United States

Department of

Agriculture

Forest Service

A Method of Assessing

Risk in Forestrv

Southern Forest

Experiment Station Investments J

New Orleans,

Louisiana

Research Paper

SO-1 89

March, 1983

Robert J. Engelhard and Walter C. Anderson
SUMMARY

A method for evaluating investments that considers associated risks is

described and its application to forestry illustrated. The outcome of many

forestry investments is highly uncertain because of the long production period involved. Nevertheless, forest managers often rely on a single predicted

rate of return as the best estimate of the payoff using that value as if it were

certain. None of the methods used for recognizing risk indicate the chances

of achieving the predicted rate of return. David B. Hertz, a management consultant, developed a practica1 means for computing the odds of achieving the

expected return from an investment. The technique, which incorporates risk

information and Monte Carlo simulation, can be applied by forest managers

to make better choices.
A Method of Assessing Risk in Forestry Investments

Robert J. Engelhard and Walter C. Anderson

INTRODUCTION

When costs are accelerating and market interest

rates for capital are high, refined techniques for analyzing forestry investments are essential. Competition for available capital is keen and forest managers,

who have little direct control over the size of their

budgets, must present complete, rational analyses to

convince decision makers, unfamiliar with forestry,

of the desirability of proposed investments. Investment decisions are also challenging because of the

difficulty of attaining long-term investment objectives when unwise investments are not easily avoided

and very costly when they occur. To screen investment proposals with greater precision, forest managers need a technique that enables them to not only

predict rates of return but also indicates the likelihood of their being achieved.

plant one-third more seeds than the number of seedlings desired. The second type of risk is that for

which statistical probabilities can be established,

such as destruction by forest fires, but an individual

owner does not know when or if fire will strike his

forest.

Knight, in Risk, Uncertainty, and Profit, a book

which has become a classic of economic literature

since its publication in 1921, pointed out that the

time required for the production of a good introduces

uncertainty (Knight 1921), and the longer the interval before the outcome is known, the less certain

the outcome. Since timber growing is one of the

longest production processes employed by man, uncertainty is always present.

Although foresters have long been aware of risk

in forestry investments, risk has usually not been

formally incorporated into investment analyses. The

deterministic models commonly used are based on

the twin assumptions of complete knowledge and

certainty of future events. Even though the model

may be mathematically precise, it predicts only a

single rate of return, considered to be the “best estimate.” When faced with single estimates, those who

make investment decisions may protect themselves

against selecting any of the riskiest investments by

setting a high expected rate of return that must be

reached or exceeded for a proposal to be accepted.

Knight recognized two classes of uncertainty in

investments: measurable and unmeasurable (Knight

1921). The term “risk” designated the former, and

the term “uncertainty” the latter.

A commonly applied technique to account for risk

in forestry is adjusting the discount rate by adding

a premium. Where the interest rate is low and duration of the investment short, this is an acceptable

and reliable method. Where these two conditions do

not exist, however, the allowance for risk is often

much too great (Duerr 1950, Guttenberg 1950). An

alternative is to either scale down prospective returns or scale up costs.

Worrell applied Knight’s classifications to situations in forestry where knowledge about future outcome is lacking (Worrell 1959). He gave as examples

of uncertainties: technological changes, sociological

changes, and legal changes. He separated risks into

two types. One type of risk exists when the characteristics of the outcomes are known in advance. For example, when germination tests show that 75 percent

of the slash-pine seed collected in an area during a

particular year is viable, the nursery manager can

Another method frequently used to recognize risk

is to calculate rates of return based on high and low

values. Although the pessimistic and optimistic estimates indicate the possible range of results, they do

not indicate which is most likely to occur.

None of the conventional techniques provide decision makers with a realistic measurement of the

risks involved in selecting opportunities for capital

investment. The reason is easily explained with an

example. If six factors have been identified as significantly affecting the outcome of a particular investment and the expected value for each has a 60 percent

chance of occurring, conventional analysis would preEngelhard is professor of forestry, University of Wisconsin-Stevens Point. Anderson is principal economist, Southem Forest

Experiment Station, USDA Forest Service, New Orleans, Louisiana. This paper was initiated while Engelhard was employed

at the Southem Forest Experiment Station under an Intergovemmental Personnel Act appointment.

