Capital Budgeting

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CONCEPT OF CAPITAL BUDGETING The term 'Capital Budgeting' refers to long-term planning for proposed capital outlays and their financing. Thus, it includes both raising of long-term funds as well as their utilisation. It may thus be defined as “the firm's formal process for the acquisition and investment of capital”. 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. However, it should be noted that investment in current assets necessitated on account of investment in a fixed assets, is also to be taken as a capital budgeting decision. For example, a new distribution system may call for both a new warehouse and an additional investment in inventories. An investment proposal of this nature must be taken as a capital budgeting decision and evaluated as a single package, not as an investment in a fixed asset (i.e. Warehouse) and in a current asset (i.e., inventory) separately. Capital Budgeting is a many sided activity. It includes searching for new and more profitable investment proposals, investigating engineering and marketing considerations to predict the consequences of accepting the investment and making economic analysis to determine the profit potential of each investment

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proposal. Its basic features can be summarised as follows: (i) It has the potentiality of making large anticipated profits. (ii) It involves a high degree of risk. (iii) It involves a relatively long-time period between the initial outlay and the anticipated return. On the basis of the above discussion it can be concluded that capital budgeting consists in planning the development of available capital for the purpose of maximising the long-term profitability (i.e. ROI) of the firm. Operating Budget and Capital Budget Most largely firms prepare two different budgets each year : (i) Operating Budget, and (ii) Capital Budget or Capital Expenditure Budget. Operating Budget shows planned operations for the forthcoming period and includes sales, production, production cost and selling and distribution overhead budgets. All these budgets have already been discussed. Capital Budget deals exclusively with major investment proposals. It assesses the economics of capital expenditure and investment. CAPITAL EXPENDITURE BUDGET Capital expenditure Budget is a type of functional

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budget. It is the firm's formal plan for the expenditure of money for purchase of fixed assets. It provides a guidance as to the amount of capital that may be required for procurement of capital assets during the budget period. The budget is prepared after taking into account the available production capacities, probable reallocation of existing resources and possible improvements in production techniques. If required, separate budgets can be prepared for each item of capital asset such as building budget, a plant and machinery budget, etc. Objectives of a Capital Expenditure Budget The objectives of a capital expenditure budget are follows: (i) It determines the capital projects on which work can be started during the budget period after taking into account their urgency and the expected rate of return on each project. (ii) It estimates the expenditure that would have to be incurred on capital projects approved by the management together with the source or sources from which the required funds would be obtained. (iii) It restricts the capital expenditure on projects within authorised limits. Control over Expenditure through Capital Expenditure Budget

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The capital expenditure budget primarily ensures that only such projects are taken in hand which are either expected to increase or maintain the rate of return on capital employed. Each proposed project is appraised and only essential project or projects likely to increase the profitability of the organization are included in the budget. In order to control expenditure on each project, the following procedure is adopted: (i) A project sheet is maintained for each project. It contains columns for entering expenditure spent according to different stages of development or construction analysed under the heads : Direct Material, Direct Labour and Overheads. (ii) In order to ensure that the expenditure on different projects is properly analyzed, the project number and the project details are supplied in advance to the concerned executives. These persons make appropriate reference on all documents relating to the project. (iii) The expenditure incurred on the project is regularly entered on the project sheets from various sources such as invoices of assets purchased, bill for delivery charges, etc. (iv) The management is periodically informed about the expenditure incurred in respect of each project under appropriate heads. (v) In case project cost is expected to increase, a

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supplementary sanction for the same is obtained. (vi) In financial books the total expenditure incurred on all the projects is separately recorded. This expenditure recorded on the project sheets. The above system has an important advantage. The persons responsible for execution are constantly able to compare the physical development of each project in relation to the total expenditure incurred on the project. TACTICAL VERSUS STRATEGIC INVESTMENT DECISIONS Investment decisions may be classified as (i) tactical decisions and (ii) strategic decisions. A tactical decision generally involves a relatively small amount of funds and does not constitute a major departure from the past practices of the company. For example, the decision of Hindustan Motors to buy a new machine tool is a tactical decision. A strategic investment decision involves a large sum of money and may also result in a major departure from the past practices of the company. Acceptance of a strategic investment decision involves a significant change in the company's expected profits associated with a high degree of risk. Such changes are likely to result in shareholders and creditors revising their evaluation of the company. For example, if the Indian

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Airlines running airbuses decides to go in for supersonic aircrafts (costing billions of dollars), this would be a strategic decision. If the Airlines falls to develop these aircrafts, as economically feasible and commercially viable, the very existence of the company would be jeopardised. IMPORTANCE OF CAPITAL BUDGETING Capital Budgeting decisions are among the most crucial and critical business decisions. Special care should be taken in making these decisions on account of the following reasons: (i) Involvement of heavy funds: Capital budgeting decisions require large capital outlays. It is, therefore, absolutely necessary that the firm should carefully plan its investment programme so that it may get the finances at the right time and they are put to most profitable use. An opportune investment decisions can give spectacular results. On the other hand, an ill-advised and incorrect decision can jeopardise the survival of even the biggest firm. For example, if a company purchases a new plant for manufacture of a new product, the company commits itself to a sizeable amount of fixed cost in terms of indirect labour such as supervisory staff salary and indirect expenses such as rent, rates, insurance, etc.

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In case the product does not come out or comes out but proves to be unprofitable, the company will have to bear the burden of fixed-cost unless it decides to write off the investment completely. A wrong decision, therefore, can provide disastrous for the long-term survival of the firm. Similarly, inadequate investment in assets would make it difficult for the firm to run the business in the long run just as an unwanted expansion results in unnecessary heavy operating costs to the firm. (iii) Irreversible decisions : In most cases, capital budgeting decisions are irreversible. This is because it is very difficult to find a market for the capital assets. The only alternative will be to scrap the capital assets so purchased or sell them at a substantial loss in the event of the decision being proved wrong. (iv) Most difficult to make: The capital budgeting decisions require an assessment of future events which are uncertain. It is really a difficult task to estimate the probable future events, the probable benefits and costs accurately in quantitative terms because of economic, political, social and technological factors. On account of these reasons, capital expenditure decisions are among the class of decisions which are best reserved for consideration by the highest level of management. In case some parts of it are delegated, a

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system of effective control by the top management should be evolved. It has already been stated that the term capital budgeting includes both planning for proposed capital outlays and their financing. However, in this discussion we are not discussing with the financing aspect. We are mainly discussing with selection of a particular capital project out of several alternative projects available. Thus, our study is restricted of the process of deciding whether or not to commit resources to a project whose benefits would spread over several time period. The objective is to correlate the benefits to costs in a manner which is consistent with the profit maximisation objective of the business. RATIONALE OF CAPITAL EXPENDITURE Efficiency is the rationale underlying all capital decision. A firm has to continuously invest in new plant or machinery for maintaining and improving its efficient. The overall objective is to maximise the firm's profits and thus optimising the return on investment. This objective can be achieved either by increased revenues or by cost reduction. Thus, capital expenditure can be of two types: (i) Expenditure increasing revenue (ii) Expenditure reducing cost.

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Expenditure increasing revenue Such a capital expenditure brings more revenue to the firm either by expansion of present operations or development of a new product line. In both cases new fixed assets are required. Expenditure reducing costs Such a capital expenditure reduces the total cost and thereby adds to the total earnings of the firm. For example, when an assets is worn out or becomes obsolete, the firm has to decide whether to continue with it or replace it by a new machine. While taking such decision the firm compares the required cash outlay for the new machine with the benefit in the form of reduction in operating costs as a result of replacement of the old machine by a new one. The firm will replace the asset only when it finds it beneficial. There is a basic difference between capital expenditure increasing revenue and capital expenditure reducing cost. The former has more uncertainties attached to it as compared to the latter. This is because in the latter case the firm is already in the line and therefore make a better estimate about the resultant savings. While in the former case the product line being new, the estimates made about revenues and costs may not be reliable.

