A FINANCIAL

RETURN

PROGRAM

FOR FORESTRY 11Si

INVESTMENTS pi|||

llmllLtl Ili4

Sensitivity

of Results

to Data Errors

U^. Department of Agriculture

Forest Service

Agriculture Handbook 488

i^-- V-.:

^ ^ ^ ^ ^ „t^-^ j
A Financial Return Program

for

Forestry Investments

Including Sensitivity of Results to Data Errors

by

Marcus H. Goforth and Thomas J. Mills

Respectively, forester Coopergtive Forestry Staff, and forest economist. Forest Economics and Marketing Research Staff

December 1975

Agriculture Handbook No. 488

U.S. Department of Agriculture Forest Service
Abstract

Goforth, Marcus H. and Milts, Thomas J.

1975. A financial return program for forestry investments

including sensitivity of results to data errors. U.S. Dep.

Agrie, Agrie. Handb. 488, 18 pp.

A generalized investment analysis computer program has been

expanded to include a sensitivity analysis system both to facilitate

the comparative analysis of competing investment opportunities

and to determine the degree of data error required to influence the

outcome of the investment analysis. Standard economic criteria

such as internal rate of return and present net worth, are

employed. Th« system is described in detail with computational

formulae and instructions for data preparation.

Keywords: Economics, valuation, investment analysis
Contents

Page

INTRODUCTION1

I. Individual Case Format2

A. Basic transaction input2

B. Transaction repetition2

C. Extended time horizon and perpetuity,_2

D. Cost and benefit inflation4

E. Incremental versus total investment analysis^-4

II. Calculation of Investment Profitability4

III. Profit Level Sensitivity to Data Changes6

IV. Comparison Among Investment Cases7

V. Punched Card Input Format Instructions , 9

A. Permanent cards9

1. Sensitivity group label cards9

2. Stop card9

B. Variable cards^9

1. Master control card^9

2. Budget level card 12

3. Case title card^ 12

4. Case area card 12

5. Transaction cards 12

LITERATURE CITED 13

APPENDIX A—PROFIT LEVEL COMPUTATION 14

APPENDDC B—SAMPLE DETAIL PROFIT LEVEL OUTPUT 15

APPENDIX C—SENSITIVITY ANALYSIS COMPUTATION 17
A Financial Return Program

for

Forestry Investments

Including Sensitivity of Results to Data Errors

INTRODUCTION

Rational land management decisions require

knowledge of the financial return expected from

forestry investments. While economic factors are

far from the only relevant aspects of decisionmaking, they are often important ones. The long-term

and complex nature of most forestry investments

makes the hand computation of financial return a

very laborious process. At best, hand computation

restricts the number of alternative investments

which can be expediently evaluated. Automation of

the calculations is advantageous, both in terms of

increased accuracy and in the volume of information which can be analyzed.

A number of well-documented computer programs are available which automate the financial

return calculation (Hall, 1962; Row, 1963 and

1974; Schweitzer, et al, 1967; and Chappelle,

1969). These financial return programs differ in

terms of user-flexibility and in the amount of data

preparation required before the program can be

used.

The objective in constructing the financial return program described in this handbook was to

keep the program format as simple and generalized as possible while retaining all the aspects of a

rigorous financial evaluation. This program is

intended to be a production tool for users who

require a very flexible program or who are relatively unfamiliar with complex computer operations. If a large number of complex investment

cases must be analyzed, input data preparation

becomes rather time consuming. One solution to

the problem is to use the program developed by

Row (1974) to provide the inputs for this program.

The objective of providing a simple tool was met

in the construction of this program, but not

without some cost. One cost is that this program

requires more preparation of data, than some

alternatives. While this forces the user to confront

directly the assumptions he is making, it may lead

to the use of rougher input data than if certain

preliminary calculations were performed by the

program. This tendency towards rougher data is

counteracted in the program here described by the

inclusion of an analysis of the sensitivity of

financial return estimates to data errors. Up to six

separate data input groups can be identified and

subjected to sensitivity analysis to help determine

if more refined data are necessary. There is little

reason to expend time and money in data refinement if it takes a change in data far beyond the

range of reasonable doubt to significantly influence

profit estimation.

Profitability of investments is measured in terms

of internal rate of return (IROR), present net

worth (PNW), benefit-cost ratio (B/C), and present

net worth per dollar of initial cost (PNW/IC).

The individual cases included in a batch run are

then ranked according to each of the four profit

level criteria in summary tables for ready comparison. If area expansion factors are provided, and

the cases are mutually exclusive, the most profitable cases which exhaust any one of several budget

levels are selected and tabulated. The average

level of sensitivity to data errors for all the cases

in the batch is also tabulated.

Sections I, II, and III of this handbook describe

in detail the options available in analyzing individual cases. Section IV discusses provisions for

comparisons among investment cases. Section V

1
contains the detailed instructions for the preparation of input cards. All technical discussions and

formulae employed may be found in the appendices. A copy of the computer program^ written in

FORTRAN IV for the Univac 1108 (BCD) computer series, is available from the authors.

I. Individual Case Format

The basic format of individual cases is discussed

in this section along with techniques employed to

simplify input preparation. The detail of card

punching specifications is presented in Section V.

A- Basic transaction input. The input for each

case must be sufficient to identify the components

of individual cost and benefit (return) transactions

by year. As many as 60 individual transactions

may be specified. Each transaction is identified by

a value and a multiplier, and as a cost or a

benefit. For example, in the loblolly pine reforestation case in figure 1, the commercial thinning

transaction in year 30 is a benefit with a physical

value of 3.1 thousand board feet and a price

multiplier of $38.21 per thousand board feet.

Similarly, a cost value may be designated in manhours of labor input with a cost multiplier of dollar

wage rate per man-hour. The multiplier can be

ignored in either the case of return or costs by

simply entering the total dollar magnitude as a

value. A default multiplier of 1.0 is then used.

This latter approach is illustrated in the figure 1

example by specifying the $135 site preparation

and planting cost transaction in year 0 in total

dollar input.

The key concept here is that a time-stream of

costs and benefit transactions must be constructed

before the financial return can be calculated. By

design, however, the program is totally insensitive

to the unit of measure of the cost and return

items. For example, the return value may be

externally identified as cords of pulpwood, thousands of board feet of sawlogs, or tons of chips. It

may also be identified as hunting days or animal

unit months of forage production. Similarly, the

return multiplier may be externally differentiated

by log grade or tree species if the user needs to

differentiate prices in this manner. The program

treats the entries merely as values and multipliers

which allows a great amount of flexibility.

Some financial return programs internaHze the

calculation of both the values and the multipliers

(Schweitzer, et al, 1967, and Row, 1974). In their

programs, the physical yield, i.e. value, may be

differentiated by product and grade. The price per

unit, i.e., multiplier, is then determined by a

regression equation internal to the program which

considers the product and grade specified in the

input. Such internal data manipulation often

serves a useful purpose, but the aim here was to

design a more general and manageable program.

This program does not exclude the use of price

equations; it merely requires their development

and use outside of the program. The sensitivity

analysis feature of this program can then be used

to indicate the level of detail required to adequately describe the situation analyzed.

B. Transaction repetition. The program input is

simplified if a cost or benefit of identical magnitude occurs at regular time intervals. An entire

series of such repetitive transactions can be specified on one computer card by providing the year of

the first transaction in the series, its value and

multiplier, the interval between occurrences of the

transactions, and the year of the last transaction of

the series. The year of the last item in the series

cannot be greater than that of the most distant

independently entered transaction. The loblolly

pine example uses this format for repeated prescribed burnings and commercial thinnings (fig. 1).

This repetition format is especially convenient if

annual carrying costs are incurred or if the

investment induces an increase in annual allowable harvest. The program generates a transaction

record for each repetition of the transaction. The

total number of transactions, which equals those

specified plus those generated through the repetition coding, cannot exceed 200.

