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NPV Vs. IRR Methods The NPV and IRR methods would in certain situations give the same accept- reject decision. But they may also differ in the sense that the choice of an asset under certain circumstances may be mutually contradictory. The comparison of these methods, therefore, involves a discussion of (1) the similarities between them, and (2) their differences, as also the factors which are likely to cause such differences. NPV and IRR: Similarities The two methods-IRR and NPV- would give consistent results in terms of acceptance or rejection of investment proposals in certain situations. Conventional Investment A conventional investment is one in which the cash flow pattern is such that an initial investment (outlay or cash outflow) is followed by a series of cash inflows. Thus, in the case of such investments, cash outflows are confined to the initial period. Independent Proposals The independent proposals refer to investments the acceptance of which does not preclude the acceptance of others so that all profitable proposals can be accepted and there are no constraints in accepting all profitable projects. 10-1 The reason why both the methods are equivalent and support or reject a proposal is simple. According to the NPV method, the decision rule is that a project will be accepted if it has a positive NPV, that is, NPV exceeds zero. The IRR method would support projects in whose case the IRR is more than the required rate of return (r exceeds k). When the NPV = zero or the IRR = k, the project may be accepted or rejected. The projects which have positive net present values will also have an IRR higher than the required rate of return. Thus, Fig. 1 portrays NPV as (i) positive; (ii) zero; and (iii) negative corresponding to three situations (a) IRR > K; (b) IRR = K; (c) IRR < K. Figure 1 shows the relationship between the NPV of a project and the discount rate. If there is no K, or discount rate is zero (a very unreal situation), NPV is maximum. As the value of K increases, the NPV starts declining. At 12 per cent rate of discount, the NPV is zero. This is the IRR also because by definition it is that rate of discount which reduces the NPV to zero. Assuming cost of capital to be 8 per cent, we find that NPV is positive by amount (a) and the project is acceptable and so is it under IRR as its value is > K (0.12 > 0.08). If we assume K to be 16 per cent, the project is unacceptable as the NPV is negative by amount (b) and so is it under IRR as IRR < K (0.12 < 0.16). The two approaches lead to identical results with regard to the accept-reject decision. 10-2 y Net present value (a) (+) x 0 8 4 12 16 20 (b) Discount rate (K) (-) Figure 1 : NPV and Discount rate 10-3 NPV and IRR Methods: Differences However, in certain situations they will give contradictory results such that if the NPV method finds one proposal acceptable, IRR favours another. This is so in the case of mutually exclusive investment projects. If there are alternative courses of action, only one can be accepted. Such alternatives are mutually exclusive. The mutual exclusiveness of the investment projects may be of two types: (i) technical, and (ii) financial. Technical Exclusiveness The term technical exclusiveness refers to alternatives having different profitabilities and the selection of that alternative which is the most profitable. Thus, in the case of a purchase or lease decision the more profitable out of the two will be selected. Financial Exclusiveness The mutual exclusiveness may also be financial. If there are resource constraints, a firm will be forced to select that project which is the most profitable rather than accept all projects which exceed a minimum acceptable level (say, k). The exclusiveness due to limited funds is popularly known as capital rationing. The different ranking given by the NPV and IRR methods can be illustrated under the following heads: 1. Size-disparity problem; 2. Time-disparity problem; and 3. Unequal expected lives. 