelings would probably place the value at several hun-
dred, the person responsible for the leak would value it as fire wood.

The following calculation may be helpful and approach a just
settlement as nearly as possible :

Cost of establishing a good tree, $15 ; interest at 5% ; 25 years
before the tree is really serving its purpose, after that the tree pays
its way, pays by its service as shade tree interest on the cost of es-
tablishing it.

The value of the tree is then 15 (i.O523) =$51.80 and this val-
ue remains as long as the tree is in good condition. Cost of caring
for the tree, etc., might also be added.

DAMAGE ESTIMATES 99

b. Young plantation of forest trees.

Spruce twenty-five years old destroyed by fire; evidently the
stuff is of little use save as inferior fire wood. Assuming the cost
value of the stand to be forty-five dollars and the value of the dam-
aged wood to be ten dollars per acre the real damage is clearly thir-
ty-five dollars.

If the wood is of no value and the man spends ten dollars per
acre to get the land cleared sufficiently to plant another crop, the
loss to him is fifty-five dollars. In the past the courts in the United
States judged the value of the timber solely as sale value. Since
the timber on this plantation has no sale value and since the man
actually incurred these losses it is only fair that he should receive
pay accordingly.

To ask damages in proportion to an expectation value of this
stand, on assumption that at the age of eighty years, or fifty-five
years hence, the stand may be worth five hundred dollars an acre,
while perfectly reasonable, would not appeal to any court of justice.

c. Older plantation of pine.

Fifty-year-old stand completely destroyed, sale value is only one
hundred and twenty dollars an acre, but the expectation value on an
eighty year rotation is two hundred dollars. Which should be al-
lowed? Evidently the latter, or at least a compromise between sale
and expectation value. In this case the costs of establishing the
stand are remote ; it may have been natural reproduction on non-
agricultural land, etc., and might be less than fifty dollars. So it
would not be fair to restrict the price to this cost value. On the
other hand, expensive planting on costly land and much extra care,
cultivating, etc., might bring the cost value to two hundred and
fifty dollars, which in all probability would not be allowed.

d. Ordinary Stand of wild woods.

Timber on forty acres of hardwoods and hemlock is largely
destroyed by fire. History and conditions of the forty acres of
forest: bought 12 years ago at $800; interest rate 5%; ready to
cut 7 years from now ; timber 400 M. feet, present stumpage price
$5 per M. feet ; land now worth $10 per acre when cut over ; expect
stumpage to go to $6 in the next 7 years. Value of timber after
fire, $500 ; tax and care for the 40, $30 per year.

100 FOREST VALUATION

Estimate of the damage may be set in one of three ways :
I. By cost value:

Value before fire : $800 (i.os12) $ 1434

30 (i. OS12— 0
Tax and care — — 480

(1.05—1)

Total $ 1914

Value after fire:

Land $400

Timber 500

Total - $900

damage, $1,014.

2. By sale value :

Value before fire : land $400

Timber 400 X 5 2000

Total $2400

damage, $1,500.

In this case it must be shown that the sale value could actually
be obtained without delay. The fact that timber is worth $5 stump-
age in the particular district is not sufficient evidence.

3. By expectation value :
Expectation value of the 40 before fire :

Value of timber 400 X 6 $2400

Value of land 400

Total gross value in 7 years. $2800

Expenses during 7 years:
3o(i.o57— i)

.$ 244

1.05—1

2556

Present value 1817

i.o57

Value after fire, $900; damage, $917.

In cases of this kind the value of the young stuff, i. e., the non-
merchantable part of the growing stock is usually left out of the
calculation, though frequently it has a greater value than the mer-
chantable stuff.

ESTIMATE: BY AVERAGE YEARLY GROWTH ioi

e. Young Stands in Wild Woods.

In the more remote districts of the United States the value of
the land, and the value of young, or non-merchantable timber is de-
batable. The determination of the cost of production of such a
stand, with calculations of compound interest, rent, charge of pro-
tection, etc., is not well understood, and not well received, and the
same is even more true with regard to the expectation value.

For such cases it has been suggested to use a method strongly
advocated for years by Frey in Germany (See Zeitschirft fur F.
and J., 1915, p. 284), and employ the sale value exclusively as the
basis of estimate. Ordinarily this would work out about as follows :

The ripe stand, 120 years old, is worth $300. A stand 40 years

300X40

old is worth— — . Generally, then, the value of any stand is
120

based on the average yearly growth in value, in the above case:

300

— — $2.50 per acre and year. Due allowance is made for de-

120

gree of stocking or condition of the stand.

The advantage of this method lies in its simplicity; it expects
the trespasser to pay only for the wood actually on the ground and
destroyed. For stands older than one-half the rotation this method
is satisfactory; for young stands it does not quite do justice to the
owner. Thus if a plantation is destroyed 4 years after being estab-
lished the $2.50 per acre and year (in above case) would hardly clean
the ground and replant, and the owner would have nothing for the
four years' growth and expenses. To charge the cost of planting
and protection, etc., to the $10.00 actual value per acre, in this case,
is really to ask pay for the stand twice, once, its actual value, and
once on basis of cost of production, or at least a large part of this.

Where natural reproduction is assumed to require 10-20 years
time, this period of reproduction is made part of the rotation ; i. e.,
the rotation includes the entire time from one harvest to the next.
For the above case the crop worth $300 is produced in 120 years.
If an additional 16 years is required for natural reproduction the

300

average yearly growth is : - — = $2.20 per acre and year. In

120 -h 16

the usual case of natural reproduction a stand of trees with an aver-
age of 20 years may contain trees from about 12 to 28 years old;

102 FOREST VALUATION

the land has been occupied and used for 28 years, and the question
arises : should the trespasser pay for a stand 20 years old or one 28
years old? Evidently the latter, at least in all cases of clear cutting.
In the shelter-woods where an old stand shares in the growth dur-
ing the 16 years in which the new stand is established, it may suffice
to charge for 20 years' growth.

It is evident that this method of computing the value of the
stand lacks analysis and must always be defective especially with
young stands, where the computation of the regular cost value of
stand is much more satisfactory.

f. The lumberman's case.

Two years after the fire, claimedly caused by the locomotive
of a railway company, the lumber company sues the railway com-
pany and claims : Lumber company bought, merely as "permit" or
"license," from the Canadian province, 460 million feet stumpage,
it had cut three years and still owned 400 million feet, it has the right
to continue lumbering on the "timber limit" as long as there is any
timber; it pays 50 cents per M. feet "royalty," or stumpage ; it in-
vested $200,000 in mill, railway and equipment, and aimed to cut
the timber in next 20 years ; was making a profit of $2 per M. feet
in the business. The fire destroyed 200 million and so reduced the
cut by nearly 10 years, since most of the timber destroyed is not
yet accessible.

The particular claim set forth:

1. Lump sum to cover loss in manufacture of lumber and for
increased cost of logging due to reduction of total stand available
for the plant.

2. Value of stumpage actually destroyed.

3. Value of equipment, camps, railway bridges, etc., de-
stroyed.

4. Logs and ties burned up.

5. Value of young timber., not yet merchantable, destroyed.

Among the questions which came up were the following:

1. Is all dead timber on the area killed by the particular fire?

2. Is all dead timber actually a loss, and if not how much has
been saved, how much could be saved, and at what gain ?

3. What is the company's basis for claiming that it can make
$2 per M. feet, and how is this affected by future logging from more
remote portions of the tract?

4. What effort did the company make to protect its logs and
equipment ?

LUMBERMAN s CASE: 103

5. What right has the company to claim pay for immature stuff
when the forest belongs to the province and the company pays
stumpage as it cuts ?

6. Is not the province the real owner of the stumpage and the
one entitled to pay for stumpage destroyed?

7. What rate of interest should be used in calculation of
damages ?

Other complications came up but need no mention here. Evi-
dently claim numbers five and two for young stuff and stumpage re-
quires a court decision as to rights of a "limit holder." If favorable,
then the expectation value or Ge should be established on basis of
growth study, and cruise.

Claims three and four are clearly right, if properly substan-
tiated.

Claims one and two are not easily separated since one depends
on two. The simplest calculation is offered by establishing the in-
come or expectation value of the whole business before the fire and
the same value after the fire and the difference should be the loss.

Expectation value before the fire: the cut is 20 million feet
per year with profit, (evidently net income and profit), $2 per M.
feet, or a total of $40,000 per year; interest -at 3% ; since this would
have continued for 20 years the present value of these 20 years
income is :

plus the provable wrecking value of the outfit at end of 20 years,
discounted to present time; let this be 10,000, then the total is
$601,000.

The expectation value after the fire on basis of only $1.50 profit,
due to extra work of logging.

30000

i.o3-i

plus the wrecking value at end of ten years, discounted to present
time ; if this is $50,000, then the present value is $307,000, and the
loss due to fire is about $294,000.

Another way of attacking this problem is to ascertain the value
of the stumpage on a liberal basis. Good stumpage is sold at $2 in
this district. Assume that 200 million feet are destroyed, that this
timber would have formed a uniform part of the cut during the 20
years. Then its present value is as follows :

104 FOREST VALUATION

Every year 10 million would have been cut, valued at $20,000 ;

(i.o320 — i)

total present value : 20,000 — - = $296,000.

(1.03 — 1) I.0320-

In questions of this kind there is still some uncertainty as to
how far a company or person should be held responsible in cases of
fire. In the city the owner of a burning building is generally not
held liable for harm which comes to other properties from the burn-
ing of his. In any case the public arid both parties to the suit are
more or less closely bound together and should suffer together.

This case sufficiently illustrates efforts at determining damage.
It is evident that it is chiefly a matter of accurate examination into
all the facts and the establishment of a reasonable basis which is
needed. Detail knowledge of the business and honest dealing should
solve these problems outside the courts.

VIII. TAXATION OF FORESTS

The subject of forest taxation is primarily one of public policy;
the attitude of government toward the forest business. But since
the basis of equitable taxation of forests must be supplied by forest
valuation a brief treatment of this subject is necessary.

a. Taxation is for public good, to collect money for public
expenses. There are three fundamental principles apparent in all
taxation except punitive forms which have no place here :

1. All people are asked to share in proportion as they are able
to pay.

2. Taxation should be no more irksome or offensive than is
necessary, indirect taxation, revenue, tariff, etc.

3. Taxation should not interfere or injure useful or necessary
business. While rarely expressed in just this way, the many modi-
fications of the methods of taxation to suit different kinds of busi-
ness were based on this principle fully as much as on the difficulty
of finding a satisfactory basis.

Even in the United States we have taxes of various kinds : or-
dinary property tax for house, farm, valuables, etc. ; income tax,
national, and also for railways by states, poll tax or head tax, "road
tax" to be worked out or paid for, tariff duties, internal revenues,
licenses to do business, special taxes, like present war tax, and other
forms.

Taxes are gathered by United States authorities for the na-
tional government and by local authorities for town, county and
state.

b. In ordinary taxation of real estate in the United States we
have to distinguish between assessment and rate.

i. The assessment sets a value on the property. It usually
takes the ordinary sale or market value, it may take the entire value
or only a certain, more or less uncertain fraction. This latter con-
dition is not always fixed by law and even where it is, it is com-
monly modified in practice and gives the assessor a chance to favor
certain persons or properties. It is clear that this local agent, an
ordinary elective officer, without special training, experience or other
qualities, can modify the amount of taxes paid on any particular
property and in this way he becomes the most important part in the
entire tax system.

106 FOREST VALUATION

That this is not easily overcome by law is well illustrated in the
report of the State Tax Commission of Michigan where it is shown
that about one half of the state, in 1914, was assessed at nearly full
value, (ninety-seven per cent), and the other half at only sixty-nine
per cent, in spite of the law which requires assessment at full cash
value, and in spite of the efforts of past tax commissioners. As
late as 1911 the assessment for the whole state was about sixty-one
per cent of the full value.

Assessment is not always simple. A i6o-acre farm with ordi-
nary buildings may make a good net income and yet sell for only
$50 an acre while a similar farm with fine brick buildings, etc., may
not pay expenses and yet sell for $TCO an acre. Fundamentally the
owner of the first farm is better able to pay. In practice the second
farmer pays double the taxes.

A store or factory doing poor business may not be worth the
land and buildings, or visible property, one doing a good business
may be worth five times the sale value of the visible property. Of
two railways from Detroit to Chicago the shorter one is the best
paying and most valuable but the longer route cost more money to
build and maintain, etc.

2. The rate of taxation is set to meet the expenses necessary
or supposed to be necessary by state, county and town. The total
taxes, state, county, town, including road, school, etc., for Michigan
have been about fifteen to eighteen per thousand dollars worth of
property. Of $16.55 total taxes in 1902, $12.26 were for local taxes,
town, school, roads, etc., $2.41 for county and only $1.88 for state.
Naturally the local taxes vary most, and vary from one school dis-
trict to another, even in the same township. The great range for
different counties in the same state is apparent from the following:
for 1901 the average tax rate for the different counties in Michigan
was as follows :

Over $ 50 per $1000 property in I county

40-49 5

30-39 13

20-29 30

15-19 18

10-14 15

Below 10 dollars i

It is apparent that in any county where timber is assessed at
full value and taxed at forty dollars per thousand of value, the inter-
est and taxes eat up the property every six or ten years. Since this
rate is an arbitrary affair without limits and left to local politicians,

UNITED STATES TAX RATES

107

it is quite common that the tax rate and not the tax assessment is
the more dreaded phase of taxation. Good, old settled, rural dis-'
tricts in southern Michigan commonly fall below ten dollars per
thousand of property while poorly settled, new, districts are normally
high in their tax rates, in fact one of the most sparsely settled coun-
ties in 1901 had an average tax rate of over sixty-three dollars per
thousand of property. It is doubtful if rural taxes should be al-
lowed to go much above ten dollars per thousand.

In this connection the following table is interesting :

Tax Rate Per Thousand Dollars of Assessed Valuation,

according to bulletin 109, Department of Commerce and Labor,
1910, p. 849 :

1890

$18.50

16.40

14.40
23.70

1880

$18.30

17.70

12.70
20.90

1870

$19.80

18.70

14.10
24.00

1860
$7-80
9.70

11.70

1002

Continental United States $20.50

North Atlantic, Maine- Penna.. . 18.30
South Atlantic, Delaware-
Florida 16.00

North Central, Ohio-Wisconsin-

Kansas-Mirmesota 24.70

South Central, Kentucky-Arkan-
sas-Alabama-Texas J7-3O

Western, including Pacific Coast 25.50

Ohio 23.80

Indiana 19.70

Illinois 5.1.50

Michigan 16.60

New York 22.20

Pennsylvania 14.90

Massachusetts 15.80

Wisconsin 13.60

The above table indicates that Michigan, in this, as many other
matters is very nearly average and also that for the entire Union
fifteen to twenty dollars per thousand is considered a reasonable
rate. The tendency to increase in rate may be expected to give way
to a tendency to decrease with about twelve dollars per thousand as
the proper minimum for the state and about six dollars for rural
property. In circular 132, A, United States Department of Agri-
culture, 1913, this rate of six dollars per thousand, of farm property,
is accepted as average for farm property in the United States. As

14.30

16.30

18.00

4.10

19.90

22.30

25-50

17.70

19.10

16.80

20. IO

IO.OO

18.20

16.40

16.30

9.00

40.90

31-30

45.20

15.70

16.10

16.70

19.90

10.80

19.80

21.30

24.70

11.00

14.00

17.10

18.70

12.10

14.60

15.40

1570

9.6O

22.90

18.70

16.20

12.50

108 FOREST VALUATION

pointed out, property is not assessed at full value and even in states
where the law demands this it is not done consistently. In most
states the assessment is at about 2/3 value for rural property and
varies from twenty-five to one hundred per cent in city property
with large amounts escaping taxation altogether.

c. When farm taxes were gathered as "tithes," or one-tenth
of the crop, not in money but in grain, etc., the tax was clearly a
personal tax and of the nature of income tax, on gross income.

When this changed to a fixed money tax, based on the value of
the farm and this latter based on the fertility of the farm, it lost the
character of a personal tax though still of the nature of a tax on an
implied or estimated income.

Today in the United States the farm or forest is assessed at its
sale value; the tax books are based on the property, it is the prop-
erty which is taxed regardless of ownership. If the owner neglects
to pay, it is not the owner who is looked up and addressed, but the
property itself which is at once taken charge of and sold for taxes,
etc.

The property tax as it applies to real estate, farm and forest,
then, is no longer a personal tax, it ignores the owner and condi-
tion of ownership, is not concerned whether the owner is able finan-
cially, or poor and in debt, whether or not he makes any income from
this property.

d. In Europe forests are taxed in various ways. Usually the
forest property is so regulated that a yearly income is secured and
the ordinary forest property resembles the farm and the ability of
the owner to pay is much more easily determined.

The three forms of forest taxation most generally applied in
central Europe are: ground tax; income tax; property tax.

