project. Annex III OUTLINE OF INVESTMENT EFFICIENCY INDICA TORS AND SIMULATION MODEL The following four parameters are usually utilized for measuring the profitability of a Payback period Benefit ratio Net present value Internal rate of return (a) Payback neriod The payback period measures the time taken for the net cash flow generated by an investment to pay back the of its initial investment. The shorter the payback period, the better the investment. With this method of investment appraisal, a project will be approved if its payback period is shorter than a limit that was set up previously. If it is a question of choosing between 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 rough measure of the amount of time that the capital is at risk. It may be the most frequently utilized method of appraisal in the industry at present. However, it has a number of serious disadvantages, for example: (a) Neglect of income after paxback The payback criterion completely ignores any cash proceeds after the payback date. These may be nil or many thousands of dollars, but the same value is indicated 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 is very important. For example, with a 4-year payback period, in a quickly changing market there would be considerable advantage in having the majority of income in the first year offset the relatively high risk. However, if the same investment with the same payback period were being made where changes are relatively few and the risk is consequently less, there might be considerable advantage in having a rising trend of net income. Both cases have the same payback periods, but very different characteristics which may influence the total amounts of discounted cash flow depending on the level of interest rate. However, the payback period indicator cannot show such differences.
The 56 (c) No indication on Qrofitabilitx Payback period gives no indication of the profitability of a project or even of whether it will ever be profitable. It assumes that once the capital outlay has been recovered, the investment proves while. It completely ignores the of raising capital as well as the opportunity investing elsewhere. Payback analysis, however, is in some circumstances a useful tool. Because it is simple and 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, 1 to 15 years are unlikely to be profitable even in mor~ conservative sectors, and are probably therefore not analyzing further.. Projects involving a relatively small capital outlay and with a short payback either absolutely or in relation to their likely lives are probably. undertaking without detailed analysis other than a payback calculation. This may be the case for 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.. (b) Benefit ratio Benefit ratio is defined as follows: Benefit ratio = Present of benefits Present of In this method, a ration of" 1" or above will indicate a project with discounted benefits greater than discounted s, and the project is therefore acceptable. A higher benefit - ratiois usually construed to mean greater profitability. To compute the ratio, it is necessary to decide on a discount rate. The best discount rate to use is probably the opportunity 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 of capital. In most developing countries this is assumed to be somewhere between 8 and 15 per cent. Another value that is sometimes used is the market rate of interest. This is, as a matter of fact, subject to error because of distortions that may occur in the market. benefit- ratio method suffers from the following disadvantages: (1) A common netting out convention is required to derive and benefit streamsto avoid misleading results in ranking projects using benefit ratios.
(2) The value of the benefit ratio depends on the discount rate used. Since selection of the right discount rate is always a problem, some doubt always exists as to the relevance of the calculated benefit- ratio. (c) Net uresent Net present is defined as follows: Net present = Present of benefits- Present of s = Present of net benefits In the above, net benefits is defined as the algebraic difference of benefit and in each year of the benefit and streams. The net benefit stream is also known as the cash flow. A positive value of the net present indicates a project where discounted benefits are greater than discounted s. The net present method has the following disadvantages: Although the net present is a measure of the profitability of a project, the measures is not tied to the amount of investment required. Two projects having the same net present may thus have widely different investment requirements. The value of net present depends on the discount rate used, and therefore suffers the disadvantage of having to select the right discount rate prior to the analysis. (3) It is necessary to ensure that all discounting is done to the same base year to allow proper comparison of alternative projects. (d) Internal rate of return Internal rate of return is defined as "the discount rate which will cause the net present 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 decreases as the discount rate is increased. There is one value of the discount rate at which the net present becomes zero as shown in Figure A-I. This discount rate is known as the internal rate of return. ~'7