10-4 1. Size-disparity problem Size disparity arises when the initial investment in mutually exclusive projects is different. Example 1 Particulars Project A Project B Project B-A Cash outlays (Rs 5,000) (Rs 7,500) (Rs 2,500) Cash inflows at the end of year, 1 6,250 9,150 2,900 IRR (%) 25 22 16 k 10 NPV 681.25 817.35 Thus, the two methods rank the projects differently. Project A has a higher IRR (0.25) than project B (0.22) but the NPV of project B (Rs 817.35) is more than that of A (Rs 681.25). The important question is which method, in such a situation, gives better results? The answer should be related to the effect of the decision on the maximisation of the shareholders’ wealth. The IRR method is not compatible with the goal of wealth maximisation. It is concerned with the rate of return on investment or yield rather than the total yield on the investment. In the above example, assuming 10 per cent to be the required rate of return, the firm would be left with Rs 750 [Rs 6,250 – (Rs 5,000 + 0.10 × Rs 5,000)] after one year in case project A is accepted and Rs 900 [Rs 9,150 – (Rs 7,500) + 0.10 × Rs 7,500] in case project B is accepted. The NPV method suggests that project B is better. This recommendation is consistent with the goal of the firm of maximising shareholders’ wealth. 10-5 Incremental Approach The conflict between the NPV and IRR in the above situation can be resolved by modifying the IRR so that it is based on incremental analysis. According to the incremental approach, when the IRR of two mutually exclusive projects whose initial outlays are different exceeds the required rate of return, the IRR of the incremental outlay of the project requiring a bigger initial investment should be calculated. This involves the following steps: 1) Find out the differential cash flows between the two proposals. 2) Calculate the IRR of the incremental cash flows. 3) If the IRR of the differential cash flows exceeds the required rate of return, the project having greater investment outlays should be selected, otherwise it should be rejected. In Example 1, the IRR of the differential cash outlay of Project B is 16 per cent. The required rate of return is 10 per cent. Thus, project B is better than project A in spite of the fact that IRR in the latter is lower because it offers the benefits offered by project A plus a return in excess of the required return on Rs 2,500, that is, differential cash outlays. 10-6 2. Time-disparity Problem Time-disparity arises when the cash flow pattern of mutually exclusive projects is different. Example 2 Year Cashflows Project A Project B 0 Rs 1,05,000 Rs 1,05,000 1 60,000 15,000 2 45,000 30,000 3 30,000 45,000 4 15,000 75,000 IRR (%) 20 16 NPV (0.08) 23,970 25,455 We find on the basis of a comparison of the internal rate of returns that project A is better, but the NPV method suggests that project B is better. Since the cost of capital is 8 per cent, given the objective of the firm to maximise wealth, project B is definitely better. Under the time-disparity problem it is the cost of capital which will determine the ranking of projects. If we take k = 0.10, we shall find project A is better as its net present value would be Rs 19,185 compared to Rs 18,435 of B. Its IRR is also more than that of B. Both the methods give identical prescription. But it does not imply that the IRR is superior to the NPV method, as the NPV is giving the same ranking as the IRR. In the event of conflicting rankings, the firm should rely on the rankings given by the NPV method. 10-7 3. Projects With Unequal Lives Another situation in which the IRR and NPV methods would give a conflicting ranking to mutually exclusive projects is when the projects have different expected lives. This is shown in Example 3. Example 3 There are two projects A and B. A has a service life of one year, while B’s useful life is five years. The initial cash outlay for both the projects may be assumed to be Rs 20,000 each. The cash proceeds from project A (at the end of the first year) amount to Rs 24,000. The cash generated by project B at the end of the fifth year is likely to be Rs 40,200. Assume that the required rate of return is 10 per cent. Compute the NPV and the IRR of the two projects. Solution IRR and NPV of Projects A and B Project IRR (per cent) NPV A 20 Rs 1,816 B 15 4,900 Obviously, the ranking given by the IRR and NPV methods is different. According to the IRR method, the recommendation would favour project A while the NPV method would support project B. The conflict in the ranking by the two methods in such cases may be resolved by adopting a modified procedure. There are two approaches to do this: 10-8 (1) Common time horizon approach Common time horizon approach makes a comparison between projects that extends over multiples of the lives of each. Example 4 Particulars Project A Project B Initial outlay Rs 10,000 Rs 20,000 Cash inflows after taxes Year-end 1 8,000 8,000 2 7,000 9,000 3 Nil 7,000 4 Nil 6,000 Service life (years) 2 Required rate