Some business problems of American forestry

Some Business Problems
of AmericQLn Forestry

Some Business Problems of
American Forestry

By C. a. SCHENCK, Ph. D.,

Forester to the Biltmore Estate, Biltmore, N. C.

Forest Assessor to the Grand Duchy of Hesse- Darmstadt, and

Principal Biltmore School of Forestry,

The French Broad Press, Ashcville, N. C.

Digitized by the Internet Archive

in 2009 with funding from

NCSU Libraries

http://www.archive.org/details/somebusinessprobOOsche

PREFACE.

FORESTRY on a large scale will not be possible in the United
States, on private holdings, unless it proves to be a remun-
erative investment of capital.

Unfortunately, ovving to the slowness of treegrowth, there
is no chance of large profits in forestry. Not one of the forest own-
ers abroad has engaged in forestry with a view of getting rich
through it. Forestry is not a maker of wealth ; it is only a pre-
server of wealth.

As a preserver of wealth, forestry is unrivalled. No business
yields interest on the capital engaged in it as steadily as forestry.
As sure as the sun shines, the wind blows and the rain falls, the
volume of a tree is compelled to increase, the increment represent-
ing the interest on tree-capital. Sunshine, air and precipitations
are the factors of treegrowth.

Abroad, all aristocratic families owning forest-estates have suc-
ceeded in the maintainance of their standing for centuries, whilst
the rich merchants and bankers of olden times have not left a trace
of their names and their wealth, in spite of the fact, that many of
them, the merchants of Leipzig, Hamburg, Midland, Nuernberg,
were richer than their sovereigns themselves.

In America, it is the well-to-do class, and pre-eminently the well-
to-do lumberman, who should be interested in forestry, wherever it
offers him a safe and remunerative chance of investment.

The " Problems of Forestry " were compiled with a view of
showing the American wood owners the financial character of pro-
fessional forestry. The object in forestry, as in any other business,
is the production of high and safe interest on capital. Some little
knowledge of elementary mathematics and of banking generally
is required for the solution of any financial problem. The banker,
the insurance company, the stock broker, constantly meet with
tasks similar to those outlined in the " Problems of Forestry."

The splendid interest tables issued by the Mutual Life Insur-
ance Company were used for the solution of the problems in order
to avoid the times-taking application of logarithms.

C.A. SCHENCK,
Forester to the Biltmore Estate.
Biltmore, N. C, March, 1900.

TABLE OF PROBLEMS.

PAGE

A Longleaf Pine Problem (Florida) 5

Another Longleaf Pine Problem (Florida) 6

A Red Fir Problem (Oregon) 8

A Yellow Poplar Problem (North Carolina) lO

Another Yellow Poplar Problem (North Carolina) la

An Adirondack Problem 13

A Spruce Problem 14

Another Spruce Problem 16

A White Pine Problem (Minnesota) 17

A Shortleaf Pine Problem (Arkansas) 18

Influence of Forest Fires on Rate of Interest 20

Stumpage — Prices of the Future 21

Forest Taxation in the United States 22

Influence of Taxes on Business Forestry 23

A National Park Problem (Minnesota) 24

State Loans for Forestry Purposes (Pennsylvania) 25

Weeding and Road-building 26

A LONGLEAF PINE PROBLEM (FLORIDA).

PREMISES : Mr.' S., of E., Florida, owns a pine forest of all
ages, so that seedlings, saplings, poles and trees are equally mixed,
and estimates that the annual growth is 250 feet board measure per
acre. The tract is 100,000 acres and he thus cuts 25,000,000 feet
board measure annually with the view of not decreasing the growing
stock. The expense for taxes and the cost of protection from fire,
etc., is 5c per acre per annum ; the value of the stumpage is $1 per
thousand feet board measure. Mr. S. thinks that the quality of the
forest will be improved gradually, and expects an increase in pro-
ductiveness, of one per cent, annually. He figures, besides, on ris-
ing stumpage prices, the rise keeping step with the increase in pop-
ulation {i}4 per cent.). He has a chance to invest money at 5 per
cent, in an equally safe manner and wants to sell the forest.

QUESTION : Below what price per acre is it not advisable
for Mr. S. to sell ?

POINTS :

1. Mr. S. must figure at 5 per cent, interest, as the equally
safe investment promises him 5 per cent, as well.

2. If the productiveness of the forest increases by i per cent,
per annum, and the stumpage price at i}4 per cent, per annum, the
receipts will grow at the rate of 2}4 per cent, per annum. In dis-
counting these receipts backwards, we have to figure at 5 per cent.
— 2)4 per cent. = 2}i per cent.

3. The present value of all annual receipts is $25,000

0.050 — 0.035

4. The present value of all expenses (taxes and protection) it
100,000 X 0.05

005

EQUATION : 25,000 100,000 x 0.05 _

0.050—0.025 0.05 ~ ^

RESULT : $900,000 for the whole forest, or $9 per acre.

