CAPITAL BUDGETING BY ASIT KUMAR NAYAK(INMANTEC)

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For purposes of investment appraisal, the cashflow is the incremental cash receipts less the incremental cash expenditures solely attributable to the investment in question. The future costs and revenues associated with each investment alternative are – Capital costs, Operating costs, Revenue, Depreciation, and Residual value

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The life of the project may be determined by taking into consideration the following factors like Technological obsolescence, Physical deterioration A decline in demand for the output of the project etc.

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Investment Appraisal Techniques, Payback Period Method The payback period is usually expressed in years, which it takes the cash inflows from a capital investment project to equal the cash outflows. The method recognizes the recovery of original capital invested in a project. At payback period the cash inflows from a project will be equal to the project's cash outflows. This method specifies the recovery time, by accumulation of the cash inflows (inclusive of depreciation) year by year until the cash inflows equal to the amount of the original investment. The length of time this process takes gives the 'payback period' for the project. In simple terms it can be defined as the number of years required to recover the cost of the investment

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Illustration 12.1 The project involves a total initial expenditure of Rs. 2, 00,000 and it is estimated to generate future cash inflow of Rs. 30,000, Rs. 38,000, Rs. 25,000, Rs. 22,000, Rs. 36,000, Rs. 40,000, Rs. 40,000, Rs.28,000 Rs. 24,000 and Rs. 24,000 in its last year.

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Solution Calculation of Payback Period In six years, Rs. 1, 91,000 are recovered. :.Pay term = 6 years + Rs. 9,000/Rs.40,000 * 12 months = 6 years 3 months Years Cash inflows Cumulative cash inflows 1 30,000 30,000 2 38,000 68,000 3 25,000 93,000 4 22,000 1,15000 5 36,000 1,51,000 6 40,000 1,91,000 7 40,000 2,31,000 8 28,000 2,59,000 9 24,000 2,83,000 10 24,000 3,07,000

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Illustration 12.2 Analysis : In this example, Project Y would be selected as its payback period of 3 years is shorter" than the 4 years payback period of Project X. Initial investment Project X (1,00,000) Project Y (1,00,000) Cash inflows Total cash inflows Cash inflows Total cash inflows Year 1 20,000 20,000 25,000 25,000 Year 2 20,000 40,000 25,000 50,000 Year3 30,000 70,000 50,000 1,00,000 Year 4 30,000 1,00,000 20,000 1,20,000 Year5 50,000 1,50,000 10,000 1,30,000

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Accounting Rate of Return Method The accounting rate of return is also known as 'return on investment' or 'return on capital employed' method employing the normal accounting technique to measure the increase in profit expected to result from an investment by expressing the net accounting profit arising from the investment as a percentage of that capital investment. The method does not take into consideration all the years involved in the life of the project. In this method, most often the following formula is applied to arrive at the accounting rate of return. Accounting Rate of Return = Average Annual Profit After Tax / Average or Initial Investment * 100 Average Investment = Initial Investment + salvage Value / 2

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Illustration12.4 Consider the following investment opportunity: A machine is available for purchase at a cost of Rs. 80,000. We expect it to have a life of five years and to have a scrap value of Rs. 10,000 at the end of the five year period. We have estimated that it will generate additional profits over its life as follows: These estimates are of profits before depreciation. You are required to calculate the return on capital employed. Year 1 2 3 4 5 Amount (Rs.) 20,000 40,000 30,000 15,000 5,000

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Solution Total profit before depreciation over the life of the machine = Rs. 1, 10,000 .: Average profit p.a. = Rs. 1,10,000 /5 years = Rs. 22,000 Total depreciation over the life of the machine (Rs. 80,000 - Rs. 10,000) = Rs. 70,000 .,Average depreciation p.a. = Rs. 70,000/5 years = Rs. 14,000 :.Average annual profit after depreciation = Rs. 22,000 - Rs. 14,000= Rs. 8,000 Original investment required = Rs. 80,000 ..Accounting rate of return = (Rs. 8,000/Rs. 80,000) X 100 = 10% Average investment = (Rs. 80,000 + Rs. 10,000)/2 = Rs.45,000 Accounting rate of return = (Rs. 8,000/Rs. 45,000) X 100 = 17.78%

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Net Present Value Method The objective of the firm is to create wealth by using existing and future resources to produce goods and services. To create wealth, inflows must exceed the present value of all anticipated cash outflows. Net present value is obtained by discounting all cash outflows and inflows attributable to a capital investment project by a chosen percentage e.g. , the entity’s weighted average cost of capital. The method discounts the net cash flows from the investment by the minimum required rate of return, and deducts the initial investment to give the yield from the funds invested. If yield is positive the project is acceptable. If it is negative the project in unable to pay for itself and is thus unacceptable.

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The exercise involved in calculating the present value is known as ‘discounting and the factors by which we have multiplied the cash flows are known as the ‘discount factors’. The discount factor is given by the following expression: 1 / (1 + r) n Where, r = Rate of interest p.a. n = number of years over which we are discounting.