of return 0.10 10-9 Solution Project A Year Cash flows PV factor Total present value 0 Rs 10,000 1.000 (Rs 10,000) 1 8,000 0.909 7,272 2 7,000 0.826 5,782 3 (10,000) a 0.826 (8,260) 3 8,000 0.751 6,008 4 7,000 0.683 4,781 NPV 5,583 a Machine replaced at the end of year 2. Project B Year Cash flows PV factor Total present value 0 Rs 20,000 1.000 Rs 20,000 1 8,000 0.909 7,272 2 9,000 0.826 7,434 3 7,000 0.751 5,257 4 6,000 0.683 4,098 Net present value 4,061 Decision Project A should be preferred to project B because of its larger NPV. If we had compared the two projects without incorporating the consequences of replacing the machine at the end of year 2, the decision would have been the reverse, because the net present value of project A then would be Rs 3,054 [Rs 7,272 + Rs 5,782 – Rs 10,000]. 10-10 (2) Equivalent annual value, (EANPV)/cost approach (EAC). The EANPV/EAC is a better approach. The EANPV is determined dividing the NPV of cash flows of the project by the annuity factor corresponding to the life of the project at the given cost of capital. The EAC is obtained dividing the total PV of cash outflows by the relevant annuity factor. While the maximisation of EANPV is the decision-criterion in the case of revenue-expanding proposals, the minimisation of EAC is the guiding criterion for cost reduction proposals. 10-11 Example 5 (Revenue-expanding Investment Proposal) A firm is considering to buy one of the following two mutually exclusive investment projects: Project A: Buy a machine that requires an initial investment outlay of Rs 1,00,000 and will generate the CFAT of Rs 30,000 per year for 5 years. Project B: Buy a machine that requires an initial investment outlay of Rs 1,25,000 and will generate the CFAT of Rs 27,000 per year for 8 years. Which project should be undertaken by the firm? Assume 10 per cent as cost of capital. Solution (i) Determination of NPV of Projects A and B Project Years CFAT PV factor (0.10) Total PV NPV A 1-5 Rs 30,000 3.791 Rs 1,13,730 Rs 13,730 B 1-8 27,000 5.335 1,44,045 19,045 10-12 (ii) Determination of EANPV: Net present value of the project EANPV (1) PV of annuity correspond ing to life of the project at given cost of capital EANPV (A) = Rs 13,730/3.791 = Rs 3,621.74 EANPV (B) = Rs 19,045/5.335 = Rs 3,569.82 On the basis of NPV criterion, Project B is preferred. However, on the basis of EANPV, project A becomes more desirable, with higher EANPV. In fact, acceptance of project A would be a right decision. Example 6 (Cost-reduction Investment Proposal) A firm is considering to instal a large stamping machine. Two machines currently being marketed will do the job satisfactorily. Machine A costs Rs 50,000 and will require cash running expenses of Rs 15,000 per year. It has a useful life of 6 years and is expected to yield Rs 2,000 salvage value at the end of its useful life. Machine B costs Rs 65,000 but cash running expenses are expected to be Rs 12,000. This machine is expected to have a useful life of 10 years with salvage value of Rs 5,000. Assume both the machines would be depreciated on straight line basis for tax purposes. If the corporate tax rate is 35 per cent and cost of capital is 10 per cent, which machine should be bought by the company? 10-13 Solution Equivalent Annual Costs of Machines A and B Particulars Costs PV Adjusted PV Machine A Machine B factor Machine A Machine B (0.10) 0 (Initial cost) Rs 50,000 Rs 65,000 1.000 Rs 50,000 Rs 65,000 (Operating cost): 1-6 years (A) 6,950 1-10 years (B) — 5,700 4.355 30,267.25 6.145 ________ 35,026.50 80,267.25 1,00,026.50 Less: Salvage value: 6th year (A) 2,000` 0.564 1,128.00 — 10th year (B) 5,000 0.386 — 1,930 Present value of total costs 79,139.25 98,096.50 Divided by annuity PV factor for 10 per cent corresponding to the life of the project (capital recovery factor) 4.355 6.145 Equivalent annual cost (EAC) 18,172 15,963.63 Recommendation Since Machine B has a lower equivalent annual cost, it is preferred investment. 