1. The ground Tax, "Grundsteuer," or "Ertragsteuer," of the
Germans is a tax on the soil, based on its estimated income or else
on an official estimate of the productivity, "Kataster," and is used
exactly like the ordinary tax on farm property or real estate in the
United States ; where the farm is largely assessed according to the
crop it produces.

2. The property tax of European states is a regulator in cases
where the property does not produce an income in keeping with its
value. An empty lot in the city is only an expense to the owner but
it has a sale value. Similarly a farm in the outskirts of a city may
be worth a thousand dollars an acre and yet as a farm may not make
as large a net income as another farm three miles away and valued

INCOME; TAX IN FOREST 109

at only one hundred an acre. Private parks, summer homes, etc.,
belong in this class. In these cases the sale value of the property is
taken in the assessment.

3. Income tax is a personal tax and takes a certain part, say
one-tenth, of the net income. The income is taken as an average of
three or five years and all expenses are deducted. In these expenses
are included also the interest which the owner of the property is
paying on debt. The following case illustrates :

Area of property, 10,000 acres ;
Forest of spruce, all one site;
Clear cut and plant, rotation, 100 years ;
Yr, $500, yearly cut, 100 acres, worth $50,000 ;
Yearly expenses, $1.50 an acre, or $15,000 total;
Tax rate, one-tenth of net income. The taxes are :
o.ioX (50,000 — 15,000) or $3,500.

This amount is seven per cent of the stumpage value of the
ripe timber cut during the year so that a yield tax of seven per cent
in this typical case is equivalent to ten per cent on net income.

If in the above case there was a mortgage of $200,000 at 4%
on the property the $8,000 of interest would be added to the expenses
and the taxes reduced to $2,700.

4. Where the forest is not regulated it does not produce a
yearly income but produces an income only at long- intervals, (inter-
mittent working of Schlich), as for instance a single plantation, all
one age and kind where, if we neglect thinnings, no income is se-
cured from time of planting till the stand is ripe. In such cases the
method of taxation by income tax is not readily applicable and vari-
ous modifications are employed. The simplest of these and most
nearly in keeping with the principle of income tax is the postponing
of payment until the timber is ripe and then paying a sufficient sum
in keeping with the large income at that "time.

In other cases the value of the intermittent income is calculated
and converted into a yearly income by the formula :

periodic income _ yearly income
i.opr — i i. op — i

periodic income

. . yearly income = ; .op.

i. op1— i

But this means practically a return to the ground tax system which
in these cases no doubt deserves preference.

I IO

FOREST VALUATION

5. The state and. local taxes in Germany are not always com-
puted by the same methods, in fact it is common for state taxes to
be levied as income tax and local taxes as ground or property tax.

Since the state forests pay local taxes, corresponding to county,
town, highway, etc., taxes with us, and since these local taxes repre-
sent probably not less than seventy-five per cent of all taxes paid, the
following figures are of interest, doubly so because they affect a
large proportion of all forests of the several states.

Local taxes paid on the state forests of Wiirttemberg on a total
area of about 490,000 acres :

Value

Local taxes paid by state.

forest
or

Yearly

Years.

net
income
capital-
ized
at 10%.

net
income
per
acre.

Total
$1000.

Per
acre.

Tax

IOOO

property.

Tax

as % of
net
income.

Tax

as%
of
stump-
age.

$per

acre.

1880-89

$2.69

80.9

.16

6.10

4.2

1890-99

3-86

105

.21

5-50

5-4

4-3

1900

5<J

5-07

117

•23

4.60

4-5

3-7

1901

5-41

119 .

.24

4-45

4-4

3-4

1902

4-73

126

•25

5-30

5-2

4.1

1903

5.10

128

.26

5-10

5.1

3-9

1904

5-79

105

.21

3.60

3-6

2.9

1905

6.10

167

•34

5-55

5-6

4.2

1906

6.78

178

•36

5-35

5-3

4-i

1907

7-47

188

.38

5.10

5-1

4-1

1908

6.50

200

.41

6.30

6-3

4-9

Assuming these local taxes to be seventy-five per cent of total
taxes the forests of Wiirttemberg were taxed in 1908 on a basis of
about $8.40 per $1,000; or 8.4 of net income, or 6.5 stumpage tax,
or 54 cents an acre. The following figures represent the same con-
dition for the state forests of Baden for the year 1002, arranged by
the political districts:

TAX RATES IN EUROPE 1 1 I

Local taxes paid by the state forests of Baden in 1002 :

Value

Local Taxes.

District.

Area
of
forests,

1000

acres.

Net
yearly
income
per
acre.

forest
on
basis
of
net
income

Tax on

$1000

prop-
erty.

Tax

as%
of
net
income.

Tax

as%
of
stump-
age.

Total

IOOO.

Per
acre.

and

10%.

$
8.48

$
84

3-5

$
.27

$
3.20

%
3-2

2.7

4-5

3-52

.18

5-10

5-1

5.98

32.5

.29

4.90

4-9

3-5

5-92

23-7

•47

8.00

6.1

6.19

4-5

.09

1.48

1.4

2.1

4-13

3-2

.40

9.80

9.8

2.04

3-2

.22

11.00

ii.

Entire
state

248

5.78

.29

5.10

5-1

4-4

The great variation in the local taxation as it appears in this
table is, no doubt, due to the fact that so many villages and towns
in parts of Baden have large communal properties which relieve
local taxation very materially.

On previous assumption of local taxes representing seventy-
five "per cent of total taxes the Baden forests were taxed in 1902
about thirty-eight cents an acre ; six dollars and eighty cents per
thousand dollars worth of property ; six and eight-tenths per cent of
net income ; or five and eight-tenths per cent of stumpage cut per
year.

In Prussia with about 6,540,000 acres of state forest the local
taxes for many years varied between three and a half and four and
a half per cent of total expenses. Taking the year 1892-93 as basis
of income and expenses, the following results :

Total income per acre $ 2.66

Total expenses per acre i • 38

Net income per acre 1 . 27

Value of forest per acre on 10% basis 12.70

Local taxes at 4% of expenses per acre: 5.2 cents,

Local taxes per $1000 property 4.20

As per cent of net income 4-2%

As per cent of stumpage 2-3%

112 FOREST VALUATION

Assuming again the local taxes to be seventy-five per cent of
total taxes these forests appear taxed at about seven cents per acre ;
or five dollars and sixty cents per thousand ; five and six-tenths of
net income, or three per cent of value of stumpage.

6. The general tendency in forest taxation in Europe is
toward some form of income tax but it is doubtful if ground tax
and property tax will ever be entirely dispensed with. An important
and interesting fact is that forestry as a business is not only possi-
ble but thrives under a variety of methods of taxation and that in
the best forest districts, Wiirttemberg, Saxony and Baden, the old-
est form of ground tax is still employed.

This clearly proves that it is not so much a matter of method
of taxation as it is an understanding of forestry as a business and
a sense of justice which is needed, here, as in many other lines of
taxation. The application of some one simple method by one au-
thority, as is done today in the United States for farm property,
would certainly be preferable to the irregular variety of taxation,
in method, rate and authority of most European countries.

e. Forest taxation in the United States.

1. Forests are taxed in all states of the Union as real estate,
the timber and the land, or crop and land being taxed together. The
taxation is not uniform : in one county the forest may be assessed
low as wild land, in another the timber is carefully estimated and
its value added. Non-resident owners and therefore a large part of
the forest owners usually fare worse than residents of the township
or county. A common mistake is to assess stumpage which can not
possibly come into use for years, as if it were ready to cut at once.
For instance — a lumber company has twenty years' supply of stump-
age; its mill is the most important enterprise in the county, furnishes
opportunity for labor, market for produce and a supply of cheap
building material. Stumpage is worth six dollars per M. feet. At
a recent revision an effort was made to assess the twenty years sup-
ply at this rate. It was shown that by doing so with the prevailing
tax rate of three per cent, the taxes and interest would eat up the
value of a large part of this stumpage long before the timber could
be used at the mill.

The complaint usually is that the present methods of taxation
force the owners to cut and thereby discourage the holding of for-
ests.

2. In actual forestry practice, the present method of assessing
the stand at full sale value and taxing it at a rate of three per cent
would prove prohibitory. To illustrate: a plantation of white pine

INFLUENCE; OF TAX RATES 113

costs ten dollars an acre and is located on land worth ten dollars
more. It is assessed at twenty dollars and pays taxes at three per
cent for thirty years. So far the owner has had no income but has
paid sixty cents per year for taxes alone. This together with inter-
est at three per cent makes thirty years holding- of the plantation
cost $28.54 for taxes. If now the value of the stand

At 30 years is $100

At 50 years is 250

At 70 years is 400

and- if the assessment is raised, as it should be according to law in
some states, to these values at thirty and at fifty years the case is
as follows :

Taxes and interest between 30-50 years $ 80

Taxes and interest between 50-70 years 200

and the growth in value of the stand between fifty and seventy years
fails by as much as fifty dollars to make good the expense of taxes.

In addition to taxes there is a charge of $39.14 between 30 and
50 and a charge of $70.68 between 50 and 70 on the original invest-
ment of land and plantation.

The above case presents no special peculiarities, the rotation of
seventy years is below the ordinary and the value of the stand at
seventy is liberal. It is evident therefore that with present methods
of assessment and rates, forestry, even at such favorable conditions
as in the above case, must be carried on at a large loss.

The fundamental fallacy of this method lies in the fact that
the same year's growth is taxed over and over again, for seventy
years, in the above case. This is never done in taxation of farm
property.

3. From the standpoint of the state or people the following
is true : To the state the taxes on standing timber are only of mod-
erate importance ; in the Lake states and east of very little import-
ance. On the other hand the secondary benefit through manufac-
ture of timber is of great value to the state. With the counties this
varies. In well settled farm counties the taxes from woodlots are
unimportant and there is no reason why woodlots should not be
treated like the rest of the farm land, i. e., the value of the timber
left out of consideration. In sparsely settled forested counties the
taxes from timber are important and there is usually clamor for
large sums and also for a steady income, to enable development.

114 FOREST VALUATION

In some localities this is justified, in most places it is not, for usually
the sawmill, etc., are worth more to the counties than any direct
taxes. Lack of state control and the unreasonable insistence on high
local taxes have repeated the story of the goose of the golden egg
a great many times in all our forest districts.

The claims of the local people are usually of this order: the
forests were not raised by their present owners but given away by
the people at nominal prices to encourage the timber business and
general development. The owners are not in the forestry business
and have no intention of perpetuating the forest. There is no reason
why a man should not pay taxes en a hundred thousand dollars
which he invests in timber exactly as if he had invested it in other
property. The holding of large areas of forest is a form of land
monopoly and generally inimical to settlement and development.

f. Reform in forest taxation in the United States.

i. For about forty years efforts have been made to encourage
forestry either by modifying taxation or by actual bonus. Among
the earliest of these efforts was the Timber Culture Act of 1873,
giving United States lands on condition of establishment of a stand
of forest trees. Since that time different states have enacted a
variety of laws. Usually the aim was to encourage planting of
woods in small tracts.

In some cases the plantation was exempt entirely or partially,
in others only the land was taxed and assessed at nominal value, etc.
In most cases these laws, excepting the United States Timber Cul-
ture Act, produced no results whatever. In the last five years, Con-
necticut, Massachusetts, New York and Pennsylvania have enacted
well planned laws.

In recent legislation the following three essential points in our
transition stages of forestry in the United States are considered :

The requirement of the local people of a continuous income is
met by a yearly tax on the land, either on its sale value, or a nominal
value.

Lack of income from plantations and immature stands is con-
sidered by deferring the tax on the timber to the time of cutting, i. e.,
making it a harvest or yield tax.

The variable and peculiar condition of merchantable timber is
taken care of by varying the amount of the yield tax.

In the Connecticut law of 1913 the following provisions are
made:

i. The application of the new tax law is optional with the
owner.

NEW TAX LAWS 115

2. Land worth twenty-five dollars or more is not considered
forest land and does not come under the provisions of the act.

3. An existing forest placed under the ne\v law pays not over
ten per mill on actual value of the forest as a yearly tax, and when
the timber is cut it pays a yield tax which is varied as follows :

If cut in first ten years, yield tax. .. . 2% of stumpage value
2nd 3% of stumpage value

3rd 4% of stumpage value

4th 5% of stumpage value

5th 6% of stumpage value

after 5th 7% of stumpage value

4. New plantations are not exempt, but pay:

a. Yearly tax on the assessed value of the land alone at not
over ten per mill ;

b. Yield tax of ten per cent of the stumpage value of the ma-
terial removed, to be paid when the timber is cut.

In the Pennsylvania law of 1913 the harvest or yield tax is
also set at ten per cent of the stumpage value, the land is assessed
at one dollar per acre and the state pays the yearly land tax and the
owner of forests is free to avail himself of the law.

g. Basis of new tax laws.

1. The various efforts at some reform in forest taxation clear-
ly show a lack of uniformity in the basis for such tax law. Even
with regard to the land we have :

Lands worth over twenty-five dollars excluded:

Lands assessed at sale value ;

Lands assessed at one dollar, in Pennsylvania, and assessment
at five dollars recommended by Massachusetts.

A reasonable sale value should be employed, and there is no
reason why even fifty dollar land should be excluded. Efforts at
tax dodging would be taken care of by the sale value assessment.

2. The greatest amount of uncertainty, however, was involved
in finding a proper rate for the yield tax. Should it be five or ten
per cent, should it be ten per cent of the stumpage, of logs at land-
ing, at mill, etc.?

Il6 FOREST VALUATION

Pennsylvania and Connecticut employed ten per cent without
apparently attempting to develop a reasonable basis or giving an
explanation.

The Massachusetts Commission, see Senate document number
426, 1914, made an effort which proves instructive. Its premises are :

Rotation, 50 years, also assumed by Connecticut and Vermont
in recent acts (setting a general rotation is of very doubtful value
and certainly 50 years will not raise proper sizes for general mar-
ket) ;

Tax rate, $17.39 per $1.000 worth of property:

Yield at 50 years, $240; value of land, $5 per acre; interest rate
for total tax, 8% ; for land tax. 5%.

The plan is to pay a yearly tax on the land and pay a yield tax
at the time of cutting the timber. The reasoning is this : the income
from this property consists in the timber cut. The tax on this in-
come or timber is the tax for the whole property, timber and land.

The land tax is paid to furnish a yearly income for the local
government but should be deducted from the yield tax which is the
principal tax which the property should pay.

Computation of yield tax or principal tax :

The present value of Yr pays taxes every year at rate of $17.39
per $1,000, and this is to be compounded at 8%, so that for $i of
Yr we have:

(— | —yield tax for each $i Yr, or $0.212.
I.Oo — I /

i.oS50/x 1000 V i.o8—i/

Of this 21 cents only 2/3 is taken, since it is customary in Massa-
chusetts to tax rural property on a 2/3 valuation. The yield tax then
is 14 cents for each dollar of final yield or thirty-three dollars and
sixty cents an acre, if $240 worth of timber is cut per acre.
The land tax is computed as follows :

W \S ', _*;Qj? / ' 3 . __ \

5 1000 \ 1.05—1 /

or $19.11 an acre, which makes about 12 cents per $i of final yield.
Again taking only 2/3 of this, or 8 cents and subtracting this from
the 14 cents yield tax leaves a final yield tax of 6 cents per dollar
of stumpage, to be paid at the end of the rotation or when the tim-
ber is cut. In this way the commission decided that a yield tax of
six per cent is a proper tax to charge.

BASIS OF TAX RATES 1 17

An attempt to use the Massachusetts plan on other rotations
gives, even with a uniform land price of five dollars an acre, the
following yield tax :

Rotation 50 years 6%

75 " 3%

100 — 10%

so that the state would be rebating as soon as reasonable rotations
are employed.

3. In seeking a proper basis for any tax rate the following
may be assumed :

The most important point of all is that the tax rate on forests
should be no higher than that on other rural property. If farm
property generally pays less than twelve per thousand in practically
all parts of the United States then forest property should pay the
same, but certainly not more. This principle is recognized in the
Massachusetts plan.

Again if the value of farm property universally is judged by
the income which it can produce the same measure is fair for forest
property.

A yield tax should be fair not only for one rotation but for all
reasonable rotations.

In judging the value of a farm or forest for taxation by capital-
izing the net income the interest rate should be fairly high, since the
owner takes all risks and the state takes none. This also seems rec-
ognized by the Massachusetts commission, and it is common practice
in valuation of real estate.

If a yield tax is fair for one stand of timber it is fair for any
other stand regardless of methods and regulation, and the proper
rate may, therefore, be found by a study of the regulated forest.

That a regulated forest property would pay more taxes, even
at the same yield tax rate than a property worked on the intermit-
tent plan, is self-evident.

