Capital Budgeting and Time value of money

Transcription

1 Capital Budgeting and Time value of money Meaning and Concepts: Capital budgeting is commonly referred to as a fixed- asset management, when integrated with the financial manager s goal of attaining proper combinations of assets (i.e. optimal asset mix ) fixed assets assume a great deal of significance. Fixed assets are also frequency termed as the earning assets of the firm since they usually generate large returns. Such return is contrary to the limited earning power of and returns from short term assets. It is the decision making process by which the firms evaluate the purchase of major fixed assets. It involves firm s decision to invest its current funds for addition, disposition, modification and replacement of long-term or fixed assets. Capital budgeting decision involve the entire process of decision making relating to acquisition of long-term assets whose returns are expected to arise over a period beyond one year, planning and control of capital expenditures is a major decision area in any organisation. Its basic features can be summarised as follows: (i) (ii) (iii) It has the potentially of making large anticipated profits It involves a high degree of risk It involves a relatively long-term period between the initial outlay and the anticipated return. Significance of Capital Budgeting There are several factors and consideration which make the capital budgeting decisions as the most important decisions of a finance manager. The relevance and signify of capital budgeting may be stated as follows: (a) (b) (c) (d) Long term effects: the most important features of a capital budgeting decision and which makes the capital budgeting so significant is that these decisions have long term effects on the risk and return composition of the firm. These decisions affect the future position of the firm to a considerable extent as the capital budgeting decisions have long term implications and consequences. By taking a capital budgeting decision, a finance manager in pact makes a commitment into the future, both by committing to the future needs of funds of the projects and by committing to its future implications. Substantial commitments: the capital budgeting decisions generally involve large commitment of funds and as a result substantial portion of capital funds are blocked in the capital budgeting decisions, otherwise the firm may suffer from the heavy capital losses in time to come. It is also possible that the return from projects may not be sufficient enough to justify the capital budgeting decision. Irreversible decisions: most of the capital budgeting decisions are irreversible decisions. Once taken, the firm may not be in a position to revert back unless it is ready to absorb heavy losses, which may result due to abandoning a project in midway. Affect the capacity and strength to compete: The capital budgeting decisions affect the capacity and strength of a firm to face the competition. A firm may lose competitiveness of the decision to modernise is delayed or not rightly taken. Similarly, a timely decision to take over a minor competitor may ultimately result even in the monopolistic position of the firm. 66

2 Kinds of Capital Budgeting Decisions Since capital budgeting includes the process of generating, evaluating, selecting and following up on capital expenditure alternatives, allocation of financial resources should be made by the firm to its new investment projects in the most efficient manner. A firm may adopt the following three types of capital budgeting decisions: (i) Mutually Exclusive Projects It means if a firm accepts one project, it may rule out the necessity for other, i.e. the alternatives are mutually exclusive and only one is to be chosen. (ii) Accept- Reject Decisions The proposals which yield a higher rate of return in comparison with a certain rate of return or cost of capital are accepted and naturally, the others are rejected. For example, if the minimum acceptable return from a project is say 10%, after tax and an investment proposal which shows a return of 12%, may be accepted and another project which gives a return of 8% only may be rejected. In other words, using Net Present Value Method Criterion an investment opportunity will be accepted if NPV>0, or, the same will be rejected if NPV< 0. That is, all independent projects are accepted under this criterion. It is to be noted that independent projects are those which do not compete with one another, i.e. the acceptance of one precludes the acceptance of other. At the same time, those projects which will satisfy the minimum investment criterion should be taken into consideration. (iii) Capital Rationing Decision Capital rationing is normally applied to situations where the supply of funds to the firm is limited in some way. As such, the term covers many different situations ranging from that where the borrowings and lending rates faced by the firm differ to that where the funds available for investments are strictly limited. In other words, it occurs when a firm has more acceptable proposals than it can finance. At this point, the firm ranks the projects from highest to lowest priority and as such, a cut-off point is considered. Naturally, those proposals which are above the cut-off point will be accepted and those which are below the cut-off point are rejected, i.e. ranking is necessary to choose the best alternatives. Capital Budgeting Techniques Traditional or Non-discounting or, Unsophisticated Time-Adjusted or Discounted Cash Flows or, Sophisticated Accounting Rate of Return Pay Back Period Net Present Internal Rate Profitability Terminate Value of Return Index Value 67

3 Traditional or non-discounted cash flow techniques. (a) Payback period The term pay-back refers to the period in which the project will generate the necessary cash to recoup the initial investment. For example, if a project requires Rs. 20,000 as initial investment and it will generate on annual cash inflow of Rs. 5,000 for 10 years, the pay-back period will be 4 years, calculated as follows:- Pay-back period = = 20,000 5,000 inititalinvestment annual cash in flow The annual cash inflow is calculated by taking into account the amount of net income on account of the asset before depreciation but after taxation. The income so earned if expressed as a percentage of initial investment, is termed as unadjusted rate of return. annual return Unadjusted rate of return = 100 initial investment Advantages (i) (ii) (iii) (iv) Disadvantages (i) (ii) (iii) (iv) (v) 5000 = % 20,000 It is simple to apply, easy to understand and of particular importance to business which lack the appropriate skills necessary for more sophisticated techniques. In case of capital rationing, a company is compelled to invest in projects having shortest payback period. This method gives an indication to the prospective investors specifying when their funds are likely to be repaid. Ranking projects according to their ability to repay quickly may be useful to firm when experiencing liquidity constraints. It does not indicate whether an investment should be accepted or rejected, unless the payback period is compared with an arbitrary managerial target. If fails to take into account the timing of returns and the cost of capital. It fails to consider the whole life of a project. The traditional payback approach does not consider the salvage value of an investment. The bailout payback method concentrates on the abandonment alternative. This method makes no attempt to measure a percentage return on the capital investment and is often used in conjunction with other methods. The investment in projects with long payback periods are made with long-term planning and may not yield highest returns for a number of years and the payback method is biased against such investments. 68