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KINDS OF CAPITAL INVESTMENT PROPOSALS A firm may have several investment proposals for its consideration. It may adopt one of them, some of them or all of them depending upon whether they are independent, contingent or dependent or mutually exclusively. (i) Independent proposals These are proposals which do not compete with one another in a way that acceptance of one precludes the possibility of acceptance of another. In case of such proposals the firm may straightway “accept or reject” a proposal on the basis of a minimum return on investment required. All those proposals which give a higher return than a certain desired rate of return are accepted and the rest are rejected. (ii) Contingent or dependent proposals These are proposals whose acceptance depends on the acceptance of one or more other proposals. For example a new machine may have to be repurchased on account of substantial expansion of plant. In this case investment in the machine is dependent upon expansion of plant. When a contingent investment proposal is made, it should also contain the proposal on which it is dependent in order to have a better perspective of the

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situation. (iii) Mutually exclusive proposals These are proposals which compete with each other in a way that the acceptance of one predicts the acceptance of other or others. For example, if a company is considering investment in one of two temperature control systems acceptance of one system will rule out the acceptance of another. Thus, two or more mutually exclusive proposals cannot both or all be accepted. Some technique has to be used for selecting the better or the best one. Once this is done, other alternatives automatically get eliminated. FACTORS AFFECTING CAPITAL INVESTMENT DECISIONS The following are the four important factors which are generally taken into account while making a capital investment decision:1. The amount of investment : In case a firm has unlimited funds for investment it can accept all capital investment proposals which gave a rate of return higher than the minimum acceptable or cut-off rte. However, most firms have limited funds and therefore capital rationing has to be imposed. In such an event a firm can take only such project or projects which are within its

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means. In order to determine which project should be taken up on this basis, the projects should be arranged in an ascending order according to the amount of capital investment required as shown below: S.No.

Project

1 2 3 4

101 102 103 104

Description

Required investments Purchase of new plant 100000 Expansion of the existing plant 130000 Purchase of New sales office 150000 Introduction of a new product line 200000

In case the funds available only Rs. 1,50,000, Project 104 cannot be taken up and it should, therefore, be rejected outright. Computation of capital investment required The term 'capital investment required' refers to the net cash outflow which is the sum of all outflows and inflows occurring at zero time period. The net outflow is determined by taken into account the following factors: (i) Cost of the new project (ii) Installation Cost (iii) Working capital: Investment in a new project may also result in increase or decrease of net working capital requirements. For example, if the new project is expected to increase sales; investment in accounts receivables. Inventories, cash balance,

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etc., is also likely to increase. A part of this increase in current assets may be offset by increase in current liabilities. For the balance additional funds will have to be arranged. This amount should therefore be taken as a part of the initial capital. The investment required in the form of net working capital will be recovered at the end of the life of the project. This amount of working capital so recovered will become part of cash inflow in the last year of the life of the project. However, investment in working capital and the recovery of working capital will not balance each other on account of time value of money. It may further be noted that the amount of working capital may show a continuous increase in each of the subsequent years on account of continuous increase in sales. Such increase in working capital should not be taken as a part of initial cash investment. It should rather be taken as an outflow of cash in the year in which additional working capital is required. Generally all capital investments proposal for increasing revenue require additional working capital, while almost all capital investment proposals for reduction in costs result in saving of working capital by increasing the firm's operational efficiency. (iv) Proceeds from sale of asset: A new asset may be

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purchased for replacement of an old asset. The old asset may therefore be sold away. The cash realized on account of such sale will reduce the cost of new investment. (v) Tax effects: The amount of profit or loss on the sale of the assets may affect the cash flows on account of tax effects. The profit / loss is ascertained by taking into account the cost of the asset. Its book value and the amount realized on its sale. The tax liability of the company will be different in each of the following cases: (a) when the asset is sold at its book value. (b) when the asset is sold at a price higher than its book value but lower than its cost. (c) When the assets is sold at a price higher than its cost. (d) When the asset is sold at a price lower than its book value. This will be clear with the help of the following illustration: Illustration 1: A company purchased a machinery a few years back for Rs. 10,000. It wants to replace this machinery by a new one costing Rs. 15,000. The company is subject to income tax @ 50% while capital gains tax @ 30%. The present book value of the machinery is Rs. 6,000. Calculate the net initial cash

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outflow if the company decides to purchase the new machine, in each of the following cases, if the old machine is sold for: (a) Rs. 6000; (b) Rs. 8000 (c) Rs. 12,000 (d) Rs. 4000 Solution (a) Cash required for the purchase of the Rs. 15,000 new machine Less: Cash realised on sale of the old machine 6,000 Net Cash Outflow 9,000 (b) Cash required for purchase of the new Rs. 15,000 machine Less: Cash realised on sale of the old Rs. 8,000 machine Rs. 7,000 Add: Income tax liability on profit made on sale of machinery (2000 x 50/1000) 1,000 Net cash Outflow 8,000 (c) Cash required for purchase of the new Rs. 15,000 machine Less: Cash realised on sale of the old 12,000 machine 3,000 Add: Income Tax Liability (6000x50/100) Capital Gains tax liability (2000x30/100)

3000 600

3,600 6,600 (b) Cash required for purchase of the new Rs. 15,000 Net Cash Outflow

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machine Less: Cash realised on sale of the old machine

4,000 11,000

Add: Saving in tax liability on account of loss on the sale of the old machine 1,000 (2000x50/100) * Net Cash Outflow 10,000 * The loss can neither be adjusted against current operational profits or be carried forward for 8 years, under existing rules, for setting off against future profits. Note: It may be noted that the method of computing depreciation under the Companies Act is different from that under the Income tax Act. As per Section 350 of the Companies Act, 1956, loss or profit on sale of individual asset is to be taken to Profit and Loss Account as a balancing charge. However, as per the current income tax provisions, the profit and loss on individual item of a fixed asset is not to be taken to P&L Account. Depreciation is to be charged on a block of assets account or accounting to Group Depreciation Method. The total amount realized on sale of an individual asset comprising a block, is to be credited to the “block of assets account” and thus reducing the written down value of the block of assets. Hence, there can be a profit and loss only when the whole block of

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assets is sold or where the block of assets comprises only of one individual assets which has been sold away. The profit or loss computed in Illustration 1, as above for “tax effect” has been computed on the presumption that the sale is of entire block of assets comprising one or more than on assets(s). (vi) Investment allowance : This is allowed to encourage capital investment in machinery and equipment. In India this allowance was allowed at 20% of the cost of new machinery and equipment for calculating income tax liability for the year in which such asset was put into service. Such allowance thus reduces the cost of the initial investment on the project. Thus, the net cash outflow on account of capital investment proposal can be ascertained as shown below: Original Cost of the Asset

Xxx

Add: Installation cost Increase in working capital requirements Increase in Tax Liability

Xxx xxx xxx

Less: Decrease in working capital requirements Decrease in tax liability Investment allowance (if any) Net cash outflow

Xxx xxx xxx

Xxx xxx

Xxx xxx

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Illustration 2: A company intends to replace an old machine with a new machine. From the following information you are required to determine the net cash required for such replacement: Cost of the old machine Life of the old machine Depreciation according to straight-line method Remaining useful life Cost of new machine Installation charges Amount realized on sale of old machine Additional working capital required Income-tax Capital gains tax Investment allowance

Rs.50,000 5 years 2 years 70,000 10,000 25,000 5,000 50% 30% 20%

Solution ESTIMATION OF CASH REQUIREMENT FOR REPLACEMENT Cost of the new machine Add: Installation charges Additional working capital required Additional tax liability ; Income tax 5,000x50/1 00 Capital gains tax

Rs.70000 10,000 5,000 2,500 87,500

Less: Amount realized on sale of old machine Investment allowance [70,000 x 20/100] Net Cash outflow