1
dict the actual outcome less than 5 percent of the

time ( 0.66 = 0.047).

An ideal method for evaluating forestry investments would explicitly consider risk. A method that

does this was developed by David B. Hertz, a management consultant (Hertz 1964).

This paper describes the Hertz method and illustrates its application to capital investments in forestry.

THE HERTZ METHOD

The Hertz method is a computer-based capital investment risk analysis procedure involving Monte

Carlo simulation. Monte Carlo simulation is a technique for numerically exploring a system by repeatedly sampling proabiltiy distributions of the variates

specified in the model. This paper describes the process in detail.

The two initial steps in the process are to indentify

both cost and income variables affecting the outcome

of investment, and to construct a risk profile for each

variable. This is done by collecting al1 available information from historical trends, statistical studies,

management records, experienced judgments, and

other sources, and then weighing and combining the

information.

A risk profile can be represented as a probability

distribution curve with the range of outcomes measured along the horizontal axis, and the chances of

each outcome value being achieved measured along

the vertical axis. A risk profile for sawtimber stumpage, for example, may show that the chance of the

price being $100 per thousand board feet at harvest

is 20 percent, while the chance of being $150 is only

5 percent. Risk profiles for various input factors may

be bell-shaped, ares, horizontal lines, or have other

forms.

In the third step, one value is randomly selected

for each independent variable from its risk profile.

The set of values selected are then used, in the fourth

step, to calculate the rate of return on investment by

conventional present net Worth, interna1 rate of return, or composite rate of retürn procedures.

These four steps, (a) identifying the significant independent variables that determine investment outcome, (b) constructing risk profiles for each key input factor, (c) randomly selecting one value from the

probability distribution for each factor, and (d) combining the selected values to calculate a return on

investment, are the basic procedures involved. The

remaining steps are based on the repetition of steps

three and four in which the computer repeats the

process of selecting additional sets of values (Step

2

3) and calculating a new rate of return for each set

(Step 4). After severa1 thousand rates of return have

been calculated, the computer lists the results from

the highest to the lowest. From this ranking, the percentage of total situations falling within given ranges

of rates of return are determined.

Finally, the probability of occurrence for each

range of rates of return is cumulated to derive a risk

profile for the proposed investment. The risk profile

will show the chance of earning any given rate of return from the investment. It will also show the maximum return which can be earned as well as the

chance of incurring a loss.

A FORESTRY ILLUSTRATION

To dembnstrate the Hertz method, an investment

in a slash pine plantation was hypothesized. It was

assumed the plantation was established on Site Index 60 (25 years) land in the West Gulf Region, and

was expected to be harvested in 30 years. The results are not intended to indicate the profitability of

growing slash pine in the West Gulf Region.

In this illustration, each step involved in the Hertz

method, as applied to a forestry investment, is described in detail.

The composite rate of return earned on the investment is determined by the present Worth of al1 costs,

and the value of the plantation at harvest.’ Probability distributions of expected costs per acre were

established in consultation with experienced, professional forest managers (table 1). It was assumed

approximately 650 trees would be planted per acre

at 8 X 8 foot spacing using seedlings grown in a contract nursery from seed furnished by the firm.

There are two ranges of planting costs: lower costs

for machine planting and higher costs for hand planting. Three-quarters of the seedlings are to be machine

planted.

Contract costs of site preparation were estimated

to range from $60 to $80 per acre.

Annual property taxes levied by local government

are the major variable in determining annual costs of

management. Ad ualorem taxes range from less than

$1 per acre per year to more than $5.

Conventional investment analyses rarely include

“unlikely” costs, but risk analysis can incorporate

them. For example, replanting with no additional Site

preparation was assumed to be necessary 28 percent

‘For a discussion of composite interna1 rate of return see

Marty, Robert. 1970. The composite interna1 rate of return.