The following case brings out the relations of property tax at
12 per 1,000 and the yield tax for the stands of a regulated forest at
different rotations.

Premises : Yr is taken at about half the normal yield in spruce,
site II, as per Schwappach,

Yr at 50 years $200

Yr at 75 years 400

Yr at zoo years 600

land, $5 per acre, p — 10% to capitalize net income and find income
value of the property,

Il8 FOREST VALUATION

Current yearly expenses $i per acre; cost of planting, $10 per
acre.

Tax rate, 12 per 1,000 as being about average for rural prop-
erty in the United States.

Relation of property tax at 12 per 1,000 and yield tax in regu-
lated forest.

Rotation, years. 50 75 100

Minimum number of acres in regulated forest,

i. e., r acres 50 75 100

Yearly gross income from r acres, neglect

thinnings $ 200 $ 400 $ 600

Yearly expenses on r acres, current and plant-
ing $ 60 $ 85 $ 1 10

Yearly net income from r acres $ 140 $ 315 $ 490

Value of the r acres regulated forest, i. e., net

income capitalized at ten per cent $1400 $3150 $4900 .

Taxes, as property tax at rate of 12 per 1000

on r acres $ 16.80 $ 37.80 $ 58.80

Property tax, 12 per looo, per acre $ 0.33 $ 0.50 $ 0.58

Property tax of 12 per 1000 as a per cent of

stumpage cut, or Yr 8.4% 9-4% 9.8%

Property tax of 12 per 1000 as a per cent of

net income 12% 12% 12%

It is evident from the above that. a twelve per mill tax on the
true value of a regulated forest corresponds closely to a yield tax
of nine or ten per cent of the stumpage value of the timber.

The introduction of the land tax disturbs the simplicity and
even the justice of the yield tax method since land values differ and
this difference is not always made up by the difference in final yield.
On lands where the timber grows slowly and requires about one
hundred years to reach marketable size the yearly land tax on five
dollar land even at twelve per mill and compounded at as low as
three per cent reaches the formidable sum of over thirty-six dollars
an acre, a sum which would seriously discourage the planting of
bare lands and frequently exceed the ten per cent yield tax. For
some time to come and only as an expedient to bring about some
tolerable reform the land tax may be necessary, but a tax rate not
to exceed ten per mill should then be employed. Cases like parks
and costly estates in the vicinity of cities should receive special treat-
ment and be taxed by the ordinary tax method.

FUTURE; IN FOREST TAXATION 119

Of late the application of the single tax has strongly been ad-
vocated for forests as well as other real property. The single tax
is well suited to forestry; it would stimulate the accumulation of a
good growing stock and the making of improvements, roads, proper
division, etc., and so put a premium on good forestry. The action
of the single tax in forestry is exactly the same as in farming, where
it stimulates building and keeping of plenty live stock, while the
present form, the property tax, in a way penalizes the good farmer
with fine buildings and plenty of stock and machinery. But in no
case should the crop, or timber and land be taxed together, as has
at times been advocated by single taxers. For the existing virgin
forest where the owner merely holds a stored mass of merchantable
timber and is in no way practicing forestry and wrhere the public is
determined to make the owner divide the goods, practically given
away by the people, there is nothing for it but to devise some com-
promise. Here the simple property tax as now applied, or a com-
bination as is represented in the Connecticut law is probably as good
as any other.

h. Future in forest taxation.

i. A yield tax is inconvenient. The owner of a small forest
cutting a few poles or a few cords of wood finds it bothersome to
record and report. This leads to exemption for domestic use, as is
done in the Connecticut law. But it is hard to set limits in these
exemptions, they lead to confusion and bad practice. With large
owners it becomes necessary to take the word of the owner, it pries
into his affairs and has all the objections commonly claimed for in-
come taxes. The local tax official has added a great deal to his
labor and where the matter is left optional it involves inspection of
state foresters who lack help, money and experience.

For a regulated forest property there is no occasion to use a
yield tax ; it can be assessed as easily as a farm and taxed in exactly
the same way.

For isolated tracts, not really managed as forest it may bridge
over, but is not satisfactory enough to recommend for permanent
practice. To receive a yield tax once in eighty years introduces too
many chances for cheating the buyer of such property and the com-
munity.

For a beginning the yield tax is to be recommended to get away
from the present methods, but the tax collecting practice in rural
properties will work for a return to the property tax, properly regu-
lated by computations based on actual income.

[20 FOREST VALUATION

2. The income tax has been recommended for forest taxation,
it is used abroad, it usually takes about ten per cent of net income,
it is simple in practice, tends to a form resembling closely the ordi-
nary property tax now in use. The ten per cent basis is arbitrary,
whether a remnant of the old "tithe" or a gradual adaptation of
public expense to personal income, yet it is generally agreed upon
as common and fair.

How a ten per cent income tax compares to our ordinary twelve
per mill property tax is shown by the following figures, the basis
taken from circular 132, A, 1913, United States Department of
Agriculture.

For the average farm of the United States the total value is
$6,343, the total income $980 and the net income is given at $538.
An income tax of ten per cent on $538 or $53 is equivalent to $8.30
per $1,000 of property and shows that ten per cent of net income
is only about 2/3 of the ordinary 12 per 1,000 rate of taxation of
rural property, where this is assessed at full value. Apparently this
was felt by rural tax officials and the assessment was adjusted to
make the rate reasonable, i. e., the custom of taking rural property
at 2/3 value brings the common, nominal twelve per mill to an
eight per mill on full value, or close to a ten per cent on net income
as above computed.

3. From the above it follows that a ten per cent yield tax
which is really ten per cent on the gross income is somewhat too
high ; that about eight per cent of the stumpage is more nearly right
and that the addition of a land tax is entirely unfair. From this
standpoint the Pennsylvania law requiring only the ten per cent
yield tax is fairest; the Massachusetts law charging six per cent
on yield and a land tax on flat rate assessment comes next, but does
not work well for rotations above fifty years, and that the Connecti-
cut law still demands an amount of tax much greater than is paid
by the average farmer.

4. Taxation and protection more than all other factors com-
bined decide whether forestry can and will be practiced by private
owners. The present methods lead to confiscation ; the recent laws
are a good beginning but they still demand more than is fair and
also lack in convenience and simplicity of application.

From the standpoint of the state it would be of great value
in all forested districts to pass some simple laws, applicable to all
forests and framed somewhat along the lines of the Connecticut
law, to provide:

a. Taxation of all woodlots as parts of occupied farms, on a
basis of simple assessment of the land, leaving out of consideration

SUGGESTIONS IN TAXATION I2i

the growing stock or crop, exactly as is done in case of wheatlands,
meadows, etc.

b. Exemption of forest plantations for twenty-five years and
then taxation on a land and yield tax, but limiting the tax rate to
five per mill and the yield tax to six per cent.

c. Taxation of existing forests, not parts of farms, on a land
tax at five per mill and a progressive yield tax with a limit of six
per cent.

d. Taxation of regulated forests on the property tax plan, ex-
actly like the farm, but the value of the forest to be the income
value on a basis of net income capitalized at ten per cent.

Or else: taxation of these forest properties by levy of income
tax taking ten per cent of the net income ; or as a third alternative,
a simple yield tax of eight per cent.

e. Providing a state control which makes it impossible for
local politicians to interpret and execute tax laws to suit their in-
terests.

IX. FIRE INSURANCE IN FORESTY

The timber or growing- stock in the forest is liable to destruc-
tion by fire at any J:ime of its existence. The danger J.s_greater for
conifers than hardwoods, greater for stands from ten to thirty
years old than for plantations or older timber; varies with the cli-
mate, soil, topography, and may be reduced greatly by proper im-
provenjents and protection. Since the timber or growing stock com-
monly makes up seveniyrfive.j>er. ce_nt or more of the value of the
forest property, fire danger is serious.

For the owner of a small forest, from forty to one hundred
acres, who may lose in one fire the greater part of all he owns, this
is no doubt true. Generally the danger is overrated. The burning
of a few plantations on a large forest property is not a serious mat-
ter ; they must be replaced and this adds to the current expense but
it does not affect the regular income for years to come. In stands
over fifty years old, the fire-injured or fire-killed timber is not a
total loss, in fact, it may be utilized often up to eighty or ninety per
cent of its full value. Here the fire may disturb the plans and or-
derly business of the forest but does not cause a serious loss. In
wild woods the case has been different. In the United States fires
have done enormous damage and even today are the greatest factor
preventing action in forestry. According to the report of the Na-
tional Conservation Commission of1 1909, the fire losses in the United
States may be estimated at about fifty million dollars per year for
merchantable timber alone. To this the report adds a much larger
sum for destruction of stuff below merchantable size and -usually
a total loss. Leaving out the latter, yearly fire losses of merchant-
able stuff for the last fifty years in the United States have been at
least ten cents per acre of forest area, and if the average value of
forest is twenty dollars an acre, the loss amounts to five dollars per
thousand dollars worth of forest, or about seventy per cent of what
good forests should pay in taxes.

The difficulty here has been a lack_oL^rgtecjiDJi_and lack of
market and roads to enable immediate use of the stuff injured or
killed. It has been the rule rather than the exception that timber
killed byjires in the United States has been a total loss.

This is all changing now and will change a great deal more even
in the near future. It may be expected that in fifty years conditions

FIRES IN EUROPE:

123

in the United States except perhaps in the high mountain country
of the west, will resemble those of Europe.

Here the fire danger is no longer considered a serious difficulty
in forestry and all large owners, state and private, do not even feel
the necessity of fire insurance. The following figures will illustrate :

DAMAGE FROM FOREST FIRES :*

Prussia.

Bavaria

Austria

All
forests.
1881-1894

State
forests.
1881-1912

state
forests.
1877-1902

not
Hungary.
1881-1895

Total area of forest, million acres. ..

20.4

6.2

2.07

24.27

Total gross' income, million dollars. .

50$

15-5

30$

Net income per acre, approximate $.

1.25$

1-25

0.30$

Value of forests on basis of 3% and

net income, million dollars

810

250

120

24O

Damage from forest fires $1000

ACfft*

For each 100,000 acres of forest the

fires burned over acres

I/*

For every $1000 gross income fire

*"j

**ff

damage is in dollars

I QO

.66

1.16

For every million dollars worth of

j. • y^

forest damage is $. .

117

•3?

17?

Average number of fires per year. . .

A A /

388

*o/

Average area burned over each year,

acres

•4955

1500

200

3420

In the statistical works for Wiirttemberg and Baden the damage
by forest fires is not even mentioned. While it is evident from the
foregoing that large f^restjDwners have little reason to seek insur-
ance, the case is different for the great number of small owners.
For this reason forest^fire insurance was discussed and planned as
early as 1877 by Burckhardt and the matter agitated from that time
tcTthis.

Insurance by the state, by cooperation of forest owners and by
commercial concerns, all have been discussed.

* See Endres Forst Politik, also Forstliche Verhaltnisse Preussens
Wurttem'burg, etc.

± May be a little high since it is based on income in state forests and
iveraged for a number of years.

124 FORF.ST VALUATION

So far only commercial organizations have worked extensively
in this field. Of these a department of the Gladbacher jfire insurance
company, starting in 1895 is the oldest and most important. In
1903 this company had more than 300,000 acres of forest covered
by insurance, mostly in the densely settled Rhine province where
the forest is in small tracts. The average rate has been about $1.80
perJjSipocLof property.

Since then the Bayerische Hypoteken und Wechselbank, the
Provincial Fire Insurance Institute of the Rheinprovinz and others
have taken up this work. The^rates usually run from one to five
dollars per thousand- dollars worth of property.

Usually it is demanded that the insurance continue for at least
ten years, that the owner insure all his holdings in one company,
and that he give to his property such protection as is customary in
the district, this point being stipulated rather in detail. The rate
of premium varies with the kind of timber and age, formerly the
rates increased with age up to thirty years, this appears to have been
given up and the rate^ starts with a maximum and decreases.

Regular published tables of yield and methods of assessing
damage are provided, the cost^ and sale value of the stand prevail,
the expectation value is permissible only under certain exceptional
conditions, the payment is to cover only actual damage, any income
from material salvaged is deducted, the interest rate for any calcu-
lation of values is three _per cent.

The following figures f rom, Vorster, director of the Provincial
Fire 'insurance Institute of the Rheinprovinz, published in Zeit-
schrift fur Forst und Jagdwesen, 1908, p. 797, etc., will illustrate
what is today good forest fire insurance as to rates, and change in
these.

v j r »• u • Premium per $1000

Kind of timber insured. , *

of property,

1. Pure 'hardwoods, coppice or timber $0.25 — .80

2. Mixed 'hardwoods and conifers in timber forest 60 — 1 . 50

3. Coppice mixed with conifers 90 — 3 .00

4. Pure conifers:

Up to 8 years old 3.00 — 4.00

8-15 2.50—4.00

15-40 i . 50— 2 .co

over 40 50 — 1.50

The following illustrates how a small forest of pine, site IV,
of Schwappach, properly regulated, with present prices for timber,
fares in this insurance. Figures of the Rhenish Institute are com-
pared with those of the Gladbach Fire Insurance company.

FIRE: INSURANCE) IN EUROPE;

125

For simplicity, the lower rates only are here considered for both

"»a TTIP>C

companies.
Cost <
acres, rotation 60 years.

panics.

Cost of insurance for a regulated forest of pine, site IV, 60

Rhein Province

Glad-bach

Institute.

Insurance Co.

Area.
Acres.

Age of
Stand.
Years.

Value of
Stand per
Acre $.

Premium.

Rate per

$1000.

Cost for
10
Acres $.

Rate per
$1000.

Cost for

Acres $.

2.50

.70

I. 12-

1.50

.78

3-40

1.76

1.50

1-37

2.80

2.56

133

i,5o

2.OO

2. 2O

2-93

165

.50

.82

1.50

2.48

197

• 50

•98

1. 00

1.97

Total 6.67

Total 12.84

Per acre .11 .21

Per $1000 worth of woods i.oo

1.94

Assuming the yearly gross income from this sixty acres to be
$225, Yr + Tq, and the total expense c -f e, $75, the insurance
would take 4.4% in one, or 8.5% in the other, of the net income of
this forest. From each $1,000 of gross income this insurance takes
$30 in one, $57 in the other company. Comparing this to the actual
yearly losses in Prussia, $1.90, and Bavaria $0.66, as seen in the
foregoing table, it is easy to see why the state forests are not insured.

So far the forest fire insurance has not been a success, the com-
panies have not made any money in this line of insurance and the
proportion of forest insured is still insignificant. Compulsory jstate
insurance would no doubt readily solye this^rjroblem and reduce the
rate to nearly the actual average loss and so reduce it to less than
twenty per cent of the present rates.

In this connection the comparison of cost of insurance and cost
of good fire protection is interesting.: For a regulated forest of pine
with a rotation of only sixty years the lowest premium is eleven
cents per acre for a hundred year rotation of the same kind of
woods, pine, it amounts to twenty-seven cents. But with any large
property and any kind of system of protection tenjcents an acre goes
a long way toward preventing fire entirely and certainly can well
reduce the damage to the insignificant minimum now secured in

126 FOREST VALUATION

Germany. In the national forests an expenditure of only about
t\vo cents an acre has reduced fire losses from an estimated ten cents
per acre to less than one cent per acre. By an expenditure of ten
cents an acre it is to be expected that this loss will be reduced still
further, and what is more important, this protection will protect
with a certainty regardless of conditions, and so prevent any of the
great forest fires which from time to time have completely devas-
tated many thousands of acres in a single season.

So far forest fire insurance has not really been tried in the
United States. All financial concerns, including insurance com-
panies have been afraid of forest properties ; some of the reasons
for this attitude are found in the following conditions :

The values are badly distributed and scattered in a forest ; there
is a large area for a relatively small amount of money. This is less
true in the well-cared for forest with good market than with the
wild woods ; and it is less true of the heavy stands of timber in the
Pacific coast states, but generally the fact remains. In the city,,
property on one acre is worth many thousands, in^the forests of
the eastern half of the United States it is worth about twenty dollars.

The value of wild woods is hard to ascertain with any degree
of accuracy. The insurance company's agent can not simply inspect
and verify; it takes a regular cruise and involves expense.

The amount of damage by a forest fire is very hard to ascertain.
A lot of hardwood timber run over by fire may all leaf out and ap-
pear practically uninjured and yet half the stuff may die and start
to decay before five years are past. Two estimators would often
fail to agree with regard to the same tree before them.

Much of our timber is owned in separated and often^videjv
scattered bodies.

The owners of timber are only holding stumpage; it is a spec-
ulative affair, and does not inspire confidence. The owners do not
practice forestry, the forest is left without improvements, roads,
etc., and there is no real care and protection.

The community, state and county. do_jj.othjng, as yet, to_niake
forest property reasonably secure.

Public opinion and habit has no regard for forest property and
is quite generally inimical to the owners of forests. This attitude
finds expression in the behavior of young and old in the forest, in
legislation and in the enforcement of law.