25,000 14,000

39,000 48,500

2. Minimum rate of return on investment: The management expects a minimum rate of return on the

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capital investment. The minimum rate of return is usually decided on the basis of the cost of capital. For example, if the cost of capital is 10%, the management will not like to accept a proposal which yields a rate of return less than 10%. The project giving a yield below the desired rate of return will, therefore, be rejected. Cut-off point The cut off point refers to the point below which a project would not be accepted. For example, if 10% is the desired rate of return, the cut-off rate is 10%. The cut-off point may also be in terms of period. For example, if the management desires that the investment in the project should be recouped in three years, the period of three years would be taken as the cut-off period. A project, incapable of generating necessary cash to pay for the initial investment in the project within three years, will not be accepted. 3. Return expected from the investment: Capital investment decisions are made in anticipation of increased return in the future. It is therefore very necessary to estimate the future return or benefits accruing from the investment proposals. There are two criteria available for quantifying benefits from capital investment decisions. They are (i) accounting profit and (ii) cash flows. The term accounting profit is identical with income concept used in accounting. While in estimating cash flows, depreciation charges and other

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amortization charges of fixed assets are not subtracted from gross revenue, because no cash expenditure is involved. The difference between the two will be clear with the following example.

Sales (i) Less: Cost of Sales (ii): Direct Material Direct Labour Depreciation Indirect expenses (ii) Net Income/Cash Flow before tax (i)(ii) Tax (say at 50% of Net Income of Rs. 3,000) Net Income/Cash after Tax

Benefit as per Benefit as per Accounting Cash flow approach approach Rs. 10,000 Rs. 10,000 3,000 2,000 1,000 1,000 7,000 3,000

3,000 2,000 1,000 6,000 4,000

1,500

1,500

1,500

2,500

The above example shows that the amount of cash flow is Rs. 1,000 more than the amount of accounting profit. The accounting approach shows that only Rs. 1,500 is available after meeting expenses while the cash flow approach shows that Rs.2,500 is available for investment. The cash flow approach for determination of benefit

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from a capital investment project is better as compared to accounting profit approach on account of the following reasons: (i) Determination of economic value While making capital budgeting decisions, a firm is interested in determining the economic value of the project which can only be determined by comparing the cash inflows (benefit) with the cash outflows associated with the project. The firm can by comparing them find out for itself whether the future economic inflows are sufficiently large to warrant the initial investment. The accounting profit approach allocates the cost of investment over the economic useful life of the asset in the form of depreciation rather than at the time when the cost is actually incurred. It, therefore, falls to reflect the original need for cash at the time of investment. It also does not bring out clearly the actual size of cash inflows and outflows in later years. On account of these reasons cash flow approach is more appropriate for capital budgeting decisions. (ii) Accounting ambiguities Accounting profit approach is full of ambiguities on account of different accounting policies and practices, regarding valuation of inventory, allocation of costs, calculation of depreciation, amortization of various other expenses. The amount of profit may therefore

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vary according to accounting policies and practices adopted while preparing the accounts. However, there will be only one set of cash flows associated with a project. Obviously, therefore, the cash flow approach is superior to the accounting profit approach. (iii) Time value of money Under usual accounting practices revenue is considered to be realized not at the time when the cash is received but at the time the sale is made. It means the amount of profit shown by the books may be simply a paper figure if the sales are not realized. Similarly, expenditure is recognized as being made not when the payment is made out but at the time it is incurred. Thus, the time taken in realizing or making payments is completely ignored. The cash flow approach recognizes the time value of money by comparing actual cash inflow:; and cash outflows. Moreover, in order to have a better picture even the future cash inflows arc discounted and their present worth is found out. On account of the above reasons, accounting profit approach, though quite useful in measuring performance of an enterprise, is less useful as a tool for managerial decisions. Conventional and non-conventional cash flows: In case of conventional cash flows, an initial cash outflows is followed by a series of cash inflows whether of uniform

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or of different amounts. Most of the capital budgeting decisions follow this pattern. For example, a firm may spend Rs.5,000 on capital asset in zero time period and may receive Rs, 1,000 each year for 8 years. In case of unconventional cash Hows, initial cash outflow is not followed by a series of cash outflows followed by a series of cash inflows. For example, a firm may purchase a plant for a sum of Rs. 10,000. This cash outflow may be followed by cash inflows of Rs.3,000 each year for 5 years. However, after 5 years the asset may need overhauling resulting in a cash outflow of Rs.3,000. This may give a new lease of life to the asset and it may be followed by a series of cash inflows. This practice may continue in future years also. 4. Ranking of the investment proposals: When a number of projects appear to be acceptable on the basis of their profitability the projects will be ranked in order of their profitability in order to determine the most profitable project. Ranking of capital investment proposals is particularly necessary in the following two circumstances; (a) Where capital is rationed, i.e., there is a limit on funds available for investment. (b) Where two or more investment opportunities are mutually exclusive, i.e., only one of the opportunities can be undertaken.

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Thus, the objective of ranking is to puf the capital available to the best possible use. This will be clear from the following illustration. Illustration 3: A Ltd. is considering the following five projects for capital expenditure. The company can spare a sum of Rs. 1,50,000 and expect a minimum return of 15% before tax on the investment. The details of the projects are as under: Projects

(i) A B C D E

Capital Expenditure (ii) Rs. 50,000 75,000 1,00,000 1,25,000 1,50,000

Estimated Percentage Savings return on (Before tax) investment (iii) (iv) Rs. 5,000 20 9,000 24 8,000 16 25,000 40 28,000 37

Tax rate may be taken as 50% Solution On the basis of information given, project D seems to be the most profitable, since it is giving the highest

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percentage return on investment. However, in case this project is taken up Rs.25,000 will be the surplus amount available with the company for alternative investment. In case project E is taken up, the full amount of Rs. 1,50,000 would be used up. The difference between the additional investment required and Rs.25,000 and additional income is Rs. Rs 3,000 respectively over D giving a return rise of 12% on the balance of Rs. 25,000 over D. In case such an opportunity is not available, the company should take up project E. 5. Risk and uncertainty: Different capital investment proposals have different degrees of risk and uncertainty. There is a slight difference between risk and uncertainty. Risk involves situations which the probabilities of a particular event incurring are known whereas in uncertainty, these probabilities are not known. Of course in most oases these two terms are used interchangeably. Risk in capital investment decisions may be due to general economic conditions, competition, technological developments, consumer preferences, labour condition etc. On account of these reasons the revenues, costs and economic life of a particular investment are not certain. While evaluating capital investment proposals, a proper adjustment should therefore be made for risk and uncertainty. Besides the above factors, various other non-monetary considerations should also be weighed before taking a

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capital investment decision. For example, if a new product is to be introduced in the market, its effect on the state of existing product must also be seen. Sometimes a heavy investment completely changes the character of the firm. It may be felt by the investors that the company has entirely changed its line of manufacture and it may adversely affect the image of the company. This may result in fall in the value of the company's shares in the stock exchange. In other words, all possible consequences must be seen and in no case the image of the company should be allowed to be lowered down. CAPITAL BUDGETING APPRAISAL METHODS In view of the significance of capital budgeting decisions, it is absolutely necessary but that the method adopted for appraisal of capital investment proposals is a sound one. Any appraisal method should provide for the following: (i) a basis of distinguishing between acceptable and non-acceptable projects; (ii) ranking of projects in order of their desirability; (iii) choosing among several alternatives; (iv) a criterion which is applicable to any conceivable project; (v) recognizing the fact that bigger benefits are preferable to smaller ones and early benefits are