ANOTHER LONGLEAF PINE PROBLEM (FLA.)

PREMISES : Near Pensacola, Florida, a tract of 50,000 acres
stocked with longleaf pine, not boxed for turpentine, is for sale, the
stumpage averaging 3000 feet board measure per acre. The present
owner offers the stumpage alone at $1 per thousand feet, or else is
willing to sell the fee simple (soil and trees together) at $3.50 per
acre.

Under conservative lumbering, the annual production of timber
is 133 feet board measure per acre, to be drawn from a growing
stock of 1500 feet board measure per acre. The land itself is prac-
tically unfit for farming. No damage is to be feared from forest
fires, as long as turpentine is not obtained from the forest. Figure
at 6 per cent, interest, and at ic taxes per acre per annum.

QUESTION : Is it advisable for a Pensacola mill firm, of
twenty-five million feet annual capacity, to buy the stumpage alone,
or is it more profitable for it to acquire stumpage and land together
with a view of practicing forestry ?

POINTS:

1. When buying the fee simple, the firm can cut, within three
years, 1500 feet per acre— the biggest trees— leaving the balance of
1500 feet on the ground, and obtaining from that balance henceforth
on an annual average as much as the annual accretion, namely 133
feet board measure (worth 13.3 cents) per acre.

2. Thus the firm obtains from the forest

(a) For three years annually 500 x 50,000 feet board measure
worth $25,000.

(b) From the fourth year on, annually 133 x 50,000 feet board
measure worth $6,650.

3. The expense for taxes will, for the whole tract, amount to
$500 annually.

4. The firm paying $3.50 x 50,000 equal to $175,000 cash
obtains assets worth 25000 (1.06*— i) , 6650 500

0.06 X 1.06^ ' 1.06^ X 0.06 0.06

EQUATION : Entrepreneur's Gain

25000 (1.06=^-1) ^ 6650 500 ^ -QQQ

0.06 X 1. 06^ ' 1.06^x0.06 0.06

= 25000 X 2.67 -{- 6650 X 14.0 — 500 X 16.7 — 175000

= 66750 ] 93100 — 8350 — 175000

RESULT : Bent on forestry, the firm seemingly incurs an
undertaker's loss of about $25,000, paying more for the forest than
the forest is able to refund.

If, however, the prices of stumpage can be expected to rise by
50 per cent, in the course of the next 20 years (corresponding with a

rise of 2 per cent, per annum), acquisition of tiie fee simple at $3.50
per acre implies a net gain of about $33,600.

In addition it must be remembered that the tract, under destruc-
tive lumbering, cannot be logged over in less than six years, the mill
capacity being 25 million feet board measure only.

Thus the firm, when engaging in ordinary lumbering, pays in
fact more than $1.00 per looo feet board measure, namely
$150,000 X 0.06 X 1. 06^

25,000 (1.066 — I) "" ^^-22

If this consideration holds good, acquisition of fee simple and
practice of forestry is preferable even under stagnating prices,
being by about $11,700 superior to destructive lumbering.

A RED FIR PROBLEM (OREGON).

PREMISES : Mr. W r, a Michigan lumberman, had a

chance to acquire, in 1862, 200,000 acres of splendid white pine forest,
at 40c per acre. He had made 7 per cent, on the investment, and a
total net gain of $1,200,000 when the last tree was cut in 1888.

In 1900 Mr. W r moved to Oregon, and had a chance in the

Cascade backwoods to exactly repeat the speculation of 1862, buy-
ing 200,000 acres of splendid Douglas fir, scaling 30,000 feet board
measure per acre, at 40c per acre.

The value of the denuded land, in Michigan and Oregon, is nill.
Taxes ic per acre per annum.

QUESTION : What must be the development of stumpage

prices in the section referred to, if Mr. W r is again to make a

net gain of $1,200,000 in addition to deriving 7 per cent, from the
investment, in the course of 26 years ?

POINTS :

The answer depends on the rate, at which the railroad system
in the section will be developed, by the establishment of which the
gradual removal of the timber will be made possible.

I. Suppose cutting begins after 16 years, in I9i6and ends in
1926.

1. The average cut will be 600 million feet board measure per
annum, worth 6oo,oooX. The receipts for stumpage, in 1926, will
have accumulated to 600,000 X (1.07'° — i)

0.07

2. The accrued expense for taxes will be, at ic per acre per
annum, 2000 (1.07^^ — i)

0.07
if we assume, that taxes on the whole land are paid until 1926.

3. The original price paid for the land, $80,000, has grown up,
at 7 per cent, compound interest, to year 1926, to $80,000 x 1.07-'^.

EQUATION :

600,000 X ( 1 .07'" — I ) 2000 ( 1 .072**— I )
1,200,000 = ^^ - ^^ _ 80,000 X 1.0726

RESULT: The stumpage price of Oregon pine, in that sec-
tion, must average about 22 cents per 1000 feet board measure, from
16 years from to-day on.