Forest Science 16: 276-279.
Table l.-Expected slash pine plantation establishment and

management costs in West Gulf, with associated

probabilities of occurrence

Cost factor

Year of

cost occurrence

-

@acre

Planting stock 5.85 0

7.15 0

7.80 0

Planting 11.00-18.50 0

22.00-25.00 0

Site preparation 60.00-67.00 0

67.01-73.00 0

73.01-80.00 0

Management 3.00-3.50 Annual

(taxes, annual 3.51-4.00 Annual

overhead, protection 4.01-4.50 Annual

and other yearly 4.51-5.50 Annual

outlays) 5.51-8.00 Annual

Probability of

occurrence

.lO

.20

.70

’ .75

.25

.30

.40

.30

.25

.33

.25

.15

.02

of the time; 18 percent after the first growing season

and 10 percent after the second. It is also assumed

that a chemical release is necessary in the fifth year

on 10 percent of the plantations. The cost is $21.80

to $28.68 per acre (Moak et al 1977). Finally, the

loss of plantations due to catastrophe or changing

land use before any return can be earned is expected

to occur 5 percent of the time.

Costs that occur during the life of the stand were

discounted tc the present at a 10 percent rate.

Similarly, probability distributions were determined for factors affecting revenues (tables 2 and 3).

The plantations were expected to grow at an average rate of from 50 to 100 cu. ft. per acre per year, as

suggested by regional studies (Dutrow 1978). Al1

surviving trees will be harvested 30 years after initial

planting with no intermediate thinnings.

Thirty-year-old slash pine plantations can be expected to yield some saw log material. For stands

having an average of 300 surviving trees per acre at

time of harvest, a ratio of pulpwood-to-sawlog volume of 80: 20 was assumed.

Twenty percent of the total stand volume for

plantations with 300 surviving trees per acre is represented by trees ll-inches d.b.h. and larger and

utilized to a 4-inch top. Ratios of pulpwood-to-sawlog volumes were computed for other average survival

rates assuming the minimum diameter for sawtimber

trees is 11 inches. Stands with fewer surviving trees

will have less total volume but a larger average diameter (Dell et al 1979) and a higher ratio of saw

timber volume, while stands with a greater number

of trees have more volume but small diameter trees

and a lesser proportion of saw timber.

Harvest values per acre in dollars per cubic foot

(table 3) are based on June 1979 prices from !#!%nber

ilhrt South for South Mississippi, Southeast Louisiana and Southeast Texas (Timber Mart South 1979).

Conversions from cord to cubic values assumed 65

cubic feet per cord.2 Scribner values were converted

using the following board foot :cubic foot conversions

by diameter class :

4.85: 1 ll-inch d.b.h.

5.10: 1 12-inch d.b.h.

5.35: 1 13-inch d.b.h.

Once the key input factors determining costs and

revenues for the investment were identified and uncertainty profiles estimated for each, the next step

was to select one value for each factor. The initial

values selected at random were:

Cost of planting stock $ 7.80 per acre

Average cost of planting $12.88 per acre

Cost of site preparation $73.00 per acre

Annual costs of management $ 4.00 per acre

Volume 24.6 CCF per acre

Value of output $ 0.320 per cu. ft.

The composite interna1 rate of return is then calculated for this combination of values by using the

formula :

FVI (1 + R)30 = Pvc

where :

R = composite interna1 rate of return

FVI = future value of allincomes

PVC = present value of al1 costs.

The values of these variables were calculated to be

$131.39 for PVC and $787.20 for FVI. When these

two values were substituted in the rate of return

equation, the value of R was found to be 61% percent.

The process of selecting a set of values and calculating the rate of return is repeated 10,000 times, a

task easily and quickly accomplished by computer.

In the computer program (Appendix) the Monte

Carlo simulation uses a random number generator

with a subroutine to select costs that are discounted

when necessary and summed to determine present

Worth. It also uses a subroutine to compute future

values by selecting the volume range according to

probability of occurrence, and then selecting a volume within the range at random. If the plantation

was selected for replanting, the expected volume is

reduced as follows:

sThe U.S. Forest Service conversion factor of 1.54 cords.per

100 cu. ft. of solid wood (65. cu. ft. per cord) is used by

Region 8 (Southern Region) in the sale of small roundwood

(pulpwood) timber.