What the future will bring is doubtful. For large owners of
forest, who practice real forestry, there is no object in insuring, as

FUTURE; IN INSURANCE; 127

is evident from the experience on the national forests today. For
the small holding, especially the wqqdlot on the farm, insurance
would be beneficial and may even become necessary if these valuable
woods are to be preserve'd. For commercial companies these wood-
lots are not inviting as objects to insure, the difficulties in appraisal
of damage alone being sufficient to discourage any company. It
will require mutual insurance as now exists in many counties, or
state insurance will have to supply security.

X. THE RIGHT USE OF LAND

FORESTRY VS. AGRICULTURE AND RANGE.

a. Nature of land. Since the area of land can not be increased
and since land can not be moved from place to place, the occupancy
of land, as by a farmer, is monopolistic, and the right use of the
land is important, in fact, fundamental to the welfare of any people.
That a farmer should have a duty, not only to himself, but to the
people or state, and that the state authorities have a duty in seeing"
that the land of the state is put to its best use for present and future,
are modern conceptions, rapidly developing and becoming influential
in public economy. Even in the past, the state felt justified in taxing
the shiftless owner of a good piece of land, farm or city lot, not in
keeping with what it produced but according to what it should pro-
duce. Today all civilized states are spending money to devise ways
and means of making the land more productive. In this effort to
maintain and better the land it is of as much importance to select
the right crop as it is to give the proper care, and it is here where
the choice between forest and field crop asserts itself.

b. Lands may roughly be divided into : agricultural, forest,
range and waste lands ; but the lines between these four classes are
rarely very sharp.

On the agricultural lands, including the garden and truck lands,
the crop is to furnish food for people or animals. The forest crop,
on the other hand, serves two very distinct purposes ; it may merely
maintain a necessary cover on mountain lands and be useful as a
protective forest, or it may serve solely to produce timber and other
products. The importance of the forest as protective cover is so
great and has of late been so well recognized by the governments
of civilized countries that Martin in his Statik classifies lands into
those used to raise products and those requiring a protective cover.

In the following paragraphs the protective forest is considered
as occupying absolute forest soil.

c. The factors which determine or limit the use of land
are chiefly: climate, (temperature and moisture,) soil, topography
and population. In mountain countries small patches of valley or
bench land may be excellent farm land and yet not desirable for this

WHAT DETERMINES USE OE LAND 1 29

use because of their location and size, a condition which applies,
however, only to a very small per cent of our lands.

i. Climate is invariably the principal factor. More than half
of N. America and Asia is too cold for agriculture; more than 35%
of North America, more than sixty per cent of Asia and Africa,
and more than eighty per cent of Australia are too dry for farming.

About forty degrees Fahrenheit average yearly temperature
limits good farming; about 30° F. ends the useful forest, except pro-
tective woods. In the United States about twenty-five inches of
rainfall for the year limits the natural forest ; about fifteen inches
sets a limit to dry farming or farming without irrigation ; at ten
inches of rainfall the prairie changes to desert.

In countries with an average yearly temperature less than fifty
degrees Fahrenheit and with dry summers and low relative humid-
ity all lean sandy lands have failed in maintaining satisfactory agri-
culture.

Topography affects agriculture ; generally a five per cent slope
washes as soon as plowed ; a ten per cent slope gullies and is ruined.
Usually steep lands become stony and lean and millions of acres of
farm lands have been abandoned in Europe because of topography.

Dense population commonly stimulates the use of land for
farming. In the United States millions of acres of good land are
not used or poorly used for lack of labor and demand. But while
it is generally true that dense population leads to the use of lands
for agriculture, this is no longer true to the same extent that it was
fifty or more years ago. Formerly the majority of the people lived
on the farm, today over sixty per cent of the people of the United
States live in town. The people do not flock to the country, they
leave the country and move to town. It is the town which furnishes
employment and a safe and comfortable living. This is as true of
Europe as it is of the United States. The result is that millions of
acres of land even in the better populated parts of the United States
and the most densely populated states of Europe are not tilled, and
large areas have been abandoned to deteriorate into waste lands.
Dense population today, means cities, manufacture and commerce,
good wages and living in the city, higher wages and less farm labor
for the farm; and intensive use of good farm lands which justify
labor and machinery ; and abandonment of poor farm lands. In
Europe this situation has shifted the use of lands from agriculture
to forestry for large areas ; it has led to regular appropriations by
the states and the development in this direction is more rapid today

130

FOREST VALUATION

than ever before. Lands worth up to fifty dollars an acre are today
being converted from field into forest in southern Germany.

England has had a special commission to work on this problem.
In its report this body cites the case of a tract of land of twelve
thousand acres, bought at ten dollars an acre, which for years had
brought only about thirty cents per acre rental, and it recommends
extensive purchase of lands and reforestation in densely populated
England.

d. The countries of the Old World are interesting in this
connection: of Scandinavia less than 8% is tilled, about 50% is
waste land; Spain and Italy are about 33% tilled and more than
25% is g°at and sheep range which will be regarded waste land as
soon as industrial conditions are such as to give the people a 50 cent
per day wage.

Russia in Europe is claimed to be about 26% tilled and 37%
forest, leaving 37% as waste land, with an uncertain portion of
range lands.

Turkey in Asia tills about 3% of its 580 million acres, the rest
being mostly waste land with various combinations of rock waste,
desert and range lands.

India, China and Japan, with about half the human race as
population, till probably less than 20% of their land.

Use of land in highly developed states :

Cities

Highways

Meadow

and waste

Fields.

and

Forest.

including

Pasture.

some

range.

Germany

France

36*

Both in France and Germany the tilled land is not on the in-
crease. Prices of land are not advancing and the rents or income
from farms is not materially better than fifty years ago.

* Includes considerable heather land.

LAND CONDITIONS

e. Land conditions in the United States.

13*

Area

Per

Cent.

Region by States.

million
acres.

Improved
land.

Forest.

Rest is

Atlantic, Maine to Georgia. . . .
Gulf, Florida to Louisiana
Texas

225
126
167

35%.
18

45%
65

cut over land
cut over land
prairie

Lake States, including Ohio,
Indiana and Illinois

207

cut over land

East Central, West Virginia to
Arkansas

146

cut over land

West Central, Oklahoma to
Dakota

250

prairie

Rocky Mountain

C4Q

I C

prairie desert

Pacific, California to
Washington

20^

brush and
waste
prairie, desert,
brush and

waste

Total United States

IpOO

Apparently over 900 million acres are neither forest nor field,
largely too dry and therefore prairie or desert. About 300 million
acres are wild woods on absolute forest soils, the lands being un-
suited to farming by reason of climate, cold mountain country, to-
pography, all large mountain ranges, and to a lesser extent, poor
soil, South and Lake states and the East.

What these conditions may be even in an old settled state is well
seen from the following figures for Michigan :

State. S. Half. N. Half.

Total area million acres 36.8 17 19.8

Per cent improved .35% 64% 6%

f. Agricultural use.

Generally the agricultural possibilities of any district finally de-
cide its use. Any good tract of agricultural land as large as an ordi-
nary county will become farm settlement in our country. This fact,
based on large experience has helped to fix in the minds of most

132 FORKST VALUATION

people, and especially the so-called representative men who are in
duty bound to "boost" and to "believe in the country," the assump-
tion that all lands are agricultural lands. That this is practically
true of Iowa and Illinois no one doubts, but that it is true of very
few other states every one who cares to can see for himself.

Formerly the policy of the states was to get people and settle
the country. Usually this policy was forcefully emphasized by the
land boomer and other people who had, or believed they had a mon-
etary interest in rapidly populating the state. Of late the author-
ities agree that the state wants :

1. Not merely many people biit rather good and prosperous
people.

2. To the state, any kind of "pauper'' industry or industry in
which the people can not make fair wages and a fair living is an
injury. Of these pauper industries the farming of non-agricultural
lands is one of the worst.

3. The state needs manufacture as well as farming, and that
even the best farming districts may lose in population and business
because of the one-industry condition. Consider Missouri and Iowa,
and some of the best farm counties of several of our states.

4. The state wants to have its people supplied with raw ma-
terial and manufactured goods by the state itself and so be as inde-
pendent of import as possible. This applies as much to timber as
to grain.

5. Every acre of land should raise the best possible crop and
make the largest return in permanent use.

6. Labor conditions should be carefully balanced, so that
labor is steadily employed and all work is well done. The great
wheat districts, though excellent farm country, waste grain for lack
of help in the harvest season, and fail to give employment all the
rest of the year.

7. Regulation of stream flow, protection from erosion and
winds and the beauty of the landscape are important and in many
cases decide the choice between field and forest.

In our country public policy regarding the proper use of land
is largely controlled by the views and wishes of the farmer and it
is interesting to see how he is affected by the choice.

i. The farmer wants not merely good crops but good prices.
A good home market is the only means of liberating the farmer

FARMER'S VIEWPOINT 133

from the speculator and the manipulator of the world markets. Two
good sawmills where twenty per cent of the land is tilled in a county
of the Great Lakes district, are worth more to these farmers of the
county than a condition of sixty per cent of the land cleared, com-
petition trebled and the local market spoiled for lack of manufac-
tures. This competition is especially painful in one-crop districts,
potato, fruit, etc., and it is doubly bad where the average farmer is
poor and compelled to sell for what he can get.

2. The farmer needs labor, cheap and convenient, usually for
short periods. Without other business a district can not keep itself
supplied.

3. The farmer needs railways. The farm furnishes about two
hundred and fifty pounds of freight per acre and year, the forest
about one thousand and the manufacturer exceeds them both.

4. The farmer wants good roads and schools and yet low
taxes. The state taxes, and these in the long run determine school
and road, are not paid by the farmer. In the United States the
farmer owns less than one-third of the property, is assessed at about
sixty per cent of its value and usually pays about sixty or seventy-
five per cent of the average tax rate for the state, so he contributes
less than twenty per cent to the state tax burden.

It is evident that to the farmer there is very little inducement to
urge agricultural use of lands wherever this brings competition and
reduces manufacture and local market. In the past this phase of
the question was clouded because, most farmers were as much spec-
ulators as they were farmers ; they wanted to feel that their farm
was increasing in value and that they would make money by selling
out if they chose to do so. The utter fallacy of this reasoning to the
real farmer is apparent ; all he gained by the boost was a larger tax
assessent, for his crop, and his income was not increased by it. A
few boost sales in a county frequently upset farm assessment though
they did not add a cent to the income of ninety-nine per cent of the
farmers.

g. The income from the land has always been regarded as an
important criterion of its use. A century ago before railway and
modern manufacture, wood was cheap, over large areas it had no
value at all, while food was a necessity and measured by a day's
wage was high in price everywhere. Accordingly, the incomes from
forests were very small and even foresters like Hundeshagen and
Cotta felt that only the state could afford forestry on anything like

134 FOREST VALUATION

fair land. Today these conditions have changed, and agriculture is
called on to explain its smaller net income from better lands. In
this discussion it is well to keep in mind the following :

1. Timber is a necessity to modern civilization. All substi-
tutes have not been able to reduce the per capita consumption and
in Europe any state with fair industrial development becomes, a
timber importer as soon as its forest area drops below thirty per cent.

2. The forest crop is safe and certain wherever forest is native
and even on prairies the forest once established modifies its own
local climate. On all lean and difficult, stony, rough, etc., lands the
forest is far more certain than any field crop. The forest crop
takes care of the land, the field crop drains it.

3. The forest crop is durable, unlike potatoes, fruit, etc. A
few years seasoning increases the value of timber.

4. Prices of forest products have gone up steadily for a cen-
tury and have more than doubled in half a century ; prices of field
crops in Europe and the United States have not changed materially
for the last half century. See Endres, Forst Politlk, p. 119, etc.
Rye, the great bread stuff, was cheaper in Prussia in 1893-1903 than
it was in 1860-1890. For the United States, see United States Dept.
Agri. Farmer's bulletin, 645, 1914, p. 23, the value per acre of the
ten most important farm crops was $15.74 in 1871, then declined
rapidly and did not regain this value until 1908.

5. Forest statistics of necessity are averages since it requires
many seasons to grow a crop of timber. To be comparable at all
the figures for farm income therefore must be ,taken as averages.
This is commonly overlooked and accidental maximum figures are
constantly quoted and repeated. "Great money in clover-seed,"
"$400 per acre in cherries," etc., are repeated in journals and by
booster orators until the average person is completely misled. It
is one of the most useful works of the United States Department of
Agriculture and the Experiment Stations to gather truthful statis-
tics of the farm. So long as the booster succeeds in making the
people believe that there is big money in sand farms, so long the
public is reluctant to pay even a decent cost price for farm products.

6. Forest statistics as used here describe large averages of
incomes not from the good lands but from inferior, largely non-agri-
cultural lands. It is doubtful if more than thirty per cent of all
German forest lands could be farmed continuously and successfully.
If all lands of Germany were arranged in five classes of equal area,

INCOME FROM FARMLANDS 135

the forest lands would take practically all of number five and about
half of number four with very little of class I-III. For this reason
it is quite safe to say that for the same use, the lands now in fields,
etc., should by virtue of their fertility produce a much larger return
than the forest lands. This as will be seen, they do only for the
gross income in which a large per cent is labor, but they fail to do
this for net income, clearly proving the superiority, at present prices,
of the forest uses when judged by net income.

i. Income from field and farm land in the United States.

For over thirty years the United States Census authorities have
gathered farm statistics. Of late the United States Department of
Agriculture and also some of our Agricultural Experiment Stations
have checked, verified and amplified this work and have generally
proven the accuracy of the work of the Census.*

In discussing the income from land used in farming it is neces-
sary to keep separate the income from the crop and that from the
animals, etc., which represent a separate investment.

The total value of the farm crops in the United States, includ-
ing the value of the material fed to live stock, was reported in cir-
cular 132, as taken from the Census of 1910, at 5,487 million dollars,
or $860 per farm. The average farm has 138 acres, of which 75
acres are improved land. Allowing only 50% for cost of produc-
tion, exclusive of rent of land, the 138 acres of farm land produce
a gross crop income of $6.24 per acre, or a net crop income of $3.12.
Even if referred to the 75 acres of improved land only the gross crop
income is $11.40 and net $5.70 an acre.

United States Bulletin 645, 1914, p. 23, gives the "Yearly value
per acre of ten crops combined." The crops are corn, wheat, oats,

* See United States Crop Reporter for 1911 for cost of producing wheat,
oats and potatoes in the United States.

Ohio Agricultural Experiment Station bulletin 266 cost of producing corn
in Ohio, 1913.

United States Farmers' Bulletin 641, 1914, cost of producing cotton.

United States Farmers' Bulletin 635, what the farm contributes directly
to the farmer's living, 1914.

United States Farmers' Bulletin 645, Agricultural Outlook, 1914, p. 23,
yearly value per acre of the ten most important crops combined for 1866-1914.

Bulletin 41, United States Department of Agriculture, 1914, farm manage-
ment survey of three representative areas in Indiana, Illinois and Iowa.

Farmers' Bulletin 665, 1915, Agricultural Outlook for farm wages in the
United States; Farmers' Bulletin 570, 1913, and circular I3^-A, 1913, which
discuss the farmers' income, using Census of 1910.

136

• FOREST VALUATION

barley, rye, cotton, potatoes, hay, tobacco and buckwheat. The data
are presented in the following diagram.

/6
/5
$14
&3
$12

Fig. 2. Chart showing the value per acre of 10 crops combined (corn,
wheat, oats, barley, rye, buckwheat, potatoes, hay, tobacco, and cotton), rep-
resenting about 90% of the total cultivated area of the United States.

These figures present the gross income per acre of fields and
meadows, actually tilled that year, and show that even at present
prices this gross income is only about $16 an acre and that for more
than 25 years prior to 1904 it was usually below $12 an acre of fields
and meadows. These fields contained 47 acres per farm, or made
only 34% of the farm itself. The following table indicates the rel-
ative importance of the principal crops, and presents some figures
on the cost of production of farm crops in the United States, 1909.

Cost of

Total
area
million

Total
Value
million

Yield
per

Value
per
acre.

production
per acre
exclusive

acres.

dollars.

acre.

of rent.

Corn

10^

i=;2O

32 bu.

8.52

Wheat

ccc

17 bu.

7.85

Oats

-ty

4.C2

W bu.

7.13

Cotton

T.J

825

240 Ibs.

3,0

16.70

Potatoes

3.6

212

iiSbu.

Hay

AT.

856

1.2 tons

Barley and rye

9-7

135

22 bu.

about like

oats.

CROP AND EXPANSES ON FARM 137

Bulletin 645, 1914, states that the thirteen principal crops occupied
three hundred million acres, and had a value at the farm of 4,919
million dollars, or about $16.38 an acre.

