Annex III

OUTLINE OF INVESTMENT EFFICIENCY INDICA TORSAND SIMULATION MODEL

The following four parameters are usually utilized for measuring the profitability of a

project.

Payback periodBenefit cost ratioNet present valueInternal rate of return

(a) Payback neriod

The payback period measures the time taken for the net cash flow generated by aninvestment to pay back the cost of its initial investment. The shorter the payback period, thebetter the investment. With this method of investment appraisal, a project will be approved if itspayback period is shorter than a limit that was set up previously. If it is a question of choosingbetween projects, then the one with the shorter payback period will be chosen.

Payback period criterion has the merit of being simple to calculate and gives a roughmeasure of the amount of time that the capital is at risk. It may be the most frequently utilizedmethod of appraisal in the industry at present. However, it has a number of seriousdisadvantages, for example:

(a) Neglect of income after paxback

The payback criterion completely ignores any cash proceeds after the paybackdate. These may be nil or many thousands of dollars, but the same value isindicated by the payback period.

(b) Neglect of timing of cash flows

It also ignores the timing of the cash flows within the payback period, which isvery important. For example, with a 4-year payback period, in a quickly changingmarket there would be considerable advantage in having the majority of incomein the first year offset the relatively high risk. However, if the same investmentwith the same payback period were being made where changes are relatively fewand the risk is consequently less, there might be considerable advantage in havinga rising trend of net income. Both cases have the same payback periods, but verydifferent characteristics which may influence the total amounts of discounted cashflow depending on the level of interest rate. However, the payback periodindicator cannot show such differences.

55

No indication on Qrofitabilitx(c)

Payback period gives no indication of the profitability of a project or even ofwhether it will ever be profitable. It assumes that once the capital outlay has beenrecovered, the investment proves worthwhile. It completely ignores the cost ofraising capital as well as the opportunity cost investing elsewhere.

Payback analysis, however, is in some circumstances a useful tool. Because it is simpleand easy to calculate, it can be used as an initial screening device to save time in the followingways:

Projects with a very long payback of more than, for example, 10 to 15 years areunlikely to be profitable even in mor~ conservative sectors, and are probablytherefore not worth analyzing further. .

Projects involving a relatively small capital outlay and with a short payback eitherabsolutely or in relation to their likely lives are probably. worth undertakingwithout detailed analysis other than a payback calculation. This may be the casefor various kinds of office machines.

However, payback analysis is a very dangerous method of investment appraisal on whichto rely for decisions involving large amounts of capital. Itis as likely to give the wrong answeras to give the right one. .

Benefit cost ratio(b)

Benefit cost ratio is defined as follows:

Present worth of benefitsPresent worth of cost

Benefit cost ratio =

In this method, a ration of" 1" or above will indicate a project with discounted benefitsgreater than discounted costs, and the project is therefore acceptable. A higher benefit -cost ratiois

usually construed to mean greater profitability. To compute the ratio, it is necessary to decideon a discount rate. The best discount rate to use is probably the opportunity cost of capital, whichis

the rate of return (or profitability) of the least possible investment in an economy given thetotal available capital. However, in practice it is very difficult to obtain the value of opportunity

cost of capital. In most developing countries this is assumed to be somewhere between 8 and 15per cent. Another value that is sometimes used is the market rate of interest. This is, as a matterof fact, subject to error because of distortions that may occur in the market.

The

benefit-cost ratio method suffers from the following disadvantages:

A common netting out convention is required to derive cost and benefit streamsto avoid misleading results in ranking projects using benefit cost ratios.

(1)

56

The value of the benefit cost ratio depends on the discount rate used. Sinceselection of the right discount rate is always a problem, some doubt always existsas to the relevance of the calculated benefit-cost ratio.

(2)

Net uresent worth(c)

Net present worth is defined as follows:Net present worth = Present worth of benefits- Present worth of costs

= Present worth of net benefits

In the above, net benefits is defined as the algebraic difference of benefit and cost in eachyear of the benefit and cost streams. The net benefit stream is also known as the cash flow. Apositive value of the net present worth indicates a project where discounted benefits are greaterthan discounted costs.

The net present worth method has the following disadvantages:

Although the net present worth is a measure of the profitability of a project, themeasures is not tied to the amount of investment required. Two projects havingthe same net present worth may thus have widely different investment

requirements.

The value of net present worth depends on the discount rate used, and thereforesuffers the disadvantage of having to select the right discount rate prior to the

analysis.

It is necessary to ensure that all discounting is done to the same base year to allowproper comparison of alternative projects.

(3)

(d) Internal rate of return

Internal rate of return is defined as "the discount rate which will cause the net presentworth of the project to be equal to zero". In other words, the internal rate of return could be called"break-even discount rate" for the project.

For normal projects where benefits follow an initial investment, the net present worthdecreases as the discount rate is increased. There is one value of the discount rate at which thenet present worth becomes zero as shown in Figure A-I. This discount rate is known as theinternal rate of return.

~'7

120

~

100

N~--+-,

80

=j==j::~

-1

~

-i~t 600~

~1-,~~

-I),...,.1""'"

,I~

-i-..;;J

J0 , I I I I

:::::j~~~~

-1-20

-+-i-40

0

2

4 6 10 12 14 16

Discount rate (%)

18 20 22 24 26

Figure A-I: Internal rate of return

The internal rate of return (IRR) is a measure of the return on and of capital for a project.The following illustration provides a simple definition of the IRR.