II. Suppose cutting begins after 10 years, in 1910, and ends in
1926.

I. The average cut will then be 6,000,000,000 =375 million feet

16

board measure per annum. The receipts from stumpage in 1926
will have accumulated to 375,000 X (1.07^^ — i)

2. and 3. asunder I. 0.07

EQUATION :

..«o,ooo= ^"■°°°^.'„7'"-"-'gg^i^g^=il-8.,..ox...7»

RESULT : The stumpage price of Oregon pine, in that sec-
tion, must average about 17 cents per 1000 feet board measure, from
10 years from to-day on.

II II

II II

II II

II II

A YELLOW POPLAR PROBLEM (N. C).

PREMISES : A careful tally of the yellow poplar trees, stand-
iug in the valley drained by Claw Hammer creek, furnishes the fol-
lowing data :
1090 trees of 1% foot diameter, containing 300 feet b. m. each,

equal to 327,000 feet b. m.

1980 trees of 2 foot diameter, containing 450 feet

b. m. each, equal to 891,000

860 trees of 2>^ foot diameter, containing 700

feet b. m. each, equal to 602,000

680 trees of 3 foot diameter, containing 1000 feet

b. m. each, equal to 680,000

270 trees of over zVz foot diameter, containing

1700 feet b. m. each, equal to 459,000

The stumpage of these trees is worth, on an average.
In the case of trees of i>^ foot diameter, . $0.75 per 1000 feet b. m.
In the case of trees of 2 foot diameter, . . 1.25 per 1000 feet b. m.
In the case of trees of 2}^ foot diameter . 2.50 per 1000 feet b. m.
In the case of trees of 3 foot diameter . . 4.25 per 1000 feet b. m.
In the case of trees of over z}i foot diameter 6.25 per 1000 feet b. m.

The trees, up to 2%. foot in diameter, are growing at a rate of
lyi inches in 10 years, and thereafter at a rate of i inch in 10 years.

The taxes are not apt to be reduced after the timber is cut.

The owner believes, that the price of poplar stumpage will
double in 25 years (annual increase of 2}^ per cent), and is satisfied
to make 5 per cent on the investment.

QUESTION : At what rate shall the owner dispose of the
trees, viz. down to what diameter limit is it advisable for him to
sell the trees ?

POINTS :

1. Atreeof I j^ foot diameter, in 40 years, attains 2 footdiameter
A tree of 2 foot diameter, in 40 years attains . . 2% foot diameter
A tree of 2>^ foot diameter, in 60 years attains. . 3 foot diameter
A tree of 3 foot diameter, in 60 years attains . . . 2% foot diameter

2. The lyi, foot tree, now worth $0.75 x 0.300 = 22>^ cents,
will be worth after 40 years $1.25 x 0.450 x i.o2S«' =z . . . $ 1.52
The 2 foot tree, now worth $1.25 x 0.450 = 56 cents, will be

worth after 40 years $2.50 X 0.700 X 1.025^ = 4.72

The 2>^ foot tree, now worth $2.50 x 0.700= 175 cents, will

be worth after 60 years $4.25 x i.ooo x 1.025'* = • • 18.70
The 3 foot tree, now worth $4.25 x i.ooo = 425 cents, will be

worth after 60 years $6.25 x 1.700 x 1.025^ = . . . . 46.80

3. All trees, growing at a 5 per cent, rate, are to remain ; those
growing at a rate of less than 5 per cent, will be cut.

10

EQUATIONS :

For lYi foot trees : 0.225 x i.oX*" = 1.52; X = 5 per cent.

For 2 foot trees : 0.562 x i.oX*^ = 4,72; X = S/4 per cent.

For 2y^ foot trees : 1.750 x loX^" = 18.70; X = 4 per cent.

For 3 foot trees: 4.250 x i.oX«o = 46.80; X = 4 per cent.

RESULT : The owner should dispose of all trees having a
diameter of 2}4 foot or more, as they grow only at a rate of 4 per
cent. Obviously, unsound trees which are apt to deteriorate, should
be cut at once whatever the diameter be.

II

ANOTHER YELLOW POPLAR PROBLEM (N.C.)

PREMISES: Pisgah forest contains 40,000 acres, stocked
with 60 million feet board measure yellow poplar of superior quality,
worth now $3.50 per thousand feet board measure. The owner
expects that the prices of yellow poplar stumpage will double within
the next 15 years (increase of 5 per cent, per annum), and that then
small logs and defective logs will have a value as well, so that 70
million feet board measure will be available in the year 1915.

The taxes and the general expenses take six cents per acre per
annum

The value of the soil, after the timber is cut, can be assumed to
be $2 per acre.

The owner figures at 6 per cent, interest.

QUESTION : What is the profit from the investment, if any
at the end of the next 15 years, aside from the interest of 6 per cent?