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preferable to later ones. There are several methods for evaluating and ranking the capital investment proposals. In case of all these methods the main emphasis is no the return which will be derived on the capital invested in the project. In other, words, the basic approach is to compare the investment in the project with the benefits derived therefrom. Following are the main methods generally used: 1. Pay-back Period Method. 2. Discounted Cash Flow Method. (a) The Net Present Value Method. (b) Present Value Index Method. 3. Accounting Rate of Return Method. Each of the above methods have been explained in detail in the following pages. Pay-back period method The term pay-back (or pay-out or pay-off) 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 an annual cash inflow of Rs.5,000 for ten years, the pay-back period will be 4 years, calculated as follows;

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Pay-back period = =

Initial Investment Annual Cash Inflow Rs.20,000 Rs. 5,000

The annual cash inflow is calculated by taking into account the amount of net income on account of the asset (or project) before depreciation but after taxation. The income so earned, if expressed as a percentage of initial investment, is termed as "unadjusted rate of return". In the above case, it will be calculated as follows: Unadjusted rate of return = =

Annual Return X 100 Initial Investment Rs.5,000 X 100 Rs.20,000 = 25%

Uneven cash inflows In the above example, we have presumed that the annual cash inflows are uniform. However, it may not always be so. The cash flow each year may be different. In such a case cumulative cash' inflows will be calculated and by interpolation, the exact pay-back period can be calculated. For example, if the project requires an initial investment of Rs.20,000 and the

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annual cash inflows for 5 years are Rs.6,000, Rs.8,000, Rs.5,000, Rs.4,000 and Rs.4,000 respectively, the payback period will be calculated as follows: Year

Cash Inflows

1 2 3 4 5

Rs. 6,000 8,000 5,000 4,000 4,000

Cumulative Inflows Rs. 6,000 14,000 19,000 23,000 27,000

Cash

The above table shows that in three years Rs. 19,000 has been recovered. Rs. 1,000 is left out of initial investment. In the fourth year the cash inflow is Rs.4,000. It means the pay-back period is between three to four years, ascertained as follows: 1,000 Pay-back period = 3 years + 4,000 = 3.25 years Accept or reject criterion The pay-back period can be used as a criterion to accept or reject an investment proposal. A project whose actual pay-back period is more than what has been predetermined by the management will be straightway rejected, The fixation of the maximum acceptable pay-

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back period is generally done by taking into account the reciprocal of the cost of capital. For example, if the cost of capital is 20% the maximum acceptable pay-back period would be fixed at 5 yeas. This can also be termed as cut-off point. Usually projects having a pay-back period of more than 5 years are not entertained because of greater uncertainties. The pay-back period can also be used as a method of ranking in case of mutually exclusive projects. The projects can be arranged in an ascending order according to the length of their pay-back periods. The project having the shortest pay-back period or highest unadjusted rate of return will be preferred provided it meets the minimum standard that has been established. For example, if the pay-back period has been fixed as 4 years, and project A has a pay-back period of 3 years and project B has a pay-back period of 4 years, project A would be preferred. Illustration 4: Payoff Ltd. is producing articles mostly by manual labour and is considering to replace it by a new machine. There are two alternative models M and N of new machine. Prepare a statement of profitability showing the pay-back period from the following information:

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Estimated life of machine Cost of machine Estimated saving in scrap Estimated savings in direct wages Additional cost of maintenance Additional cost of supervision Ignore taxation

Machine M 4 years Rs.9,000 500 6,000 800 1,200

Machine N 5 years Rs. 1 8,000 800 8,000 1,000 1,800

Solution: STATEMENT SHOWING ANNUAL CASH INFLOWS Estimated saving in scrap Estimated savings in direct wages Total Savings (i) Additional cost of maintenance Additional cost of supervision Total Additional costs (ii) Net Cash Inflow (i) - (ii) Pay-back period = Original Investment Annual Average Cash Inflow

Machine M Rs. 500 6,000 6,500 800 1,200 2,000 4.500

Machine N Rs. 800 8,000 8,800 1,000 1,800 2,800 6,000

Machine M 9,000 = 4,500 = 2 years

Machine M has a shorter pay-hack, hence it should be preferred to Machine N.

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Illustration 5: An Engineering company is considering the purchase of a new machine for its immediate expansion programme. There are three possible machines suitable for the purpose. Their details are as follows:

Capital Cost Sales (at standard prices) Net Cost of Production: Direct Material Direct Labour Factory Overheads Administrative Costs Selling and Distribution Costs

1 (Rs.) 3,00,000 5,00,000 40,000 50,000 60,000 20,000 10,000

Machine 2 3 (Rs.) (Rs.) 3,00,000 3,00,000 4,00,000 4,50,000 50,000 30,000 50,000 10,000 10,000

48,000 36,000 58,000 15,000 10,000

The economic life of machine No. l is 2 years, while it is 3 years for the other two. The scrap values are Rs.40,000, Rs.25,000 and Rs. 30,000 respectively. Sales are expected to be at the rates shown for each year during the full economic life of the machines. The costs relate to annual expenditure resulting from each machine.

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Tax to be paid is expected at 50% of the net earnings of each year. It may be assumed that all payable and receivables will be settled promptly, strictly on cash basis with no outstanding from one accounting year to another, Interest on capital has to be paid at 8% per annum. You are requested to show which machine would be the most profitable investment on the principle of "payback method". Solution STATEMENT SHOWING THE NET CASH FLOW OF THREE MACHINES

Capital Cost Sales (i) Cost of Production Administrative Costs Selling and Distribution Costs Total Cost (ii)

1 (Rs.) 3,00,000 5,00,000 1,50,000 20,000 10,000

Machine 2 3 (Rs.) (Rs.) 3,00,000 3,00,000 4,00,000 4,50,000 1,30,000 1,42,000 10,000 15,000 10,000 10,000

1,80,000 1,50,000 1,67,000

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Profit before depreciation and interest (i)-(ii)=(iii) Cost less scrap value Economic life Interest on Borrowings Depreciation and Interest (iv) Profit before tax (iii)-(iv) Taxation (50%) Add: Depreciation Net Cash Inflow Pay-back period

3,20,000 2,50,000 2,83,000 1,30,000

91,667

90,000

24,000 24,000 24,000 1,54,000 1,15,667 1,14,000 1,66,000 1,34,333 1,69,000 83,000 67,167 84,500 1,30,000 91,667 90,000 2,13,000 1,58,833 1,74,000 1.41 1.89 1.72 years years years

Machine No,. 1 is most profitable. Notes: (i) It has been presumed that interest on borrowings will have to be paid throughout the economic life of the assets. (ii) Factory overheads do not include depreciation. (iii) No borrowings will be required for working capital. Merits The pay-back method has the following merits: 1. The method is very useful in evaluation of those projects which involve high uncertainty. Political instability, rapid technological development of cheap substitutes, etc., are some of the reasons

35

2.

3. 4.

which discourage one to take up projects having long gestation period. Pay-back method is useful in such cases. The method makes it clear that no profit arises till the pay-back period is over. This helps new companies in deciding when they should start paying dividends. The method is simple to understand and easy to work out. The method reduces the possibility of loss on account of obsolescence a the method prefers investment in short-term projects.

Demerits The method has the following demerits: 1. The method ignores the returns generated by a project after its pay-back period, projects having long gestation period will never be taken up if this method is followed though they may yield high returns for a long period. Consider the following example.

36

Example: Initial Investment Cash Inflows;

Project A Rs. 1 0,000

Project B Rs. 10,000

Year 1 2 3 4 5 Pay-back period

4,000 4,000 2,000 -----3yrs.

3,000 3,000 3,000 3,000 3.33 yrs.