C. Extended time horizon and perpetuity. As

long as the limit on number of transactions is not

violated, transactions can be specified for any

number of rotations beyond the first one. For

example, if the case analysis involves precommercial thinning of a 15-year-old pine stand, the

management regime in the second rotation will not

be identical to that in the first. The second will

start with site preparation and planting which

hopefully establishes stocking conditions that render another precommercial thinning unnecessary.

Before profitability of alternative investments

can be validly compared, the alternatives must

cover the same time horizon. Since the initial

investments seldom mature at the same time, endto-end repetition of rotations into perpetuity is one

technique for achieving equal time horizons. Alternatively, any transaction or a whole rotation of

transactions can be carried to perpetuity merely by
u

INTEREST RATES TO BE USED FOR

PRESENT NET WORTH AND BENEFIT-COST

ANALYSIS

BENEFIT

INFLATION

RATE

COST

INFLATION

RATE

SENSITIVITY PARAMETERS

PRESENT

NET

WORTH

AMOUNT

INTERNAL

RATE OF

RETURN

AMOUNT

35 36[37 a8|3a|40|4iÍ4; «44««47«49 50 21 72 73 74 :re 7« 77 71 7110

03

BUDGET LEVELS

— DOLLARS —

10

0.0

CASE TITLE CASE

CODE

11 2| 31 4| a| » I 7 I » j 9 [10 [ll|l2|l3ÍH|l5|l6[lTL>a|l»[20[ail22|23l24|2g|2e|27[?é[29[30l3l|«l33[^ 36|37 ^8 3a|«[4l[<2|43l44|4s|46|47|4e[49|50|5l|52 53|M|55|56|57 SelsalsO 6t|62 63 MlssleS 67 6a|M|70Í71 72 73|74 75

8.Í. OR B\S TA

CASE

CODE

AREA

(THOUSANDS

OF

ACRES)

12 13 14 15 1Í 17 ,1B 19 65 «67 W 69 70 71 K 73 74 75 7S 77 75 7*

YEAR VALUE GROUP

CODE MULTIPLIER GROUP

CODE

RER

INT.

(YEAR)

RER

STOP

(YEAR)

PERR

YEAR

knATiof^

ITEM DESCRIPTION

7 9 9 10 11 12 13 14 15 16 20 21 22 23 24 25 26 27 26 29 87 68 69 TOlTI 72 73 74 75 78 77 79 79

TE

PR

OM

HA

NA

Figure L—Sample card layout for a program execution.
designating the interval at which each transaction

reoccurs into perpetuity.

D. Cost and benefit inflation. Studies have

revealed that real stumpage prices have risen

relative to the wholesale price of other commodities (USDA Forest Service, 1973, and Row, 1973).

This program enables the user to assume any rate

of real value change in cost and/or benefits, called

"inflation rates" in this handbook. Real prices and

costs should be used in financial analysis. Rates of

value change should only be used under an

assumption of relative price or cost increases (or

decreases) and not merely to reflect changes in the

value of the dollar, the true inflation rate.

The inflation rates can be used for either finite

or perpetual rotations. When using a perpetual

series of rotations, no PNW or B/C ratio is

calculated if the discount rate is less than the

higher inflation rate specified. The true PNW or

B/C ratio in that instance would be infinite and the

equations used for the calculations would fail.

E. Incremental versus total investment analysis.

Individual cases can be evaluated as either incremental or total investments. A total investment

analysis includes the costs and returns of a

particular investment without regard for the foregone costs and returns of some alternative level of

investment for the same area. An incremental or

marginal analysis represents the costs and returns

of the management regime of interest as positive

numbers and the costs and returns of an alternative regime as negative inputs. The loblolly pine

reforestation example is framed as an incremental

investment (fig. 1).

The advantage of the marginal approach is that

all costs and returns which remain the same under

both investment levels, such as annual taxes, land

value, and annual protection costs, can be ignored.

The disadvantage of this approach is that, while

the incremental investment may be profitable, the

total investment might not be. The profitability of

the total investment can only be estimated by

evaluating the total investment.

Whichever combination of these options for

formulating an investment case is used, the program provides a detailed input hsting of the major

options selected and of the case input (fig. 2). This

listing provides good documentation of the case

investment analyzed for future reference.

II. CaJculation of Investment Profitability

Once the time stream of cost and return transactions has been constructed from any of the

permissible steps previously outlined, the financial

return of that stream is measured by four parameters. The first is internal rate of return (IROR),

which is the discount rate that equates the present

value of discounted costs and returns. Stated

alternatively, IROR is the rate at which the

investment ''grows''' into the accrued returns.

The second parameter is present net worth

(PNW) which is the present value of the return

minus the present value of the cost transactions.

This is calculated for each of up to four specified

discount rates. The PNW is a measurement for

either the riet return per acre or the net return for

an entire tract, depending solely upon whether the

program input is provided on a per acre or total

tract basis. Third is the benefit-cost ratio (B/C)

which is the ratio of discounted benefits to discounted costs, with discounting done at the same

discount rates used in PNW calculations. The

fourth parameter is the ratio of PNW to initial

investment cost. This standardizes for the scale of

investment among the competing investments.

This makes them more comparable just as perpetual rotation standardizes the investment horizon of

alternative investments. The formulae for these

various calculations are shown in Appendix A.

The relative merits of these alternative financial

return measures have received considerable attention in the technical literature. Each selection

criterion, as typically employed, has its own

disadvantages. For example, IROR does not standardize the reinvestment rate for intermediate returns. Instead, the intermediate returns of each

case are assumed to be reinvested at the IROR of

that case. Similarly, PNW alone does not standardize for different scales of investment between

cases.

These differences among criteria can and do

result in different rankings of forestry inviestments.

Studies bave shown, however, that the ranking

differences are of little importance if the investments are not mutually exclusive (Haley, 1969, and

Webster, 1965). Investments are mutually exclusive if the execution of one investment precludes

undertaking another. A mutually exclusive example is precommercial thinning of the same area to

two different stocking levels. Only the highest

return investment of mutually exclusive investments should be included in the analysis. When