POINTS:

1. The present value of the investment is $60,000x3.50 for the
trees and $40,000 x 2.00 for the soil.

2. The value of the forest in 1915 is $70,600 x 7.00 for the trees
and $40,000 X 2.00 for the soil.

3. The running expenses from 1900 to 1915 are, per annum,
$0.06 X 40,000. They accumulate up to 1915, to the sum

0.06 X 40,000 (1.06'^ — I )

0.06

EQUATION : X = 70,000 x 7.00 J^ 40,000 x 2.00 —

0.06 X 40,000 (i.o6'5 _ i)
1.061^(60,000 X 3.50 -\- 40,000 X 2.00) ^-^

RESULT : The owner will find himself $182,000 short. He
will lack a good deal from making 6 per cent, on his investment.
As a matter of fact, he will make about 4 per cent, on the invest-
ment and no more, unless the stumpage prices do more than double
within the next 15 years.

13

AN ADIRONDACK PROBLEM.

PREMISES : A tract of land in the Adirondacks, acquired in
the year 1876 at $5 per acre, was cut over in i888, yielding then,
per acre, 1800 feet b. m. White pine, worth $3 per thousand feet
b. m., and 2600 feet b. m. Spruce, worth $1 per thousand feet.

In the year 1896, there were cut per acre another 6550 feet b. m.
of spruce, worth $1.50 per thousand feet b. m.

The taxes on the forest were Sc per acre per annum ; the
expense of administration and protection 2c per acre per annum.
Figure at 6 per cent.

QUESTION : At what cost were those last 6550 feet b. m.
produced ?

POINTS:

I. The price paid for the land, in 1876, was $5 per acre, which
accrued, at compound interest, and up to the year 1896, to $5.00x1.06^

a. The running expenses, during the period 1876 to 1896, were
7 cents per acre per annum, and sum up to the amount of

0.07 (1.06^0 — I)
0.06

3. The yield made in 1888 was $3.00 x 1.8 J- $1.00 x 2.6=$8.oo

Discounted forward to the year of calculation, 1896, this yield,

(which is of course to be subtracted from the various outlays)

amounts to $8.00 x 1.06^.

EQUATION: ^ ^,„ 0.07(1.0620-1)

X = 5 x I.O620 -f ~^-\;^ - 8x i.o6«

RESULT : The cost of producing those 6550 feet was $5.80.
As the value of the 6550 feet is $9.82, the owner has gained, aside
from making 6 per cent, interest on the investment and aside from
having the value of the culled forest for an additional asset, about
$4.00 per acre.

13

A SPRUCE PROBLEM.

PREMISES : A spruce forest contains in the year 1899 per
acre about 4228 feet b. m., consisting of trees scaling 10 inches or
more at four feet from ground.

First case : Suppose that the owner actually cuts down to 10
inches diameter, thus removing now 4228 feet. Then, in the year
1929 he will be able to again cut 2420 feet b. m., cutting again
down to 10 inches. Every 34 years thereafter he will have the
same yield of 2420 feet b. m. The price of the stumpage is $1.40
per thousand feet. The taxes are, on an average, 3c per acre per
annum.

Second case : Suppose the owner cuts only down to 12 inches.
Then the forest will yield,to begin with,36o8 feet b. m. In the year 1919
the owner will be able to cut 2115 feet b. m., and thereafter the same
amount every 24 years. The value of stumpage in this case is $1.50
per 1000 feet. The taxes are, on an average, 4c per acre per
annum.

Third case : Suppose the owner cuts only down to 14 inches.
Then the first yield will be, in the year 1899, 2846 feet b. m. In the
year 1919 the owner will be able to cut 2624 feet b. m., and thereaf-
ter every 21 years the same amount. The value of the stumpage is
$1.60 per thousand feet; the taxes are, on an average, 5c per acre
per annum.

The owner wants to derive 5 per cent, interest and believes in a
gradual increase of the prices, the increase to average 2 per cent,
per annum. The cost of administration and protection is in all cases
5c per acre.

QUESTION : Had the owner of the forest better cut down to
10 inches, to 12 inches or to 14 inches?

POINTS:

1. The maximum difference between expected yields and ex-
pected expenses determines the best course to be followed.

2. In the 10 inch case the yields are

1.03* X 2,420 X 1.40 «- ,^

4,228x1.40 -L 1.03^^ - I ^ * *

In the 12 inch case the yields are

, „ , 1.03* X 2,115 ^ I-SO (to o

3,608x1.50 ^- 1.0324 - I = ^^'^^

In the 14 inch case the yields are

2,846x1.60 4- 1.03x2,624x1.60 _ ^^^^

3. In the 10 inch case the expenses are 0.03 -\- 0.05 $1 60

0.05 ~

*4

In the 12 inch case the expenses are 0.04 -\- 0.05 ,. q

0.05
In the 14 inch case the expenses are 0.05 -p 0.05 «

0.05
EQUATION : (8.14 - 1.60) = (8.86 - 1.80) = (9.56 - 2.00)

6.54 7-o6 7.56

RESULT : Cutting down to 14 inches only, the most con-
servative practice, pays best. It pays by $1 per acre, better than cut-
ting down to 10 inches, and by Soc. per acre, better than cutting
down to 12 inches.