In the above ease Project A has a shorter payback period and therefore it should be preferred over B. But his may not be rational decision since project B continues to give return after the pay-back period which fact has been completely ignored. As a matter of fact, on the whole Project B is more profitable as compared to Project A. 2. The method does not take into account the time value of money. In other words, it ignores the interest which is an important factor in making sound investment decisions. A rupee tomorrow is worth less than a rupee today. The following example makes this point clear: Example: There are two projects A and B. The cost of the project is Rs.30,000 in each case. The cash

37

inflows are as under: Cash Inflows Year Project 'A' 1 Rs. 10,000 2 10,000 3 10,000

Project 'B' Rs. 2,000 4,000 24,000

The pay-back period is 3 years in both the cases. However, project 'A' should be preferred as compared to project CB' because of speedy recovery of the initial investment. Suitability In spite the above limitations, ,the pay-back method can profitability be used in each of the following cases: (i) Hazy long-term outlook: Where an account of political or other conditions, long-term outlook (say, exceeding three years) seems to be quite hazy, pay-back method is appropriate. (ii) Firms suffering from liquidity crisis: A firm which suffers from liquidity crisis is more interested in quick return of funds rather than profitability. Payback method suits them most because it also Emphasizes on quick recovery of funds. (iii) Firms emphasizing short-term earning performance. Pay back method is also suitable for a firm which emphasizes on short-term earning

38

performance of the firm rather its long-term growth. It may, therefore, be said that pay-back period is a measure of liquidity of investment rather than their probability. It should more appropriate of be treated as a constraint to be satisfied than as a profitability measure to be maximised. Discount Pay-Back Period method: The method discussed above is Traditional Pay-Back Period Method. However in order to overcome the criticism that this method does take into account the time value of money, the discounted pay-back period method is recommended. In case of this method, the present value of cash inflows arising at different time intervals at the desired rate of interest (depending upon the cost of capital) are found out. The present values so calculated are not taken as the real cash inflows for determination of the pay-back period, This technique can better be understood by the students after studying NPV Method discussed later. 2. Discounted Cash Flow (DCF) Method or Time Adjusted Technique The discounted cash flow technique is an improvement on the pay-back period method. It takes into account both the interest factor as well as the return after the pay-back period, the method involves three stages:

39

(i) Calculation of cash flows, i.e., both inflows and outflows (preferably after tax) over the full life of the assets, (ii) Discounting the cash flows so calculated by a discount factor, (iii) Aggregating of discounted cash inflows and collaring the total with the discounted cash outflows. (iv) Aggregating of discounted cash inflows and comparing the total with the discounted cash outflows. Discounted cash flow technique thus recognizes that Re. 4 of today (the cash outflow) is worth more than Re. 1 received at a future date (cash inflow). Discounted cash flow methods for evaluation capital investment proposals are of three types as explained below: (a) The Net Present Value (NPV) Method This is generally considered to be the best method for evaluating the capital investment proposals. In case of this method cash inflows and cash outflows associated with each project are first worked out. The present value of these cash inflows and outflows is then calculated at the rate of return acceptable to the management. This rate of return is considered as the

40

cut-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. Cash outflows represent the investment and commitments of cash in the project at various points of time. The working capital is taken as a cash outflow in the year the project starts commercial production. Profit after tax but before depreciation represents cash inflows. 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 outflows. The equation for calculating NPV in case of conventional cash flows can be put as follows:

In case of non-conventional cash inflows (i.e. where there are a series of cash inflows as well cash outflows) the equation for calculating NPV is as follows:

41

Where: NPV = Net Present Value, R = Cash Inflows at different time periods. K = Cost of Capital or Cut-off Rate, I = Cash Outflows at different time periods. Accept or reject criterion The Net Present Value can be used as an 'accept or reject' criterion, In cash the NPV is positive (i.e. present value of cash inflows is more than present value of cash outflows) the project should be accepted. However, if the NPV is negative (i.e., present value of cash inflows is less than the present value of cash outflows) the project should be rejected. Symbolically, the accept/reject criterion can be put as follows: NPV > Zero accept the proposal NPV < Zero reject the proposal Or where PV > C accept the proposal PV < C reject the proposal PV stands for Present Value of Cash Inflows and C for Present Value of Cash Outflows (or outlays). Illustration 6: Calculate the net present value for a small sized project requiring an' initial investment of Rs.20,000, and which provides a net cash inflow of Rs.6,000 each year for six years. Assume the cost of funds to be 8% p.a. and that there is no scrap value.

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Solution: The present value of an annuity of Re. 1 for 6 years at 8% p.a. interest is Rs. 4,623 Hence, the present value of Rs. 6.000 comes to: 6,000 x 4.623 = Rs. 27.738 Less: Initial Investment Rs. 20,000 Net Present Value (NPV) Rs. 7,738 Illustration 7: The Alpha Co. Ltd. is considering the purchase of a new machine. Two alternative machines [A and B] have been suggested, each having an initial cost of Rs.4,00,000 and requiring Rs.20,000 as additional working capital at the end of the 1st year. Earnings after taxation are expected to be as follows: Cash Inflows Year Machine A Machine B 1 Rs. 40,000 Rs. 1,20,000 2 1,20,000 1,60,000 3 1,60,000 2,00,000 4 2,40,000 1,20,000 5 1,60,000 80,000 The company has target of return on capital of 10% and on this basis, you are required to compare the profitability of the machine and state which alternative you consider financially preferable. Note: the following table gives the present value of Re.l due in 'n' number of years:

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Year 1 2 3 4 5

Present Value at 10% 0.91 0.83 0.75 0.68 0.62

Solution The Alpha Company STATEMENT SHOWING THE PROFITABILITY OF THE TWO MACHINES Year

Discount Factor

1 0.91 2 0.83 3 0.75 4 0.68 5 0.62 Total Present Value of Cash Inflows Total Present Value of Cash Outflows (Rs. 4,00,000 + 20,000 x 0.91) Net Present Value

Machine A Cash Inflow Rs. 40,000 1,20,000 1,60,000 2,40,000 1,60,000

Machine B

Present Cash Value Rs. Inflow Rs. 36,400 1,20,000 99,600 1,60,000 1,20,000 2,00,000 1,63,200 1,20,000 99,200 80,000 5,18,400

4,18,200 1,00,200

Present Value Rs. 1,09,200 1,32,800 1,50,000 81,600 49,600 5,23,200

4,18,200 1,05,000

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Recommendations: Machine B is preferable to Machine A. Though total cash inflow of Machine A is more than that of Machine B by Rs.40,G00, the net present value of the cash inflows of Machine B is more that of Machine A. Moreover, in case of Machine B cash inflow in the earlier years is comparatively higher than that in case of Machine A. It is to be noted that the present value method (on the basis of discounted cash inflows) assumes that the available funds would immediately be reinvested at the chosen rate of interest. 10% in the above case. If this assumption is not valid, the decision should be on the basis of gross cash inflows and not according to discounted cash inflows. In that case Machine A would be preferable to Machine B. Another assumption while deciding in favour of Machine B is that, in both cases, one is equally sure that these cash inflows will arise. In other words, the probability of cash inflows as given in die question for both the machines is the same. In case one is not sure about the cash inflows one should have adjusted the discounted cash inflows of the machine's with the probability factor and then only a proper comparison would be possible.

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Illustration 8: A choice is to be made between two competing projects which require an equal investment of Rs.50,000 and are expected to generate net cash flows as under; Project 1 Project 2 End of year 1 Rs. 25,000 Rs. 10,000 End of year 2 15,000 12,000 End of year 3 10,000 18,000 End of year 4 Nil 25,000 End of year 5 12,000 8,000 End of year 6 6,000 4,000 The cost of capital of the company is 10 percent. The following are the Present Value Factors @ 10% per annum; Year P. V. Factors @ 10% p.a. 1 0.909 2 0.826 3 0.751 4 0,683 5 0,621 6 0.564 Which project proposal should be chosen and why? Evaluate the project proposals under:

46

(a) Pay-back Period, and (b) Discounted Cash Flow methods, pointing out their relative merits and demerits. Solution PAY-BACK PERIOD METHOD Project I Project II Cash inflows End of year 1 End of year 2 End of year 3 End of year 4 End of year 5 End of year 6

Rs. 25,000 15,000 10,000 Nil 12,000 6,000

Cum. Cash Cum. CashCashinflows inflows inflows Rs. 25,000 Rs. 10,000 Rs. 10,000 40,000 12,000 22,000 50,000 18,000 40,000 50,000 25,000 65,000 62,000 8,000 73,000 68,000 4,000 77,000

Project I has the pay-back period of 3 years while project II has a pay-back period of 3-4 years [i.e. Rs.40,000 in 3 years and Rs. 10,000 in the 4th year]. Thus, Project I has to be preferred because it has a shorter pay-back period.