3
15.0-20.6 C cu. ft. 50 cu. ft. per acre per year

20.7-24.6 C cu. ft. 70 cu. ft. per acre per year

24.7-30.0 C cu. ft. 90 cu. ft. per acre per year

Next, a value class is selected according to probability, and a value is selected within the range at random. The volume is multiplied by this value. The rate

of return is computed by assigning a negative rate 5

percent of the time to account for plantation loss due

to catastrophe or reversion to another land use. The

investigator can experiment with the number of computations until the distribution of results indicates

that virtually all possible combinations of significant factors have been sampled.

The computer then lists each composite rate of return result, from highest to lowest (table 4). Of the

10,000 calculations made for this investment, 503

resulted in negative returns. From the frequency

table, showing the possible financia1 outcomes for

this investment, the computer determines the percentage of each falling within given ranges of the

positive rate of return, i.e., the probability of their

occurrence.

Finally, these percentages are summed to obtain

the cumulative probability (table 5) and used to derive a risk profile for the investment (fig. 1). This

curve shows the highest return possible and the range

of returns. More importantly, it shows the chances

of equalling or exceeding a particular rate of return.

This method of risk analysis provides decision

makers with more useful information than a conventional analysis. Conventional analysis, using

“most likely” numbers, would predict an expected

return of about 5.1 percent. The results of risk analysis, using 10,000 iterations, indicates that a return

of precisely 5.1 percent can be expected to occur only

about 5 percent of the time (table 4). Risk analysis

also shows that returns from 2.1 to 7.9 percent are

possible. The decision maker will be more interested

in learning that 5.1 percent will be equalled or exceeded 42.7 percent of the time (fig. 1). Also, there

is a 50/50 chance of earning 4.9 percent or more, and

two chances in three of earning 4.3 percent or more

on the investment.

DISCUSSION

An investment in a slash pine plantation in the

West Gulf region was used to illustrate the application of the Hertz method of risk analysis to forestry,

and show what useful information it provides. This

example was chosen because of its suitability for describing the steps involved in the method, and because it is a type of investment foresters are frequently called on to analyze.

The Hertz method is not limited to investments

Table 2.-Expected slash pine pkzntation yields, in West Gulf, with associated probabilities of occurrence

Volume class

at 30 years

(C cu. ft./acre)

Surviving

trees

Ratio of

pulpwood volume

to sawlog volume

Probability of

occurrence

15.1-20.6 200 75:25 .33

20.7-24.6 300 80:20 .50

24.7-28.6 400 85: 15 .15

28.8-30.0 500 85: 15 .02

Table 3.-Expected value of output per cubic foot from slash pine plantation, in West

Gulf, with associated probabilities of occurrence

Value

class

Ratio of pulpwood volume to sawlog volume Probability of

75:25 80:20 85: 15 occurrence

--------.------------. $/C cu. f& --_________ - ---- -_--

Low .220-.290 .195-.260 .170-.230 .25

Medium .291-.360 .261-.320 .231-.280 .60

High .361-.400 .321-.360 .281-.320 .lO

Highest .401-.500 .361-.460 .321-.420 .05
Table 4.-Ranking from lowest to highest of frequencies with which rates of return

occurred, based on 10,000 iterations, for slash pine plantation, in West Gulfl

Rate of

return Rate of return in tenths of percent

(percent) .ooo .OOl .002 .003 .004 .005 -006 .007 .008 .ooQ

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

____ --________ 2-w __________ number- _________-__________------------------.

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 2 0 1 2 5 7 10 l l 2 0

2 6 3 9 3 8 6 7 7 1 8 7 105 134 153 196

211 274 271 322 355 388 419 403 433 453

471 505 482 503 465 453 374 345 267 237

186 160 117 8 8 8 2 6 3 51 3 1 2 9 3 1

2 1 14 5 3 3 4 1 2 0 1

0 0 0 0 0 0 0 0 0 0

1503 null iterations.