IS

ANOTHER SPRUCE PROBLEM.

PREMISES: A lumberman owns 20,000 acres of spruce land,
from which he has just cut 6000 feet board measure per acre, Z2
inch and over in diameter at the stump, worth $1.50 per thousand.
After another 20 years he will be able to obtain 3320 feet per acre,
cutting again down to 12 inch diameter, and we may expect, that,
after 40 years, the same yield will be obtainable and so on.

The land, when cleared, is said to have some value for pasture
purposes. The taxes are 4cts., the expense for administration, pro-
tection, etc., 8 cts. per acre per annum. Figure at 6 per cent.

QUESTION : What is the forest worth at the present mo-
ment?

POINTS:

1. After 20, 40, 60 (and so on) years, a yield of 3320 feet b. m.,
worth $4.98 can be obtained.

2. The necessary expenses are 4 cents plus 8 cents per acre
per annum.

3. The value of a forest, like the value of a house or a farm or
a business is equal to the present value of all returns, minus all ex-
penses, expected from it.

EQUATION: X= ,^T "^ = "•"" " "^^

RESULT : The forest, after lumbering, is worth 22cts per acre.

If the owner can sell it, for farming purposes, at over 22cts. per
acre, he should certainly do it, provided that he can make, by re-
investing the proceeds of the sale, 6 per cent, in an equally safe
manner.

If the taxes, or the expense necessary for administration, pro-
tection, etc., are 2cts higher per acre per annum than is supposed in
the premises, the owner had better give up the land after the first
cutting, unless he can sell it, for in that case its forestry value is
negative, the necessary expenses devouring all possible profits.

If, on the other hand, there is a good chance for the stumpage

prices to rise, say at the average rate of 2 per cent, per annum, the

cut over forest has a value of

4.08 0.12 _

-^-^ 7- = $2.15 per acre.

1. 042*— I 0.06

The study of future prices of stumpage is of the very greatest

importance for the wood-owner.

z6

A WHITE PINE PROBLEM (MINNESOTA.)

PREMISES : A Minnesota lumberman owns 10,000 acres of
white pine forest, containing 6000 feet b. m. per acre, worth $3 per
thousand. The agricultural value of the land is $5 per acre, when
the timber is removed. Under conservative lumbering, an annual
production of 300 feetb. m. per acre can be expected. Taxes Sets per
acre per annum. Protection from fire, under forestry, i2cts per acre per
annum. Extra logging expenses, under forestry, $4 per acre, at
the first cutting. Lumber prices expected to double in 35 years
(= annual rise of 2 per cent.) Proper growing stock for forestry
2000 feet b. m. per acre.

QUESTION : What interest on the investment will forestry
yield ?

POINTS:

1. The investment, to begin with, is 6000 feet b. m. worth
$3 — $18 per acre plus value of soil worth $5 per acre.

2. The yield under forestry is 4000 feet worth $3 = $12 per
acre to be derived at once, and 300 feet worth poets to be derived
annually thereafter, being the annual production of the 2000 feet left
standing, per acre. The future yields are to be discounted at (X
per cent. — 2 per cent.)

3. The annual expenses, under forestry, are 20 cents. The
extraordinary expenses are $4 per acre, spent at the first cutting.

EQUATION : 18 i 5 = 12 ^ # _ '^° _ 4

^ ^ ^ ' 0.0 X — 0.02 o.oX ^

RESULT: About 7 per cent.

17

A SHORT LEAF PINE PROBLEM (ARK.)

PREMISES: The S. & A. Lumber Co., of B., Arkansas,
owns 100,000 acres of forest stocked, per acre, with 6000 feet board
measure merchantable short leaf pine, and has a mill of thirty
million feet board measure annual capacity. The stumpage is worth
$1 per 1000 feet board measure. The land is unfit for agriculture.
Under conservative cutting the forest will continuously produce 200
feet board measure per acre per annum, after the "Virgin Surplus"
of the forest, consisting per acre of 4500 feet of hypermature and
mature trees, has been removed. Under conservative cutting, the
logging expenses are 10 cents higher per thousand feet board meas-
ure. Prices are expected to rise at i 1-2 per cent per annum. Fig-
ure at 6 per cent. Taxes are ict per acre per annum. Protection
from fire, under conservative lumbering, will cost 3cts per acre per
annum.

QUESTION: Which pays better, conservative or exhaustive
lumbering ?