4
iNVeSTMtNÍ ANALYSIS SYSTtM

WITH

MhASUKtMtNT Dl- THE SE.NSITIVITY

OK

iNTfcKNAL RATt ÜF K£TUKN

ANU

PKtSENT NtT WORTH

10

CHANbES IN INPUT

CUNTKOL UPTIUNS

¿ = OUTPUT LEVEL

2 = SfNSlTiViry II^TthfEST RATt SLLECTOW

¿.SüüOO = FIRS! IlMTtKEST NAT£

5.U0UÜÜ 3 SECOND INTEREST RATE

lU.UÜüOU = THIRU INTEREsr RATE

is.uuüoo = (-OUHTH INTEREST RATE

.UÜÜÜÜ = bENEP'IT INFLATION HATE

•UJUUO = COST iNFLATIuN RATE

2 = PRESENT NET WORTH SENSITIVITY CODE

iÜ.UOUUO «= PRESENT NET wORTH SENSITIVITY AMOUíNT

1 = KAU, OF RETURN SENSITIVITY COOt

1.UÜUÜ0 = RATE OF RETUKIM SENSITIVITY AMOUNT

dUOOtî LEVELS IN THOUSANDS OF DOLLARS

bÜOU.ü lOOOü.O ISOÜÜ.O JüUOÜtÜ tbUÜ 7500Ü.Ü 'JnoOO.Ü 105000,0 120000.0

CASE iNJO, 2 OF THIb RUN

INHUT FOR PRECOMMERCIAL TMIN |^ObtLOLLY -SHORT HitGION ii SITE 85-120

INTENSIFIED HANAOEMêNT

YEAR

0

lü

20

¿0

5ü

MARveST

UROUP

CODE PRICE

ORUUP

CODE BENEFIT COST

GROUP

CODE

REPETITION

INT, STOP

PERPETUITY

YEAR

31,00 2 0 0 0

Ö.00 0 0 0 0

5.2200 i* ití.21 6 199.46

a,00 Ü 0

g

0

0

0

0

0

0

0

0

Ü

^.B600 4 Jö,21 b lÔb.7u 0

í+O 7.2900 4 30.21 b 27tí.Í5b 0

bO 31.2000 5 50,94 b 15Ü9.3J 0 0 ÙO

ro

du

ÍO

135.00 1 0 0 70

0,00 0 0 0 70

H.OO 0 0 0 70

d.OO 0 0 0 70 :fü 5.2200 Í* 3tí.2i b 199,46 0 l) 70

70

70

lOü 4.80ÜIJ 4 Jd.21 6 lb5.70 0 0

0

llü 7.2900 if 3b.21 6 27Ö.55 0

i Jü JÍ.200U b 50.95 6 I5tiy,b4 0 0 70

CURRÉIS T i^MNAOEMENT

OKOUP GROUP GROUP REPETITION PERPETUITY YEAR I-IAKVESI COüE PRICE CUOE bEiMEFIT COST CODE INT, STOP YEAR ib

Jb

-7.3BU0 5 b0.9íf 6 -375.94 0 0 45

-135.00 1 0 0 45

DESCRIPTION

PRECOMMERCIAL THINNING

PRESCRIBED BURN

PRESCRIBED BURN

COMMERCIAL THINNING

COMMERCIAL THINNING

COMMERCIAL THINNING

FINAL MARVEST

SITE PREP AND PLANT

PRESCRIBED BURN

PRESCRIBED BURN

PRESCRIBED BURN

COMMERCIAL THINNING

COMMEKCIAL THINNING

COMMERCIAL THINNING

FINAL HARVEST

DESCRIPTION

FINAL HARVEST

SITE PREP AND PLANT

AKtA FOH CASE 3b IS 36.00 THOUSAND ACRES

RATt UF KLTUKN StAHCH FlNlbhED

AT 13.00* SUM OF DISCOUNIED öENEFIfS 25.19Ö IS LESS THAN INITIAL COST 31.000

Figure 2.—Output of program controls and individual case input.

investments are not mutually exclusive, the lower

return ones are simply moved farther down the

investment rank to be selected when and if

budgets are adequate.

If cost and return schedules include large transactions with alternating costs and returns, more

than one IROR may exist (Marty, 1970, and

Gansner and Larson, 1969). This sometimes occurs

when evaluating incremental investments. Such a

case might have an investment cost in year 0,

followed by a positive value for the harvest of the

intensified management regime, and finally a negative value for the foregone harvest of the less

intense regime. This situation is a phenomenon of

the cost and return stream and not of the IROR

selection criterion. The use of IROR merely

exposes some details of the shape of the PNW

function. This program locates and reports all

IROR's between 0 percent and 50 percent. The

highest IROR where PNW is decreasing is the
IROR about which the sensitivity to data errors is

measured and is the IROR used in ranking

investments.

The standard profitability output from the program repeats the case title card and lists the

values of the four financial return parameters (fig.

3). More detail is available if desired. By inserting

a code on the master control card, the present

value of each transaction in the cost-revenue

stream at each of the specified discount rates is

available. Appendix B shows the detailed output

for the loblolly pine sample case. The transactions

created by use of the repetition code are also

listed in this detailed output instead of being

condensed as they are in the briefer input listing

in figure 2.

III. Profit Level Sensitivity to Data

Changes

Anyone who has ever estimated the financial

return from forestry investments knows that much

of the data input must be estimated with varying

degrees of certainty. For example, the estimated

final harvest may deviate from the actual harvest

by several percent either way. The same can be

said of stumpage price and treatment cost estimates. These estimates can usually be further

refined, but at a cost in both time and money.

An alternative course to refining estimates

across the board is first to determine if data

changes within the bounds of data uncertainty

have any significant influence upon estimated

financial return. If estimated financial return is

influenced little by possible data errors, there is no

reason to develop more refined data.

The first step in this sensitivity analysis is to

record possible percentage deviations of actual

data about the estimated data point. This should

be done for each data element which will be

subjected to separate sensitivity analysis. The

second step is to establish the amount of acceptable fluctuation or error between the estimated

financial return and the financial return associated

with some data change. This predetermined financial return deviation can be specified in a number

of alternative ways with this program:

(1) an absolute ± change about the base profit

level, expressed as either a dollar change for

PNW or an interest rate change for IROR,

(2) a ± percentage change about base profit

level for either PNW or IROR, or

(3) a ± percentage change about the base PNW

equal to the acceptable percentage change in

the base IROR criterion. This last threshold

concept, called the "computed" PNW

threshold in the program output, places the

IROR and PNW criteria on a comparable

basis for sensitivity comparison.

Once the cost-return stream is constructed and

these error thresholds established for data elements and financial return, the program answers

the question:

''How much of a percentage change in separate

data elements must occur before the estimated

financial return deviates from its base estimate

PKtCOHHtiKClML THIN LOtíLULLY-ShÜKÍ

tíASt ÜATA PHüFiT LEVELS

iNífcj-^NAL HATE Of HtíU^h ÍU.64U

HEGION Ö SITE tí5-i^ü

SPEClFUü

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¿.50UU

b . O O O O

i U • O (i U ü

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Ö»9öo7

• ^177

PKESENT NET

WüHTh PEK ít

INITIAL CuST

1Ö.9Ü64

4.9y8b

.2356

Figure 3.—Profit level output for example investment case.
enough to violate the predetermined financial

return error threshold?"

The calculated data change necessary to violate

the error threshold is compared with the possible

bounds of data error previously recorded. If the

calculated data change exceeds the possible data

error range, further data refinement is not required. If, however, the calculated data change is

less than the previously recorded data error range,

more refined data must be collected to bring the

estimated financial return within the predetermined error thresholds.

Six separate data element groups can be subjected to sensitivity analysis, three for costs and

three for returns. The sensitivity groups codes can

be assigned to either the transaction value or

multiplier, and different sensitivity group codes

can be assigned to the value and the multiplier of

the same transaction. The same code cannot be

used on both the value and multiplier of the same

transaction, however, because of the way the

allowable percentage changes are calculated. The

sensitivity group codes can also be applied to

either or both of the management regimes of an

incremental analysis.

The sensitivity of each of the six data groups is

calculated separately. The allowable percentage

data change is separately calculated for each

group of similar elements assuming all other data

are unchanged. The data are then returned to their

original values before sensitivity to the next group

is calculated. The sensitivity to joint changes is

not included in the program because of the large

number of joint changes possible.

Four data groups were subjected to sensitivity

analysis in the loblolly pine sample case. The

position of the group codes is shown in figure 2

and the sensitivity analysis output is shown in

figure 4. The allowable percentage changes are

just that, percentage changes rather than direct

multipliers. For example, the actual stumpage

price must be 50.33 percent higher than the

estimated stumpage price of the case before the

estimated IROR of the case would increase by 1

percent from 3.4827 percent to 4.4827 percent.

The base prices were $38.21 and $50.94 per

thousand board feet for commercial thinnings and

final harvests of the intense management regime,

respectively. Thus, the actual prices must be as

high as $57.44 and $76.58 per thousand board feet,

respectively, before the estimated IROR underestimates the actual IROR by 1 percent. Conversely,

actual stumpage prices must be 32.95 percent

below the input prices before the actual IROR is 1

percent below the estimated IROR. The allowable

data change must be applied to all of the data

elements identified by the code before the profitability error threshold is violated. Appendix C

provides the formulae used to calculate the allowable percentage data change.