4 (b) Average rate of return (ARR) method According to this method, the capital investment proposals are judged on the basis of their relative profitability. For this purpose, capital employed and related incomes are determined according to commonly accepted accounting principle and practices over the entire economic life of the project and then the average yield is calculated. Such a rate is termed as accounting rate if return. It may be calculated according to any of the following methods. Annual Average net earnings (I) 100 original investment Annual Average net earnings (II) 100 Average investment Average Investment: - ½ (Initial Cost +Installation Expenses-Salvage Value) + Salvage Value Advantages of ARR (i) The most significant attribute of ARR is that it is very simple to understand and easy to calculate, (ii) It can be easily computed on the basis of accounting data which are furnished by the financial statements. Disadvantages of ARR (i) The principal shortcoming of ARR is that it recognises only the accounting income instead of cash flows. (ii) It does not recognise the time value of money. (iii) It does not take into consideration the length of lives of the projects. (iv) It does not consider the fact that the profits may be re-invested Modern or Discounted Cash Flow Techniques Time Value of Money One of the most important principles in all of finance is the relationship between value of a rupee today and value of rupee in future. This relationship is known as the 'time value of money'. A rupee today is more valuable than a rupee tomorrow. This is because current consumption is preferred to future consumption by the individuals, firms can employ capital productively to earn positive returns and in an inflationary period, rupee today represents greater purchasing power than a rupee tomorrow. The value of money received today is different from the value of money received after some time in the future. The preference of money now, as compared to future money is, known as time preference for money. A rupee today is more valuable than a rupee after a year due to several reasons. Inflation: Under inflationary conditions the value of money, expressed in terms of its purchasing power over goods and services, declines. Risk: Re. 1 now is certain, whereas Re.1 receivable tomorrow is less certain. This bird-in-the-hand principle is extremely important in investment appraisal. Personal consumption preference: Many individuals have a strong preference for immediate rather 69

5 than delayed consumption. The promise of a bowl of rice next week counts for little to the hungry man Investment opportunities: Many like any other desirable commodity have a price, given the choice of Rs. 100 now or the same amount in one year s time it is always preferable to take the Rs. 100 now because it could be invested over the next year at say) 16 per cent interest rate to produce Rs. 116 at the end of one year. If 16 per cent is the best return available then you would be indifferent to receiving Rs. 100 now or Rs. 116 in one year s time. Expressed another way, the present value of Rs. 116 receivable one year hence is Rs The time value of the money may be computed in the following circumstances. (a) Future value of a single cash flow (b) Future value of an annuity (c) Present value of a single cash flow (d) Present value of an annuity Future Value of a Single Cash Flow For a given present value (PV) of money, future value of money (FV) after a period t' for which compounding is done at an interest rate of r, is given by the equation FV = PV (1 + r) t This assumes that compounding is done at discrete intervals. However, in case of continuous compounding, the future value is determined using the formula FV = PV * e rt Where e' is a mathematical function called 'exponential' the value of exponential (e) = The compounding factor is calculated by taking natural logarithm (log to the base of ). Example 1: Calculate the value of a deposit of Rs.2,000 made today, 3 years hence if the interest rate is 10%. By discrete compounding: FV = 2,000 * (1+0.10) 3 = 2,000 * (1.1) 3 = 2,000 * = Rs. 2,662 By continuous compounding: FV = 2,000 * e ( 0.10*3 ) =2,000 * = Rs Example 2. Find the value of Rs. 70,000 deposited for a period of 5 years at the end of the period when the interest is 12% and continuous compounding is done. Future Value = 70,000* e (0.12*5) = Rs. 1,27, The future value (FV) of the present sum (PV) after a period 't' for which compounding is done m' times a year at an interest rate of r, is given by the following equation: FV = PV (1 + (r/m)) ^mt Example 3: How much a deposit of Rs. 10,000 will grow at the end of 2 years, if the nominal rate of interest is 12 % and compounding is done quarterly? Future value = 10,000 *(1+0.12/4) 4*2 = Rs. 12,