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Illustration 12.5 A firm can invest Rs. 10,000 in a project with a life of three years. The projected cash inflows are: Year 1 - Rs. 4,000, Year 2 - Rs. 5,000 and Year 3 - Rs. 4,000. The cost of capital is 10%p.a. should the investment be made? Solution Firstly the discount factors can be calculated based on Re. 1received in with 'r' rate of interest in 3 year 1 / (1 + r) n Year 1 = 1 / 1+ 10 / 100) = 1 / (1.10) = 0.909 Year 2 = 1 / 1+ 10 / 100) 2 = 1/ (1.10) 2 = 0.826 Year 3 = 1 / 1+ 10 / 100) 3 = 1/ (1.10) 3 = 0.751

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In this chapter, the tables given at the end of the book are used wherever possible. Obviously where a particular year or rate of interest is not given in the tables, it will be necessary to resort to the basic discounting formula. Analysis-Since the net present value is positive, investment in the project can be made. Year Cash flow (Rs.) Discount factor Present value (Rs.) 0 (10,000) 1,000 (10,000) 1 4,000 0.909 3,636 2 5,000 0.826 4,130 3 4,000 0.751 3,004 NPV = 770

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Internal Rate of Return Method Internal rate of return (IRR) is a percentage discount rate used in capital investment appraisals which brings the cost of a project and its future cash inflows into equality. It is the rate of return which equates the present value of anticipated net cash flows with the initial outlay. The IRR is also defined as the rate at which the net present value is zero. The rate for computing IRR depends on bank lending rate or opportunity cost of funds to invest which is often called as personal discounting rate or accounting rate. The test of profitability of a project is the relationship between the IRR (%) of the project and the minimum acceptable rate of return (%).The IRR can be stated in form of a ratio as shown below: Cash Inflows / Cash Outflows = 1 P.V. of Cash Inflows - P.V. of Cash Outflows = Zero

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The IRR is to be obtained by trial and error method to ascertain the discount rate at which the present values of total cash inflows will be equal to the present values of total cash outflows. If the cash inflow is not uniform, then IRR will have to be calculated by trial and error method. In order to have an approximate idea about such discounting rate, it will be better to find out the , actor: The factor reflects the same relationship of investment and cash inflows as in case of payback calculations F = I / C Where, F = Factor to be located I = Original Investment C = Average cash inflow per year

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Illustration 12.6 A company has to select one of the following two projects: Using the internal rate of return method, suggest which project is preferable. Particulars Project A Project B Cost 11,000 10,000 Cash inflows Year 1 6,000 1,000 Year 2 2,000 1,000 Year 3 1,000 2,000 Year 4 5,000 10,000

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Solution Factor in case of Project A = 11,000/ 3,500 = 3.14 Factor in case of Project B = 10,000/ 3,500 = 2.86 The factor thus calculated will be located in table given at the end of the book on the line representing number of years corresponding to estimated useful life of the asset. This would give the expected rate of return to be applied for discounting the cash inflows in finding the internal rate of return. In case of Project A, the rate comes to 10%while in case of Project B it comes to 15%.

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Project A The present value at 10% comes to Rs. 11,272. The initial investment is Rs. 11,000. Internal rate of return may be taken approximately at 10%. Year Cash inflows (Rs.) Discounting factor at 10% Present value (Rs.) 1 6,000 0.909 5,454 2 2,000 0.826 1,652 3 1,000 0.751 751 4 5,000 0.683 3,415 Total present value 11,272

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In case more exactness is required another trial rate which is slightly higher than 10 % ( since at this rate the present value is more than initial investment) may be taken. Taking a rate of 12%, the following results would emerge: The internal rate of return is thus more than 10%but less than 12%.The exact rate may be calculated as follows: P.V. required = 11,000 PV. at 10% = 11,272 PV. at 12% = 10,844 Actual IRR = 10 + 272 / 272-(-156)* 2 = 11.27% Year Cash inflows (Rs.) Discounting factor at 12% Present value (Rs.) 1 6,000 0.893 5,358 2 2,000 0.797 1,594 3 1,000 0.712 712 4 5,000 0.636 3,180 Total present value 10,844

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Project B Since present value at 15%comes only to Rs. 8,662, a lower rate of discount should be taken. Taking a rate of 10% the following will be the result. Year Cash inflows (Rs.) Discounting factor at 15% Present value (Rs.) 1 1,000 0.870 870 2 1,000 0.756 756 3 2,000 0.658 1,316 4 10,000 0.572 5,720 Total present value 8,662

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The present value at 10%comes to Rs. 10,067 which is more or less equal to the initial investment. Hence, the internal rate of return may be taken as 10%. Year Cash inflows (Rs.) Discounting factor at 10% Present value (Rs.) 1 6,000 0.909 909 2 2,000 0.826 826 3 1,000 0.751 1,502 4 5,000 0.683 6,830 Total present value 10,067

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In order to have more exactness to internal rate of return, can be interpolated as done in case of Project 'A' P.V. required 10,000 PV. at 10% 10,067 PV. at 12% 8,662 Actual IRR = 10 + 67 / 67 - (-1,338) X 5 = 10.24% Analysis - Thus, internal rate of return in case of Project A is higher as compared to Project B. Hence, Project A is preferable.