IV. Comparison Among Investment Cases

Up to 60 individual investment cases in any one

computer run can be compared or compiled in

three ways once the profit measure and sensitivity

analysis on each case have been conducted. First,

the cases are ranked according to each of the four

profit measures. This merely automates the ranking that is often done by hand and provides a

ready summary of cases analyzed. Each case is

identified by its title card, its assigned case

number (CASE), and the order that case was

entered in that particular computer run (ISN). The

PNW, B/C ratio, and PNW per dollar of initial

investment are all discounted at the same discount

rate selected for the sensitivity analysis. Figure 5

displays a sample ranking of the investment cases

by IROR.

Second, the program selects investment cases

down each of the four rankings until each of up to

ten budget levels is exhausted. If the cases are

analyzed on a per-acre basis, an acreage expansion

factor must be specified in the input. If the total

costs and returns of an entire case area are

directly included, an acreage expansion factor of 1

must be provided. Only initial (year zero) treatment costs are charged against the budget levels.

Future costs are not.

Cases are sequentially added down a particular

ranking until the summation of initial costs for the

case areas equals the first budget level. The last

case selected for budget inclusion and the proportion of that marginal case employed are reported

along with the PNW of the investments included

in that budget. The discount rate used in calculation of the budget PNW is the same one used in

PNW ranking. Additions to smaller budgets are

made by starting from where that budget left off in

the rank and adding cases until the next budget

level is exhausted. Figure 6 shows the budget

output of the program.

The budget construction phase of the program

will execute whenever budget levels and acreage
CO

StNbll Í^HY ANALYSIS

PHihCOHMthfCI AL I HXí>i LOBLOLLY-SrJCNf híLGlON Ô SUt tí5-l¿ü 36

TMHLSMüLü StLtXTIÜiM CRITLKIA

HAÎt OF KLrtjríN - >-LüS U^ MINUS AN AbSOLU Tt i. OU PüRCEN I NATE ÜF KETU^^N

PKtSLNi NEÎ tiUHÍh - PLUS ÜH MINUS iU.OO PEKCtNT Of OASE PPESENT NET WORTH

THHESNULUS SELECT EL)

BASE PATE up KLTUKN IS iü,ri*i*ll PANGE IS

COPKESPONüING PKEStNT NET WOPÍH KAi^íOE IS

9.ö4il THROUGH U.tí^ll

B.9135 THROUGH -6.6112

fcíASE PbïEStNT l^íEÎ wORTrt AT 5.Ü0 PERCENT IS lS4»9b34 RANGE IS i39,45tíl THROUGH i70.4^^67

RATE OF KtTUHN THHESnOLiJ IS PLUS UK MINUS 9.¿Z PERCENT Oh THE BASE RATE OF RETURN

(HIS PERCENTAGE APPLlEu TO THE dASE PRESENT NET ivORTH GIVES A RANGE OF 140,6602 THROUGH 169.2466

PERCt«>)7 CnANGE IN INPUT KEUUIKED TU KEACM UPPEK A'V»D LOWER THRESHOLDS (ÖY GROUP)

INPUT UAÎA GKOUPS

SPEClFItD LIMIT'-

RATE OF RtiTURN

UPPER LüWEK

THRESHULU THRESHOLD

ll.d411 9,04 il

•—SPECIFIED LIMIT*-

—PRESENT NET wOKTHUPPER LOWER

THRESHOLU THRESHOLD

170.4487 139.45Ö1

—COMPUTED LIMIT

'-PRESENT NET WORTHUPPER LüWER

THRESHOLD THRESHOLD

169#2466 14Ü.6602

COST ITEf^S

i. KtrOKtSTATiON 26Ü.19í¿iO -191,9345

¿# PRLCOKMEKCIAL THINNING -¿I.3¿ó3 28./S32

77»22U7

-49.96S0

-77.2207

49.9850

7U2297 -71#2297

-46.1070 46.1070

KETOR'^i UE'^S

A. COi^hlEKClAL THINNING

5. FiîM^L HARVtiST

6. SrUHPAGE PRICE

¿1.3ri06 -la.HbSO

-117.9946 103.6867

2<D.il2I -22.4ööl

9.S025 -9.5025

137.2656 -137.2656

6.6672 -6.8672

8.7653 -6.7653

126.6163 -126.6163

8.1977 -Ö.1977

Figure 4.—Sensitivity analysis output for example investment case.
CAStS kAiNKtu fcjY INTERNAL. RATE OF RETURN

RANK ISN CASE LAtíEL CASE VALUE

1 1 RELEASE DUUbLAS f IR REGION 6 SITE 120* 39 14.7541

Z ¿ PRECOMMERCIAL TMlN LübLOLLY-SHURT REGION Ö SITE 85-120 36 10.8411

3 j RELEASE LUNULEAF-SLASH REGION 8 SITE 85-120 48 8.8233

¿t ^ PKECUMMEKCIAL THIN LObLOLLr-SHURT REGION tí SITE 50-85 37 8.6254

b 'Ö RELEASE LOBLOLLY-SHORT REGION 8 SITE 50-85 51 7.0204

6 5 RELEASE FlRrSPRuCE REGION 6 SITE 50-85 45 5.3315

1 r RtKüKESTATiÜN LONÜLEAF-SLASh REGION Ö SITE 85-120 16 4.9365

Ö d REf-URESTATlON LOBLOLLY-SHORT REGION 8 SITE 85-120 20 4.8636

9 9 REFüRESTATIüN PONUEROSA PINE REGION 5 SITE 120'^ 8 4.3920

1Ü 10 RRECOMMEKClAL ThiN FIR-SPRUCE REGION 6 SITE 85-120 33 3.8909

ii 11 RELEASE PONUEROSA PINE REGIUN 5 SITE 85-120 42 3.5747

12 i¿ REFORESTATiüN PONÜERÜSA PINE REGION 1 SITE 85-120 5 3.2525

13 13 REFüRESTATIüN UOUOLAS fi\i REGION 5 SITE 85-120 2 2.8304

H 1^4 REFÜRESTATIÜN FIR-SPRUCE REGION 1 SITE 85-120 12 2.4017

lb 15 RELEASE FIR-SPRUCE REGION 5 SITE 85-120 44 2.3094

16 ib REFORESTATION PONUEROSA PINE KEGÍON 6 SITE 50-85 10 2.0073

17 17 PRECÜN-MEKCIAL TMlN LODÛEPOLE PINE REGION 1 SITE 120* 34 1.6096

Id 18 RELEASE LOüüEPOLE PINE REGION 1 SITE ti5-120 46 1.5624

IV 19 REFüRESTATIüN LODGEPOLE PINE REGION 1 SITE 85-120 15 1.5055

¿Ü ¿0 PRECOMMERCIAL ThlN DOUGLAS FIR REGION 3 SITE 50-85 25 • 9866

21 ¿i REFORESIATIÜN LODiiEPOLE PINE REGION 2 SITE 50-85 16 .5110

Figure 5.—Sample IROR ranking for all cases included in a single computer run.

expansion factors are provided. The budgeting

aspect should not be used, however, if any of the

investment cases included in the run are mutually

exclusive. The program treats all cases as if they

were not mutually exclusive.

Third, a summary table of the sensitivity analysis results is constructed. The sensitivity to data

errors is often quite variable from case to case.

The summary table calculates the mean allowable

data change for each of the data groups identified

in the cases and the standard deviation about the

mean. The average sensitivity of the IROR, PNW,

and '^computed" PNW,thresholds are all reported.

The mean includes the sensitivity to any data

element in the cases identified by the same

sensitivity group code. Therefore, it is essential

that the codes be applied to data elements in each

case which are comparable enough to have some

meaning when averaged together. Figure 7 shows a

sample of the sensitivity analysis summary table.