POINTS:

1. If prices rise at i 1-2 per cent., future yields must be dis-
counted back to the present moment at 6 per cent — i 1-2 per
cent equal to 4 1-2 per cent.

2. Under exhaustive lumbering, the forest will yield 30,000,000
feet b. m. for 20 years, and nothing more. The land, being non-
agricultural, will be thrown away after 20 years. The value of all
yields expected from the forest, minus taxes for 20 years, is there-
fore :

30000 (1.0452" — i) 1000 (i.o62o — i)

0.045 X 1.045^ 0.06 X 1.0620

3. Under conservative lumbering, we withdraw as well annu-
ally 30 million feet from the forest, as long as the mature stock of
4500 X 100,000 equal to 450 million feet lasts, namely for 15 years.

4. From the i6th year on, we cut only the annual production,
namely, 200 x 100,000 equal to 20 million feet per annum.

5. As the extra logging expenses, in this case, are 10 cents
higher, the timber has a stumpage value of 90 cents only, instead of
$1 per 1000 feet board measure.

6. Taxes and protection from fire will cost annually 0.04 x
100,000 equal to $4000.

7. Thus, under conservative management, the present value
of all expected yields, minus expenses for taxes and protection is :

27000 (1.045^^ — i) I 18000 4000

0.045x1.04515 ~ 0.045x1.045^5 ~ ^;5J5

18

EQUATION :
30000 (1.045^ — I) 1000 (1.06^) >^ 27000 (1.045^^ — I) ,

0.045x1.04520 o.o6xi.o6»> < 0.045x1.045'*

18000 4000

0.045x1.045'^ ~ 0.06

30000x13.0 — loooxii.s = 27000x10.7 -}- 400,000x0.5 — 66,700
RESULT: Conservative lumbering pays, by about $43,700,
better than exhaustive lumbering.

«9

INFLUENCE OF FOREST FIRES ON RATE OF

INTEREST.

PREMISES: Absolutely safe investments (f. i. U. S. bonds)
yield about 3 per cent, interest on the principal.

Forestry in America is a less safe investment. Of course, trees
live and grov7 as sure as the sun shines, the wind blows and the
rain falls, for sunshine, air and rainwater are the components of
wood fibre. Still the ravages of forest fires endanger both capital
and returns from capital.

In the Southern Alleghanies, 2 per cent, of the woodlands, on
an average, are annually damaged by fire. Nature will require 20
years for the restoration of the burned forest to its former value and
productiveness.

QUESTION : What is the minimum rate of annual interest
which forest-growth, under these conditions, must yield ?

POINTS:

1. 98 acres out of 100 acres are left intact, 2 acres out of 100
acres suffer a reverse resulting in a setback of 20 years.

2. Hence the value of those 2 acres is reducd to yao of
what it was to begin with.

3. The growth of every 98 units of value left intact must
make up for the loss through burning in such a way, as to bring the
value of the total investment, at the end of the year, up to 103.

4. The 98 develop into the value 98 x i.oX. This value, plus
what remains of the 2 units damaged by fire, must be 103 if the in-
vestor shall make 3 per cent, on the original principal.

EQUATION : 98 x i.oX ' — %^ =- 103

RESULT : 4 1-4 per cent. Unless those sections of the forest,
which are left intact, grow at a rate of 4 1-4 per cent., the owner
does not make 3 per cent, of absolute interest on the whole
investment. It will pay the owner to annually spend up to i 1-4
per cent, of the investment for forest protection, if by such expen-
sive precaution fires can be entirely avoided.

Where fires result, on the annual average, in the entire destruc-
tion of 5 per cent, of the forest, the annual production on areas left
intact must amount to at least 8.4 per cent, if the entire investment
is to bring 3 per cent, interest. Such a production is impossible,
unless the price of standing timber doubles within the next 15
years.

20

STUMPAGE PRICES OF THE FUTURE.

PREMISES: Virgin forest is unproductive, because, annu-
ally, just as much timber is lost, through death and decomposition
of trees, as there is produced under the influence of sun, rain and
wind.

Cut over forest is, as a general rule, almost unproductive,
owing to fires following the removal of the virgin growth.

Hence it is safe to say, that the annual production of timber in
the 700 million acres of American woodlands is not over one-fifth of
what it might be, (namely, 200 feet board measure per acre) and is
not likely to exceed 40 feet board measure per annum per acre, or
28 billion feet board measure on the whole.

The total growing stock of timber in the United States is esti-
mated to be 900 billion, and the annual consumption is estimated to
be 39 billion feet board measure, (exclusive of firewood).

It is expected that, after the exhaustion of the American virgin
surplus of timber, prices of stumpage will be at a level with those
prevailing in No-Surplus countries, where, f. i., prime white oak
stumpage is worth $75 instead of $3 here, and prime pine stumpage
is worth $15 instead of $1.50 here, per thousand feet board meas-
ure.

QUESTION : At what annual rate can we expect the stump-
age prices of oak and pine to rise, whilst our surplus is being grad-
ually exhausted ?