Table 5.-Cumulatiue probabilities of occurrence by rates of return, based on 10,000 iterations, for

slash pine plantation in West Gulf

Rate of

return

(percent)

--..-...-

.ooo .OOl

Rate of return in tenths of percent

.002 .003 .004 .005 .006 .007 .008 .OOQ

0.00 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950

0.01 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950

0.02 0.950 0.950 0.950 0.949 0.949 0.949 0.948 0.948 0.946 0.945

0.03 0.943 0.939 0.936 0.930 0.923 0.915 0.906 0.894 0.880 0.862

0.04 0.842 0.818 0.790 0.761 0.727 0.690 0.649 0.608 0.566 0.522

0.05 0.476 0.427 0.378 0.328 0.280 0.234 0.193 0.157 0.126 0.101

0.06 0.080 0.063 0.049 0.039 0.030 0.023 0.017 0.013 0.010 0.007

0.07 0.004 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000

0.08 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

in plantations as in the example, however. It can be

used with capital outlays for a range of diverse purposes such as timber stand improvement, purchase

of a feller-buncher, or installation of a chipping headrig.

In the example, the composite rate of return on

investment was the criteria selected for assessment

of the investment. The Hertz method, however, is not

tied to this single yardstick. Other criteria such as

payback, net present value or average rate of return

can be used if preferred.

There are severa1 respects in which the Hertz

method is superior to conventional techniques for determining the profitability of investment proposals.

One is that it utilizes al1 of the quantitative information available on costs, returns, and risks. It resurrects the early days of profitability analysis by using

many possible values. In those times, foresters agonized over the selection of specific “most likely”

values because so many values were possible. The

risk analysis technique described here allows the use

of al1 possible values weighted by their probabilities.

Also, the Hertz method not only displays conventional “likely” outcome, but specifies the chances of

that result occurring. In addition, a variety of other

choice criteria such as maximums, minimums, means

or variance, together with their expectations, are also

shown. The results, too, are more likely to approximate future outcomes than are predictions from conventional analysis (MacKinnon 1976).

Further, the risk analysis method can be used with

either of the two types of investment decisions forest

managers make. One is to accept or reject a particular propósition. The other, which is a more common

type of decision, is to choose among alternative propositions. This involves comparisons of investment alternatives. The method can also realistically compare

investments of different risk levels, long term investments with short term investments, and forestry with

nonforestry investments.

5
RATE OF RETURN (PERCENT)

Figure l.-Rtik profile for investment in the slash pine plantation based on cumulative probabilities for 10,000

iterations.

An additional benefit of the technique is that it

can show a decision maker the logical conclusion of

a peculiar set of expectations. The individual can

learn the chances of earning at least some particular

rate of return for the magnitudes and probabilities

that were indicated for the various prices and other

factors. This approach is helpful, especially when the

analysis can pinpoint a specific factor as the cause

of most of the uncertainty.

Although the Hertz method is a powerful..and highly useful method of risk analysis, it is based on subjective estimates of the likelihood of various values

for determining variables. This is shown by the illustration. The subjective nature of the process is a

principal reason the results imply lower rates of return than foresters familiar with the region would

expect. Generalized regional data were used that, of

necessity, exaggerated the risks for an individual firm.

A forest manager usually has some control over certain aspects of risk. In the illustration, for instance,

planting losses could be reduced by grading the seedlings and properly handling the stock between the

nursery and the planting site. The assumption that

the results of the risk analysis are representative of

the “real world” may be incorrect.

Another example of how the process is based on

subjective estimates of the likelihood of various values for determining variables is the group of stumpage values used in the illustration (table 3). These

values cannot arise from any objective sampling of a

future market, but are the decision maker’s best

guess about the likelihood of various prices occurring.

This means that the probability function (fig. 1)

derived from these estimates is also subjective, and

therefore may not represent the real world as an objective function would. Also, in the subjective case,

it is not possible to determine how closely the estimate approximates reality. A confidente band cannot

be established around the curve.

The Hertz method of risk analysis provides a

formal procedure for quantifying risk in forestry investments. It is a tool for majo, decisions. When

properly used, it will enable forest managers to make

better investment choices.

LITERATURE CITED

Dell, T. R.; Feduccia, D. P.; Campbell, T. E.; Mann,

W. F. and Polmer, B. H. Yields of unthinned slash

pine plantations on cutover sites in the West Gulf

region. Research Pap. SO-147, New Orleans, LA:

U.S. Department of Agriculture, Forest Service,

Southern Forest Experiment Station; 1979. 84 p.

Duerr, William A. Fundamentals of forestry economics. McGraw-Hill Book Co., Inc., New York.

1960.579 p.