V. Punched Card Input Format

Instructions

This section contains the instructions for preparing the computer cards necessary to perform the

analysis described. There are two groups of cards:

those which are permanent and those which vary

from run to run. There are two types of permanent

cards: sensitivity data element group names, and

the STOP card. There are five types of variable

cards: a master control card, a budget level card,

a case title card, a case area card, and a set of

cost and benefit transaction cards.

A. Permanent cards. Seven permanent data

cards are required for each run in addition to the

control and transaction cards which may vary from

run to run.

1. Sensitivity group label cards. Each run requires six of these cards. They contain (in columns

1-26 ) the names of the six sensitivity analysis

groups respectively. Thus, the names of the

groups may be changed without program modification.

2. Stop card. One stop card is required for each

run. This card is punched ''STOP" in columns 1-

4. It is the last data card in the deck.

B. Variable cards. The data in these cards

varies according to the purpose of the run. The

first three cards contain data pertaining to all

cases being analyzed in the run and must always

be present. The number of the remaining cards

will vary both with the number of cases being

analyzed and with the number of transactions for

each case.

1. Master control card. This card contains 14

data fields as follows:

Card

Field columns Format

1 1 II

information

Output control code—Code 1

for detailed discounted benefit-cost tables for each interest
COMPAKATIVE CASE KANKir^JGS -

—KAT£ UF KtTUKN—

KANK CASt VALUE

1 (39) 14.7541

¿ (36) 10,0411

3 (4b) Ö.B233

4 (37) b.62b4

b (bi) 7,ü¿04

b (^b) 5.331b

7 ÍIH) 4.yJ6b

H (¿0) 4.fcb36

9 ( b) 4.39¿ííj

ro (33) 3.6909

il (42) 3.5747

i¿ ( b) 3.2S2b

13 ( ¿) ¿.Ö3U4

i4 (12) ¿.401/^

IS (44) ¿.3094

16 (10) ¿.ÜÜ73

17 (34) 1.6096

Ití (4ó) 1.SÖ24

19 (ib) l.büSb

¿0 i?,b) .9066

¿í (16) .Silo

PkESENT i^tr viO^

-PRESENT NET

CASE

(39)

(36)

(4ö)

(37)

(Si)

Í4b)

(16)

(20)

(42)

(33)

(-fr6)

(44)

tab)

( 6)

(34)

( b)

(12)

(lb)

( 2)

(lü)

(16)

> AND tíEiMLFlT-CÜST kATIOS AT 5.0% INTEREST

NET wÜr^TH BENEFIT--CUST RATIO

VALUE CASE VALUE

187.b9l4 (36) 8,9867

lb4.9S34 (39) 7,0860

123.4543 (48) 4.3111

74.66UÜ (37) 3.8790

b4.6óüO (bl) 2.1900

4,6343 (45) 1.1205

-4.2434 (18) .9660

-9.15b6 (20) .9281

-19,3460 ( 8) .^411

-28-1709 Í33) .7088

-32,9b60 (42) .3884

~^b^bQö3 ( 2) .3396

-45.2013 ( 5) 3213

-46.4142 (12) ,1789

-^0.2173 (44) .1482

'•79.l¿o'i (10) .0982

-y5./2ó^ (15) .0906

-116,17/4 (34) .0824

•119.76Ô2 (46) ,0679

-169.Ö074 (16) ,0230

-I9b.l5b7 (25) .0192

-PNW/INITIAL COSTCASE VALUE

(39) 6.2530

(36) 4,9985

(48) 2.4207

(37) 2.4084

(51) 1,0718

(45) .1220

(18) -.0314

(20) -*0678

(33) -.2934

( 8) -.3316

(42) -.6241

{ 5) -.0074

( 2) -.8147

(44) -,8685

(34) -.9300

(46) -.9416

(12) -.9768

(25) -.9826

(15) -1.0562

(10) -1.0613

(16) -1.1616

TOlAL PKESLNT Ntl wOKlH Al HlXtü bUütjET LtVfcLS wlTH HANK ÜF MAROIi^JAL CASES

(dUUt^ET LtVfcLS Atiu PKESEiJl NE í ^üKTHS IN THOUSANDS OF DOLLARS)

bUuütT CASI

LEVELS KA'MI

boOO. 0 5

luuoo.o Ö

15000.0 8

30000,0 13

45000.0 19

6oOOU,ü »«

7b0 00.0 «■■a9 0 0 0 0,0 «<^

10bOÚO,0 « «

12 U 0 0 0 . 0

•u-*

—INÏEKIMAL KATE ÜF KETUKIM —

i^'AKGlNAL TUIAL % MARPKESENT blNAL

NET WORTH CASi^

17896,16 68.1

18004,22 9.0

1766b.12 69.6

6800.29 60.1

^^b¿3^o¿ 39.2

223d¿,7b .0

22382. /b .0

22382,75 .0

'2238¿;.7b .0

•223tí¿,75 .0

RANKING CRITERIA

PKESENT NET WORTH tíENEFíT/COST RATIO

MAR(3ÍNAL TOTAL % MAR- MARGINAL TOTAL % MARCASE PKESëNT tilNAL CASE PRESENT OINAL

KANK NtT ^OHih CASE RANK NET wORTH CASE

b

ó

Ö

if

20

L fÖ-fö^Lt 88,1

160 04,22 9.0

17665,12 89.6

6120,04 11.4

-5482,82 54,0

223ö2,75 ,0

¿2382./5 ,0

223d2,7b • 0

22382,75 ,0

22382,/S ,0

5

8

8

12

19

««

17898,16

18004,22

17665,12

8793.95

-5631,16

-22382,75

-22382.75

-22382.75

-22382.75

-22382.75

88.1

9,0

89,6

92.4

50.4

,0

,0

.0

.0

.0

-PNW PER

MARGINAL

CASE

RANK

5

8

8

13

20

it«

$ OF INITIAL COSTTOTAL % MARPRESENT GINAL

NET WORTH CASE

17898.16

18004.22

17665.12

8808.29

-5482.82

-22382.75

-22382.75

-22382.75

-22382.75

-22382.75

88.1

9.0

89.6

68.1

54.0

.0

.0

.0

.0

.0

* liMOICATES IHAT iHd CASE AT ThlS RANK USES UP THt STATEU bUÜGET EXACTLY

«^ i.^UlCATES THAT THIS HUDOET LEVEL wlLL COVER ALL TriE CASES IN fhlS RUN

Figure 6.—Sample output of case ranking by four profit criteria and budget level constraints.
MEANS AND STANüAWÜ ÜEVlAflÜNS OF StNSIlIVHY PEKCENTAüES BY CHITêHION ANO ITEM

-CHíTtHION AND LIMITÓOS f íTtMS

1. KtFOhlt&TATlÜN

c. PKtCUMMEHCÍAL THÍNNlNü

J. KtLtASt;

KElUHiN ITLMS4. CUMMtKCIAL THÍNiMlNÜ

b. F I NAL hAKVtSr

Ö. SfÜMPAGE HKICE

hiUW-UPPtK LÍMH

N MEAN * Si)

lo -¿ldt>.07 5999,3871

7 -3(i,bb 19.7255

PUW-LÜWER LIMIT

N HEAN % SD

16 2btí.95 815,2870

15 1U252¿».00***»**»***

7 143.79 171.2711

—PN;N-SPECIFIED LIMITMEAN % Su

21

21

21

129.93 111.9öb3

5342.7421965.9ÜÓ4

86.43 55.0972

19

19

19

-?2.14 46,2010

-1607.56 7033.6333

-42.U3 13.9182

18

17

7

21

21

21

8330.8322504.8637

269.56 574.0387

17.57 21.0300

98.01 181.6389

?523.32 9313,1119

75.41 137.5107

"PNW-COMPUTEO LIMIT—

N MEAN % SD

18 68873.2Û*««»<******

17 805.15 1538.610Ô

7 28.96 19.4452

21 1115.40 3126.2472

21 23932.4594565.2352

21 802.78 2052.8686

ÍHt 21 CAStS HAD A M£AN KATE ÜF KETUKN ÜF <+,5/29% WlfH A STANÜAHD DEVIATION OF 3.6299

Ü CASES HAü MÜHE THAN ONL INTtHNAL KATE OF PtTUKN

Figure 7.—Sample sensitivity analysis summary table.