10-14 Working Notes Determination of Operating Costs Particulars Machine A Machine B Cash running cost Rs 15,000 Rs 12,000 Less: Tax shield @35 per cent (assuming profitable 5,250 4,200 operations) Less: Tax advantage on depreciation charged every year: Machine A (Rs 8000 × 0.35) 2,800 — Machine B (Rs 6,000 × 0.35) — 2,100 Effective operating cash outflows 6,950 5,700 10-15 Reinvestment Rate Assumption The conflict between the NPV and IRR methods is mainly ascribed to the different reinvestment rate assumptions of intermediate cash inflows accruing from projects. The IRR method implicitly assumes that the cash flows generated from the projects are subject to reinvestment at IRR. In contrast, the reinvestment rate assumption under the NPV method is the cost of capital. The assumption of the NPV method is conceptually superior to that of the IRR as the former has the virtue of having a uniform rate which can consistently be applied to all investment proposals. The IRR can be modified (to overcome the deficiency of the reinvestment rate assumption) assuming the cost of capital to be the reinvestment rate. Implicit investment rate Implicit investment rate is the rate at which interim cash flows can be invested. 10-16 The superficiality of the reinvestment rate under the IRR method can be demonstrated by comparing the following two investment projects. Project Initial investment Cash inflows Year 1 Year 2 A Rs 100 Rs 200 0 B 100 0 Rs 400 Under the IRR method, both projects have a rate of return of 100 per cent. If Rs 100 were invested for one year at 100 per cent, it would grow to Rs 200, and if invested for two years, to Rs 400. Since both the projects have the same IRR, the firm should be indifferent regarding their acceptability, if only one of two projects is to be picked up as both the projects are equally profitable. For this to be true, it is necessary that Rs 200 received at the end of year 1 in case of project A should be equal to Rs 400 at the end of year 2. In order to achieve this, it necessarily follows that the firm must be able to reinvest the first year’s earnings at 100 per cent. If not, it would be unable to transform Rs 200 at the end of the first year into Rs 400 at the end of the second. And if it cannot transform Rs 200 into Rs 400 in a year’s time, the two projects A and B cannot be ranked equal. There is no reason to believe that a firm can find other investment opportunities at precisely the required rate. In contrast, the present value method does not pose any problem. Let us calculate the present value of Example 7, assuming cost of capital (k) as 10 per cent. 10-17 Example 7 Year Project A Project B Cashflows PV factor Total PV Cashflows PV factor Total PV 1 Rs 200 0.909 Rs 181.80 0 — — 2 0 — ______ Rs 400 0.826 Rs 330.40 181.80 330.40 Less: Initial outlay 100.00 100.00 Net present value 81.80 230.40 The PV method indicates that project B is preferable to project A as its net present value is greater. The reinvestment rate in the PV method seems more realistic and reasonable. It assumes that earnings are reinvested at the same rate as the market cost of capital. However, the IRR can be modified assuming the cost of capital to be the reinvestment rate. The intermediate cash inflows will be compounded by using the cost of capital. The compounded sum so arrived at and the initial cost outflows can be used as the basis of determining the IRR. Thus, the assumption regarding the reinvestment rate of the cash inflows generated at the intermediate stage is theoretically more correct in the case of NPV as compared to the IRR. 10-18 Computational Problems IRR method also suffers from computational problems. These may be discussed with reference to two aspects. Computation in Conventional Cash Flows It has been shown while computing the IRR that the calculation of the IRR involves a trial-and-error procedure as a result of which complicated computation has to be done. In conventional proposals having a constant cash inflow stream (i.e. annuity) the computation, is not so tedious. Computation in Non-conventional Flows The problem of computation of IRR gets accentuated when cash flow patterns are non-conventional. The complications in such cases are a) that the IRR is indeterminate, and b) there may be multiple IRRs 10-19 Indeterminate IRR For the following pattern of cash flows of an investment proposal, the IRR cannot be determined. Example 8 CO0 = Rs 1 CFAT1 2 CO2 2 Where subscripts 0, 1, 2 refer to respective time periods, CFAT = cash inflows, CO = cash outflows The required equation to solve the IRR is: 2 2 1 , which leads to r 2 1 1 r 2 1 r Clearly, the value of IRR is intermediate. On the other hand, the NPV of this project, given k as 10 per cent, can be easily ascertained. This would be negative (Rs –0.834), as shown below: 10-20 Clearly, the value of IRR is intermediate. On the other hand, the NPV of this project, given k as 10 per cent, can be easily ascertained. This would be negative (Rs –0.834), as shown below: Year Cash flows PV factor Total present value 0 Rs (1) 1.000 Rs 