Dutrow, George F. Economic management opportunities to increase timber supplies in southern United

States-some preliminary and tentative results.

In, McMillin, Charles W., ed. Complete Tree Utilization of Southern Pine: Proceedings of a symposium; 1978 April17-19; New Orleans. Madison, WI:

Forest Products Research Society;’ 1978: 6-14.

Guttenberg, Sam. The rate of interest in forest management. Journal of Forestry. 48 (1) :3-7. 1950.

Hertz, David B. Risk analysis in capital investment.

Harvard Business Review. 42 (1) :95-106. 1964.

Knight, Frank H. Risk, uncertainty and profit. London School of Economics and Political Science. Reprints of Scarce Tracts No. 16. 1921. 381 p.

MacKinnon, D. A. Risk must be known and assessed

before selecting capital projects. Pulp & Paper.

50(6) :108-111.1976.

Moak, James E.; Kucera, James M.; and Watson,

William F. Current costs and cost trends for forestry practices in the South. Forest Farmer. 34 (5) :

16-21. 1977.

Timber Mart South. Vol. 4, No. 6. June 1979.

Worrell, Albert C. Economics of Ameritan Forestry.

John Wiley & Sons, Inc.; New York. 1959.441 p.
INITlALlfE VARIABLES

NUMBER SEED

FOR THE NUMBER

OF ITERATIONS

-7

CALL CDST I

SUBROUTINE

I

DETERMINE RANDOM PLANTING COSTS

CALL YIELD

SUBROUTINE

DETERMINE RANDOM PLANTING LABOR COSTS

+,

DETERMINE RANDOM

YIELD AT HARVEST CALCULATE CIRR

I DETERMINE RANDOM SITE PREP COSTS

l

DETERMINE RANDOM INCREMENT TAELE VALVES ---I

DETERMINE PLANTATION SURVIVAL STUMPAGE VALUE

CALCULATE PRINT MEAN

DETERMINE RANDOM CALCULATE THE FUTURE MEAN 8 S.D. - S.D. 8 NULLS

CHEMICAL WEED TREATMENT COST VALUE OF INCOME FROM HARVEST

DETERMINE RANDOM

ANNUAL LAND MANAGEMENT COST

CAtCULATE PRESENT VALUE OF LAN0

MANAGEMENT COST OVER 30 YEARS
i~****t*t**tt**~f*******~***~*~~~~*~~~*~******~*~**~~***~*******~~*~***~

c- HERTZ-MONTE CARLCI PROFITABIL.ITY MEASUREMEN7

i:-.

c -’ HMCF’M IS A SIMULATIQN QF MANAGEIIIENTPROFITABILITY FOR PLANTED

(:; . . . . SL.ASH PINE IN THE GIJLF: COAST +

cc -. DEVELOPED EY : ROEfEHT 3.1 i ENGELHARD

c- I~‘HOGRAMMED BY : FREDER I C:K M e H ILF:‘E:R”l -\l-., IJMIVERSITY OF WISCONSINY STEVENS P:‘T.)INT

c -. 1979

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REAL IHR

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15 CONTINUE

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I

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8
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Y =-el0

DO 80 I=i,âO

WRITE(697O)Y9 (PERC(J) 9 J::IFr Il,>

7 0 FORMAT( ’ ‘9F5,29iX9iOF6,3)

IF=IF+IO

ILr=ILtlO

Y=Yt *Ql.

80 CONTINUE

l

.’ .

.,

c”- CALCULATE AUl3AGE AND STANIlARD DEVIATIUN

cN- I’l’El?-4IJLL..

AUG-SUM/N

SB-SQWT ( ( SS- ( SUMdSlJM 1 /N 1 /‘N 1

WRITE~69S’O~AVG9SD9NULL

90 FClRMAT(//‘O’r’AVERAGE= rFb+3/‘0* 9’S+ II+=’ 9F8+3/'0'9

* ‘NUL.1.. ITERATIONS? 9 Iá/////>

CALL EXIT

END

c9
[:: _...._..........__” .-.....--“_..” -....- ---.I-.-------..” -.---.-....-.--. - -.--....--..I . . . . . . ..-.. I_““..” ..-..--.--.._^ . . . . . . . . ..-............- _...._.I.”. .._..^._-.-