POINTS :

1. The annual consumption of timber exceeds the annual pro-
duction by at least 11 billion feet.

2. Hence our surplus stock of 900 billion will be consumed in

equal to 82 years.

3. After 82 years, stumpage of oak will be worth about 25
times, and stumpage of pine will be worth about 10 times of what
it is worth now.

EQUATION : Oak : 3.00 x i.o X^^ = 75.00
Pine : 1.50 x i.o X^^ = 15.00

RESULT : The price of oak stumpage can be expected to
rise at a rate of about 4 per cent, per annum ; the price of pine
stumpage at a rate of about 3 per cent, per annum.

21

FOREST TAXATION IN THE UNITED STATES.

PREMISES: In America taxes depend on the value of prop-
erty. In the less densely settled sections, where most of our for-
ests are situated, the taxes amount to i per cent, of the property
value.

Given a forest, vrhich when 90 years old contains $20 worth of
timber per acre. The soil alone, when cleared, is worth only $1
per acre. Rate of interest 4 per cent.

QUESTION : What taxes ought to be justly imposed upon
the owner,— if taking i per cent, of the forest value is just taxation
— at the 6oth and 30th year of the development of the forest, and
further, in the year, in which the seedlings were just starting ?

POINTS:

1. The taxes being i per cent, of the value of the forest, that
value — a prospective value— must be ascertained for the years 60,
30 and o.

2. The forest 90 years old is worth $21.00— $0.21, the 21 cents
being the amount of taxes due in the year 90,

go
$21.00 — $0.21 equals $^^ x 21

... , , $ 99 X 21 $ 99 X 21 ^ I

The forest 89 years old is thus worth- ^^ ^ ^ ^^— ^^^ ^ ^ ^^ x -_

^q"^^ *° [^]

21

100 J 1.04

The forest 88 years old is thus worth f 99 T ^ 21

I 100 J 1.042

The forest 87 years old is thus worth f 99 ] ^ 21

I 100 J

3. The forest 60 years old is thus worth

4. ""The forest 30 years old is thus worth f

5. The forest o years old is thus worth

EQUATIONS:
Taxes in forest 60 years old i ( 99 1 ^' ^i

L 100 J

100 i^ 100 J 1.04^"

Taxes in forest 30 years old i f 99 1 " 21

L 100 J

100 L 100 J 1.04^
Taxes in forest o years old i f 99 1 *' 21

100 I 100 i 1.04**
RESULT: At 60 years 4 7-10 cent.
At 30 years i i-io cent.
At o years 2-10 cent.

22

INFLUENCE OF TAXES ON BUSINESS
FORESTRY.

PREMISES : The premises are just as in foregoing problem.

QUESTION : To what figure do the taxes (paid from the first
to the 90th year of the forest) accumulate up to the time at which
the timber is mature, namely, up to the 90th year ?

POINTS:

I. Taxes in the year 0 of the forest are

I r 99 1 ®^ 21

100

100

1.04'

90

which, discounted to

the year 90, amount to
2

to

21

L 100 J

91

100 I- 100

Similarly, the taxes paid in the year i of the forest accrue
21
100 ^- 100

f 99 ^ 90

I ] and the taxes paid in the year

f 99 1 s**

— ^^- and so on.
L 100 J

2 of the forest accrue to —

100 >- 100

3. Thus the discounted values of the taxes form a geometrical

99
progression of 91 numbers, with ^^ for the constant factor.

EQUATION : Sum of taxes equal to
21 L 100

100

LiooJ

z=2I

1 100 J

RESULT: The sum of taxes paid, accrued at compound
interest is $12.60, and thus takes away 60 per cent, of the final
yield obtainable.

It is especially noteworthy, that the rate of interest used does
not influence the accrued sum of taxes in the least. The sum simply
depends upon the number of years required to develop merchantable
timber out of seedling trees.

It is safe to say that, under the conditions now prevailing in
America, the taxes consume over one-half of the value of the yield
derivable from forestry, if they are "justly " imposed. No wonder,
then, that people are averse of engaging in forestry.

If the rotation is 150 years, the taxes curtail the final yield by
77 per cent!

23

A NATIONAL PARK PROBLEM (MINNESOTA).

PREMISES : It is proposed to establish a national park in
Northern Minnesota, on land unfit for farming, stocked with about
6000 feet board measure pine timber per acre, worth $2.50 per
thousand feet board measure.

Four thousand feet board measure, per acre on an average, con-
sists of mature or hypermature timber, whilst the balance is thrifty,
and can be expected to yield by its own growth and by giving rise
to a second growth, 150 feet board measure per acre per annum,
under conservative management.

In this case the first logging expenses •will by 50 cents per acre
exceed the logging expenses under destructive lumbering.