1.000 1 +2 0.909 1.818 2 (2) 0.826 (1.652) (0.834) Multiple Rates of IRR Another serious computational deficiency of IRR method is that it can yield multiple internal rates of return. This is illustrated in Example 9. Example 9 Initial cost Year 0 (Rs 20,000) Net cash flow 1 90,000 Net cash flow 2 (80,000) 10-21 Rs 90,000 Rs 80,000 The required equation is : Rs 20,000 1 r 1 r 2 Let (1 + r) be = X and divide both sides of equation by Rs 10,000, 2 = [(9/X) – (8/X)2] = 0 Multiplying by X 2, we can transform the equation into the quadratic form, 2X 2 – 9X + 8 = 0 Such an equation with a variable to the second power has 2 roots which can be identified as: b b 2 4ac X (2) 2a where a = coefficient of the variable raised to the second power b = coefficient of the variable raised to the first power c = constant or coefficient of the variable raised to the zero power Substituting the values for a, b, and c into the quadratic formula produces value for X of 1.21. Since X = (1 + r), the internal rates for this project are 21.9 and 228 per cent. 10-22 Thus, the project yields a dual IRR. This kind of problem does not arise when the NPV method is used. The problem with the IRR is that if two rates of return make the present value of the project zero, (21.9 and 228 per cent respectively in our example), which rate should be used for decision-making purposes? To conclude the discussion relating to the comparison of NPV and IRR methods, the two methods would give similar accept-reject decisions in the case of independent conventional investments. They would, however, rank mutually exclusive projects differently in the case of the 1) Size-disparity problem, 2) Time-disparity problem, and 3) Unequal service life of projects. The ranking by the NPV decision criterion would be theoretically correct as it is consistent with the goal of maximisation of shareholders’ wealth. 10-23 Net Present Value Vs. Profitability Index In most situations, the NPV and PI, as investment criteria, provide the same accept and reject decision, because both the methods are closely related to each other. Under the PI method, the investment proposal will be acceptable if the PI is greater than one; it will be greater than one only when the proposal has a positive net present value. Likewise, PI will be less than one when the investment proposal has negative net present value under the NPV method. However, while evaluating mutually exclusive investment proposals, these methods may give different rankings. Example 10 Year Project A Project B 0 (Rs 50,000) (Rs 35,000) 1 40,000 30,000 2 40,000 30,000 Present value of cash inflow (0.10) 69,440 52,080 NPV 19,440 17,080 PI 69,440/50,000 = 1.39 52,080/35,000 = 1.49 Thus, project A is acceptable under the NPV method, while project B under the PI method. Which project should the firm accept? The NPV technique is superior and so project A should be accepted. 10-24 Project Selection Under Capital Rationing The capital rationing situation refers to the choice of investment proposals under financial constraints in terms of a given size of capital expenditure budget. The objective to select the combination of projects would be the maximisation of the total NPV. The project selection under capital rationing involves two stages: (1) identification of the acceptable projects. (2) selection of the combination of projects. The acceptability of projects can be based either on profitability index or IRR. The method of selecting investment projects under capital rationing situation will depend upon whether the projects are indivisible or divisible. In case the project is to be accepted/rejected in its entirety, it is called an indivisible project; a divisible project, on the other hand, can be accepted/rejected in part. These are illustrated in Examples 11 and 12 respectively. 10-25 Example 11 (Divisible Project) A company has Rs 7 crore available for investment. It has evaluated its options and has found that only 4 investment projects given below have positive NPV. All these investments are divisible. Advise the management which investment(s)/projects it should select. Project Initial investment (Rs NPV (Rs crore) PI crore) X 3.00 0.60 1.20 Y 2.00 0.50 1.25 Z 2.50 1.50 1.60 W 6.00 1.80 1.30 Solution Ranking of the Projects in Descending Order of Profitability Index Project and (rank) Investment outlay Profitability index NPV (Rs crore) (Rs crore) Z (1) 2.50 1.60 1.50 W (2) 6.00 1.30 1.80 Y (3) 2.00 1.25 0.50 X (4) 3.00 1.20 0.60 Accept Project Z in full and W in part (Rs 