6 Future Value of an Annuity An annuity is a stream of equal annual cash flows. The future value (FVA) of a uniform cash flow (CF) made at the end of each period till the time of maturity t for which compounding is done at the rate V is calculated as follows: r (1+ r) t -1 FVA = CF*l + r) t CF* (1+ r) t CF*(l + r) 1 +CF = CF (1+r) t - 1) r The term (1+r) t - 1) is referred as the Future Value Interest factor for an annuity (FVIFA). r The same can be applied in a variety of contexts. For e.g. to know accumulated amount after a certain period,; to know how much to save annually to reach the targeted amount, to know the interest rate etc. Example 4: Suppose, you deposit Rs.3,000 annually in a bank for 5 years and your deposits earn a compound interest rate of 10 per cent, what will be value of this series of deposits (an annuity) at the end of 5 years? Assume that each deposit occurs at the end of the year. Future value of this annuity is: = Rs.3000*(1.10) 4 + Rs.3000*(1.10) 3 + Rs.3000*(1.10) 2 + Rs.3000*(1.10)+ Rs.3000 = Rs.3000*(1.4641) + Rs.3000*(1.3310) + Rs.3000*(1.2100) + Rs.3000*(1.10)+ Rs.3000 = Rs Example 5: You want to buy a house after 5 years when it is expected to cost 40 lakh how much should you save annually, if your savings earn a compound return of 12 %? The annual savings should be: /6.353 = 6,29, In case of continuous compounding, the future value of annuity is calculated using the formula: FVA = CF * (e rt -1)/r. Present Value of a Single Cash Flow Present value of (PV) of the future sum (FV) to be received after a period 't' for which discounting is done at an interest rate of V, is given by the equation In case of discrete discounting: PV = FV / (1+r) t Example 6: What is the present value of Rs.5,000 payable 3 years hence, if the interest rate is 10 % p.a. PV =5000/(1.10) 3 i.e. = Rs In case of continuous discounting: PV = FV * e -rt Example 7: What is the present value of Rs. 10,000 receivable after 2 years at a discount rate of 10% under continuous discounting? Present Value = 10,000/(exp^(0.1*2)) = Rs

7 Present Value of an Annuity The present value of annuity is the sum of the present values of all the cash inflows of this annuity. Present value of an annuity (in case of discrete discounting) PVA = FV[{(l + r) t - 1}/{r*(l + r) t }] The term [(1+r) 1-1/ r*(1+r)t 1 ] is referred as the Present Value Interest factor for an annuity (PVIFA). Example 8: What is the present value of Rs. 2000/- received at the end of each year for 3 continuous years = 2000*[1/1.10] *[1/1.10]^2+2000*[1/1.10]^3 = 2000* * * = = Rs Example 9: Assume that you have taken housing loan of Rs.10 lakh at the interest rate of Rs.ll percent per annum. What would be you equal annual installment for repayment period of 15 years? Loan amount = Installment (A) *PVIFA n = 15, r=ll% 10,00,000 = A* [(1+r) t -1/r*(1+r) t ] 10,00,000 = A* [(1.11)^15-1/ 0.11(1.11^15] 10,00,000 = A* ,00,000/ = A A = Rs. 1,39, Present value of an annuity (in case of continuous discounting) is calculated as: PV a - FV a * (l-e -rt )/r (a) Net present value method This is generally considered to be the best method for evaluating the capital investment proposals. In case if this method cash inflows and cash outflows associated with each project are first worked out. The present value of these cash inflows and outflows in then calculated at the rate of return acceptable to the management this rate of return is considered as the out-off rate and is generally determined on the basis of cost of capital suitably adjusted to allow for the risk element involved in the project. The working capital is taken as cash out flow in the year the project starts commercial production. The net present value (NPV) is the difference between the total present value of future cash inflows and the total present value of future cash inflows and future cash outflows. Equation for NPV NPV = R0 R 1 R n 1 K 0 1 K 1 K 1 K 1 K R 3 R n R = cash inflows at different time K = cost of capital The decision Rule: the decision rate under the NPV method is: accept the proposal if its NPV is positive and reject the proposal if the NVP is negative. NPV represents the excess of benefits over the costs in real terms. 72

8 In case of ranking of mutually exclusive proposals, the proposal with the highest positive NVP is given the top priority and the proposal with the lowest positive NPV is assigned the lowest priority. The proposals with negative NPV should be rejected. However, if NVP is 0 then firm may be indifferent between acceptance and rejection of the proposal. (i) It recognizes time value of money. (ii) It also recognizes all cash flows throughout the life of the project. (iii) It helps to satisfy the objectives for maximizing firm's values. (iv) This method is particularly useful for the selection of mutually exclusive projects. Disadvantages (i) (ii) It is difficult to calculate as well as understand it as compared to accounting rate of return method or payback method. It does not present a satisfactory answer when there are different amounts of investments for the purpose of comparison. (iii) It does not also present a correct picture in case of alternative projects or where there are unequal lives of the project with limited funds. (iv) The NPV method of calculation is based on discount state which again depends on the firm's cost of capital. The latter is to some extent difficult to understand as well as difficult to measure in actual practice. (b) Profitability Index (PI) PI is defined as the benefits (in present value terms) per rupee invested in the proposal. This technique which is a variant of the NPV technique, is also known as benefit-cost ratio, or present value index the PI is based upon the basis concept of discounting the future cash flows and is ascertained by comparing the present value of the future cash inflows with the present value of the future cash outflows. The PI is calculated by dividing the former by the latter. PI = Total present valueof Total present vaueof cash inf lows cashoutflows The decision Rule: under the PI technique, the decision rule is: accept the project if its PI is more than I and reject the proposal if the PI is less than I. if the PI is equal to 1, then the firm may be indifferent because the present value of inflows is expected to be just equal to the present value of outflows. (c) Internal Rule of return (IRR) Internal rate of return is the rate at which the sum of discounted cash inflows equals the sum of discounted cash outflows. In other words, it is the rate which discounts the cash flows to zero. It can be stated in the form of a ratio as follows: Cach inf lows 1 Cash outflows Thus, in case if this method the discount rate is not known bit the cash outflows and cash inflows are known. For example, if a sum of Rs. 800 invested in a project becomes Rs at the end of a year, the rate of return comes to 25% calculated as follows: R I = I V I = cash outflow K = cash inflow 73