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Project I Year

Cash Inflow

1 Rs. 25,000 2 15,000 3 10,000 4 Nil 5 12,000 6 6,000 Total Present value of Future cash inflow Initial Investment Net Present value Project II Year

Cash Inflow

1 10,000 2 12,000 3 18,000 4 25,000 5 8,000 6 4,000 Total Present value of Future cash inflow Initial Investment Net Present value

Discount Present Value Factor at 10% p.a. .909 Rs. 22,725 .826 12,390 .751 7,510 .683 -.621 7,452 .564 3,384 53,461 50,000 3,461 Discount Present Value Factor at 10% p.a. .909 9,090 .826 9,912 .751 13,518 .683 17,075 .621 4,968 .564 2,256 56,819 50,000 6,819

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Both projects need the same investment of Rs,50,000. However, in case of Project I, there is a surplus of Rs,3,461, while in case of Project II, there is a surplus of Rs.6,819. Hence Project II is to be preferred. Relative merits and demerits of the two methods: Pay-back period method is relatively simple to understand and may easy to work out as compared to the discounted cash flow method. However, it does not take into account the return after the pay-back period. Moreover, pay-back period ignores the time value of money, Discounted cash flow method does not have these disadvantages. It takes into account the returns over the effective life of the asset besides considering the future cash inflows. The method is, therefore, more scientific and dependable. Illustration 9: Home Gadgets Company is considering building an assembly plan. The decision has been narrowed down to two possibilities. The company desires to choose the best plant at a level of operation of 10,000 gadgets a month. Both plants have an expected life of 10 years and are expected not to have any salvage value at the time of their retirement. The cost of capital is 10 per cent. Assuming a zero income-tax rate, suggest what would be the desirable choice?

49

Cost of 10,000 gadgets per Month Output Level

Initial Cost Direct Labour: First Shift Second Shift Overheads

Large Plant (Rs.) 30,00,000 p.a. 15,00,000 p.a. --- p.a. 2,40,000 p.a.

Small Plant (Rs.) 22,93,500 p.a. 7,80,000 p.a. 9,00,000 p.a. 2,10,000 p.a.

The Present Value of an ordinary annuity of Re. 1, for 10 years at 10 per cent, is 6.1446. Solution SAVING PER ANNUM OF INSTALLING LARGE PLANT Saving in Direct labour (both shifts) Rs. 1,80,000 Savings in Overhead costs (-) 30,000 Savings per annum of using large plant 1,50,000 Present value of recurring annual savings of Rs. 1,50,000 per year, at 10 per cent opportunity rate = 1,50,000 x 6,1446 Rs. 9,21,690 Cost of Large Plant Rs. 30,00,000 Cost of Small Plant Rs. 22,93,500 Additional outlay for large plant Rs. 7,06,500

The present value of savings, Rs.9,21,690 resulting from the use of the large plant is substantially higher than the extra capital initial outlay of Rs.7,06,500 required for its. Therefore, it is advisable to go in for the large plant.

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(b) Excess Present Value Index This is a refinement of the net present value method. Instead of working out the net present value, a present value index is found out by comparing the total of present value of future-cash inflows and the total of the present value of future cash outflows. This can be put in the form of the following formula; Excess Present Value Index [Or Benefits Cost (B/C) Ratio] Present value of future cash inflows x 100 = Present value of future cash outflows Excess Present Value provides ready comparison between investment proposals of different magnitudes. For example, Project 'A' requiring an investment of Rs. 1,00,000 shows excess present value of Rs.20,000 while another project 'B' requiring an investment of Rs. 10,000 shown an excess on present value of Rs. 5,000. If absolute figures of net present values are computed, Project 'A' may seem to be profitable. However, if excess present value index method is followed Project 4B' would prove to be profitable. 1,20,000 X100 Present Value Index for Project A =1,00,000 = 120%

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15,000 X 100 Present Value Index for Project B =10,000 Illustration 10: On the basis of figures given in the illustration 8, state which project is profitable according to the Present Value Index Method. Solution Present Value Index = Present value of future cash inflows x 100 Present value of future cash outflows Project I

=

Project II

=

53,461 X 100 50,000 56,819 X 100 50,000

= 107% (approx.) = 114% (approx.)

Since, Project II has a higher Present Value Index hence it is more profitable as compared to Project I. Illustration 11: S Ltd. has Rs, 10,00,000 allocated for capital budgeting purposes. The following proposals and associated profitability indices have been determined:

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Project 1 2 3 4 5 6

Amount Rs. 3,00,000 1,50,000 3,50,000 4,50,000 2,00,000 4,00,000

Profitability Index 1.22 0.95 1.20 1.18 1.20 1.05

Which of the above investments should be undertaken? Assume that projects are indivisible and there is no alternative use of the money allocated for capital budgeting. Solution STATEMENT RANKING OF PROJECTS ON THE BASIS OF PROFITABILITY INDEX Project Amount Rs. Profitability Rank Index 1 3,00,000 1.22 1 2 1,50,000 0.95 5 3 3,50,000 1,20 2 4 4,50,000 1.18 3 5 2,00,000 1.20 2 6 4,00,000 1.05 4 Since projects are indivisible and there is no alternative

53

use of the money allocated for capital budgeting on the basis of P.I., hence S Ltd. is advised to undertake investment in projects 1,3 and 5. However, in case of alternative projects, the allocation should be made to the project which adds the most to the shareholders' wealth. The NPV method in such a case will give the best results. Project Amount Profitability Rs. Index (i) (ii) (iii) 1 3,00,000 1.22 2 1,50,000 0.95 3 3,50,000 1.20 4 4,50,000 1.18 5 2,00,000 1.20 6 4,00,000 1.05

Cash Inflows of Projects Rs. (iv) = [(ii) x (iii)] 3,66,000 1,42,500 4,20,000 5,31,000 2,40,000 4,20,000

N.P.V. of Project Rs. (v)-[(iv)-(ii)] 66,000 (-) 7,500 70,000 81,000 40,000 20,000

The above table shows that allocation of funds to the projects 1, 3 and 5 (as selected according to P.I.) will give NPV of Rs. 1,76,000 and Rs. 1150,000 will remain unspent. However, the NPV of the project 3,4 and 5 is Rs. 1,91,000 which is more than the NPV of projects 1,3 and 5. Moreover, by undertaking projects 3, 4 and 5 no money will remain unspent. Hence S Ltd. is advised to undertake investments in project 3, 4 and 5.

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(c) Internal Rate of Return Internal Rate of Return is that 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: Cash Inflows Cash Outflows

=1

Thus, in case of this method the discount rate is not known but the cash outflows and cash inflows are known. For example, if a sum or Rs.800 invested in a project becomes Rs. 1,000 at the end of a year, the rate of return comes to 25%, calculated as follows: R I = I+r Where I = Cash Outflow i.e., initial investment R = Cash Inflow r = Rate of return yielded by the Investment (or IRR) Thus: 800=l,000/l+r or 800 r +800 =1,000 or 800 r = 200 or r = 200/800 = .25 or 25%

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In case of return is over a number of years, the calculation would take the following pattern in case of conventional cash flows:

In case of return is over a number of years, the equation would be as follows:

where I = Cash Outflow (or outflow) at different time periods. R = Cash Inflows at different time periods. r = Rate of return yielded by the Investment (or IRR). Since I and R are known factors, r is the only factor to the calculated. However, calculations will become very difficult over a long period if worked out according to the above equations. Tabular values are therefore, used.