Card

Field columns Format

n

Information

rate specified in fields 3-Ó of

this card and for each interest

rate involved in the rate of

return sensitivity (as in Appendix B). Code 2 for present net

v^orth and benefit-cost ratio

summary tables only (as figure

3).

Interest rate selector code—I,

2, 3, or 4, respectively to

indicate which of the four interest rates entered in fields

3-6 of this card is to be used

as the base in the sensitivity

analysis of present net v^orth.

Use code zero (0) to suppress

all sensitivity analysis and

summary tables.

3 3-10 F8.4 First interest rate (expressed

as a percentage)—the first

(usually but not necessarily

the lowest) interest rate to be

analyzed for each case. If 0.0

percent is to be analyzed it

must be entered in this field

(field 3). A zero or blank in

fields 4 or 5 precludes the

analysis of any interest rates

subsequently entered in fields

4-6.

Note: The 0.0 percent interest

rate cannot be analyzed for

cases involving perpetual series as specified in field 10 of

the Transaction Cards.

4-6 11-34 3F8.4The second, third, and fourth

Card

Field columns Format Information

interest rates respectively to

be analyzed for each case—

Any or all may be omitted.

The first zero or blank field of

fields 4-6 negates any valid

interest rates to the right of it.

7 35-42 F8.4 Benefit inflation rate^ (expressed as a percentage)—

Must be less than any interest

rate in fields 3-6 if perpetual

discounting is used for any

transaction.

8 43-50 F8.4 Cost inflation rate^—See field

7 above.

9 51 II Present net worth sensitivity

code—Code I if the value in

field 10 is an absolute amount

to be added to and subtracted

from PNW to establish upper

and lower thresholds. Code 2

if the value in field 10 is a

percentage of the PNW.

Leave blank if no sensitivity

analysis is wanted.

10 52-59 F8.4 PNW sensitivity amount—See

field 9 above.

IROR sensitivity code—Code

I if the value in field 12 is an

absolute amount to be added

to and subtracted from the

IROR to establish upper and

11 60 II

^ Inflation rate as used here, in appendix A. and in figure 1

refers to rates of real value or real price increases or decreases

and not to changes in the value of the dollar alone.

11
Card

Field columns Format Information

lower thresholds. Code 2 if the

value in field 12 is a percentage of the IROR. Leave blank

if no sensitivity analysis is

wanted.

12 61-68 F8.4 IROR sensitivity amount—See

field 11 above.

13 69 II Data sift code—Code i if only

intensified management Transaction Cards are to be included in the financial analysis. Code 2 if only current

management Transaction

Cards are to be included in

the financial analysis. (Current

management Transaction

Cards must be distinguished

by the minus sign on the value

in field 4). Code 3 if all Transaction Cards are to be included, i.e., an incremental

investment is subjected to financial analysis.

14 70 11 Summary suppression code—

Code 1 to suppress summary

tables or leave blank to print

tables.

2. Budget level card. This card contains up to

ten budget levels in the format 10F8.4. The

expanded initial costs of the ranked cases will be

examined at each budget level to determine which

cases would be made operational at that budget

level for each of four ranking criteria, (Expanded

initial cost is the product of the total cost in the

beginning year times the area expansion factor

from the Case Area Card,) This card must be

included, but it may be left blank if no budget

levels are to be used.

3. Case title card. One of these cards is required

for each of up to 60 cases in a run. Columns 1-72

contain any alpha-numeric information which will

identify the case in the program output. Columns

73-75 contain a unique numeric case code for each

case in the run. This code is assigned by the user.

Columns 76-80 should be blank.

4. Case area card. If the values in the Transaction Cards are per-acre estimates, this card carries

the area expansion factor for that case in thousands of acres. Columns 1-3 contain the same

unique case code as columns 73-75 of the Case

Title Card. Columns 4-11 contain the area expansion factor in the format F8.4. This card is

mandatory for each case. If the expansion factor is

zero or blank, it will be set at 1.0 by the program

implying that the Transaction Cards carry the

costs and returns for the whole tract.

5. Transaction cards. The program allows up to

60 of these cards for each case to be analyzed.

Repetitious transaction records generated by fields

8-9 may add records up to a total of 200 transactions. These cards each provide for 11 fields of

information as follows:

Card

Field columns Format Information

1 1 Al Alphabetic benefit-cost code—

Code B for Transaction Cards

describing benefit transactions

or C for cards describing cost

transactions. Any other code

will be reset to B and a warning printed.

2 2 11 Stop Code—Code 1 on the last

Transaction Card of each

case. Leave blank on all others. Cards with field 2 coded

must be followed either by a

Case Title Card or by the Stop

Card,

3 3-6 14 Year-Enter the year of the

transaction relative to zero as

the present or base year.

4 7-16 F10.4 Value-For benefits, this may

be harvest volume per acre.

For costs, this may be the

number of units of expenditure. Enter the value as a

negative number for the current management regime of a

marginal analysis. The current

management Transaction

Cards must all follow the intensified management cards.

5 17-19 13 Value sensitivity group code—

Enter the group to which the

value belongs for sensitivity

analysis. Enter 7, 2, 3, 4, 5, or

6 depending upon which group

the value falls in. The codes

correspond sequentially to the

titles in Sensitivity Group Label Cards, Leave blank if no

12
Card

Field columns Format Information

sensitivity analysis is wanted

for this value.

6 20-29 F10.4 Value multiplier—for benefits,

this may be stumpage price.

For costs this may be the cost

per unit of expenditure. This

multiplier must not be negative. If zero or blank, it will be

reset to 1.0.

7 30-32 13 Multiplier sensitivity group

code—Enter a sensitivity code

from among those described in

the Sensitivity Group Label

Cards. The code must be different than that shown in field

5 or may be blank. It cannot

be the same as the code in

field 5.

8 33-36 14 Repetition interval—For identical transactions occurring at

regular intervals, beginning at

the year specified in field 3,

enter the interval in years.

The additional transaction records are generated by the program, bypassing the necessity

of coding and keypunching a

separate card for each occurrence of the transaction.

Leave blank for nonrepetitive

transactions.

9 37-40 14 Repetition stop year—Enter

the year (relative to zero as

the present or base year) beyond which repetitious transaction records will not be generated. This entry may not be

higher than the highest year

specified in field 3 of any

Transaction Card for the case.

If it is equal to the highest

year, or if the transaction is

nonrepetitive, this entry may

be omitted.

10 41-44 14 Perpetuity year—If the transaction is to be discounted as a

perpetual series, enter the recurrence period in years. If

this field is coded, any 0.0

percent interest rates specified

on the Master Control Card

Card

Field columns Format Information

will be ignored for the case in

question. Any or all of the

Transaction Cards may include a perpetuity year and

the perpetuity codes may differ among transactions. Leave

this field blank when discounting a terminable or finite series.

11 45-72 7A4 Description—Up to 28 alphanumeric characters may be

used as a label for the transaction described by each Transaction Card.

LITERATURE CITED

Chappelle, Daniel E.

1969. A computer program for evaluating forestry opportunities

under three investment criteria. USDA Forest Serv. Res.

Pap. PNW-78, 64 p.

Gansner, David A. and David M. Larson.

1969. Pitfalls of using internal rate of return to rank investments in forestry. USDA Forest Serv. Res. Note NE>-106, 5

p.

Haley, David.