9 R = rate of return yielded by the investment In case of return is over a number of years, the calculation would take the following pattern I = R 1 R 2 Rn v 1 v 1 v 1 v n R 3 I = cash outflow R = cash inflow at different time periods R = Rae of return yielded by the investment The decision Rule: - In over to make a decision on the basis of IRR technique the firm has to determine, in the firm instance, its own required rate of return (K) A particular proposal may be accepted if its IRR (v) is more than the minimum rate I.e. (k), otherwise rejected. However, if the IRR is just equal to the minimum rate, k, the firm may be indifferent. In case of mutually exclusive proposals, the proposal with the highest IRR is given the top priority Advantages (i) (ii) (iii) (iv) It recognises the time value of money like Net Present Value Method; It also takes into account the cash flows throughout the life of the project; This method also reveals the maximum rate of return and presents a fairly good idea about the profitability of the project even if the firm's cost of capital is absent since the latter is not a precondition for use of it; The percentage which is calculated under the method is more meaningful and justified and that is why it is acceptable to the users since it satisfies them in relation to cost of capital. Disadvantages (i) (ii) (iii) (iv) The method of calculation is no doubt complicated and it is difficult to use and understand the same. This method does not present unique answers under all circumstances and situations. It may even present a negative rate or multiple rates under certain circumstances. This method recognizes the fact that intermediate cash inflows which are generated by the project are re-invested at the internal rate whereas the NPV method recognises that cash inflows are reinvested at the firm's cost of capital which is more appropriate and justified in comparison with IRR method. It may present inconsistent result with the NPV method when the projects actually differ from their expected life or cash outlays or timing of cash flows. Conflict in results under NPV and IRR NPV and IRR methods may give conflicting results in case of mutually exclusive projects, i.e., projects where acceptance of one world result in non-acceptance of the other such conflict of result may be due to any one or more of the flowing reasons: (i) The projects require different cash outlays (ii) The projects have unequal loves. (iii) The projects have different patterns of cash flows. 74

10 In such a situation, the result given by the VPN method should be relied upon. This is because the objective of a company is to maximise its shareholder s wealth. IRR method is concerned with. The rate of return on investment rather than total yield on investment hence it is not compliable with the goal of wealth maximisation. NPV method considers the total yield on investment. Hence, in case if mutually exclusive projects, each having a positive NVP, the one with largest NPV will have the most beneficial effect on shareholder is wealth. The IRR approach solves for a rate unique to each project, while the NPV approach solves for the trade-off cash inflows and outflows using a general required rate of return. On the basis of the above discussion of NPV and IRR, a comparison between the two may be attempted as follows: (a) Advantage of IRR over NPV: IRR may be considered superior to the NPV for the following reasons : i) IRR gives percentage return while the NPV gives absolute return. ii) For IRR, the availability of required rate of return is not a pre-requisite while for NPV it is must. (b) Advantage of NPV over IRR: The NPV is said to have superiority over IRR for i) NPV shows expected increase in the wealth of the shareholders. ii) NPV gives clear cut accept-reject decision rule, while the IRR may give multiple results also. iii) The NPV of different projects are stabilizer while the IRR cannot be added. iv) NPV gives better ranking as compare to the IRR. Terminal Value (TV) Method Under this method, it is assumed that each cash inflow is re-invested in another asset at a certain rate of return and calculating the terminal value of net cash flows at the end of project life. In short, the NCF and the outlay are compounded forward rather than backward by discounting which is used by NPV method. Acceptance Rule From the foregoing discussion it becomes clear that if the value of the total compounded re-invested cash flows is greater than the present value of outflow, i.e. if NCF have a higher terminal value in comparison with the outlay, the project is accepted and vice-versa. The accept-reject rule can, thus, be formulated as under: (1) If there is a single project : Accept the project if the terminal value (TV) is positive, (2) If there are mutually exclusive projects : The project will be more profitable which has a highest positive terminal value (TV). It can also be stated that if TV is positive, accept the project and if TV is negative, reject the project. It should be remembered that TV method is similar to NPV method. The only difference is that in case of former, values are compounded while in case of latter, values are discounted, of course, both of them will present the same result provided the rate is same. 75

11 LEASE FINANCING CONCEPT OF LEASING: Leasing, as a financing concept, is an arrangement between two parties, the leasing company or lessor and the user or lessee, whereby the former arranges to buy capital equipment for the use of the latter for an agreed period to time in return for the payment of rent. The rentals are predetermined and payable at fixed intervals of time, according to the mutual convenience of both the parties. However, the lessor remains the owner of the equipment over the primary period. By resorting to leasing, the lessee company is able to exploit the economic value of the equipment by using it as if he owned it without having to pay for its capital cost. Lease rentals can be conveniently paid over the lease period out of profits earned from the use of the equipment and the rent is cent percent tax deductible. FORMS OF LEASE RENTALS: The lease rentals may be quoted in several forms, for instance (i) Level or constant period (ii) Stepped where the lease rental increases at a fixed percentage over the earlier period, (iii) Deferred, where the rental is deferred for certain periods to accommodate gestation period, (iv) Ballooned under which major part of the rentals is collected in a lump sum at the end of the primary period, (v) Bell shaped where the rental is gradually stepped up, rises to its peak in the middle of the lease period and is then gradually stepped down and (vi) Zig-zag where the rental is stepped up in one period and then stepped down in the succeeding period and so on. 76