4,50,000) as it will maximise the NPV. 10-26 Example 12 (Indivisible Project) A company working against a self-imposed capital budgeting constraint of Rs 70 crore is trying to decide which of the following investment proposals should be undertaken by it. All these investment proposals are indivisible as well as independent. The list of investments along with the investment required and the NPV of the projected cash flows are given as below: Project Initial investment (Rs NPV (Rs crore) crore) A 10 6 B 24 18 C 32 20 D 22 30 E 18 20 Which investment should be acquired by the company? Solution NPV from investments D, E and B is Rs 68 crore with Rs 64 crore utilised leaving Rs 6 crore to be invested in some other investment outlet. No other investment package would yield an NPV higher than this amount. The company is advised to invest in D, E and B projects. Trial and error process is an integral part of selecting optimal investment packages/set in capital ratinoning situation. Consider Example 13. 10-27 Example 13 Sound Limited has a financial resource constraint of a maximum of Rs 65 lakh in the current year. It has evaluated a large number of investment projects but has discarded all except those listed below. All the listed investment proposals are independent. The selected list of investments provide investment outlays, gross present value, NPV and present value index. Project Investment NPV Gross present Present value outlay value index A Rs 21,85,000 Rs 15,07,500 Rs 36,92,500 1.69 B 19,10,000 10,70,000 29,80,000 1.56 C 15,50,000 2,15,000 17,65,000 1.14 D 13,00,000 2,75,000 15,75,000 1.21 E 11,45,000 15,80,000 27,25,000 2.38 F 9,40,000 4,25,000 13,65,000 1.45 G 6,75,000 6,20,000 12,95,000 1.92 H 5,35,000 3,90,000 9,25,000 1.73 I 4,65,000 6,10,000 10,75,000 2.31 J 4,30,000 4,77,500 9,07,500 2.11 K 4,10,000 2,95,000 7,05,000 1.72 L 3,50,000 3,05,000 6,55,000 1.87 M 2,75,000 1,07,500 3,82,500 1.39 N 2,45,000 2,05,000 4,50,000 1.84 O 1,90,000 3,00,000 4,90,000 2.58 1,26,05,000 83,82,500 2,09,87,500 Which investments should be acquired by Sound Limited? 10-28 Solution First, we should arrange the investment projects in descending order of present value (PI) index. The optimal investment portfolio/set will be one which yields the maximum NPV. The investment projects are accordingly listed below. Project PI Investment outlays of NPV of Project Cumulative Project Cumulative O 2.58 Rs 1,90,000 Rs 1,90,000 Rs 3,00,000 Rs 3,00,000 E 2.38 11,45,000 13,35,000 15,80,000 18,80,000 I 2.31 4,65,000 18,00,000 6,10,000 24,90,000 J 2.11 4,30,000 22,30,000 4,77,500 29,67,500 G 1.92 6,75,000 29,05,000 6,20,000 35,87,500 L 1.87 3,50,000 32,55,000 3,05,000 38,92,500 N 1.84 2,45,000 35,00,000 2,05,000 40,97,500 H 1.73 5,35,000 40,35,000 3,90,000 44,87,500 K 1.72 4,10,000 44,45,000 2,95,000 47,82,500 A 1.69 21,85,000 66,30,0001 15,07,500 — B 1.56 19,10,000 63,55,000 10,70,000 58,52,5002 F 1.45 9,40,000 4,25,000 M 1.39 2,75,000 1,07,500 D 1.21 13,00,000 2,75,000 C 1.14 15,50,000 2,15,000 1 Not feasible at this stage; cumulative investment outlays exceed Rs 65 lakh. 2 Investment outlay as well as NPV consist of projects (from O to H) plus project B. 10-29 In case the company is guided simply by the PI index, then it selects the first nine projects (numbered from O through K) plus project B. This investment package yields an NPV of Rs 58,52,500. Project Investment outlays of NPV of Project (s) Cumulative Project (s) Cumulative O to H — Rs 40,35,000 — Rs 44,87,500 A Rs 21,85,000 62,20,000 Rs 15,07,500 59,95,000 M 2,75,000 64,95,000 1,07,500 61,02,500 Such a substitution exercise involves a trial and error approach. Thus, the optimal investment package consists of 10 projects (O, E, I, J, G, L, N, H, A and M) requiring a total investment outlay of Rs 64.95 lakh, yielding a total NPV of Rs 61,02,500. 10-30 Fallout of Capital Rationing Capital rationing limits the amount to be spent on capital expenditure decisions. The firm may impose such a limit primarily for two reasons: (i) there may be a paucity of funds and(ii) corporate managers/owners may be conservative and may not like to invest more than a specified/stated sum in capital projects at one point of time; they may like to accept projects with a greater margin of safety, measured by NPV. Whatever might be the reasons for capital rationing, it usually results in an investment policy that is less than optimal. The reason is that capital rationing does not allow the business firm to accept all profitable investment projects which could add to net present value and, thus, add to the wealth of shareholders. Another notable consequence is that capital rationing may lead to the acceptance of several small investment projects (promising higher return per rupee of investment) rather than a few large investment projects. Acceptance of such a package of investment projects is likely to have a bearing on the risk complexion of the business firm (perhaps it may decrease). Finally, selection criterion of investment projects under capital rationing (based on one-period analysis) does not reckon intermediate cash inflows expected to be provided by an investment project. 