[; -....._._.-.__.-.-.._ -.-.. “.““-- -.--..--.-I..^_.I.I.I__ “” -..........“._.” . . . . ..---...... “.-II . . . .“--. . . . . . . . . . . . . . . ..-.- “” . . . . . . . . . . . . . .“.I”..I.“._.“..“.” -.....--........

c:- . SIJBRIJUTINE: L:C)ST (‘JAL P ISEED Y IFLAG 1

c:-

c .‘.. IIETURNS PRESENT UAL.UE QF ESTABLIStJMENT AND MANAGEMENT CGST +

I

.’ -

.,

~;““....--.*- . . . . . “.“......-*..-..“--....-.““....--”......--..”....““.-.-..”.-”” I......“..I_.”.--...... I . . . ..-..- - -._.-_._..^_-.---..” .. . . ...” . . . . . . “___” ..-....._.“...“_

CC- ICIETERMINE PLANTING CGSï

cX=RANBGM ( ISEEKl)

IF~X~GT,O+AND,X+LE~ ,iO~UAL~=5,85

IF(X,GT+ +IOIAND+X+LE+ ,301 UAL. -7+%5

IFtX.GT,+ZO) UAL=7+80

cc .‘.. KSETERMINE L.A.BOR COST

c....

X=l?ANDO# ( ISEEKl)

IFtX,GT,,75) GO TO 10

Y=RANDQM ( ISEEIïl)

XLAE=11+00+7+50bX

GO TG 20

10 X-RANDOM( ISEED)

XLAE=22+00+3+00*X

20 UAL=UAL+XL.AB

c-

(1; . . . . DETEWIINE SITE F’REF:‘AWATION CGST

c....

X=RANDOM ( ISEED 1

IF(X+GT 0 + 301 GO ‘ro 30

X:-RANDOM ( 1 CEE11 1

SITE=7;3,Ol+&+WtX

GO TO SO

30 IF(X+GT, +70) 60 TO 40

X=RANDOM ( ISEE:D ZJ

SITE=67,01$5+V$‘SX

GO TO 50

4 0 X=RANDOM ( I SEED 1

SITE:= + OO+7 + OOrkX

SO UAL=UAL+SITE

(.; “..

c -‘. DETERMINE SIJRUIUAL..

c .“.

X=RANDQM ( ISEED 1

IF(X,GT+,ìS) GO TC) 60

IFLAG=1

UAL=:UAL+~ (UAL-SITE)/i s1.1

GO TO 80

60 IFIX.GT+,28) GO TC) 70

1 FLAG=2

UAL=UAL.+ I f UAL-SITE )/ ( % + ltf2) 1

GO TO 80

70 IFLAG=3

c-
(1; .. . . DETERMINE: CHEMICAL.. WEED TREATMENT COST

cso x-RANSIOMt 1 SEED 1

w (X,GT,0+10) GC? TO 85

X-RANDOM( ISEED 1

CtiE’M=%l e #+6 o 886X

Vhl.hAL+CHE:M/ ( i c 1.tsk5)

cc: -. IKZTERI~INE MANAGE:MENT COSI

c85 X=RANDOM I ISElk 1

IFCX,ET,,f55) GO 10 90

X=RANDOM ( ISEED) ”

CMAN=J * ooa J 5*x

GO TO 130

90 IFo(,GT+ .“jSl cm TO x00

X=+wwlM( :I:SE:ED 1

CMAM=3+51++49SX

GO TO %30

100 IFCX.GT, .83) GO -TO ll.0

X:=RANDOM ( ISEED 1

CMAN= i Oá+ + 49tX

GO TO 130

3.10 IF(X,GT++95) GO TO 120

X-~:rwNXSOMI ISEELI 1

CMAN=4,51+*99tX

GO TO 130

120 X::+2Ah!DOM ( ISEED 1

CMAN= <, 5:l.+:?+ 49SX

C -

C; -, ITERATIOW G’JI,:t? 30 YE:#aHt;

f

- . ..”