12 Practice Questions 1. The cost of plant of Rs. 6,00,000. It has an estimated life of 5 years after which it would be disposed-off (scrap value nil). Profit before depreciation, interest and taxes (PBIT) is estimated to be Rs. 2,50,000 p.a. Find out the yearly cash flow from the plant. (Given the tax 40%). 2. RMS Ltd. is evaluating a capital budgeting proposal for which relevant figures are as follows: Cost of the plant Rs. 15, 00,000 Installation cost Rs. 5,000 Economic life 7 years Scrap value Rs. 50,000 Profit before depreciation and tax Rs. 2,50,000 Tax rate 40% Calculate yearly cash flows. 3. A firm buys an asset costing Rs. 2,00,000 and expects operating profits ( before 15% WDV and 40%) of Rs. 35,000 p.a. for the next 4 years after which the asset would be disposed-off for Rs. 1,40,000. find out the cash flows for different years. 4. Following is the income statement of a project, on the basis of which calculate the annual cash inflows. Income statement of the project Net sales revenue Rs. 5,75,000 - Cost of goods sold Rs. 2, 00,000 - General expenses Rs. 1, 00,000 - Depreciation 60,000 3,60,000 profit before interest and taxes 2,15,000 - interest 25,000 Profit before tax 1,90, % 76,000 Profit after tax 1,14, Jaydev Ltd. in considering an investment proposal for which the relevant information is as follows: Rs. Purchase price of the new asset 10,00,000 Installation costs 2,00,000 Increase in working capital in year zero 2,50,000 Scrap value of the new assets after 4 years 3,50,000 Revenues from new asset (annual) 21,50,000 Cash expenses on new asset (annual) 9,50,000 Current book value (old asset) 3,00,000 Present scrap value (old asset) 5,00,000 Revenue from old asset (annual) 19,25,000 Cash expenses on old asset 11,25,000 Planning period, 4 years. Tax rate 30% 77

13 Depreciation on new asset: 94% the cost is to be depreciated in the ratio of 5:6:7:4 over 4 years. Existing asset is depreciated at a rate of Rs. 1,10,000 p.a. 6. Ramjee & Co. is considering a proposal to replace one of its old plant costing Rs. 80,000 and having a written down value of Rs. 25,000. The remaining economic life of the plant is 4 years after which it will have no salvage value. However, if sold today, it has a salvage value of Rs. 20,000. The new machine costing Rs. 1,50,000 is also expected to have a life of 4 years with a scrap value of Rs. 15,000. The new machine, due to its technological superiority, is expected to contribute additional annual benefit (before depreciation and tax) of Rs. 65,000. Find out the cash flows associated with this decision given that the tax rate applicable to the firm is 40%. (The capital gain or loss may be taken as not subject to tax.) 7. Gopikant Ltd. is interested in assessing the cash flows associated with the replacement of an old machine by a new machine. The old machine bought a few years ago has a book value of Rs. 95,000 and it can be sold for Rs. 95,000. It has a remaining life of five years after which its salvage value is expected to be nil. It is being depreciated annually at the rate of 15% per cent (written down value method). The new machine costs Rs. 4,20,000. It is expected to fetch Rs. 2,00,000 after five years when it will no longer be required. It will be depreciated annually at the rate of 30% (written down value method.) The new machine is expected to bring a saving of Rs. 1,30,000 in manufacturing costs. Investment in working capital would remain unchanged. The tax rate applicable to the firm is 40 %. 8. Ramlal & co. firm is currently using a machine which was purchased two years ago for Rs. 70,000 and has a remaining useful life of 5 years. It is considering to replace the machine with a new one which will cost Rs. 1,40,000. The cost of installation will amount to Rs. 10,000. The increase in working capital will be Rs. 30,000. The expected cash inflows before depreciation and taxes for both the machines are as follows; Year existing machine new machine 1 30,000 50, ,000 60, ,000 70, ,000 90, ,000 1,00,000 The firm use straight line method of depreciation. The average tax on income as well as on capital gain/loss is 40%. Calculate the incremental cash flows assuming sale value of existing machine. (i) Rs. 80,000 (ii) Rs. 60,000 (iii) Rs. 50,000, (iv) Rs. 30, Kailashgiri Ltd. is trying to decide whether it should replace a manually operated machine with a fully automatic version of the same machine. The existing machine, purchased ten years ago, has a book value of Rs. 1,60,000 and remaining life of 10 years. Salvage value was Rs. 50,000. The machine has recently begun causing problems with breakdowns and is costing the company Rs. 24,000 per year in maintenance expenses. The company has been 78