Taxes, protection from fire and administration will take locts per
acre per annum. Five and one-half per cent, interest. — Stumpage
prices expected to double in 35 years (corresponding with an annual
increase of 2 per cent.)

QUESTION: Will conservative lumbering, in this case, pay
better than destructive lumbering ?

POINTS:

1. Under destructive lumbering, the value of the forests is 6000
X 2.50 equal to $15 per acre.

2. Under conservative lumbering, 4000 feet are cut at once,
and 2000 feet are left standing as a permanent investment, yielding
annually 0.150 x 2.50 equal to 37 )4 cents per acre, from which fig-
ure, however, the annual expenses of locts must be deducted.

EQUATION : 15 ^ 10.00 - 0.50 4 °-^75
< 0.035.

RESULT : Under conservative lumbering, an enterpren-
eur's gain of about $2.50 per acre is obtained. Hence conservative
lumbering pays better.

Unless the first logging expenses under forestry are by $3.00 per
acre higher than is usually the case, destructive lumbering is finan-
cially inferior to conservative lumbering.

After destructive lumbering, the land is left worthless. Under
conservative lumbering $10 are withdrawn from the forest, and
there remains a permanent asset of about $8 per acre on the
ground, yielding SH Pcr cent, interest per annum.

24

STATE LOANS FOR FORESTRY PURPOSES.

PREMISES : The state of P. decides to engage in state for-
estry, and to that end takes up a loan of $1,450,000, at 4 per cent.,
which is to be used as follows :

$1,000,000 for purchase of 1,000,000 acres at the headwaters of
the rivers,

$ 50,000 for lawyer's fees, surveys, demarkation, etc.,

$ 150,000 for roads, etc.,

$ 250,000 for defraying the annual salaries of superintendents
and rangers. After the road system is developed, 12 years from
today, an annual revenue of 10 cents per acre per annum will be
derived, under conservative management, and it is expected that
this revenue will gradually increase at the rate of 3 per cent, per
annum.

QUESTION: A: Within how many years will the forest
itself be able to redeem the loan ?

B : What is the forest worth after the loan is
redeemed ?

POINTS :

1. The annual interest on the loan is $58,000.

2. The revenue from the 12th year on is o.io x 1,000,000 =
$100,000, of which $58,000 are used, from that time on, to pay the
interest on the loan, whilst $42,000 or more are available annually
for redemption of loan.

3. As the revenue rises at 3 per cent, per annum, the receipts

are to be discounted at 4 per cent. — 3 per cent. — i per cent.

EQUATION: . 42000(1.01" — i)

A: ^- ^ ^— 1,450,000

o.oi X 1. 01" '^^ '

3. 100,000 X 1.03^" _

o.oi ~

RESULT : A : The loan can be entirely redeemed within 43

years after the 12th year, or within 55 years from today.

B : The forest, freed from all incumbrances after

55 years, and producing annually $356,000 with prospect of an

annual increase of revenue equalling 3 per cent., is worth about

$35,600,000.

If the people are ready to spend $58,000 for 12 years, they will

gradually build up a very valuable forest.

Far-leading calculations in forestry might seem fallacious and

absurd, if forest-history had not proved the very contrary.

25

WEEDING AND ROAD-BUILDING.

PREMISES : Given a spruce forest in the Adirondacks,
containing 50,000 acres stocked with 4,000 feet b. m. per acre. The
forest is to be cut over at once in such a v^ay as to reduce the
average stumpage to 1,200 feet b. m., which are expected to produce
thereafter 140 feet b. m. per acre per annum. Stumpage is worth
$1.50 per 1,000 feet b. m. Cuttings recur every 10 years.

QUESTION : A : Is it advisable for the owner, to remove, by
way of an additional "weeding," the misshapen trees at an expense
of 50 cents per acre, if by so doing the annual production can be
raised from 140 feet to 175 feet b. m. per acre ?

B : Is it advisable for the owner to build the
skidding roads more solidly, at an expense of $10,000 so as to make
them available for future operations, and so as to be less depend-
ent on the snow-covering, if by so doing the logging expenses
per 1000 feet b. m. can be reduced by Sets ?

POINTS : A : The additional expense of 50 cents results

in producing, every ten years, an additional 350 feet b. m. worth

52>^ cents.

B : The additional expense of $10,000, reduces

the cost of logging, and hence increases the value of stumpage,

by 5cts per 1000 feet. The first cut, therefore, of 50,000 x 2800 =

140,000,000 feet b. m., gains $7,000 ; the subsequent cuttings, of

50,000 X 1750 = 87,500,000 feet b. m., gain $4,375.

EQUATION : A : 0.50 == ^^^^

B : 10,000 = 7,000 -?- -^^f

i.oX'" — I

RESULT: The "weeding" as well as the solid construction
of roads are advisable, the former paying 7 per cent, and the latter
g)4 per cent, interest on the additional outlay required. The advan-
tage derived is greater still, if stumpage prices are on the increase.

26