1969. A comparison of alternative criteria for the evaluation

of investment projects in forestry. Univ. of British Columbia, Vancouver, B.C., 93 p.

Hall, O. F.

1962. Evaluating complex investments in forestry and other

long-term enterprises using a digital computer. Purdue

Univ. Res. Bull. 752, 11 p.

Marty, Robert.

1970. The composite internal rate of return. Forest Sei.

16{3):276-279.

Row, Clark.

1963. Determining forest investment rates-of-return by electronic computer. USDA Forest Serv. Res. Pap. SO-6, 13

PRow, Clark.

1973. Probabilities of financial returns from southern pine

timber growing. Unpubl. Ph.D. disser. Tulane Univ., NewOrleans, La., 428 p.

Row, Clark.

1974. System "Muhiploy"—a computer tool for simulation

and evaluation of forest land management regimes. USDA

Forest Serv. Wash.. D. C. (Manuscript in preparation.)

Schweitzer, Dennis L., Allen L. Lundgren, and Robert F.

Wambach.

1967. A computer program for evaluating long-term forestry

investments. USDA Forest Serv. Res. Pap. NC-10, 34 p.

USDA Forest Service,

1973. The outlook for timber in the United States. Forest

Resource Rep. 20, 367 p.

Webster, Henry H.

1965. Profit criteria and timber management. J. For.

63(4):260-266.

13
APPENDIX A—PROFIT LEVEL

COMPUTATION

Present net worth (PNW) and benefit-cost ratios

(B/C) are computed from the discounted values of

each transaction in the schedule of transactions

which defines an investment opportunity. The sum

of the discounted benefit transactions minus the

sum of the discounted cost transactions is the

PNW of the investment opportunity. The corresponding quotient of these two sums is the B/C

ratio for the investment opportunity.

One of the following two equations is used to

discount each transaction depending upon whether

the transaction is to be discounted as a one-time

occurrence (finite discounting) or as a perpetual

series into infinity (perpetual discounting).

A. Finite discounting formula:

DV = A X

B. Perpetual discounting formula:

DV =A X

(S) P-l

Where:

A = The value of the transaction expressed in current dollars.

DV = The discounted value of A.

Y = The year of first occurrence of the

transaction in ternis of zero as the

current year.

P = The number of years between recurrences of the transaction (when discounting perpetually).

R = The annual interest (or discount) rate

expressed in decimals plus 1. (e.g.,

when the interest is 5 percent then R

= LOS.)

N = The estimated rate of annual inflation

expressed in decimals plus 1. (e.g.,

when the inflation rate is estimated to

be 2.5 percent N = 1.025.)

R must be greater than N when equation (B)

is to be used.

The internal rate of return (IROR) is defined as

the interest rate at which the PNW of the

investment is zero and the B/C ratio is 1.0. For

any given investment, there will usually be only

one such interest rate. However, there may be

more than one such rate depending upon the

magnitude and the signs of the transaction values.

The search for IROR begins at one of two

interest rates. If all transactions are to be finitely

discounted (Equation A used throughout) or if the

estimated rate of inflation is zero, the starting

interest rate is 0.0001 percent. If any transaction

is to be discounted perpetually, and the highest

inflation rate is not zero, the starting interest rate

is equal to the inflation rate plus 0.0001 percent.

In the first instance, zero percent cannot be used

because transactions cannot be discounted perpetually at zero percent interest. In the second

instance, the benefit inflation rate cannot be used

as a starting point because with perpetual discounting, the interest rate must be greater than

the inflation rate (R>N).

Starting with the beginning interest rate, subsequent internal rates are tested in increments of

1,0 percent until a change in the sign of the PNW

occurs. At this point an IROR has been detected.

The estimate of IROR is refined by subtracting 1.0

from the interest rate and further testing at an

interval of 0.1 percent again until another change

in the sign of the PNW occurs. This process is

repeated until IROR is correct to five decimal

places.

After each IROR is computed, the testing rate

returns to the rate which detected the presence of

that IROR. The testing then resumes at 1.0

percent intervals.

Seldom will the testing continue up to the

maximum test rate of 50 percent interest. A rate

would commonly be attained before that where the

sum of the discounted benefit transactions is less

than the sum of the positive costs in the year zero.

Beyond this point, no higher interest rates need be

tested because the sign of the present net worth

cannot change again. The search is terminated at

this point.

14
APPENDIX B—SAMPLE DETAIL PROFIT LEVEL OUTPUT

rüKESrATIÜN LÜSLÜLLY PlNfc: SITE 50-Ö5 CU.FT,/ACKt/YEAH

DISCOUNTtD ÖENEFITS AND COSTS AT 2,5000% INTEREST

YEA«

30

40

50

70

40

TOTAL

BENEFIT GROUP DESCRIPTION

60,66179501 4 6 COMMERCIAL THINNING

53.6384Ö452 4 6

55.4X916863 4 6

205.20710134 5 b

-76,10037790 0 6

306.74617180

COMMERCIAL THINNING

COMMERCIAL THINNING

FINAL HARVEST

FINAL HARVEST

PNW' a 124,42949829 BCR « ^ 1,68249105

YEAR

0

10

20

COST

164,14443056

7,59877729

5,93615268

GROUP

1 0

0 0

0 0

DESCRIPTION

SITE PREP AND PLANT

PRESCRIBED BURN

PRESCRIBED BURN

30 4,63731298 0 0 PRESCRI&ED BURN

TOTAL 182,31667351

DISCOUNTED öENEFITS AND CUSÍS AT 5*0000% INTEREST

YEAR BENEFIT GROUP DESCRIPTION

30 28,33826018 4 6 COMMERCIA-L THINNING

PNW

YEAR

0

10

20

-78,78712867

COST

BCR .47369081

GROUP DESCRIPTION

139,58771317 1 0

5.07820724 0 0

3,11757873 0 0

SITE PREP AND PLANT

PRESCRIBED BURN

PRESCRIBED BURN

30 1,91392290 0 0 PRESCRIBED BURN

40 17.39723351 4 6 COMMERCIAL THINNING ^

50 14.12568004 4 6 COMMERCIAL THINNING

70 32.30227194 5 6 FINAL HARVEST

40 --21.25315230 0 6 FINAL HARVEST

TOTAL 70.91029336 TOTAL 149.69742204

DISCÜUNÍED BENEFITS AND COSTS AT 10.0000% INTEREST PNW = -130.85081364 BCR s ,06474422

YEAR BENEFIT GROUP DESCRIPTION YEAR COST GROUP DESCRIPTION

0 135.17115755 1 0 SITE PKEP AND PLANT

10 3,08825675 0 0 PRESCRIBED BURN

20 1.19065667 0 0 PRESCRIBED BURN

30 6.79686183 4 6 COMMERCIAL THINNING

30 ,45904969 0 0 PRESCRIBED BURN

40 2.62048447 4 6 COMMERCIAL THINNING

50 1.33621672 4 ö COMMERCIAL THINNING

70 1,2U512719 b 6 FINAL HARVEST

40 -2,9003ö317 0 Ö FINAL HARVEST

TOTAL 9,05830702 TOTAL 139,90912066

DISCOUiN TED BENEFITS AND GUSTS AT 15.0000% INTEKEST PNW = -135,64641326 BCR s .01416077

YEAR BENEFIT GROUP DESCRIPTION YEAR COST GROUP DESCRIPTION

0 135,00761219 1 0 SITE PREP AND PLANT

10 1,97758915 0 à PRESCRIBED BURN

20 .48882979 0 0 PRESCRIBED BURN

30 1,78907278 4 6 COMMERCIAL THINNING

30 ,12003125 0 0 PRESCRIBED BURN

40 .44223143 4 6 COMMERCIAL THINNING

50 .14^^57505 4 6 COMMERCIAL THINNING

^0 .05359771- 5 6 FINAL HARVEST

40 -,40102786 0 b FINAL HARVEST

TOTAL 1,94044912 TOTAL 137,59486238

15
APPENDIX B- -SAMPLE DETAIL PROFIT LEVEL OUTPUT

(Continued)