~1-,,I~ :::::j ~ -+-i -4 2 2 1 N~--+-, =j==j::~ 12 1 8 ~ t 6 ~ -2, I I I I -1 ),...,.1 ""'" -..;;J J -i -I -1 -i 4 6 1 12 14 16 Discount rate (%) 18 2 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. Investment (1) Return of capital (1) Return on capital Year 2 3 4 5 6 7 8 9 1 In this project, the original investment of 1 produces a return (profit) of 2 in each year of the life of the project. At the end of the project life, the project also generated sufficient additional profit to provide for the return of the capital (original investment) of 1. This project then has an IRR of 2 per cent (2 divided by 1). Of course, in practice, the investment sums and 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-anderror procedure and consequently is a little bit troublesome. However, standard computer programmes are available in many spread sheet software forms for personal computer, from which the IRR can be computed rapidly for any given cash flow (net benefit) stream as explained below. 58
Adjustable Constraints: The +H=O+H=O +E4>+4> (e) Simulation model of.investment efficienc~ indicators A printout of a simulation model which is designed to compute the four investment efficiency indicators simultaneously for two cases is contained in tables 1-III(a) and (b). The model which is programmed on the basis of Lotus 1-2-3 can compare the respective indicators of 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 tables l-iii(a) and l-iii(b) respectively. In each table, capital s, operating and maintenance s and gross benefits should be entered to Column C, 9 and F respectively. Be careful not to enter values to any other parts, since these cells contain formulas which will return values in accordance with the independent variables. Three indicators, vis. (B) Payback period, (c) Benefit ration and (d) Net present will be automatically returned for tables l-iii(a) and (b) when the above-mentioned values are duly entered. The attached printout shows such indicators at discount rates of8. and 12. per cent on the same cash flow in tables l-iii(a) and (b) respectively. The user may utilize only one table if two are not needed. The last item in the head panel, ( e) Result of @IRR indicates internal rates of return of Tables 1 and 2. The user must supply an initial estimate-of the 'internal rate of return. When it is too far from the correct rate, the function will return ERR: If that occurs, enter another estimate to recalculate the fonnula. Note also that if the range contains multiple negative values, @IRR may return inconsistent or inaccurate results. The user may easily verify the accuracyof a returned internal rate of return by copyingcommands the value to cell E4 and/or G4. In this case, the are:/,range, Value, press Enter, up 4 rows, press Enter. If the value was correct, the: net present value in E7 and G7 will turn to Zero. The internal rate of return will also be calculated by using the "Solver" function of Lotus-2-3 under the following definition: cells: E4 and 4 (discount rate) total net present value (H and H ) shall be zero, viz. and discount rates shall be negative, viz. 59
Table B Tables I-ill: (a) and (b) Investment efficiency indicators (simulation model) IT~~LE1.~2 b) TABLE2~ 8.% ~.i.~.~f!;.~~.~.:':~.~.e.: Payback period (year): 12.% 1 c) Benefit d) Net e) Result ratio: present : of (Q}IRR: Enter estimated IRR in 18 and/or K8 13 1.2482526 1.697564 8,49 13.795% 2,41 13.795% 'TABLE I 11 'TABLE 2.%1 I Table I-III (a) Yrl Discount factor B 1. III.9259.8573.7938.735 Capital O+M D C 125 75 14 15 Total Gross benefit NPW NPV Return (C+D)xB F FxB G-E SUM H Pre;sent 451 4168 3859 3573 1457 135 125.686 1 11 12 13 Present 6944 1157.632.5835.543.52.46.4289.3971.3677.345.3152 21 171 729 992 91.8 85 787 675 625 579 65 7475 ~==:~~ 536 238, -6944-19444 344-1641 2818-13583 269-1973 2416-87 2237-6 271-4249 1918-2331 338 363 2836 2626 24 2252 1776' 1644 1523 285 193 1787 249 447 status 141-5 -.., 189. 261 57 422 ~ 135 129 -~ 6536 849 8491 to + Discount factor Capital C 1..8929 (C+D)xB 1.566 13 14 15 Total D 1 3.7118.63.5674 12 Present 125 75.7972 1 11 O+M.4523.439.366.2.2875.2567.2292.246.1827 2~ 125 6696 13 121 18 965 861 769 687 613 547 489 436 39 348 311 238 29257 Gross benefit F 65 7475 6 Cash flow F-(C+D) 26 27 28 29 3 31 26 395 l-iii(b) Yr~ 2.%1 (' US$) 125 2 I -75 48 (' US$) Present FxB NPW NPV Return - status to G-E SUM H + 4185 3737 3336 2979-6696 -19196 283-16366 2527.1384 2256-11583 214-9569 266 2375 212 1893 169 1799-7771 166-6165 1434-4731 128-3451 1143-238 159 1348 123 174 1188 121-1287 911-376 814 438 726 1164 877 241 31298 241 52 53 54 52 Cash flow F-(C+D) -75 48 395