10-31 Case 1 Avon Chemical Company Ltd is presently paying an outside firm Re 1 per gallon to dispose of the waste material resulting from its manufacturing operations. At normal operating capacity the waste is about 40,000 gallons per year. After spending Rs 40,000 on research, the company discovered that the waste could be sold for Rs 15 per gallon if it was processed further. Additional processing would, however, require an investment of Rs 6,00,000 in new equipment, which would have an estimated life of 5 years and no salvage value. Depreciation would be computed by the reducing balance method @ 25 per cent. There are no other assets in the 25 per cent block. Except for the costs incurred in advertising Rs 20,000 per year, no change in the present selling and administrative expenses is expected if the new product is sold. The details of additional processing costs are as follows: variable—Rs 5 per gallon of waste put into process; fixed (excluding depreciation)—Rs 30,000 per year. In costing the new product, general factory overheads will be allocated at the rate of Re 1 per gallon. There will be no losses in processing, and it is assumed that all of the waste processed in a given year will be sold in that very year. Waste that is not processed further will have to be disposed off at the present rate of Re 1 per gallon. Estimates indicate that 30,000 gallons of the new product could be sold each year. The management, confronted with the choice of disposing off the waste, or processing it further and selling it, seeks your advice. Which alternative would you recommend? Assume that the firm’s cost of capital is 15 per cent and it pays, on an average, 35 per cent tax on its income. 10-32 Solution Cash outflows: Cost of additional investment Rs 6,00,000 (i) Present value of cash inflows (excluding depreciation), t = 1 – 5 Particulars Amount Increase in sales revenue (30,000 × Rs 15) Rs 4,50,000 Cost saving: reduction in disposal costs (30,000 × Re 1) 30,000 Less: Incremental costs: 4,80,000 Variable (30,000 × Rs 5) Rs 1,50,000 Fixed, manufacturing or processing 30,000 Advertising 20,000 2,00,000 Earnings before taxes 2,80,000 Less: Taxes 98,000 CFAT 1,82,000 × PVIFA (×)3.352 Total present value 6,10,064 10-33 (ii) PV of tax shield due to depreciation Year Depreciation Tax advantage PV factor Total PV 1 Rs 1,50,000 Rs 52,500 0.870 Rs 45,675 2 1,12,500 39,375 0.756 29,767 3 84,375 29,531 0.658 19,431 4 63,281 22,148 0.572 12,669 1,07,542 (iii) PV of tax advantage due to short-term capital loss: [0.35 × (Rs 1,89,844) × 0.497] = Rs 33,023. (iv) Determination of NPV Gross present value [(i) + (ii) + (iii)] Rs 7,50,629 Less: Cost of additional investment 6,00,000 NPV 1,50,629 Note: Rs 40,000 spent on research is irrelevant cost and so is the allocated share of factory overheads. Recommendation: Since the NPV is positive, the company is advised to purchase new equipment. 10-34 Case 2 An educational institute is planning to install airconditioners for its new computer centre. It has received proposals from 2 manufacturers. The first proposal is for the installation of 6 window airconditioners @ Rs 25,000 each. The other is for the installation of split airconditioners of an equal capacity costing Rs 2,00,000. The useful life of window airconditioners is 6 years and that of split airconditioners is 10 years. The cash operating costs associated with each proposal are given below: Year Proposal 1 Proposal 2 1 Rs 20,000 Rs 18,000 2 20,000 18,000 3 20,000 18,000 4 25,000 22,000 5 25,000 22,000 6 25,000 22,000 7 26,000 8 26,000 9 26,000 10 26,000 The salvage value of the window airconditioners at the end of 6 years is expected to be Rs 10,000 and that of the split airconditioners Rs 15,000. Advise the educational institute which proposal should be selected by it if its opportunity cost of funds is 10 per cent. 10-35 Solution Equivalent Annual Cost