56

Accept/Reject criterion Internal Rate of return is the maximum rate of interest which an organisation can afford to pay on the capital invested in a project. A project would qualify to be accepted if IRR exceeds the cut-off rate. While evaluating two or more projects, a project giving higher internal rate of return would be preferred. This is because the higher the rate of return, the more profitable is the investment. (l) Where cash inflows are uniform: In the case of those projects which result in uniform cash inflows, the internal rate of return can be calculated by locating the Factor in Annuity Table II. The factor is calculated as follows: I F = C where F = Factor to be located I = Original Investment C = Cash Inflow per year Illustration 12: An equipment requires an initial investment of Rs. 6,000. The annual gash flow is estimated at Rs.2,000 for 5 years. Calculate the internal rate or return.

57

Solution The annual cash flow is uniform at Rs.2,000 for five years. Hence, the 'Factor' or the 'Pay-back' is 3, calculated as follows: F = where F = I = C = F

I C Factor to be located Initial Investment Cash Inflow per year

6,000 =Rs. 2,000

=3

The discount percentage would be somewhere between 18% [Rs.3.127 present value of annuity of Re.l) and 20% (Rs. 2.99 present value of annuity of Re.l). It indicates that the internal rate of return is more than 18% but less than 20%. A more exact interpolation can be done (as explained in the next illustration). However, such an effort may not be very useful in the present case since Rs.2.99 is very near to 3 and hence the internal rate of returns can be taken as 20%. Rs.2.99 is as a matter of fact the present value of Re. l received annuity for five years at 20% interest rate. In case this amount is multiplied by the annual cash

58

inflows it will be equal to the initial investment as shown below: Rs. 2,000 x 2.99 = Rs.5,980 (or say Rs.6,000) Relationship between pay-back reciprocal and rate of return Pay-back reciprocal is exactly equal to the unadjusted rate of return, Unadjusted rate means a rate which has not been adjusted by taking into account the time value of money. For example, in the illustration given above the pay-back period comes to 3 years. Its reciprocal is 1/3 or .33 or 33%. The annual return is Rs.2,000 on an investment of Rs.6,000. It also comes to 33%. Pay-back reciprocal also gives a reasonable approximation of the time adjusted rate of return as is proved by the above illustration. Of course, for calculating the discounted rate. However, there are two assumptions to the use of pay-back reciprocal: (i) The useful life of project/asset should be at least twice the pay-back reciprocal. In any case the pay-back reciprocal will always exceed the true or the discounted rate of return, (ii) The cash inflows should be uniform over the life of the project/asset. (2) Where cash inflows are not uniform: When cash

59

inflows are not uniform, the internal rate of return is calculated by making trial calculations in an attempt to compute the correct interest rate which equates the present value of cash inflows with the present value of cash outflows. In the process, cash inflows are to be discounted by a number of trial rates. The first trial rate may be calculated on the basis of the same formula which is used for determining the internal rate of return when cash inflows are uniform, as explained above. However, in this case 'C' stands for 'annual average cash inflow', in place of 'annual cash inflow'. After applying the first trial rate the second trial rate is determined when the total present value of cash inflows is greater or less than the total present value of cash outflows. In case the total present value of cash inflows is less than the total present value of cash outflows, the second trial taken will be lower than the first rate. In case the present total value of cash inflows exceeds the present total value of cash outflows, a trial higher than first trial rate will be used. This process will continue till the two flows more or less set off each other. This will be the 'internal rates of return'.

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Illustration 13. A company has to select one of the following two projects: Project A Project B Cost Rs.l 1,000 10,000 Cash inflows: Year l 6,000 1,000 Year 2 2,000 1,000 Year 3 1,000 2,000 Year 4 5,000 10,000 Using the Internal Rate of Return Method suggest which project is preferable. Solution The cash inflows are not uniform and hence the Internal Rate of Return will have to be calculated by the Trial and Error Method. In order to have an approximate idea about such rate it will be better to find out the "Factor". The factor reflects the same relationships of investment and 'cash inflows' as in case of pay-back calculations: Thus. I F= C where F = Factor to be located I = Original Investment C = Average cash flow per year

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The 'factor' in case of project A would be; 11,000 F= Rs. 3,000 = 3.14 The 'factor' in case of project B would be; 10,000 F = Rs. 3,000 = 2.86 In case of project A, the rate comes to 10% while in case of project B it comes to 15%. Project A: Year 1 2 3 4 Total

Cash Inflows Rs. 6000 2000 1000 5000

Discounting Present value Factor at 10% 0.893 Rs. 5454 0.826 1652 0.751 751 0.683 3415 Present value 11272

The present value at 10% comes to Rs. 11,272. The initial investment is Rs. 11,000. Internal rate of Return may be taker, approximately at 10%. 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

62

taken, Taking a rate of 12%, the following results would emerge: Year 1 2 3 4

Cash Inflows Rs. 6000 2000 1000 5000

Total

Discounting Present value Factor at 10% 0.893 Rs. 5,358 0.797 1,594 0.712 712 0.636 3,180 Present value 10,844

The internal rate of return is thus more than 10% but less than 12%. The exact rate may be calculated as follows: Internal Rate of Return = Difference in calculated present value and required net cash outlay Difference in calculated X Difference in rate present values = 100% +

11,272-11,000 11,272-10,844

= 100% +

272 X 2 428

X 2

=

11.3%

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The exact internal rate of return can also be calculated as follows: At 10% the present value is + 272 At 12% the present value is - 156. The internal rate would, therefore, be between 10% and 12% calculated as follows: =

10 +

272 272+156 10+1.3= 11.3%

=

x 2

Project B Year 1 2 3 4 Total

Cash Inflows Rs. 1,000 1,000 2,000 10,000

Discounting Present value Factor at 10% 0.870 Rs. 870 0.756 756 0.658 1,316 0.572 5,720 Present value 8,662

Since the present value at 15% comes only to Rs.8,662, a lower rate of discount should be taken. Taking a i#e of 10%, the following will be the result:

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Year 1 2 3 4

Cash Inflows Rs. 1,000 1,000 2,000 10,000

Total

Discounting Present value Factor at 10% 0.909 Rs. 909 0.826 826 0.751 1,502 0.683 6,830 Present value 10,067

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%. In order to have exactness, the internal rate of return can be interpolated as done in case of project A. At 10% the present value is + 67 At 12% the present value is - 1,338 = 10 = 10

+ +

67 67+1,338 67 1,405

x 5 x 5

= 10+ .24 = 10.24% 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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Illustration 14: M/s Diwali Traders install plant and machinery is rented premises for the production of a luxury article, the demand for which is expected to last for only 5 years. The total capital put in by the firm is an under: Plant and Machinery Working Capital Total

Rs. 2,70,500 40,000 Rs. 3,10,500

The working capital will be fully realised at the end of 1990. The scrap value of the plant expected to the realised at the end of 1990 is only Rs.5,500. The earnings of M/s Diwali Traders are expected to be as under: Year Cash Profit Tax Payable (Before depreciation and tax) 1986 90,000 20,000 1987 1,30,000 30,000 1988 1,70,000 40,000 1989 1,16,000 26,000 1990 19,500 5,000 Present value factors at various rates of interest are given below:

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11% 0.9009 0.8116 0.7312 0.6587 0.5935

12% 0.8920 0.7972 0.7118 0.6355 0.5674

13% 0.8850 0.7831 0.6931 0.6133 0.5428

14% 0.8772 0.7695 0.6750 0.5921 0.5194

15% 0.8696 0.7561 0.6575 0.5718 0.4972

You are required to compute the present value of cash inflows discounted at the various rates of interest given above and state the return from the project. Solution Year 1986 1987 1988 1989 1990 Total

Cash 11% 12% 13% 14% 15% Inflows 70,000 63,063 62,503 61,950 61,404 60,872 1,00,000 81,160 79,720 78,310 76,950 75,610 1,30,000 95,056 92,534 90,103 87,750 85,475 90,000 59,283 57,195 55,197 53,289 51,462 60,000 35,610 34,044 32,568 31,164 29,832 3,34,172 3,25,996 3,18,128 3,10,557 3,03,251

Note: Cash inflows in years 1986 to 1989 are profits are given less tax. In 1990 the amount also includes Rs.5,500 the expected scrap value and Rs. 40,000, the working capital to be released. At 14% the inflows are almost equal to the outflow. The project, therefore, yields an internal rate of return of 14%.