Another reliable measure of farm-crop income is the rent act-
ually paid to owners of farms. While in a few localities the rent
has been boosted up to as high as $8, the general average of cash
rent seems to be close to $3, closely agreeing with the average net
crop income. Even this $3 rent per acre and year is not a net in-
come to the owner since taxes and repair of buildings, etc., must
still be deducted. It is also quite generally conceded that the farm
is rarely well kept up in the cash rent system.

The following figures describe the crop income conditions in
Germany. They are taken from Helferich "Deuts Maud's Wohl-
stand',' and represent average yields for 1909-1913, valued at cur-
rent prices.

Rye $14-56 per acre

Wheat 21.50

Barley 13

Potatoes 19-20

Oats 11.80

Hay 12

Which would indicate a general average close to $16 or the same as
the present average for the United States.

Since less machinery is used in Germany and the fields are gen-
erally too small for economical farming, the cost of production is
higher in spite of cheaper labor. The "Schlesische Landschaft," see
Martin, Statik, p. 259, estimates the cost of producing the crop as
follows : on lands of

Class i cost is 55-65% of value of crop

2 57-6;

3 60-70

4 65-75

5 72-82

Taking land of class 3 as average and using the above $16 aver-
age for crop, the net income even from these fields and meadows in
Germany is only $5.60 or about the same as from the improved land
in the United States.

As regards the regularity of income the figures of the United
States Department of Agriculture, see Farmer's bulletins 629, 641,
645, indicate that in hay even, the average is below seventy per cent
of a fair stand. As stated in part one, the state forests of Wurttem-
berg today cut about seventy-three per cent of normal, are still im-

138

FOREST VALUATION

proving and may be expected to be eighty per cent normal in their
yield before another twenty years.

2. Income from the forest.

Since there are no forests in the. United States in a regulated
business condition, it is necessary to consider European results.
Even in Europe it is only the state forests and the holdings of other
large owners, cities, etc., which can be considered as properly taken
care of in a way at all comparable to the farmer's fields.

The following table represents large averages and the figures
are reliable. The great difference between Prussia on one hand and
Wurttemberg and Saxony on the other is due to soil, sand, and
climate, and in part, market ; the smaller income in Bavaria is large-
ly due to topography, mountain woods, and to a lack of develop-
ment. In Bavaria and Prussia a further development, road build-
ing, etc., will continue to absorb much of the yield. Later on, in
twenty-five or fifty years, this will cease and then the net income
will be a much larger part of the total income.

Incomes from state forests in Germanv:*

Area.

Wurttemberg 1908.

Saxony 1911.

Bavaria 1912.

Prussia 1912.

Acres.

490,000

431,000

2,330,000

6,796,000

Total

yearly

$4,906,000

$4,015,000

$16,156,000

$38,490,000

income.

Years.

Income per acre.

Gross.

Net.

Gross.

Net.

Gross.

Net

Gross.

Net.

1850-59

$ 3-6o

$ 2.1 1

$ 3-03

$ 1-94

•

$ -97

$ -54

1860-69

4-73-

2.89

4.46

3.21

$ 2.32

$ 1.35

1-43

.83

1870-79

5-77

3-45

5.76

3-92

2.95

1.66

1.98

.97

1880-89

4-99

2.70

6.47

4-33

2.64

1.30

2.2O

I.OI

1890-99

6.35

3-87

7-13

4-50

3-73

1.81

2.68

1.29

1905

9.20

6.10

8-44

5-39

4-5-5

2. 2O

4.26

2.42

1906

10.05

6.78

8.28

5-o8

4-95

2.55

4.27

2.27

1907

10.90

7-47

9.60

6.17

4.90

2.55

4-54

2.51

1908

10.00

6.50

9.22

5.58

5-50

2.95

445

2.21

1909

9.90

6.35

8.96

5-24

6.30

3-30

4-53

2.O2

1910

9-15

5.36

4.22

1-93

1911

•

9.20

6.03

5-19

2.98

* See Endres, Forst Politik ; Verhaltnisse Wiirttembergs ; Tharander
Forstliches Jahrbuch und Zeitschrift fur Forst und Jagdwesen. Figures round.

FARM OR FOREST 139

From the preceding it appears :

1. The gross income per acre in the well kept forests of Wurt-
temberg and Saxony with present prices of timber is larger than
the gross income from the field and meadow when the quality of
soil is considered ; and that it is about sixty per cent of crop income
even if no allowance is made for the difference of soil.

In Prussia the gross income from forest is about thirty per cent
of the gross income from the fields, a difference fully accounted for
by the poor quality of the pinery sands devoted to forestry.

2. The net income from forests in Wiirttemberg, Baden, Sax-
ony, etc., state forests, is as large and often larger than the net
income from farm lands in the same districts. This, of course, is
chiefly due to the smaller cost of production since this cost is nor-
mally below7 fifty per cent of the value of the crop in forestry and
above sixty-five per cent in farming.

3. The gross crop income and net crop income from farmland
in the United States is smaller than that obtained from the state
forests of Wiirttemberg, Baden, Saxony, etc., and is but. little higher
than that from the poor pinery forests of Prussia.

Even if only the improved lands of our farms are considered,
the gross income is little higher than that of the state forests of
Wurttemberg and Saxony and the net income is even lower.

To some extent this condition is due, no doubt, to the fact that
farm products in the United States and abroad are not paid for at
a proper price in keeping with the value of soil and the cost of pro-
duction. If correctly adjusted the field with its better soil and large
amount of labor should produce at least twice the gross income ob-
tained from the forest. But the fact remains that the growth pro-
duced in the forest is very large and also that the forest, owing to
the large crop-capital in the form of growing stock is entitled to a
correspondingly large net income.
Summing up:

1. The forest can utilize colder, frostier sites.

2. It can use rough, steep, stony and poorly drained land.

3. It can use poor soils, especially sands.

4. It maintains the fertility of the soil and therefore is a much
surer crop than any farm crop.

5.- Bad seasons are averaged up in forestry, an excellent stand
harvested in 1914 may have been through many poor seasons but
their effect is no longer seen.

6. Its products are enduring and generally gain in value by
storage.

140 FOREST VALUATION

7. The crop is not ripened in a few days or even months, but
can be cut at any time from the age of fifty to one hundred and
fifty years.

8. It requires less labor than the farm crop.

Agricultural use on the other hand :

1. Is possible or practicable on probably less than fifty per
cent of the land area of the United States.

2. It is the most important use of land.

3. It uses more unskilled labor than forestry.

4. It furnishes greater values only from better lands.

5. It furnishes less material per acre for transportation and
further manufacture.

6. It encourages erosion, rapid run off of water and so injures
land and disturbs water distribution.

3. Use of land for range.

Real range lands occur chiefly in dry districts, prairie and des-
ert, and mountain countries where the forest can not hold its own
on account of conditions of temperature, or moisture, or both. On
better prairies of the West the range has given way to the farm. On
poor soils in forest districts like the southern pinery and the sands
of the Great Lake region the forage plants are readily crowded out
by more frugal but useless plants, so that grazing on these lands is
of very little value, and can not be compared with the use of these
same lands for forest. The poor jack pine lands will grow fifty
cents worth of jack pine and scrub oak per acre and year, but they
will never be worth ten cents per acre and year continuously as
range.

The following general averages describe the range conditions
in western United States :

Number of head of range live stock and their equivalent in
sheep.

United States. West. Equivalent in sheep

West of plains. in the West.

Cattle 61 million 9 million, or 15% 50 million

Horses 24 million 2.5 million, or 10% 20 million

Sheep 52 million 28 million, or 54% 28 million

Assuming that the feed of a sheep is worth sixty cents per year
and that the four million acres of tilled agricultural land in the west
furnish one-third of all the feed, the range lands, approximately

RANGE: is WASTE: 141

four hundred million acres furnish about forty million dollars worth
of feed or ten cents per acre and year.

Where range lands are leased as by the state of Texas and oth-
ers, or where stock is grazed at fixed rate per head as by the United
States Indian Office and the United States Department of Agricul-
ture, the price is generally below five cents per acre and year, or
season. From these few figures it is clear that where land can be
used for forestry or for farming the use as range is an inexcusable
waste.

APPENDIX.

A. Normal Yield Tables.

These tables will prove useful in giving actual reliable data con-
cerning forestry as a business. They will be helpful in preparing
problems for class use.

American yield tables are still deficient ; practically all data
come from wild woods ; the growth of the individual tree is usually
determined on dominant trees only, the yields per acre on stands far
beyond a justifiable rotation; the effects of man's care in thinning
are yet to be learned. None of these data are as yet accepted by a
representative body of men.

Under these conditions it seemed best to use the German tables
as worked out in connection with the forest experiment stations
and compiled by Professor Doctor Adam Schwappach, the foremost
authority in this line of study.

The division into five sites was agreed to by the Experiment
Stations in 1888, and bases the division on the total volume of the
main stand and provides for the stand one hundred years old the
following relations:

Site. Pine. Spruce and fir. Beech.

I 100 100 100

II 78 82 80

III 60 66 64

IV 43 • 50 49

V 29 36 35

In Schwappach's tables this relation is fairly adhered to as is
apparent from the following: total volume of the pure fully stocked
normal stand one hundred years old is :

Site. Pine. Spruce. Oak. Beech.

I
I

II
III
IV
V

6600 c. ft.

11600

6200

IOIOO

100

IOO

ICO

—

144

FOREST VALUATION

Since these German tables can not be used in the United States
without modification, it seemed unnecessary to tabulate for all rive
sites, and only the figures for site II as nearly a good average, are
here reproduced. Most of the figures are rounded off. The graphs,
figures 3-8, follow Schwappach's as given in his admirable "Fvrtrag-
stafeln d. wichtigeren Holzarten," 1912.

How far these tables may serve to guide and check in our work
in the United States is yet to be learned. It seems reasonable, how-
ever, that for trees of similar habits, tolerance and soil requirements,
etc., the yield per acre is well indicated by height growth, and that
as a provisional check we may assume that if spruce in a certain
district in the United States has # height growth equal to that of
spruce site III in Germany, the yield per acre will also approximate
that of site III, etc.

MONEY YIELD TABI& FOR SPRUCE, SITE II.

Middle and N. Germany : Sdhwappach ; 1902.

Only wood 3" and over (Derbholz) considered.

Age.

Main Stand.
Price Value

Thin-
nings
added.

Total
value.
Main
stand
and

Average Tree
Main Stand.

TreVs

per

total

Value

thin-

Diam

per

100

per

nings

Height

b.h.

Vol-

Value

acre.

c. ft.

acre.

per

o.b.

ume

acre.

. '$

ft.

inch.

c. ft.

1800

4.80

3-2

0.5

0.03

1 020

6.70

172

182

4-8

2-5

0.17

680

8.60

366

407

6.4

0-54

485

9-30

54i

104

645

12.8

i. n

372

1 1. 60

803

207

IOIO

9-5

>i8.8

2.15

295

12.60

9/2

336

1308

10.8

26.5

3-28

239

13-25

1092

483

1575

12. 1

34-5

4-50

100

198

13-80

1183

648

1831

13-3

44-

5-9^

167

14.40

1260

814

2074

101

14-3

53-

7-50

120

140

14.80

T305

969

2274

105

15-6

64-

9-25

APPENDIX 145

MONEY YIELD TABLE FOR PINE, SITE II.

In N. Germany, Schwappach, Kiefer, 1908.

Only for wood 3" and over (Derbholz).

Main Stand.

Thin-
nings

Total
value.
Main
stand

Average Tree of
Main Stand.

Age.

Price

Value

added.

and

Trees

per

total

Value

thin-

Height

Diam.

Vol-

Value

per

IOO

per

nings

ulme

acre.

c. ft.

acre.

per

acre.

ft.

inch.

c. ft.

1560

5.8o

133

150

3-7

.0.9

0.08

840

6.10

201

,256

5-3

0.24

550

6.40

267

365

6-7

0.48

400

6.70

333

143

476

8.0

9-5

0.83

290

7.10

423

190

613

9-2

14.

1-45

240

7.70

499

242

74i

10.5

19.

2.05

200

8.40

567

299

866

n-5

24-5

2.83

IOO

160

9.20

623

36o

983

12.5

32.

3-90

140

IO.20

700

428

1128

13-5

37-

5-00

120

II. 2O

770

501

1271

145

44-

6.40

130

105

I2.OO

838

574

1412

15-2

50.

8.00

140

12.80

859

639

1498

15-6

54-

8.90

146

VALUATION

MONEY YIELD TABLE FOR OAK, SITE II.

In N. Germany, Schwappach, 1905.
Only the Yield of Stuff 3" and over (Derbholz).

Main Stand.
Price Value

Thin-
nings
added.

Total
value.
Main
stand
and

Average Tree of
Main Stand.

Age.

Trees

per

total

Value

thin-

per

100

per

nings

Height

Diam.

Vol-

Value

acre.

c. ft.

acre.

per

ume

acre.

ft.

inch.

c. ft.

2650

7.85

O.OI

1240

7.85

109

—

0.06

610

7.85

196

4-9

2.5

0.18

370

7.85

150

155

305

0.40

260

7-85

202

222

424

8.5

10.5

0.77

195

7.85

244

28l

525

10.

17-5

1.25

145

7-85

295

332

627

11.5

27.

2.06

100

125

8.60

373

374

747

13-

36.

3.00

IO.OO

476

410

886

15-

44-

4-34

120

11.50

584

442

1026

16.

54-

6.05

130

13.60

735

472

1207

17.

64-

8.50

140

15.80

895

503

1398

18.

74-

11.40

150

17.20

I02O

535

1555

. 88

19.

86.

14.30

160

18.00

IIOO

564

1664

19.7

97-

16.90

I/O

18.60

1177

645

1822

20.5

108.

19.60

180

19.40

1242

690

1932

21.2

120.

22.50

190

19.40

1277

736

2013

22,

130.

25.00

200

19.40

I206

786

2082

22.6

I4O.

27.00

*For the Stand below looy the value of n Mark pro. F. m. was used as
the nearest average.

APPENDIX

MONEY YIELD TABLE FOR BEECH, SITE II.

N. Germany; Schwappach; ion.
Only wood 3" and over (Derbholz).
Heavy Thinning (Lockerer Schluss).

Main Stand.
Price

Value

Thin-
nings
added.

Total
value.
Main
stand
and

Average Tree of
Main Stand.

Age.

Trees

per

total

Value-

thin-

Diam

per

100

per

nings

Height

b.h.

Vol-

Value

acre.

c. ft.

acre.

per

o.b.

ume

acre.

ft.

inch.

c.ft.

2900

2IOO

3-10

2.8

0.6

O.O2

1360

3-8o

107

3-8

i-7

O.O6

780

4-15

127

184

5-i

4.0

0.16

430

4-50

166

103

269

6.8

8-5

0.38

260

4-90

205

154

359

8-5

15-6

0.79

187

5-30

248

208

456

10.4

23-

1.30

100

153

5-6o

292

267

559

II.2

3i.

1.90

131

5-90

34i

328

669

12.2

39-

2.60

120

112

6.30

388

393

78i

IOI

13.2

47-

3-45

130

6.60

428

460

888

105

14-3

59-

4.60

140

7.00

458-

529

987

109

15-8

70.

6.00

148

FOREST VALUATION

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APPENDIX

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APPENDIX

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SO 60 10 80 <JO too

Fig. 3. Pine; North Germany Sites I-V; Normal Yield of main stand in cubic feet
<acre. Also the points indicating the age at whic'h the average tree attains a diameter
8", 10", 12" and a 'height of 30 ft., 40 ft., etc. Only wood 3" and over is here considered.

152

60 70 #0 JO /CO

per acre
CjOOO c.jJ

H/ta

7ooo
6ooo

Sooo
i

^000

H50-

yFig. 4. Spruce; Middle and North Germany; Sites I-V; Normal Yield of
Main Stand in cubic ft per acre. Also the points indicating at what age the average
tree attains a diameter of 8", 10" and 12", and a height of 40 ft, 50 ft, etc. Only
wood 3" and over is here considered.

153

13000

60 70 SO <?0

/CO //O

/soo<

6000

//o

Fig. 5. White fir; South Germany; Sites I-IV; Normal Yield of
Main Stand in cubic feet per acre. Also the points indicating at what age
the average tree attains a diameter of 8", 10", etc., and a height of 60 ft.,
70 ft, etc. Only wood 3" and over is here considered.

154

7O SO 70 100 //O /ZO /30

/SO /60 /7O /#O /<?0

8000 c. J

6000

2.000

/ooo c.

Vooo

3ooo

^000

/ooo

/JO

Fig. 6. White Oak ; N. Germany ; Sites I-III ; Normal Yield of Main Stand in cubic feet
per acre. Also points indicating at what age the average tree attains a diameter of 12", 16",
24", and a height of 60 ft., 70 ft., etc. Only wood 3" and over is here considered.