Proposal 1 Particulars Year Cost PV factor (at PV 10%) Purchase cost 0 Rs 1,50,000 1.000 Rs 1,50,000 Operating costs 1 20,000 0.909 18,180 2 20,000 0.826 16,520 3 20,000 0.751 15,020 4 25,000 0.683 17,075 5 25,000 0.621 15,525 6 25,000 0.564 14,100 Salvage value 6 (10,000) 0.564 (5,640) Total PV Rs 2,40,780 Equivalent Annual Cost (EAC) = (Total present value of the project / PV of annuity corresponding to the life of the project at the given cost of capital. Rs 2,40,780/4.355 = Rs 55,288.17 10-36 Proposal 2 Particulars Year Cost PV factor (at 10%) PV Purchase cost 0 Rs 2,00,000 1.000 Rs 2,00,000 Operating costs 1 18,000 0.909 16,362 2 18,000 0.826 14,868 3 18,000 0.751 13,518 4 22,000 0.683 15,026 5 22,000 0.621 13,662 6 22,000 0.564 12,408 7 26,000 0.513 13,338 8 26,000 0.467 12,142 9 26,000 0.424 11,024 10 26,000 0.386 10,036 Salvage Value 10 (15,000) 0.386 (5,790) Total PV Rs 3,38,174 Equivalent Annual Cost (EAC) = Rs 3,32,384/6.145 = Rs 55,032.38 Recommendation The educational institution should go for split airconditioners as their equivalent annual cost is lower. 10-37 Case 3 Bhushan Organics supplies chemicals and dyes to various units in and around NCR Delhi. The onsite delivery of chemicals and dyes every month is 2,000 units. The unit sale price is Rs 100. The cost per unit is Rs 50. It is using a tempo which can carry a maximum of 80 units. The total distance covered in one trip is 400 kms. The cost of diesel in the NCR Delhi is Rs 25.5 per litre. The average consumption of diesel is 8 kms per litre. Due to increase in demand for dyes for industrial use, Bhushan Organics has an opportunity to make and deliver 2,500 units per month. To cater to the increased demand, the company is contemplating buying a mini truck with a capacity to carry 165 units. The required mini truck is available from Tata for Rs 14,00,000. The tempo being currently used has a book value of Rs 6,00,000. It can be sold for Rs 4,00,000. The salary of the tempo driver is Rs 6,000 per month. If the mini truck is acquired, Bhushan Organics would have to increase his monthly salary to Rs 8,000. The consumption of diesel by the truck would average 5 kms per litre. The maintenance cost of the mini truck would be Rs 8,500 compared to Rs 6,200 maintenance cost of the tempo. Bhushan Organics uses straight line method of depreciation for tax purposes. The tempo has a remaining useful life of 5 years. The mini could truck serve the need of the Bhushan Organics for the next 5 years. The applicable tax rte is 35 per cent. Ravindra Arora, the CEO of Bhushan Organics , has asked the CFO, Sunil Joshi, to examine the financial viability of the proposal to replace the tempo by the mini truck and make appropriate recommendation in this regard. Assume a required rate of return of 14 per cent. 10-38 Solution: Financial Analysis of Replacement of Tempo by Mini Truck (A) Incremental cashoutflow (t = 0) Cost of mini truck Rs 14,00,000 Less sale value of tempo 4,00,000 Less tax advantage on loss on sale of tempo: Current book value Rs 6,00,000 Sale value 4,00,000 Loss on sale 2,00,000 Tax advantage x 0.35 70,000 Rs 9,30,000 10-39 (B) Increment cash outflows (t = 1 – 5) Incremental revenue1 (500 units x 12 months x Rs 100 6,00,000 Less incremental costs: Cost of additional units2 2,40,000 Diesel charges3 (15,300) Maintenance cost4 2,300 Driver’s salary5 24,000 Depreciation6 1,60,000 4,71,000 Earnings before taxes 1,29,000 Less taxes (0.35) 45,150 EAT 83,850 Add depreciation 1,60,000 CFAT (t = 1 – 5 years) 2,43,850 PVIFA5.14 x 3.433 Total PV 8,37,137 NPV (B – A) (92,863) 1 [ 500 units (2,500 units – 2,000 units) x 12 months x Rs 100] 2 (500 units x 12 x Rs 50) 3 Diesel charges 10-40 3 Diesel charges Truck Tempo Mileage km/lit 5 8 Kms per trip 400 400 Trips/month (2,500 units ÷ 165 units per trip) 15 - (2,000 units ÷ 80 units per trip) - - 25 Kms annually (12 months x 15 x 400) 72,000 - (12 months x 25 x 400) - 1,20,000 Diesel consumed (72,000 ÷ 5) 14,400 - (1,20,000 ÷ 8) - 15,000 Total cost (14,400 x Rs 25.5) Rs 3,67,700 - (15,000 x Rs 25.5) - Rs 3,82,000 Savings in diesel cost (Rs 3,82,500 – Rs 3,67,200) = (Rs 15,300) 4 Maintenance cost (Rs 7,500 – Rs 6,200) 5 Drivers salary [(Rs 8,000 – Rs 6,000) x 12 months) 10-41 6 Depreciation: Depreciation on truck (Rs 14,00,000 ÷ 5) Rs 2,80,000 Depreciation on tempo (Rs 6,00,000 ÷ 5) 1,20,000 1,60,000 Recommendation The proposal to acquire the mini truck and dispose off the tempo is financially viable. The CEO may approve it and initiate follow-up action. 10-42