Return of capital(100)

Investment(100)

Return oncapital

20202020202020202020

Year 0

1

2 3 4 6 85 7 9 10

In this project, the original investment of 100 produces a return (profit) of 20 in each yearof the life of the project. At the end of the project life, the project also generated sufficientadditional profit to provide for the return of the capital (original investment) of 100. This projectthen has an IRR of 20 per cent (20 divided by 100). Of course, in practice, the investment sumsand profits will not take on such a simple pattern, and a different method to compute the IRR is

required.

Although manual computation of internal rate of return is possible, it involves a trial-and-error procedure and consequently is a little bit troublesome. However, standard computerprogrammes are available in many spread sheet software forms for personal computer, fromwhich the IRR can be computed rapidly for any given cash flow (net benefit) stream as explainedbelow.

58

(e) Simulation model of .investment efficienc~ indicators

A printout of a simulation model which is designed to compute the four investmentefficiency indicators simultaneously for two cases is contained in tables 1-III(a) and (b). Themodel which is programmed on the basis of Lotus 1-2-3 can compare the respective indicatorsof two cases for deciding their priority. It consists of three parts, namely the head panel, table 1-lII(a) and table 1-III(b) of one case and Table 2 of the other case.

In the head panel, the entry of discount rates should be made to cells E4 and G4 for tablesl-III(a) and l-III(b) respectively. In each table, capital costs, operating and maintenance costsand gross benefits should be entered to Column C, 9 and F respectively. Be careful not to entervalues to any other parts, since these cells contain formulas which will return values inaccordance with the independent variables.

Three indicators, vis. (B) Payback period, (c) Benefit cost ration and (d) Net presentworth will be automatically returned for tables l-III(a) and (b) when the above-mentioned valuesare duly entered. The attached printout shows such indicators at discount rates of8.0 and 12.0per cent on the same cash flow in tables l-III(a) and (b) respectively. The user may utilize onlyone table if two are not needed.

The last item in the head panel, ( e) Result of @IRR indicates internal rates of return ofTables 1 and 2. The user must supply an initial estimate-of the 'internal rate of return. When it istoo far from the correct rate, the function will return ERR: If that occurs, enter another estimateto recalculate the fonnula. Note also that if the range contains multiple negative values, @IRRmay return inconsistent or inaccurate results.

The user may easily verify the accuracythe value to cell E4 and/or G4. In this case, the4 rows, press Enter. If the value was correct, the:

The internal rate of return will also be calculated by using the "Solver" function of Lotus-2-3 under the following definition:

Adjustable

cells: E4 and 04 (discount rate)

Constraints:The

total net present value (H 32 and H 55) shall be zero, viz.

+H32=O+H55=O

and discount rates shall be negative, viz.

+E4>0+04>0

59

of a returned internal rate of return by copyingcommands are:/,Range, Value, press Enter, up

net present value in E7 and G7 will turn to Zero.

Tables I-ill: (a) and (b) Investment efficiency indicators (simulation model)

IT~~LE 1 TABLE2~8.000% 12.000%

10 13

1.2482526 1.0697564

8,049 2,04113.795% 13.795%

.~2 ~.i.~.~f!;.~~.~.:':~.~.e.: b) Payback period (year):

c) Benefit cost ratio:

d) Net present worth:

e) Result of (Q}IRR:

Enter estimated IRR

in 18 and/or K8

'TABLE 11 'TABLE 2 I

I 20.000%1 I 20.000%1

Table I-III (a) ('000 US$)

CapitalcostC

125007500

O+Mcost

D

Grossbenefit

F

Returnstatus

SUM H

-12500

-19444

-16401

-13583

-10973

-8557

-6320

-4249

-2331

-555

1089-.., .

DiscountfactorYrl

B1.00000.92590.85730.79380.73500.6806

III

1700170017001700

5250525052505250

0.63020.58350.54030.50020.4632

0.42890.39710.36770.34050.3152

261~4022 5327

6536

8049

-to+

323232323232

3232323226

2728293031

26

101112131415

Total 200001

17001700170017001700

17001700170017001700

23800

Presentworth

(C+D)xB12500

6944

1457

1350

1250

1157

1071

99291.8

850

787

729

675

625

579

536~==:~~

5250525052505250525052505250525052506500

74750

Pre;sentworth

FxB00

4501416838593573

33083063283626262432

, 2252

2085193017872049

40470

Cashflow

F-(C+D)-12500

-7500

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

4800

30950

NPWNPV

G-E-12500

-6944

3044

2818

2609

2416

2237

2071

1918

1776'1644

1523

1410

1305

1209

-~80491

Table

l-III(b) ('000 US$)

O+McostD

Grossbenefit

F

Returnstatus

SUM H

Cashflow

F-(C+D)

DiscountfactorYr~

B

Presentworth

FxB

1.00000.89290.79723.71180.63550.5674

CapitalcostC

125007500

-12500

-19196

-16366

.13840

-11583

-9569

-7771

-6165

-4731

-3451

-2308

17001170011700

1700

5250525052505250

0.50660.45230.40390.36060.3220

0.28750.25670.22920.20460.1827

-1287

-376

438

11642041

10

1112131415

Total 200~

17001700170017001700

17001700170017001700

23800

Presentworth

(C+D)xB125006696135512101080965

861769687613547

489436390348311

29257

52505250525052505250

52505250525052506500

74750

04185373733362979

26602375212018931690

15091348120310741188

31298

NPWNPV

G-E-12500

-6696

2830

2527

2256

2014

1799

1606

1434

1280

1143

1021

911

814

726

877

2041

-12500

-7500

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

3550

4800

30950

-to+

5555555555555555555555555552535452

60