SENSillVilY ANALYSIS

ÜISCüUNÍtÜ BENEFITS AND COSTS AT 4.4Ö27* ÍNTtREST

YEAR BENEFIT GROUP UESCRIPriON

30

40

50

70

^0

TOTAL

33,33227^16 4 6 COMMERCIAL TtllNNINO

21.499223Ö6

10,34014679

46,2943742b

-26.06731117

92,59870590

4 6 COMMERCIAL ThINNiNG

¿t 6 COMMERCIAL THINNING

5 6 FINAL HARVEST

0 6 FINAL HARVEST

YEAR

0

10

20

30

TOTAL

-60.12090889

COST

141.57493414

5.41120552

3.49026420

OCR » .60629938

GROUP DESCRIPTION

1 0 SITE PREP AND PLANT

0 0 PRESCRIBED BURN

0 0 PRESCRIBED BURN

2,25121006 G 0 PRESCRIBED BURN

152,72769479

DISCOUNTED BENEFITS AND COSTS AT 3,4027% INTEREST PNW = ,00000007 BCR « 1.00000000

YEAR BENEFIT GROUP DESCRIPTION YEAR COST GROUP DESCRIPTION

0 148.52266774 I 0 SITE PREP AND PLANT

10 6.24990180 0 0 PRESCRIBED BURN

20 4,43810351 0 0 PRESCRIBED BURN

30 46.66275014 4 6 COMMERCIAL THINNING

30 3.15153156 0 0 PRESCRIBED BURN

40 33,13550476 4 6 COMMERCIAL THINNING

50 31.12010372 4 6 COMMERCIAL THINNING

70 95.21364445 S 6 FINAL HARVEST

40 -43.769Ö063Ö 0 6 FINAL HARVEST

TOTAL 162.3622046Ö TOTAL 162.36220461

DISCOUNTED BENEFITS AND COSTS AT 2,4tí27% INTEREST PNW » 127.70121759 BCR » 1.69641789

YEAR BENEFIT GROUP DESCRIPTION YEAR COST GROUP DESCRIPTION

0 164.56772517 1 0 SITE PREP AND PLANT

10 7.63127427 0 0 PRESCRIBED BURN

20 5.97163461 0 0 PRESCRIBED BURN

30 69.1Ö917677 4 6 COMMERCIAL THINNING

. . 30 4,67293154 0 0 PRESCRIBED BURN

40 54,14200565 4 6 COMMERCIAL THINNING

50 56,03413633 4 6 COMMERCIAL THINNING

70 208.1Ö753562 5 6 FINAL'HARVEST

40 -77.00807119 0 6 FINAL HARVEST

TOTAL- 310.54476338 TOTAL 182.64356579

16
APPENDIX C—SENSITIVITY COMPUTATION

Sensitivity analysis as used here refers to the

measurement of the sensitivity of certain profit

level criteria such as internal rate of return and

present net worth to changes in the input transaction values which define a given investment opportunity. The measurement is expressed as the

percentage change in the transaction value (or

group of values) required to effect a specified

change in the profit level criterion. These specified

changes are expressed by the user in terms of an

absolute change or a percentage change in the

criterion. For example, the user could measure the

amount of change in input required to change the

internal rate of return by plus or minus an

absolute 1.0 percent interest or by plus or minus

10 percent of the internal rate of return. The

specification of change in criteria effectively defines an upper threshold and a lower threshold for

each criterion with respect to sensitivity.

Transactions may be considered independently

or in groups. Each transaction may be in more

than one group, and any group may include one or

more transactions. All the transactions in any

group must be of the same type, i.e., costs or

benefits.

Where:

PC = The percentage change in the transaction values of the group required to

change the IROR to the error threshold interest rate.

PNW/ = The present net worth when transactions are discounted at the error

threshold interest rate.

zBGy = The sum of the discounted transactions in a benefit group discounted at

the threshold interest rate.

SCGr = The sum of the discounted transactions in a cost group discounted at the

threshold interest rate.

Example:

Given discounted values of transactions at the

threshold interest rate (X percent) are:

Group A

Discounted Discounted

benefits costs

fóio.oo

1 22.00

43.00

154.00

93.00^

lO.OOj

Group B

$75.00 $157.00

I. Sensitivity of Internal Rate of Return

When the transactions which define a given

investment opportunity are discounted at an interest rate equal to the IROR, the PNW is zero by

definition. When the discounting is done at the ±

error threshold interest rates, the PNW will not be

zero. In order to change the IROR from the base

rate to the threshold rate, the PNW must be

changed to zero when computed at the error

threshold interest rate. Changes in the PNW can

be effected either by changing benefits or costs.

The two formulae used to calculate percentage

changes in sensitivity data groups are:

a. for benefit transaction groups:

PC = - {I!^) X

iBGy

100

b. for cost transaction groups:

PC = (H^) X 100

^ XCGT )

Using equation (a) for group A:

-$82.00

PC = - X 100 = 256.25 percent

$32.00

If each value in the benefit transactions in

Group A is raised 256.25 percent, the schedule

will be:

Group A

Discounted Discounted

benefits costs

ÍI35.625

I 78.375

$ 54.00

93.00^

43.000 10.001

Group B

$157.00 $157.00

PNW = zero

Using equation (b) for Group B:

^^ -$82.00

If the cost transactions in Group B are lowered

by 79.61 percent, the schedule will be:

17
Group A

Discounted Discounted

benefits costs

ÍI10.00

I 22.00

$54.00

18.96 \

43.00 2.04) Group B

$75.00

PNW = zero

$75.00

IL Sensitivity of Present Net Worth

The value of PNW for an investment opportunity always implies some specified interest rate at

which the transactions have been discounted. The

sensitivity thresholds for PNW must be reached

assuming that same discount rate. The two formulae for calculating the percentage change in sensitivity groups are:

c. for benefit transaction groups:

PC =

/PNWT PNW\

5BG

for cost transaction groups

PC

/PNW - PNWT\

X 100

X 100

2CG

Where:

PC = The percentage change in the transaction values of the group, required to

change present net worth to the present net worth threshold.

PNW = The present net worth of the transaction schedule discounted at a specified interest rate.

PNWT = The specified present net worth

threshold.

2BG = The sum of the discounted transactions in a benefit group, discounted at

the specified interest rate.

2CG = The sum of the discounted transactions in a cost group discounted at the

specified interest rate.

Example:

Given the same schedule of discounted values as

used in th« IROR example and a specified PNW

error threshold level of $10:

Group A

Discounted

benefits

Í $10.00

\ 22.00

43.00

$75.00

Discounted

costs

$54.00

93.(

IOJ

$157.00

i.OO^

).OQf

Group B

PNW = -$82.00

Using equation (c) for Group A:

$10 -{-:

PC =

$32 X 100 = 287.5 percent

If the benefit transactions in Group A are raised

by 287.5 percent, the schedule will be:

Discounted

benefits

i$38.75 Group A

I 85.25

43.00

$167,00

PNW = $10.00

Discounted

costs

$54.00

93.00 \

10.00 Í

$157.00

Group B

Using equation (d) for Group B:

^^ -$82 - $10

" $103 ^ ^^^ ^ "^^-^^ P^'""^"*

If the cost transactions in Group B are lowered

by 89.32 percent, the schedule will be:

Discounted

benefits

Group A '$10.00

I 22.00

43.00

$75.00

PNW =$10.00

Discounted

costs

$54.00

9.'.93^

1.07 f

Group B

$65.00

ïV I'.S. GOVERNMENT PRINTING OFFICE: 1975 0^587-898

18