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Profitability Index Method It is a method of assessing capital expenditure opportunities in the profitability index. The profitability index (PI) is the present value of an anticipated future cash inflows divided by the initial outlay. The only difference between the net present value method and profitability index method is that when using the NPV technique the initial outlay is deducted from the present value of anticipated cash inflows, whereas with the profitability index approach the initial outlay is used as a divisor. In general terms, a project is acceptable if its profitability index value is greater than l. Clearly, a project offering a profitability index greater than 1 must also offer a net present value which is positive. When more than one project proposals are evaluated, for selection of one among them, the project with higher profitability index will be selected. Mathematically, PI (profitability index) can be expressed as follows: Profitability Index (PI) = Present Value of Cash Inflows / Present Value of Cash Outlay This method is also called 'cost-benefit ratio' or 'desirability ratio' method.

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lIIustration12.8 The following mutually exclusively projects can be considered: (Rs.) Analysis - According to the NPV method, Project A would be preferred, whereas according to profitability index Project B would be preferred. Although PI method is based on NPV, it is a better evaluation technique than NPV in a situation of capital rationing. For example two projects may have the same NPV of Rs. 10,000 but Project A requires initial outlay of Rs. 1,00,000 whereas B only Rs.50,000. Project B would be preferred as per the yard stick of PI method. Particulars Project A Project B PV of cash inflows (i) 20,000 8,000 Initial cash outlay (ii) 15,000 5,000 Net present value 5,000 3,000 Profitability Index (i)/ (ii) 1.33 1.60

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Capital Rationing Capital rationing is a situation where a constraint or budget ceiling is placed on the total size of capital expenditures during a particular period. Often firms draw up their capital budget under the assumption that the availability of financial resources is limited. Capital rationing refers to the selection of the investment proposals in a situation of constraint on availability of capital funds, to maximize the wealth of the company by selecting those projects which will maximize overall NPV of the concern. In capital rationing situation a company may have to forego some of the projects whose IRR is above the overall cost of the firm due to ceiling on budget allocation for the projects which are eligible for capital investment.

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Situations of Capital Rationing Capital rationing decisions can be studied under the following situations: Situation I- Projects are Divisible and Constraint is a Single Period One The following are the steps to be adopted for solving the problem under this situation: Calculate the profitability index of each project. Rank the projects on the basis of the profitability index calculated in (a) above. Choose the optimal combination of the projects.

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Illustration 12.11 Total fund available is Rs. 3, 00,000. Determine the optimal combination of projects assuming that the projects are divisible. Project Required initial investment NPV at the appropriate cost of capital A 1,00,000 20,000 B 3,00,000 35,000 C 50,000 16,000 D 2,00,000 25,000 E 1,00,000 30,000

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Solution Project Required initial outlay (Rs.) NPV at the appropriate cost of capital (Rs.) Profitability index [(3) / (2)] Rank (1) (2) (3) (4) (5) A 1,00,000 20,000 0.2 3 B 3,00,000 35,000 0.117 5 C 50,000 16,000 0.32 1 D 2,00,000 25,000 0.125 4 E 1,00,000 30,000 0.3 2

*(Rs. 2, 00,000 X 1/4) Therefore, the optimal combination of projects is C, E, A and 1/ 4th portion of D. Situation II - Projects are Indivisible and Constraint is a Single Period One The following steps to be followed for solving the problem under this situation: a. Construct a table showing the feasible combinations of the project (whose aggregate of initial outlay does not exceed the fund available for investment). b. Choose the combination whose aggregate NPV is maximum and consider it as the optimal project mix.: 

*(Rs. 2, 00,000 X 1/4) Therefore, the optimal combination of projects is C, E, A and 1/ 4th portion of D. Situation II - Projects are Indivisible and Constraint is a Single Period One The following steps to be followed for solving the problem under this situation: a. Construct a table showing the feasible combinations of the project (whose aggregate of initial outlay does not exceed the fund available for investment). b. Choose the combination whose aggregate NPV is maximum and consider it as the optimal project mix. Rank of Investment Project Required initial (Rs.) 1 C 50,000 2 E 1,00,000 3 A 1,00,000 4 1 / 4th of D 50,000* Total 3,00,000

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Illustration 12.12 Using the same data as used in the previous illustration, determine the optimal project mix on the basis of the assumption that the projects are indivisible. Solution (Rs.) Feasible Combinations Aggregate of NPVs A,C 36,000 A,D 45,000 A,E 50,000 C,D 41,000 C,E 46,000 D,E 55,000 A,C,E 66,000 By a careful inspection of the feasible combinations constructed in the above table, we can conclude that the optimal project mix is A, C and E because the aggregate of their NPVs is maximum.