14 offered Rs. 1,00,000 for the old machine as a trade-in on the automatic model which has a deliver price (before allowance for trade-in) of Rs. 2,10,000. It is expected to have a tenyear life and a salvage value of Rs. 25,000. The new machine will require installation costing Rs. 50,000 to the existing facilities, but it is estimated to have a cost savings in materials of Rs. 85,000 per year. Maintenance costs are included in the purchase contract and are borne by the machine manufacturer. The tax rate is 40% (applicable to both revenue income as well as capital gains/losses). Straight line depreciation over ten years will be used. Find out the relevant cash flows. 10. Udarraj Ltd. purchased a special machine one year ago at a cost of Rs. 25,000. At that time the machine was estimated to have a useful life of 6 years and no salvage value. The annual cash operating cost is approximately Rs. 21,000. A new machine has just come on the market which will do the same job but with an annual cash operating cost of only Rs. 15,000. The new machine costs 30,000 and has an estimated life of 5 years with zero salvage value. The old machine can be sold for Rs. 10,000 to a scrap dealer. Straight line depreciation is used. And the company s income tax rate is 40 %. Assuming a cost of capital of 10%, you are required to compute the incremental cash flows after taxes: 11. Tiripati Ltd. is considering installing a machine costing. Rs. 5,00,000 with an additional investment of Rs. 1, 50,000 for its installation. The salvage value at the end of year 10 is estimated at Rs. 2,50,000. The machine is estimated to generate sales revenue of Rs. 20,00,000 in the first year and the sales are expected to grow at 5% p.a. for the remaining life of the machine. The profit after tax is expected at 10% of the sales while the working capital requirement is expected to be 5% of the sales. Find out the cash flows generated by the machine given that 1. The machine is depreciated as per straight line method, and 2. The additional working capital is required in the beginning of the year and is fully salvageable year The initial outlay of the project is Rs. 1,00,000 and it generates cash inflows of Rs. 50,000, Rs. 40,000, Rs. 30,000 and Rs in the four years of its life span. You are required to calculate the following: (a) Net Present Value (NPV) (b) Profitability Index (PI) (c) Discounted payback period of the project assuming 10% rate of discount. Present value of Re. 1 due at the end of a periods at 10% rate of discount. Year PV Fatl0% Siddhvinayak Ltd. is considering the purchase of a new machine. Two alternative machines have been suggested, each costing Rs. 4,00,000 earnings after tax but before depreciation are expected to be as follows: Year Cash-Flows Machine Machine B 1 40,000 1,20, ,20,000 1,60, ,60,000 2,00, ,40,000 1,20, ,60,000 80,000 7,20,000 6,80,000 79

15 The company has a target rate of return on 10% and on this basis, you are required: (i) Compare profitability (NPV) of the machines and state which alternative you consider financially preferable. (ii) Compute the payback period for each project and. (iii) Compute annual rate of return for each project. 14. Gopi Ltd. is considering the purchase of new machine. Two machine A and B are available, each costing Rs. 5 lakhs. In comparing the profitability of the machine, a discounting rate of 10% is to be used and machine is to be written off in five years by straight line method of depreciation with nil residual value. Cash inflows after tax are expected as follows: Year Machine A Machine B (Rs. In lakhs) (Rs. In lakhs) Indicate which machine would be profitable using the following methods of ranking investment proposals; (i) Pay back method; (ii) Net present value method; (iii) Profitability index method ; and (iv) Average rate of return method. The discounting factors at 10% are Year Discounting factor Hariom Ltd. has decided to purchase a machine to increase the installed capacity. There are three machines under consideration. The relevant details including estimated yearly expenditure are sales are given below: All sales are on cash and income tax rate is 40%. Machine A Machine B Machine C Initial investment required Rs. 6, 00,000 Rs. 6, 00,000 Rs. 6, 00,000 Estimated annual sales 9, 00,000 8, 00,000 8, 50,000 Cost of production (estimate): Direct materials 80,000 90,000 88,000 Direct labour 90,000 60,000 76,000 Factory overheads 90,000 90,000 88,000 Administration costs 30,000 20,000 35,000 Selling and distribution costs 30,000 20,000 30,000 The economic life of machine A is 2 years, while it is 3 years for the other two. The scrap values are Rs. 70,000, Rs. 45,000 and Rs. 60,000 respectively. You are required to find most investment based on Pay Back Method. 80

16 16. Nitse Ltd. decided to purchase a machine to increase the installed capacity. The company has four machines under consideration. The relevant details including estimated yearly expenditure and sales are given below. All sales are for cash. Corporate Tax 33.99% (inclusive of 10%, Eduction 2% and Secondary & Higher Education 1%) Particulars M1 M2 M3 M4 Initial Investment (Rs. lacs) Estimated Annual Sales (Rs. lacs) Cost of Production (Estd) (Rs. lacs) Economic Life (yrs) Scrap Values (Rs. lacs) Calculate Payback Period 17. A project costing Rs. 10 lacs. EBITD (Earnings before Depreciation, Interest and Taxes) during the first five years is expected to be Rs. 2,50,000; Rs. 3,00,000; Rs. 3,50,000; Rs. 4,00,000 and Rs. 5,00,000. Assume 33.99% tax and 30% depreciation on WDV Method. 18. Project Cost Rs. 1,10,000 Cash Inflows : Year 1 Rs. 60,000 Year 2 Rs. 20,000 Year 3 Rs. 10,000 Year 4 Rs. 50,000 Calculate the Internal Rate of Return. 19. The Income Statement of Bertrand Russell Ltd. for the current year is as follows: Sales 7,00,000 Less: Costs Material 2,00,000 Labour 2,50,000 Other operating costs 80,000 Depreciation 70,000 6,00,000 EBIT 1,00,000 Less: 40% 40,000 EAT 60,000 The plant manager proposes to replace an existing machine by another machine costing Rs. 2,40,000. The new machine will have 8 years life having no salvage value. The old machine will realise Rs. 40,000. Income statement does not include the depreciation on old machine (the one that is going to be replaced) as the same had been fully depreciated, for a few years more. It is believed that there will be no change in other expenses and revenues of the firm due to this replacement. The company requires an after tax return 10%. The rate of tax applicable to company s income is 40%. Should the company buy the new machine, assuming that the company follows straight line method of depreciation and the same is allowed for tax purposes?. 20. A firm whose cost of capital is 10% is considering two mutually exclusive projects A and B, the details of which are: Year Project A Project B Cost 0 2,00,000 2,00,000 Cash inflows 1 20,000 1,00, ,000 80, ,000 40, ,000 20, ,20,000 20,000 81