155

SO 60 70 gO CfO 100 HO I2O 130

Aae
« H

froooe^h

70 OO

bOQO

/3O

Fig. 7. Beech; N. Germany; Sites I-V; Normal Yield of Main Stand
in cubic ft. per acre. Also points indicating at what age the average tree
attains a diameter of 8", 10", etc., and a height of 50 ft., 60 ft., etc. Only
wood 3" and over is here considered.

156

APPENDIX 157

B. Tables of prolongation and discount.

The following tables follow Kraft's in his "Zuwachsrechnun-
gen." Their use is best illustrated by a few examples:

1. To find capital, Cn.

A stand of timber has now 5,500 cubic feet per acre; a growth
study determines that it is growing at 2.5%. What will this stand
contain in 15 years, growth being assumed to continue at present
rate?

Under 2.5% find figure 1.448 opposite 15 years; multiply 5,500
by 1.448, result is the volume per acre in 15 years. The figure 1.448
is I.O2515.

2. To find the initial capital Co. Same stand during the last
10 years grew at rate of 3%. What was the volume 10 years ago?
Find in column of 3% the figure 1.343 opposite 10 years. Divide
5,500 by 1.343, result is the volume 10 years ago.

3. To find the growth in per cent. A stand now 50 years old
can be sold at $6.10 per 100 cubic feet. From a growth study it is
evident that if kept until 70 years old the stand would bring $10 per
100 cubic feet. What is the per cent growth in quality these 20

Cn 10

years? Keeping in mind that is i.opn we have i.op20 = =

Co 6.10

1.638 and p the rate of growth, 2.%. In teresting and convenient to
use in this connection is the fact that the capital growing at com-

pound interest doubles, approximately, every — • years. To illus-

trate, one dollar, or one cubic foot grows into two dollars or two

cubic feet at 3% in — =-.24 years.
3

158 FOREST VALUATION

Short Table .of

Years

Values of 1.0pn, where p —

2,5

3,5

4,5

1,21

1,28

1,34

1,41

1,48

1,55

1,62

1,48

1,63

1,80

1,98

2,19

2,41

2,65

1,81

2,09

2,42

2,80

a,24

3,74

4,32

2,20

2,68

3,26

3,95

4,80

5,81

7,04

2,69

3,43

4,38

5,58

7,10

9,03

11,46

3,28

4,39

5,89

7,87

10,51

14,02

18,67

3,99

5,63

7,91

11,11

15,57

21,78

30,42

4,87

7,20

10,64

15,67

23,04

33,93

49,56

5,94

9,22

14,30

22,11

34,11

52,53

80,73

100

7,24

11,81

19,21

31,19

50,50

81,58

131,5

110

8,83

15,12

25,82

43,9?

74,75

126,7

214,2

120

10,76

19,35

34,71

62,06

110,6

196,7

348,9

130

13.12

24,78

46,64

87,54

163,8

305,5

568,3

140

15,99

31,72

62,69

123,4

242,4

474,5

925,7

150

19,49

40,60

84,25

174,2

358,9

736,9

1507

160

23,76

51,97

113,2

245,7

531,2

170

28,97

66,53

152,1

346,6

786,4

180

35,32

85,17

204,5

488,9

1164

190

43,05

109,0

274,8

689,7

1723

200

52,48

139,5

369,3

972,9

2550

APPENDIX

159

Years
n

0,1

0,2

Values of :
0,3 0,4

L.0pn, where p
0,5 0,6

0,7

0,8

0,9

1,0

1,001

1,002

1,003

1,004

1,005

1,006

1,007

1,008

1,009

1,010

1,002

1,004

1,006

1,008

1,010

1,012

1,014

1,016

1,018

1,020

1,003

1,006

1,009

1,012

1,015

1,018

1,021

1,024

1,027

1,030

1,004

1,008

1,012

1,016

1,020

1,024

1,028

1,032

1,036

1,041

1,005

1,010

1,015

1,020

1,025

1,030

1,035

1,041

1,046

1,051

1,006

1,012

1,018

1.024

1,030

1,037

1,043

1,049

1,055

1,062

1,007

1,014

1,021

1,028

1,036

1,043

1,050

1,057

1,065

1,072

1,008

1,016

1,024

1,032

1,041

1,049

1,057

1,066

1,074

1,083

1,009

1,018

1,027

1,037

1,046

1,055

1,065

1,074

1,084

1,094

1,010

1,020

1,030

1,041

1,051

1,062

1,072

1,083

1,094

1,105

1,011

1,022

1,033

1,045

1,056

1,068

1,080

1,092

1,104

1,116

1,012

1,024

1,037

1,049

1,062

1,074

1,087

1,100

1,114

1,127

1,013

1,026

1,040

1,053

1,067

1,081

1,095

1,109

1,124

1,138

1,014

1,028

1,043

1,057

1,072

1,087

1,103

1,118

1,134

1,149

1,015

1,030

1,046

1,062

1,078

1,094

1,110

1,127

1,144

1,161

1,016

1,032

1,049

1,066

1,083

1,100

1,118

1,136

1,154

1,173

1,017

1,035

1,052

1,070

1,088

1,107

1,126

1,145

1,165

1,184

1,018

1,037

1,055

1,075

1,094

1,113

1,134

1,154

1,175

1,196

1,019

1.039

1,059

1,079

1,099

1,120

1,142

1,163

1,186

1,208

1,020

1,041

1,062

1,083

1,105

1,127

1,150

1,173

1,196

1,220

1,021

1,043

1,065

1.087

1,110

1,134

1,158

1,182

1,207

1,232

1,022

1,045

1,068

1,092

1,116

1,141

1,166

1,192

1,218

1,245

1,023

1,047

1,071

1,096

1,122

1,148

1,174

1,201

1,229

1,257

1,024

1,049

1,075

1,101

1,127

1,154

1,182

1,211

1,240

1,270

1,025

1,051

1,078

1,105

1,133

1,161

1,190

1,220

1,251

1,282

1,026

1,053

1,081

1,109

1,138

1,168

1,199

1,230

1,262

1,295

<>r-

». 1

1,027

1,055

1,084

1,114

1,144

1,175

1,207

1,240

1,274

1,308

1,028

1,058

1,087

1,118

1,150

1,182

1,216

1,250

1,285

1,321

1,029

1,060

X091

1,123

1,156

1,189

1,224

1,260

1,297

1,334

1,030

1,062

1,094

1,127

1,161

1,197

1,233

1,270

1,308

1,348

1,036

1,072

1,111

1,150

1,191

1,233

1,277

1,322

1,368

1,417

1,041

1,083

1,127

1,173

1,221

1,270

1,322

1,375

1,431

1,489

1,046

1,094

1,144

1,197

1£52

1,309

1,369

1,431

1,497

1,565

1,051

1,105

1,162

1,221

1,283

1,349

1,417

1,490

1,565

1,645

1,057

1,116

1,179

1,246

1,316

1,390

1,468

1,550

1,637

1,729

€0

1,062

1,1-27

1,197

1,271

1,349

1,432

1,520

1,613

1,712

1,817

1,067

1,139

1,215

1,296

1,383

1,475

1,574

1,679

1,790

1,909

1,072

1,150

1,233

1,322

1,418

1,520

1,630

1,747

1,872

2,007

1,078

1,162

1,252

1.349

1,454

1,566

1,687

1,818

1,958

2,109

1,083

1,173

1,271

1,376

1,490

1,614

1,747

1,892

2,048

2,217

1,089

1,185

1,290

1,404

1,528

1,663

1,809

1,969

2,142

2,330

1,094

1,197

1,309

1,432

1,567

1,713

1,874

2,049

2,240

2,449

1,100

1,209

1,329

1,461

1,606

1,765

1,940

2,132

2,342

2,574

100

1,105

1,221

1,349

1,491

1,647

1,819

2,009

2,219

2,450

2,705

110

1,116

1,246

1,390

1,551

1,731

1,931

2,154

2,402

2,680

2,988

120

1,127

1,271

1,433

1,615

1,819

2,050

2,310

2,602

2,931

3,300

i6o

FOREST VALUATION

Years
n 1,1

1,2

Values of 1.0pn, where p
1,3 1,4 1,5 1,6

1,7

1,8

1,9

2,0

• 1,011

1,012

1,013

1,014

1,015

1,016

1,017

1,018

1,019

1,020

1,022

1,024

1,026

1,028

1,030

1,032

1,034

1,036

1,038

1,040

1,033

1,036

1,040

1,043

1,046

1,049

1,052

1,055

1,058

1,061

1,045

1,049

1,053

1,057

1,061

1,066

1,070

1,074

1,078

1,082

1,056

1,061

1,067

1,072

1,077

1,083

1,088

1,093

1,099

1,104

1,068

1,074

1,081

1,087

1,093

1,100

1,107

1,113

1,120

1,126

1,080

1,087

1,095

1,102

1,110

1,118

1,125

1,133

1,141

1,149

1,091

1,100

1,109

1,118

1,126

1,135

1,144

1,153

1,163

1,172

1,103

1,113

1,123

1,133

1,143

1,154

1.164

1,174

1,185

1,195

1,116

1,127

1,138

1,149

1,161

1,172

1,184

1,195

1,207

1,219

1,128

1U40

1,153

1,165

1,178

1,191

1,204

1,217

1,230

1,243

1,140

1,154

1,168

1,182

1,196

1,210

1,224

1,239

"1,254

1,268"

1,153

1,168

1,183

1,198

1,214

1,229

1.245

1,261

1,277

1,294

1,166

1,182

1,198

1,215

1,232

1,249

1,266

1,284

1,302

1,319

1,178

1,196

1,214

1,232

1,250

1,269

1,288

1,307

1,326

1,346

1,191

1,210

1,230

1,249

1,269

1,289

1,310

1,330

1,352

1,373

1,204

1,225

1,246

1,267

1,288

1,310

1,332

1,354

1,377

1,400

1,218

1,240

1,262

1,284

1,307

1,331

1,355

1,379

1,403

1,428

1,231

1,254

1,278

1,302

1,327

1,352

1,378

1,404

1,430

1,457

1,245

1,269

1,295

1,321

1,347

1,374

1,401

1,429

1,457

1,486

1,258

1,285

1,312

1,339

1,367

1,396

1,425

1,455

1,485

1,516

1,272

1,300

1,329

1,358

1,388

1,418

1,449

1,481

1,513

1,546

1,286

11,316

1,346

1,377

1,408

1,441

1,474

1,507

1,542

1,577

1,300

1,331

1,363

1,396

1,429

1,464

1,499

1,535

1,571

1,608

1,315

1,347

1,381

1,416

1,451

1,487

1,524

1,562

1,601

1,641

1,329

1,364

1,399

1,435

1,473

1,511

1,550

1,590

1,631

1,673

1,343

1,380

1,417

1,456

1,495

1,535

1,576

1,619

1,662

1,707

1,358

1,397

1,436

1,476

1,517

1,560

1.603

1,648

1,694

1,741

1,373

1,413

1,454

1,497

1,540

1,585

1,631

1,678

1,726

1,776

1,388

1,430

1,473

1,518

1,563

1,610

1,658

1,708

1,759

1,811

1,467

1,518

1,572

1,627

1,684

1,743

1,804

1,867

1,932

2,000

1,549

1,611

1,676

1,744

1,814

1,887.

1,963

2,041

2,123

2,208

1,636

1,710

1,788

1,869

1,954

2,043

2,135

2,232

2,333

2,438

1,728

1,816

1,908

2,004

2,105

2,211

2,323

2,440

2,563

2,692

1,825

li,927

2,035

2,148

2,268

2,394

2,527

2,668

2,816

2,972

1,928

2,046

2,171

2,303

2,443

2,592

2,750

2,917

3,094

3,281

2,036

2,171

2,315

2.469

2,632

2,806

2,991

3,189

3,399

3,623

2,151

2,305

2,470

2,646

2,835

3,038

3,254

3,486

3,734

4,000

2,272

2,446

2,635

2,837

3,055

3,289

3,541

3,811

4,103

4,416

2,399

2,597

2,810

3,041

3,291

3,560

3,852

4,167

4,508

to*

2,534

2,756

2,998

3.260

3,545

3,854

4,191

4,556

4,952

5,383

2,677

2,926

3,198

3,495

.3,819

4,173

4,559

4,981

5,441

5,943

2,827

3,.106

3,411

3,746

4,114

4,518

4,960

5,446

5,978

6,562

100

2,986

3,296

3,639

4,016

4,432

4,891

5,396

5,954

6,568

7,245

110

3,331

3,714

4,140

4,615

5,144

5,732

6,387

7,116

7,928

8,831

120

3,717

4,185

4,711

5,303

5,969

6,718

7,560

8,506

9,570

10,77

APPENDIX

161

Years
n

2,1

2,2

Values of 1.0pn, where p
2,3 2,4 2,5 2,6

2,7

2,8

2,9

3,0

1,021

1,022

1,023

1,024

1.025

1,026

1,027

1,028

1,029

1,030

1,043

1,045

1,047

1,049

1.051

1,053

1,055

1,057

1,059

1,061

1,064

1,068

1,071

1,074

1,077

1,080

1,083

1,086

1,090

1,093

1,087

1,091

1,095

1.100

1,104

1,108

1,113

1,117

1,121

1,126

1,110

1,115

1,120

1,126

1,131

1,137

1,140

1,148

1,154

1,159

1,133

1,140

1,146

1,153

1,160

1,167

1,173

1,180

1,187

1,194

1,157

1,165

1,173

1,181

1,189

1,197

1,205

1,213

1,222

1,230

1,181

1,190

1,200

1,209

1,218

1,228

1,238

1,247

1,257

1,267

1,206

1,216

1,227

1,238

1,249

1,260

1,271

1,282

1,293

1,305

1,231

1,243

1,255

1,268

1..280

1,293

1,305

1,318

1,331

1,344

1,257

1,271

1,284

1,297

1,312

1,326

1,341

1,355

1,370

1,384

1,283

1,299

1,314

1.329

1,345

1,361

1,377

1,393

1,409

1,426

1,310

1,327

1,344

1,361

1,379

1.396

1,414

1,432

1,450

1,468

1,338

1.356

1,375

1,394

1,413"