.,

130 SUM=O +

nro .l.40 1=1 Y3Q

cjUM:::SUI”I+CMAM/i + :LOSt f I-i 1

140 CONTI NUE:

VRI..ïrVAL:~!iil.JM

wcrutw

E:ND

c-

(:;.“.....-“” ._..“I.“”-.-....-.....-. “...“..” .._.._..I --.---..- --..---.- ““- ---.. “...“_“” -... I---...-..- ““-.--I”-“-- -.--.....-..“..““““_“” . . . . . . . ..- -.“..--

c . . . . . . “” .--..-._.I..._ “-““.--_...- .I..“““..“.”.-...... * -.-..I.” ..-.-.. ““...“._“._“” --.- “_” .._...”.-.-..--..“.““---.. “.._“” . .._I ..-............._._---.” ..-.__

CSUBFi’OlJTINE Y IELD (Yi., Y IFLAG 9 IcìEEILl)

c....

1.; . . . RETIJRNC FUTIJRE VALUE OF INCOME FRCIM THE STANII

[; ..”

1; . . . .

i:;

. ..‘

I UETERMINE: UOLUME F-OR O-, 33

cX=RANDC)M ( ISEED )

IF(X+G’I + .33) GO TO 70

IF(IFLAG,NE+l) GO TO i0

X-RANXSC)M ( ISEED 1

uC1L=14ãQ+5&O*X

GO 10 30
10 TF (IFLAGeNEeZ) GCI TCI 20

X=RAND0M~1SEED)

u0L=1400+560*X

GO TO 30

2 0 X=RANCIOM ( :C SEED )

uOL=1!500+56o*X

cc:- flETEl?MTNE UALIJE FGR 0-., 33 ‘JQLUME

c30 X=fZANWM ( ISEEI5 1

:CF CX.GT ..25) GO TO 40

X-RANIIOM ( ZSEEIl)

UAL- ,22+*07sx

GO 70 250

40 IF(X,GT,,85) GO TE1 50

X-RANDOM C 1SE:ED)

UAL.= + 29s+ + 069*x

($0 ‘ro 250

50 IF(X+GT++95) GG TO 60

X=RANDOM t ISEEII)

UAL= *36I+*o;39*X

(30 TO 250

40 X=RANISOM ( :CC;E:ED 1

UAL=+401C+099~X

60 ‘ro 250

cc- DETERMINE: UOLIJME F’GR + 34-. + 83

(.; .

70 IFtX+GT+ ,831 GO TC1 140

IF tTFLAG+NE:,I) GO TO 80

X-RANISOM ( ISEl,D 1

u(JL:=19'"1C399*X , \

GO TO 100

30 IF (IFL.AG,NE,2) GO TO 90

X:=RANDOM ( ISEI...D j

u(‘)L::~l~?21~~‘399*x

Gil TO 100

\.

90 X=RANBOM ( TSEED 1

UoL~f0~:13399rlr.X

c-

(; I.. DETERMINE UALIJE FIJI? + 34- c S3

C”..

1 OO X+?ANIKlM ( ISEIEXS 1

IF’ (X+GT,,25) GG T(n :t:tO

X:=RANDGM I ISE:ED )

UAL..:::: e S95+ i OSSXX

GO 7’0 250

1.10 Xi o(,GT+,S’ci~ GO TI:) :l.ZO

>(=F;i’ANDOM t l:SEli.:X:l)

VAL.::::. ~?&:l.+ +0:59*X

G 0 ‘l’ 0 2 5 0

120 :tF (X+GT+ + 92 1 fi 0 Ti3 :t 30

X :::: I:2 A i’4 D 0 M ! :K 8 E E: X:1 )

UAL.= b 32:1+ + 0398.X

60 TO 350

1.3 0 X :i: li A N 15 I5 M ( :E S f: E: X:1 1

UAL_:= e 3<s1.+ t 099*x

GO ‘i-0 250

C : -.

12

1

ENGELHARD, ROBERT J. and WALTER C. ANDERSON

1983. A method of assessing risk in foresty investments.

U.S. Dep. Agrie. For. Serv. Res. Pap. SO-189, 13~.

South. For. Exp. Stn., New Orleans, La.

A practica1 procedure for computing the likelihood that expected returns will be realized.

Additional keywords: Uncertainty, Monte Carlo simulation,

probability distribution curve.

*U.S. GOVERNMENT PRINTING OFFICE: 1983- 669-085/29