17 Compute the net present value at 10%. Profitability index and internal rate of return for the two projects. 21. Ramveer Ltd. considers following mutually exclusive projects. Project A Project B Present Value of cash inflows Rs. 20,000 Rs. 8,000 Initial cash outlay 15,000 5,000 Net present value 5,000 3,000 Profitability index Which project should be preferred and why? 22. Following details are provided you to evaluate which machine should be selected on the basis of NPV approach? Machine A costs Rs. 2,00,000 payable at Zero time. Machine B costs Rs. 1,90,000 half payable immediately and half payable in one year s time. Receipt costs expected are as follows: Year (at end) Machine A Machine B 1 Rs. 30,000 10, ,000 70, ,000 80, ,000 70, , At 8% opportunity cost, which machine should be selected on the basis of NPV? 23. Jayram Ltd. is considering a new project for which the investment data are as follows: Capital outlay Rs. 3, 00,000 Depreciation 20% p.a. Estimated annum income before charging depreciation, but after all other charges are as follows: Year 1 1,50, ,50, , , ,000 You are required to evaluate above project on the basis of following technique. (a) Payback Period method. (b) Rate of return on original investment. 24. Ram managing director of a private company has to consider the following project. Cost Rs. 5,00,000 Cash inflows: Year 1 50, , ,00, ,80,000 Calculate the IRR and comment on the project if the cost of capital is 14%. 82

18 25. Arundev Ltd. is considering a new five year project. Its investment costs and annual profits are projected as follows: Investment Profits Year Rs. (5,00,000) 1,80,000 1,60,000 40,000 1,20,000 80,000 The residual value at the end of the project is expected to be Rs. 40,000 and depreciation of the original investment is on straight line basis. Using average profits and average capital employed calculated the ARR for the project and the payback period. 26. An investment of Rs. 1,36,000 yields the following cash inflows (profits before depreciation but after tax). Year Cash flows 30,000 40,000 60,000 30,000 20,000 PVF at 10% PVF at 12% Calculate NPV at discount rate 10% and 12%. Also calculate IRR. 27. Ramdayal Ltd. proposes to install a machine involving a capital cost of Rs. 3,60,000. The life of the machine is 5 years and its salvage value at the end of the life is nil. The machine will produce the net operating income after depreciation of Rs. 68,000 per annum. The company's tax rate is 45%. The Net Present Value factors for 5 years are as under: Discounting Rate 14% 15% 16 % 17% 18% Cumulative factor You are required to calculate the internal rate of return of the proposal. 28. Following are the data on a capital project being evaluated by the management of Gopal Ltd.: Annual cost saving Rs. 40,000 Useful life 4 years I.R.R. 15% Profitability Index (P.I.) NPV? Cost of capital? Cost of project? Payback? Salvage value 0 Find the missing values considering the following table of discount factor only: Discount factor 15% 14% 13% 12% 1 year year year year Kailash Ltd. has an investment opportunity costing Rs. 3,00,000 with the following expected cash inflow (i.e. after tax and before depreciation): 83

19 Year Inflows PVF (10%) year inflows PVF (10%.) 1 50, , , , , , , , , , Using 10% as the cost of capital determine the (i) (ii) Net present value; and Profitability index. 30. Tirupati Ltd. requires an initial investment of Rs. 1,00,000. The estimated net cash flows are as follows: Year Net cash 16,000 17,000 18,000 17,000 15,000 Year ,000 30,000 40,000 25,000 10,000 Using 10% as the cost of capital (rate discount) determine the following: (i) Pay Back (ii) Net Present Value and (iii) Internal Rate of Return. 31. Ramdeen Ltd. is considering the replacement of its existing machine which is outdated and unable to meet the rapidly rising demand for its product. The company has two alternatives: (i) (ii) to buy machine A which is similar to the existing machine or to go in for machine B which is more expensive and has much greater capacity. The cash flows at the present level of operations under the two alternatives are as follows; Cash flows ( in lacs ) at the end of year: Time Machine A Machine B The company s cost of capital is 10%. The finance manager tries to evaluate the machines by calculating the following: 1. Net present value, 2. Profitability index, 3. Pay- Back period, At the end of his calculations, however, the finance manager is unable to make up his mind as to which machine to recommend. You are required to make these calculation and in the light thereof to advise the finance about the proposed investment. Present values of re. 1 at 10% discount rates is as follows: Year P. V