1,433

1,453

1,472

1,492

1,513

1,366

1,386

1,407

1,427

1,448

1,470

1,492

. 1,513

1,536

1,558

1,395

1,417

1,439

1.462

1,485

1,508

1,532

1,556

1,580

1,605

1,424

1,448

1,472

1,497

1,522

1,547

1,573

1,599

1,626

1,653

1,454

1,480

1,506

1,533

1.560

1,587

1,615

1,644

1,673

1,702

1,484

1,512

1,541

1,569

1,599

1,629

1,659

1,690

1,721

1,753

1,515

1,545

1,576

1,607

1,639

1,671

1,704

1,737

1,771

1,806

1,547

1,579

1,612

1,646

1,680

1,714

1,750

1,786

1,823

1,860

1,580

1.614

1,649

1,685

1/722

1,759

1,797

1,836

1,876

1,916

1,613

1,650

1,687

1,726

1,765

1,805

1,846

1,887

1,930

1,974

1,647

1,686

1,726

1,767

1,809

1,852

1,895

1,940

1,986

2,033

1,681

1,723

1,766

1,809

1,854

1,900

1,947

1,995

2,044

2,094

1,717

1,761

1.806

1,853

1,900

1,949

1,999

2,050

2,103

2,157

1,753

1,800

1,848

1,897

1,948

2,000

2,053

2,108

2,164

2,221

1,790

1,839

1,890

1,943

1,997

2.052

2,109

2,167

2.227

2,288

1,827

1,880

1,934

1,989

2,046

2,105

2,165

2,227

2,291

2,,357

1,865

1,921

1,978

2,037

2,098

2,160

2,224

2,290

2,358

2,427

2,070

2,142

2,216

2,294

2,373

2,456

2,541

2,629

2,720

2,814

2,296

2,388

2,483

2,581

2,685

2.792

2,903

3,017

3,138

3,362

2,548

2,663

2,782

2,907

3,038

3,174

3,316

3,465

3,620

3y782

2,827

2,969

3.117

3,274

3,437

3,609

3,789

3,978

4,176

4,384

3,136

3,310

3,493

3,686

3,889

4,103

4,329

4,567

4,818

5,082

3,480

3,690

3,913

4,150

4,400

4,665

4,946

5,243

5,558

5,892

3,861

4,115

4,385

4,672

4,978

5,304

5,650

6,019

6.412

6,830

4,284

4.587

4,912

5,260

5,632

6,030

6,455

6,911

7,397

7,918

4,753

5,115

5,504

5,923

6,372

6,856

7,375

7,934

8.534

9,179

5,273

5,703

6,167

6,668

7,210

7,795

8,426

9,109

9,845

10,64

5,850

6,358

6,909

7,508

8,157

8,862

9,627

10,46

11,35

12,34

6,491

7,089

7,741

8.452

9,229

10,06

11,00

12,01

13,10

14,30

7,702

7,904

8,673

9,517

10,44

11,46

12,57

13,78

15,12

16,58

100

7,991

8,812

9,718

10,72

11,81

13,02

14.36

15,82

17,44

19,22

110

9,836

10,83

12,20

13,58

15,12

16,60

18,74

20,86

23.21

25,83

120

12,11

13.62

15,31

17,21

19,36

21,76

24,46

27,49

30,89

34,71

162

FOREST VALUATION

Years
n

3,1

3,2

Values of 1
3,3 3,4

..Opn, where p
3,5 3,6

3,7

3,8

3,9

4,0

1,031

1,032

1,033

1,034

1,035

1,036

1.037

1,038

1,039

1,040

1,063

1,065

1,067

1,070

1,071

1,073

1,075

1,077

1.080

1,082

1,096

1,100

1,102

1,106

1,109

1,112

1,115

1,118

1,122

1,125

1,130

1,134

1,139

1,143

1,148

1,152

1,157

1,161

1,165

1,170

1,165

1,171

1,176

1,182

1,188

1,194

1199

1,205

1,211

1,217

1,201

1,208

1,215

1.222

1,229

1,236

1,244

1,251

1,258

1,265

1,238

1.247

1,255

1,264

1,272

1,281

1,290

1,298

1,307

1,316

1,277

1,287

1,297

1,307

1,317

1,327

1,337

1,348

1,358

1,369

1,316

1,328

1,339

1,351

1,363

1,375

1.387

1,399

1,411

1,423

1,357

1,370

1,384

1,397

1,411

1,424

1,438

1,452

1,466

1,480

1,399

1,414

1,429

1,445

1,460

1,476

1,491

1,507

1,523

1,539

1,443

1,459

1,476

1,494

1,511

1,529

1,547

1,565

1,583

1,601

1,487

1,506

1,525

1,545

1,564

1,584

1.604

1,624

1,644

1,665

.1,533

1,554

1,576

1,597*

1,619

1,641

1,663

1,686

1,709

1,732

1,581

1,604

1,628

1,651

1,675

1,700

1,725

1,750

1,775

1,801

1,630

1,655

1,681

1,707

1,734

1,761

1,788

1,816

1,844

1,873

1,680

1,708

1,737

1,766

1,795

1.824

1,855

1,885

1,916

1,948

1,733

1,763

1,794

1,826

1,857

1,890

1,924

1,957

1,991

2,026

1.786

1,819

1.853

1,888

1,923

1,958

1.994

2,031

2,069

2,107

1,842

1,878

1,915

1,952

1,990

2,029

2,068

2,108

2,149

2,191f

1,899

1,938

1,978

2,018

2.059

2.102

2,145

2,189

2,233

2,279

1,958

2,000

2,043

2,087

2,132

2,177

2,224

2,272

2,320

2,370

2,018

2,064

2,110

2,158

2,206

2,256

2,306

2,358

2,411

2,465

2,081

2,130

2,180

2,231

2,283

2,337

2,392

2,448

2,505

2,563

2,145

2,198

2,252

2,307

2,363

2,421

'2,480

2,541

2,603

2,666

2,212

2,268

2,326

2,385

2,446

2,508

2,572

2,637

2,704

2,772

2,280

2,341

2,403

2,467

2,532

2,599

2,667

2,737

2,810

2,883

2,351

2,416

2,482

2,550

2,620

2,692

2,766

2,841

2,919

2,999

2,424

2,493

2,564

2,637

2,712

2.789

2,868

2,949

3,033

3,119

2,499

2,573

2,649

2,727

2,807

2,889

2,974

3,061

3,151

3,243

2,911

3,012

3.115

3,223

3,334

3,448

3,567

3,689

3,815

3,94£

3,391

3,525

3,664

3,809

3,959

4,115

4,277

4,445

4,620

4,801

3,951

4,127

4,310

4,50,2

4,702

4.911

5,129

5,357

5,594

5,841

4,602

4,830

5,070

5,321

5,585

5,861

6,151

6,455

6,776

7,107 '

5,361

5,654

5,964

6,290

6,633

6,995

7,376

7,778

8,201

8,646

6,245

6,619

7,015

7,434

7,878

8,348

8,846

9,373

9,930

10,52

7,275

7,748

8,251

8,784

9,357

9,963

10,61

11,29

12,02

12,80

8,473

9,069

9,706

10,39

11,11

11,89

12,78

13,59

14,56

15,57

9,872

10,62

11.42

12,28

13,20

14,19

15.26

16,40

17,63

18,95

11,50

12,43

13,43

14,51

15,68

16,94

18,29

19,76

21,34

23,05

13,40

14.56

15,80

17,15

18,62

20,21

21,94

23,81

25,84

28,04

15,61

17,03

18,58

20,27

22,11

24,12

26,31

28,69

31,29

34,12

18,18

19,93

21.85

23,96

26,26

28,79

31,55

34,58

37,89

41,51

100

21,16

23,33

25,71 •

28,32

31,19

34,36

37,83

41,66

45,87

50,50

110

28,74

31,97

35,57

39,56

44,00

48.93

54,41

60,50

67,25

74,76

120

39,00

43,81

49,21

55,27

62,06

69,69

78,25

87,84

98,59

110,7

APPENDIX

163

Years

4,1

4.2

Values of l.Op", where p
4,3 4,4 4,5 4,6

4,7

4,8

4,9

5,0

1,041

1,042

1,043

1,044

1,045

1,046

1,047

1,048

1,049

1,050

1,083

1,086

1/088

1,090

1,092

1,094

1,096

1,098

1,100

1,103

1,128

1,131

1,135

1,138

1,141

1,145

1,148

1,151

1,154

1,158

1,174

1.179

1,184

1,188

1,193

L,197

1,202

1,206

1,211

1,216

1,223

1,228

1,234

1,240

1,246

1,252

1,258

1,264

1,270

1,276

1,273

1,280

1.287

1,295

1,302

1,310

1.317

1,325

1,333

1,340

1,325

1,334

1,343

1,352

1,361

1,370

1,379

1,389

1,398

1,407

1,379

1,390

1,401

1,411

1,422

1,433

1,444

1,455

1,466

1,478

1,436

1.448

1,461

1,473

1,486

1,499

1,512

1,532

1,539

1,551

1,495

1,509

1,524

1,539

1,553

1,568

1,583

1,598

1,614

1,629

1,556

1,573

1,589

1,610

1,623

1,640

1,657

1,675

1,6-93

1,710

1,620

1.638

1,657

1,677

1,696

1,716

1,735

1,755

1,776

1,796

1,686

1,707

1,729

1,750

1,772

1,794

1,817

1,840

1,863

1,886

1,755

1,779

1,803

1,827

1,852

1,877

1.902

1,928

1,954

1,989

1,827

1,854

1,881

1,908

1,935

1,963

1,992

2,020

2,050

2,079

1.902

1932

1,961

1,992

2,022

2.054

2,085

2,117

2,150

2,183

1,980

2,013

2,046

2,079

2,113

2,148

2,183

2,219

2,255

2,292

2,061

2,097

2,134

2,171

2,208

2,247

2.286

2,326

2,366

2,407

2,146

2,185

2,225

2,266

2,308

2,350

2,393

2,437

2,482

2,527

2,234

2,277

2,321

2,366

2,412

2,458

2,506

2,554

2,603

2,653

2,325

2,373

2,421

2,459

2,520

2,571

2,624

2,677

2,731

2,786

2,421

2,472

2,525

2,579

2,634

2,690

2,747

2,805

2,865

2,925

2,520

2,576

2,634

2,692

2,752

2,813

2,876

2,940

3,005

3.072

2,623

2.684

2,747

2,811

2,876

2.943

3,011

3,081

3,152

3,225

2,731

2,797

2,865

2,934

3,005

3,078

3,153

3,229

3,307

3,386

2,843

2,915

2.988

3,064

3,141

3,220

3.301

3,384

3,469

3,556

2,959

3,037

3,117

3,198

3,282

3,368

3,456

3,546

3,639

3,733

3,081

S.164

3,251

3.339

3,430

3.523

3,618

3,716

3,817

3,920

3,207

3,297

3,390

3,486

3,584

3,685

3,788

3,895

4,004

4,116

3,338

3,436

3.536

3,640

3,745

3,854

3,967

4,082

4,200

4,322

4,081

4,221 •

4,365

4,514

4,667

4,826

4,990

5,160

5,335

5,516

4,989

5.1S5

5,387

5,598

5,816

6,043

6,279

6,523

6,777

7,040

6,099

6,369

6,650

6,943

7,248*

7,567

7,900

8,246

8,608

8,985

7,257

7,823

8.208

8,611

9,033%

9,475

9.939

10,43

10,93

11,47

9,116

9,610

10,13

10,68

11,26

11,87

12,51

13,18

13,89

14,64

60 '

11,15

11.81

12,51

13..25

14,03

14,86

15,73

16,66

17,64

18,68

13,62

14,50

15,44

16,43

17,48

18,60

19,79

21,06

22,41

23,84

16,66

17,81

19,05

20,37

21,78

23,29

24. ,90

26,63

28,46

30,43

20,36

21,88

23,52

25,27

27,15

29,17

31,33

33,66

36,16

38,83

24,84

26,88

29,03

31,34

33,93

36,52

39,42

42,55-

45,93

49,56

30,43

33,02

35,82

38,86

42,16

45,73

49,60

53,79

58,33

63,25

37,20

40,56

44,22

48,20

52,54

57.26

62,41

68,00

74,10

80,73

45,48

4982

54,58

59,78

65,47

71,70

78,51

85,97

94,12

103,0

100

55,60

61,20

67,37

74,14

81,59

89.78

98,78

108,7

119,6

131,5

110

83,10

92,35

102,6

114,0

126,7

140,8

156,4

1*73,7

192,9

214,2

120

1-24,2

139.4

156,4

175,4

196,8

220,7

247,5

277,5

311,2

348,9

1 64

ST VALUATION

Years

1,1

5,2

Values of l.Op", where p
5,3 5,4 5,5 5,6

5,7

5,8

5,9

6,0

1,051

1,052

1,053

1,054

1,055

1,056

1,057

1,058

1,059

1,060

1,105

1,107

1,109

1,111

1,113

1,115

1,117

1,119

1,122

1,124

1,161

1,164

1,168

1,171

1,174

1,178

1,181

1,184

1,188

1,191

1,220

1,226

1,230

1,234

1,239

1,244

1,248

1,253

1,258

1,262

1,282

1,289

1,295

1,301

1,307

1,313

1,319

1,326

1,332

1,338

1,348

1.356

1,363

1,371

1,379

1,387

1,395

1,403

1,411

1,419

1,417

1,423

1,436

1,445

1,455

1,464

1,474

1,484

1,494

1,504

1,489

1,500

1,512

1,523

1,535

1,547

1.558

1,570

1,582

1,594

1,565

1,578

1,592

1,604

1,619

1,633

1,647

1,661

1,675

1,689

1,645

1,660

1,676

1,692

1,708

1,724

1,741

1,757

1,774

1,791

1,729

1,747

1,765

1,783

1,802

1,821

1,840

1,859

1,879

1,898

1,817

1,837

1,859

1,880

1,901

1,923

1.945

1,967

1,990

2,012

1,909

1,933

1,957

1,981

2,006

2,031

2,056

2,081

2,107

2,133

2,007

2,033

2,061

2,088

2,116

2,144

2,173

2,202

2,231

2,261

2,109

2,139

2,170

2,201

2,233

2,265

2,297

2,330

2,363

2,397

2,216

2,250

2,285

2,320

2,355

2,391

2,428

2,465

2,502

2,540

2,329

2,367

2,406

2,445

2,485

2,525

2,566

2,608

2,650

2,693

2,448

2.491

2,534

2,577

2,621

2,667

2,712

2,759

2,806

2,854

2,573

2,620

2,668

2,716

2,766

2,815

2,867

2,919

2,972

3,026

2,704

2,756

2,809

2,863

2,918

2,974

3,030

3,088

3,147

3,207

2,842

2,900

2,958

3,018

3,078

3,140

3,203

3,267

3,383

3,400

2,987

3,050

3,115

3,181

3,248

3,316

3,386

3,457

3,530

3,604

3,136

3,209

3,280

3,352

3,426

3,502

3,579

3,657

3,738

3,829

3.300

3,376

3,454

3,533

3,615

3,698

3.783

3,870

3,958

4,049

3,468

3,551

3,637

3,724

3,813

3,905

3,998

4,094

4,192

4,292

3,645

3>,V36

3,830

3,925

4,023

4,124

4,226

4,332

4,439

4,550

3,831

3,930

4.033

4,137

4,245

4,354

4,467

4,583

4,701

4,822

4,026

4,135

4,246

4,361

4,478

4,598

4,722

4,850

4,978

5,112

4,231

4.350

4,471

4,596

4,724

4,856

4,993

5,130

5,272

5,418

4,447

4..576

4,708

4,844

4,984

5,128

5,275

5,427

5,583

5,744

5.703

5,896

6,095

6,301

6,514

6.734

6.960

7,195

7,436

7,686

7,313

7,596

7,891

8,197

8,513

8,842

9,184

9,537

9,905

10,29

9,378

9,788

10,22

10,66

11,13

11,61

12,12

12,64

13,19

13,77

12,03

12,61

13,23

13,87

14,54

15,25

15,99

16,76

17,57

18,42

15,42

16,25

17,02

18,04

19,01

20,02

21,09

22,23

23,40

24,65

19,78

20,94

22,17

23,47

24,84

26,29

27,83

29,45

31,17

32,99

25,36

26..9S

28,70

30,52

32,46

34,53

36,72

39,05

41,52

44,14

32,52

34,76

37,15

39,71

42,43

45,34

48,15

51,76

55,30

59,08

41,71

44,79

48,10

51,65

55,46

59,54

63,92

68,62

73,66

79,06

53,48

57,71

62,27

67,18

72,48

78,18

84,33

90,96

98,10

105,8

68,59

74,36

80,62

87,38

94,73

102,7

111,3

120,6

130,6

141,6

87,95

95,81

104,4

113,7

123,8

134,8

146,8

159,9

174,0

189,5

112,8

123,4

135,1

147,9

161,8

177,0

193,7

211,9

231,8

253,5

100

144,6

159,1

174,9

192,3

211,5

232,5

249,8

280,9

305,8

339,3

110

237,9

264.1

293,2

325,4

361,2

400,9

444,9

493,7

547,7

607,6

120

391,1

438,4

491,4

550,7

617,0

691,3

488,7

867,5

971,7

1088

APPENDIX

165

Years
ft

6,2

6,4

Values of 1.0pn, where p

6,6 6,8 7,0 7,2

7,4

7,6

7,8

8,0

1,062

1,064

1,066

1,068

1,070

1,072

1,074

1,076

1,078

1,080

1,127

1,132

1,136

1,141

1,145

1,149

1,154

1,158

1,162

1,166

1.198

1,205

1,211

1,218

1,225

1,232

1,239

1,246

1,253

1,260

1,272

1,282

1,291

1,301

1,311

1,321

1.331

1,341

1,351

1,361

1,351

1,364

1,377

1,390

1,403

1,416

1,429

1,442

1,456

1,469

1,435

1,451

1,467

1,484

1,501

1,518

1,535

1,552

1,569

1,587

n
i

1.524

1,544

1,564

1,585

1,606

1,627

1,648

1,670

1,692

1,714

. 8

1,618

1,643

1,668

1,693

1,718

1,744

1,770

1,797

1,824

1,851

1,718

1,748

1,778

1,808

1,839

1,870

1,901

1,933

1,966

1,999

1,825

1,860

1,895

1,931

1,967

2,004

2,042

2,080

2,119

2,159

1.938

1,979

2,020

2,062

2,105

2,149

2,193

2,238

2,285

2,326

2,058

2,105

2,153

2,202

2,252

2,303

2.355

2,409

2,463

2,518

2,186

2,240

2,295

2,352

2,407

2,469

2,530

2.592

2,655

2,720

2,321

2.383

2,447

2,512

2,579

2,647

2,716

2,789

2,862

2,938

2,465

2,535

2,608

2,683

2,759

2,838

2,918

3,001

3,085

3,172

2,618

2,698

2,781

2,865

2,952

3,042

3,133

3,229

3,326

3,426

2,781

2,870

2,964

3,060

3,159

3,261

3,366

3i,474

3,585

3,700

2,953

3,055

3,160

3.268

3,380

3,496

3,615

3,738

3,865

3,996

3,136

3,250

3,368

3,490

3,617

3,747

3,882

4,022

4,166

4,316

3,330

3,458

3,590

3,728

3,870

4,017

4,170

4,328

4,491

4,661

3,537

3,679

3,827

3,981

4,141

4,306

4,478

4,657

4,842

5,034

3,756

3,915

4,080

4,252

4,431

4,616

4,810

5,010

5,219

5,437

3.989

4,165

4,349

4,541

4,741

4,949

5,165

5,391

5,627

5,872

4,236

4.432

4,636

4,850

5,072

5,305

5.548

5,801

6,065

6,341

4,499

4,716

4,942

5,180

5,428

5,687

5,958

6,213

6,538

6,849

4,778

5.018

5,269

5,532

5,807

6,096

6,399

6,716

7,048

7,396

5.074

5,339

5,616

5,908

6,214

6,535

6,873

7,227

7,598

7,988

5,389

5,680

5,987

6,310

6,649

7,005

7,381

7,776

8,191

8,627

5.723

6,044

6,382

6,739

6,794

7,510

7,927

8,367

8,830

9,317

6,078

6,431

6,803

7,197

7,612

8,051

8,514

9,003

9,518

10,06

8.210

8,769

9,365

10,00

10,68

11,40

12,17

12,99

13,86

14,79

11,09

11,96

12,89

13,90

14,98

16,14

17.39

18,73

20,17

21,73

14,98

16,31

17,75

19,31

21,00

22,85

24,84

27,01

29,37

31,92

20,24

22.24

24,43

26,82

29,46

32,34

35,50

38,96

42,75

46,90

27,34

30,33

33,62

37,28

41,32

45,79

50,73

56,19

62,24

68,92

36,94

41,35

46,29

51,79

57,95

64,82

72,49

81,05

90,60

101,3

49,90

56,39

63,71

71,97

81,27

91,76

103,5

116,4

131,9

149,1

67,41

76,90

87,70

100,0

114,0

129,9

148,0

168,6

192,0

218,6

91,06

104,9

120,7

139,0

159,9

183,9

211,5

243.2

279,5

321,2

123,0

143,Q

166,2

193,1

224,2

260,4

302,2

350,7

406',9

472rO

166.2

195,0

228,8

268,3

314,5

368,6

431,9

505,8

592,4

693,5

224,5

265,9

314,9

372,8

441,1

521,8

617,1

729,6

862,4

1019

303,3

362.6

433,5

517,9

618,7

738,8

881,9

1052

1256

1497

100

409,7

494,5

596,7

719,7

867,7

1046

1260

1518

1828

2200

i66

FOREST VALUATION

Years
n

8,2

8,4

Values of l.Op", where p

8,6 8,8 9,0 9,2

9,4

9,6

9,8

1,082

1,084

1,086

1,088

1.090

1,092

1,094

1,096

1,098

1,100

1,171

1,175

1,179

1,184

1,188

1,193

1,197

1,201

1,206

1,210

1,267

1,274

1,281

1,288

1,295

1,302

1,309

1,317

1.324

1,331

1,371

1,381

1,391

1,401

1,412

1,422

1,432

1,443

1,454

1,464

1,483

1,497

1,510

1,525

1.539

1,552

1,567

1,582

1,596

1,611

1,605

1,623

1,641

1,659

1,677

1,696

1,714

1,733

1,752

1,772

1,736

1,759

1,782

1,805

1,828

1,852

1,876

1.900

1,924

1,949

1,878

1,907

1,935

1,964

1,993

2,022

2,052

2,082

2,113

2,144

2.033

2,067

2,101

2,136

2,172

2,208

2,245

2,282

2,320

2,358

2,199

2,240

2,282

2,324

2,367

2,411

2,456

2,501

2,547

2,594

2,380

2,429

2,478

2,529

2,581

2,633

2,687

2,741

2,797

2,853

2.575

2,632

2,691

2,751

2,813

2.875

2,939

3,004

3,071

3,139

2,786

2,854

2,923

2,994

3,066

3,133

3,215

3,293

3,372

3,452

3,014

3,093

3,174

3,257

3,337

3,429

3,518

3,609

3,702

3,798

3,262

3,353

3,447

3,544

3,643

3,744

3,848

3,955

4,065

4,177

3.529

3,635

3,744

3,855

3,970

4.089

4,210

4,334

4,463

4,595

3,818

3,940

4,066

4,195

4,328

4,465

4,606

4,751

4,901

5,055

4,131

4,271

4.415

4,564

4,417

4,875

5,038

5,207

5,381

5,560

4,470

4,630

4,795

4,965

5,142

5,324

5,512

5,707

5,908

6,116

4,837

5,019

5,207

5,402

5,605

5,814

6,030

6,254

6,487

6,728

5,233

5,440

5,655

5,878

6,109

6,349

6,597

6,855

7,123

7,400

5,662

5,897

6,141

6,395

6,659

6,933

7.217

7,513

7,821

8,140

6,127

6,393

6,669

6,958

7,258

7,571

7,896

8,235

8,587

8,954

6,629

6,930

7,243

7,570

7.911

8,267

8,638

9,025

9,429

9,850

7,173

7,512

7,866

8,236

8-,623

9,028

9,450

9,892

10,35

10,84

7,761

8,143

8,542

8.961

9,399

9,858

10,34

10.84

11,37

11,92

8,397

8,827

9,277

9,750

10,25

10,77

11,31

11,88

12,48

13,11

9,086

9,568

10,08

10,61

11.17

11,76

12,37

13,02

13,71

14,42

9,831

10,37

10,94

11,54

12,17

12,84

13,54

14,27

15,05

15,86

10,64

11,24

11,88

12,56

13,27

14,03

14,81

15,64

16,52

17,45

15,78

16,83

17,95

19,14

20,41

21,77

23,21

24,73

26,37

28,10

231.39

25,19

27,11

29,19

31.41

33,80

36,37

39,12

42,08

45,26

34,69

37,70

40,96

44,49

48,33

52,48

56,99

61,87

67,16

72,89

51,45

56,43 •

61,87

67.83

74,36

81,50

89.30

97,84

107,2

117,4

76,30

84,45

93,46

103,4

114,4

126,6

140,0

154,7

171,1

189,1

113x2

126,4

141,2

157,7

176,0

196,5

219,3

244,7

273,0

304,5

167,8

189,2

213,3

240,4

270,8

305,1

343,7

387,0

435,7

490,4

248,8

283,2

322,2

366.5

416,7

473,8

538.5

612,0

695,3

789,8

369,0

423,8

486.7

558,7

641,2

735,7

843,9

967,8

1110

1272

'547,3

634,4

735,2

851,8

986,6

1142

1323

1531

1771

2048

APPENDIX 167

C. Suggestions for problems for use in teaching.

The following problems are offered here merely as suggestions.
Some practice in the use of the analyses and formulae has been
found necessary to fix these matters in the minds of the students.

1. Capital Co = $50, p = 3%; what does this capital grow
into in 7, 19, 37, and 83 years?

2. Capital now is $500; has been out at 2l/2% compound in-
terest; what was it worth 17, 43, and 120 years ago?

3. $140 grew into $190 in 17 years; what is i.op17 and what
is p?

4. - A tree contains 430 cubic feet ; it is growing at 1.2% ; what
is the growth for 5 years in cubic feet ?

5. A tree now has 430 cubic feet ; 23 years ago it had 375 ; at
what p did it grow, wThat is i.opn in this case?

400

6. Schneider's formula says: pv=- for older timber (D

being dbh and n the number of rings in outer one inch). Suppose
stand of timber has 40,000 cubic feet; average D 21 inches, and n
12 ; at what rate is this stand growing, what is the value of five years
growth at 7 cents per cubic foot ?

7. A locomotive sets fire to a stand of pine planted 25 years
ago ; it cost 10 dollars an acre to plant ; what is the loss if only
planting expense and interest at 3% is counted?

8. A stand is now 35 years old. We expect it to be worth
$350 when 80 years old; what is its present value; p — 3%, and no
expenses figured.

9. A farm rents at 100 dollars, clear, over and above expenses.
Rate per cent 3% and also 2%. What is the value of the farm and
what is the value of 25 years use of it?

10. A forest property is worth $10,000, based on income, but
it can not be sold until 15 years from now ; the property is used and
no change is expected. What is its value today at 2% and at 4% ?

11. A note for $500 at 4% is due in 7 years; it has run 3
years ; all interest and capital to be paid in at end of 7 years. What
is the note worth now to a man who is willing to take 3% on his
money ?

12. A stand of timber contains 550 cords ; it contained 470,
10 years ago; what was pv for this time? If this timber now brings
$4.50 per 100 cubic feet but brought only $3.75 per 100 cubic feet,
10 years ago, what is pq, quality growth, in per cent? If there is
no price growth, what is pf, i. e., the growth in value of this stand?

1 68 FOREST VALUATION,

13. What is the growth, in quality in' per cent, for each decade
which will keep the growth in value constant between the ages 40
and 100 years in spruce, site II, as in Schwappach tables?

14. Eight hundred acres of timber is cut over every 10 years
and nets $12 per acre at each cut. Expenses per acre: taxes 15
cents, protection 10 cents. What is the value of the forest at 2%
and at 3% ? What is 100 years lease worth if the last cut came 6
years ago?

15. One hundred acres of land may be farmed. At farming
it brings 75 cents per acre net. If planted to pine and r = 80 years ;
Yr=6o cords at $3; C — $10; €==25 cents; p = 4, 3, and 2% —
which use is more profitable?

1 6. Six thousand acres of North Carolina pinery cut over lands
bought at $5 per acre ; expenses per acre : taxes 10 cents, protection
5 cents, p = 3% ; what is Fc in 25 years? If timber is $6 per M.
feet, how much must one get to make interest and expenses, and
leave the forest as good as when bought?

17. Mountain lands in Pennsylvania; can return every 15
years for 6 cords of hardwood stuff, mostly coppice, worth $2 per
cord on stump. Taxes 5 cents per acre ; no other charges ; what is
the value of the woods at 3% ?

18. A farmer has 60 acres inferior lands ; he paid $18 an acre.
He has rented this at $i per acre for pasture. Expenses per acre:
taxes 15 cents, fences 10 cents, p = 3%. He plants up 30 acres to
hardwoods. C — $10, first cut when 15 years old. How much must
he cut if income is to be as good as at pasture use, if he values stuff
at $2 per cord?

19. One hundred acres coppice ; non-agricultural land, can be
cut every 20 years for 15 cords of stuff, last cut 9 years ago, stump-
age now $i per cord. Expected rise in market price 20 cents per
cord for each of the next 5 rotations ; after this constant. What is
this woods worth at 3% ?

Y 20. Four thousand acres of pine woods in North Carolina can
^ Y be cut over every 15 years for 5 M. feet." Last cut 7 years ago.
What yearly payment or annuity can a trust company pay if they
rate money at 3% ?

21. One thousand acres of coppice woods in Pennsylvania have
cut 15 cards every 25 years for iron furnace; stumpage $1.50. Plan
is to concert into spruce for pulp on 50 year rotation. If Yr = 3O
cords at %;t£=$io; thin. = o; taxes in first case 15 cents, in new
case i6% of stumpage as yield tax ; protection and care = 10 cents ;
pz^3%. How do the two compare?

APPENDIX J 69

22. Spruce forest.

a. Present practice : Natural reproduction, takes 10 years,
requires no artificial help ; rotation 90 years, i. e., 90 from end of one
reproduction to end of next; thinning needed early, 15 years after
reproduction is started, costs $5 an acre.

Second thinning costs $2 per acre at age of 25.

Third thinning at 40 years brings $5 net.

Fourth thinning at 60 years brings $20 net.

Fifth thinning at 80 years brings $40 net.

Yr at 90 years would be $600 but owing to extra cost of logging
is only $560.

e is $i per acre and year, including taxes; p = 3%. What is
Sehere?

b. Plan is now to change this as follows :

Plant 5 year transplants space 6x6; plants cost $3 per M, set-
ting costs $5 per M.

First thinning at 20 years pays expense.

Second thinning at 40 years pays $20.

Third thinning at 60 years pays $40.

Fourth thinning at 80 years pays $iop.

Yr should be $600 but heavy thinning reduces volume but raises
quality so that we still have $540, saving $40 on cost of logging.

e and p same as before. What is the new Se, and how does this
compare to the old plan?

23. Beech forest, site II, is not satisfactory as to income.
Make concrete case from Schwappach to show how this would work
out if changed to spruce and to pine. Put p — 3 %, e = $i, C = $10.

24. State of Michigan has been selling land inclusive of some
growing stock at $i per acre. If put in pine, C = $10, e = 50 cents,
p = 2% and r^=8o years, how much pine must the state cut per
acre to beat the $i, with stumpage at $10 per M?

25. Work out Se at 2, 4 and 5% for spruce, pine and oak,
all for site II; C = $io, e = $i, and r = 4O, 60, 80, 100 and 120
years.

Yr and thinnings as by Schwappach. Tabulate.

26. What is Se in coppice, rotation 25 years ; Yr 20 cords at
$2 ; thinnings cover expenses and taxes, planting costs $2 in each-
rotation, i. e., at each cut; p — 3%. Is this really Se?

27. Fe, pine in North Carolina ready to cut over* n&w, for
10 M. feet at $6, can return every 20 years ; e — 50 cents, soil = $5,

= . Find Fe.

1 70 FOREST VALUATION

28. What is °-<r-'>Gc and °-<r-OGe in Spruce, Yr and thinnings
as by Schwappach, site II, r = 8o years and 100 years, e = $i, p =
3%, Sc = $2o.

29. What is Fc and Fe in the above case if Sc is replaced by
Se in the calculation?

30. If the state of Michigan wanted to go into forestry and
establish one million acres of forest in regulated condition what in-
vestment, i. e., what is Fc. if : soil = $5 per acre ; C = $10 per acre ;
e — 50 cents ; p = 2%; r = So y ; Yr = $200 ; thinnings neglected.
What is Fc if Se is substituted and what is Fe then?

31. What rate of interest is made in the following case: stand
at 80 years worth $350; at 60 worth $200, with land worth $10 an
acre, e — 50 cents and rate of interest 3%. Explain principle in-
volved, and write out formula.

32. If C==$TO, 6 = 50 cents, p = 3%, soil = $io, r = 8o
years, and Yr = $3OO, what pf is made here in raising the crop?

33. A lumber company bought 10 sections of timber 10 years
ago at $15 per acre, land and timber; p = 5% ; will cut 12 M. feet
per acre ; expenses per acre, assessment at J^ cost value ; tax rate =
12 per i ,000; protection, etc., — 5 cents ; no net growth, no fires, etc.
losses so far. What is Fc now?

What is Fe if the cut expected is 12 M. feet at $6 and the
company expects to get at this timber in 8 years? Expenses to con-
tinue uniform. How does the Fc and Fe compare did they pay
too much?

34. If average stumpage costs $5 per M. feet what must the
lumber be worth which will be cut in 40 years from now if : milling
= $4 ; logging = $6 ; taxes 5 cents per M. feet ; protection = i cent
per M. feet; pr=5%; and land in 40 years to be worth $10; to
justify buying this now at $5 per M. feet.

35. A saw mill costs: for buildings, $10,000, life of this 30
years, wreckage value $1,000; for steam engines, etc., $15,000, life
15 years, wreckage value $1,000; saw mill machinery $25,000, life
10 years, wreckage value $3,000. What is depreciation cost in this
mill per year, if p — 5% ?

36. A lumber company has 25 years timber on hand. It cuts
20 million feet ; lands cut 10 M. feet per acre. They paid $6 per
acre. As fast as lands are cut over they sell for $i to a realty com-
pany. They pay 20 cents tax an acre, and also 5 cents for protection.
Interest rate =5%. What does the stumpage cost them on their
20 million feet per year?

APPENDIX 171

37. A lumber company bought 30 thousand acres of timber
lands; which cut 12 M. per acre; no net growth ; they paid $10 an
acre, build a saw mill, planing mill and other buildings at a cost of
$150,000, and buy logging equipment at $50.000 more. They log
for $6 and mill for $4 which includes all expenses. They get $18,
per M. feet on board car at mill ; cut 20 million per year. Taxes on
y2 value at 10 per 1,000, interest at 5% ; depreciation and replace-
ment as follows :

Xone for buildings, the repairs are paid by milling costs.

All machinery is replaced once during the entire cut. Buildings
cost new $60,000 and are worth at end $10,000. Machinery at start
$90,000, at end $10,000. The logging outfit is kept up by logging-
charge of $6.

a. What is the yearly depreciation on buildings? What on
machinery ?

b. What does the 20 million feet lumber cost them and what
is their net income per year?

c. What is the expectation value of the whole enterprise at
start and after 7 years cut?

d. If a fire reduces their forest by 5 years cutting what is the
damage to the company?

UNIVERSITY OF CALIFORNIA LIBRARY
BERKELEY

Return to desk from which borrowed.
This book is DUE on the last date stamped below.

FEB IB 194*

LD 21-100m-9,'47(A5702sl6)476

U.C. BERKELEY LIBRARIES

UNIVERSITY OF CALIFORNIA LIBRARY

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