20 32. Prabhu Ltd. is forced to choose between two machines A and B. The two machines are designed differently, but have identical capacity and do exactly the same job. Machine A costs Rs. 1,50,000 and will last for 3 years. It costs Rs. 40,000 per year to run. Machine B is an economy' model costing only Rs. 1,00,000, but will last only for 2 years and costs Rs. 60,000 per year to run. Cost of capital is 10%. Which machine should buy? 33. Ramjee Ltd. is considering installing either of the two machines which are mutually exclusive. The details of their purchase price and operating costs are: Year Machine X Machine Y Purchase cost 0 Rs. 10,000 Rs. 8,000 Operating cost 1 Rs. 2,000 Rs. 2,500 Operating cost 2 Rs. 2,000 Rs. 2,500 Operating cost 3 Rs. 2,000 Rs. 2,500 Operating cost 4 Rs. 2,500 Rs. 3,800 Operating cost 5 Rs. 2,500 Rs. 3,800 Operating cost 6 Rs. 2,500 Rs. 3,800 Operating cost 7 Rs. 3,000 Operating cost 8 Rs. 3,000 Operating cost 9 Rs. 3,000 Operating cost 10 Rs. 3,000 Machine X will recover salvage value of Rs. 1,500 in the year 10, while Machine Y will recover Rs. 1,000 in the year 6. Determine which machine is cheaper at 10 per cent cost of capital, assuming that both the machines operate at the same efficiency. 34. A project with 5 years life requires initial investments as under Plant and Machinery Rs. 2,70,500 Working Capital Rs. 40,000 Rs. 3,10,500 The working capital will be fully realized at the end of the 5 th year. The scrap value of the plant expected to be realized at the end of the 5 th year is only Rs. 5,500. The earnings from project are: Year Cash flows Rs. 90,000 Rs. 1,30,000 Rs. 1,70,000 Rs. 1,16,000 Rs. 19,500 (before depreciation & tax) Tax payable Rs. 20,000 Rs. 30,000 Rs. 40,000 Rs. 26,000 Rs 5,000 You are required to compute the present value of cash follows discounted at the various rates of interests given below and state the return from the project. PVF at Interest rate 15% 14% 13% 12% 1Year Year Year Year Year

21 35. Bramha Ltd. is considering two different investment proposals, A and B details are as under: Proposal A Proposal B Investment cost Rs. 9,500 Rs. 20,000 Year1 4,000 8,000 Year 2 4,000 8,000 Year 3 4,500 12,000 Suggest the most attractive proposal on the basis of the NPV method considering that the future incomes are discounted at 12% also find out the IRR of the two proposals. 36. The cash flows from two mutually exclusive projects A and B are as under; Years Project A Project B 0 Rs. 22,000 Rs. 27, (annual) 6,000 7,000 Project life 7 years 7 years i) Calculate NPV of the proposals at discount rates of 15%, 16%, 17%, 18%, 19% and 20%. ii) Advise on the project on the basis of IRR method. 37. Tirudev Ltd. had the option to buy either Machine A or Machine B. Machine A has a cost of Rs. 75,000. Its expected life is 6 years with no salvage value at the end. It would generate net cash flows of Rs. 20,000 per year. Machine B on the other hand would cost Rs. 50,000. Its expected life is 6 years with no salvage value at the end. It would generate net cash of Rs. 15,000 per year. Assuming that the cost of capital of both the machines is 10%, you are required to calculate: a) Net present value for each machine. b) Internal rate of return for each machine c) Which machine should be recommended and shy? 38. Harigovind Ltd. is evaluating three investment situations. If only the project in question is under taken, the expected present values and the amounts of investment required are Project Investment Required $200, , ,000 Present value of future cash flows $290, , ,000 If projects 1 and 2 are jointly undertaken, there will be no economics, there will be no economics, the investments required and present value will simply be the sum of the parts. With projects 1 and 3, economics are possible in investment because one of the machines acquired can be used in both production processes. The total investment required for projects 1 and 3 combined is $ 440,000. If projects 2 and 3 are undertaken, there are economics to be achieved in marketing and producing the products but not in investment. The expected present value of future cash flows for projects 2 and 3 is $ 620,000. If all three projects are undertaken simultaneously, the economics noted will still hold. However, a $125,000 extension on the plant will be necessary, as space is not available for all three projects. Which project or projects should be chosen? 86

22 39. Surya Ltd. Has Rs. 30 lacs available for investment in capital projects. It has the option of making investment in projects 1,2,3 and 4. Each project is entirely independent and has a useful life of 5 years. The expected present value of cash flows the projects are as follows: Projects Initial Outflow PV of Cashflows 1 8,00,000 10,00, ,00,000 19,00, ,00,000 11,40, ,00,000 20,00,000 Which of the above investment should be undertaken? Assume that the cost of capital is 12% and risk free interest rate is 10% per annum. Compounded sum of Re. 1 at 10% in 5 years is Rs and discount factor of Re. at 12% rate for 5 years is Radheshyam Ltd. is considering its capital investment (Rs. 12 lacs) programme for next year. It has five projects all of which give a positive NPV at the company cut-off rate of 15%. The investment outflows and PV being as follows: Project Investment (Rs.) 15% (Rs.) A B C D E You are required to optimize the returns from a package of projects within the capital spending limit. The projects are independent of each other and are divisible (i.e. part-project is possible). 41. Five Projects M, N, O, P and Q are available to a company for consideratio. The investment required for each project and the cash flows it yields are tabulated below. Projects N and Q are mutually exclusive. Taking the cost of 10%, which combination of projects should be taken up for a total capital outlay not exceeding Rs. 3 lakhs on the basis on NPV and Benefit-Cost Ratio (BCR)? Project Investment Cash flow p.a. No of years 10% M 50,000 18, N 1,00,000 50, O 1,20,000 30, P 1,50,000 40, Q 2,00,000 30, Total Capital outlay < Rs lakhs 42. Gopi Ltd. is considering 5 capital projects for the years 2002, 2003, 2004, The company is financed by equity entirely and its cost of capital is 12%. The expected cash flows of the projects are as follows: project A B C D E Years and cash flows (70,000) 35,000 35,000 20,000 (40,000) (30,000) 45,000 55,000 (50,000) (60,000) 70,000 80, (90,000) 55,000 65,000 (60,000) 20,000 40,000 50,000 87