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Comparison of the Internal Rate of Return Approach with the Present Value Approach Though both Net Present Value Method (NPV) and Internal Rate of Return Method (IRR) are the species of the same sequence, i.e., discounted cash flow method, yet they are different from each other in several respects. The chief points of difference between the two are as fellows: 1. The Net Present Value Method takes the interest rate as a known factor while Internal Rate of Return Method takes it as an unknown factor. 2. The Net Present Value Method seeks to find out the amount that can be invested in a given project so that its anticipated earnings will exactly suffice to repay this amount with interest at the market rate. On the other hand, Internal Rate of Return Method seeks to find the maximum rate of interest at which the funds invested in the project could be repaid out the cash inflows arising out of that project. 3. Both the Net Present Value Method and Internal Rate of Return Method proceed on this presumption that cash inflows can be-reinvested at the discounting rate in the new projects. However, reinvestment of funds at the cut-off rate is more possible than at the internal rate of return. Hence, Net Present Value Method is more reliable than the Internal Rate of Return Method for ranking two or more capital investment

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projects. Similarities in results under NPV and IRR Both NPV and IRR will give the same result (i.e., acceptance or rejection) regarding an investments proposal in following cases: (i) Projects involving conventional cash flows, i.e., when an initial outflow is followed by a series of inflows; (ii) Independent investment proposals, i.e., proposals the acceptance of which does not preclude the acceptance of others. The reason for similarity in results in the above cases is simple. In case of NPV method, a proposal is acceptable if its NPV is positive. NPV will be positive only when the actual return on investment is more than the cut-off rate. In case of IRR method a proposal is acceptable only when the IRR is higher than the cutoff rate. Thus, both methods will give consistent results since the Acceptance or rejection of these proposal under both of them is based on the actual return being higher than the cut-off rate.

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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 would result in non-acceptance of the other. Such conflict may be due to any one or more of the following reasons: (i) The projects require different cash outlays, (ii) The projects have unequal lives, (iii) The projects have different patterns of cash flows. In such a situation, the result given by the NPV method should be relied upon. This is because the objective of a company is to maximise its shareholders' wealth IRR method is concerned with the rate of return on investment rather than total yield on investment hence it is not compatible with the goal of wealth maximisation. NPV method considers the total yield on investment. Hence, in case of mutually exclusive projects, each having a positive NPV, the one with the largest NPV will have the most beneficial effect on shareholders' wealth. In case of projects requiring different cash outlays, the problem can also be resolved by adopting incremental approach, a modified form of IRR method. According to this approach in case of two mutually exclusive 'projects requiring different cash outlays, the IRR of

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incremental outlay of the project requiring a higher investment is calculated. In case this IRR is higher than the required rate of return, the project having greater non-discounted cash flows should be accepted otherwise it should be rejected. Illustration I5: A firm has to make a choice between two projects A and B which are mutually exclusive. The cash flows are as follows: Year Project A Project B 0 Rs. 5,000 Rs. 7,500 1 Rs. 6,000 Rs. 8,800 The cost of capital is 10%. Suggest which project should be taken up using (i) NPV Method and (ii) IRR Method. Solution NPV Method Project Present value of cash Inflows (6,000 x .909) Initial Investment NPV Project Internal Return

Rate

of

A Rs. 5,454 (8,800 x.909) 5,000 454 IRR Method A 20%

B Rs. 7,999 7,500 499

B 17.33%

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Thus, according to NPV method, Project B is superior to Project A since its NPV is higher than that of B. But according to IRR method, Project A is superior to Project B since it has a higher IRR. Since acceptance of Project B would result in maximisation of wealth of the shareholders as indicated by NPV, it will be appropriate to reject Project A. The same conclusion can be drawn by adopting the Incremental Approach, as shown below: Project A Cash Outlays Rs. 5,000 Cash Inflows Rs. 6,000 IRR for Incremental cash inflows

B B-A Rs. 7,500 Rs. 2,500 Rs. 8,800 Rs. 2,800

The IRR of differential cash outlay of Project B comes to 12% while the required return is 10%. Project B is therefore better than Project A inspite of its having a lower IRR. This is because it offers the benefits offered by the Project A and also a return in excess of the required rate of return on incremental investment of Rs.2,500. Merits The merits of discounted cash flow method are as follows:

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(i) Discounted cash flow technique takes into account the time value of money. Conceptually, it is better than other techniques such as payback or accounting rate of return. (ii) The method takes into account directly the amount of expense and revenues over the project's life. In case of other methods simply their average are taken. (iii) The method automatically gives more weight to those money values which are nearer to the present period than those which are farther from it. While in case of other methods, all money units are given the same weights which seems to be unrealistic. (iv) The method makes possible comparison of projects requiring different capital outlay, having different lives and different timings of cash flows, at a particular moment of time because of discounting of all cash flows. Demerits The following are the demerits of discounted cash flow method: (i) The method is difficult to understand and work out as compared to other methods of ranking capital investment proposals. (ii) The method takes into account only the cash inflows on account of a capital investment decisions. As a matter of fact the profitability or otherwise of a capital investment proposal can be judged only when the net

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income (and not the cash inflow) on account of operations is considered. (iii) The method is based on the presumption that cash inflows can be reinvested at the discounting rate in the new projects. However, upon the available investment opportunities. Accounting or 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 income are determined according to commonly accepted accounting principles 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 of Return. It may be calculated according to any of the following method: Annual Average Net Earnings X 100 (i) Original Investment Annual Average Net Earnings X 100 (ii) Average Investment The term "average annual net earnings" is the average of the earnings (after depreciation and tax) over the whole of the economic life of the project. Increase in expected .future annual net earnings X (iii) Initial increase in required investment

100

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The amount of "average investment" can be calculated according to any of the following methods: Original investment (iv) (a) 2 (b)

Original investment - Scrap value of the asset 2

Original investment + Scrap value of the asset (c) 2 (d)

Original investment - Scrap value + 2

Add. Net + Scrap Working Capital Value

Out of the four methods of calculating average investment, method (d) seems to be theoretically more logical on account of the following reasons: (i) Presuming that depreciation is charged according to fixed instalment method, the average investment in the asset is only 50% of original cost less scrap value. (ii) The amount required for additional net working capital (current assets - current liabilities) remains tied up during the lifetime of the asset. Its entire amount is therefore a pert of investment in the assets. (iii) Scrap value is realised only at the end of the life of the asset. Depreciation is charged on the asset after

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deducting scrap value. Hence, the whole amount of scrap value remains tied up in the project throughout its lifetime. It may be noted that results obtained under each of above methods will be quite different from each other. It is, therefore, necessary that while evaluating capita investment proposals, the same method is followed in each case. Accept/reject criterion Normally, business enterprises fix a minimum rat of return. Any project expected to give a return below this rate will be straightway rejected. In case of several projects, where a choice has to be made, the different projects may be ranked in the ascending or descending order of their rate of return. Projects below the minimum rate will be rejected. In case of projects giving rates of return higher than the minimum rate, obviously projects giving a higher rate of return will be preferred over those giving a lower rate of return. Illustration 16: The directors of Alpha Limited are contemplating the purchase of a new machine to replace a machine which has been in operation in the factory for the last 5 years.

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Ignoring interest but considering tax at 50% of net earnings, suggest which of the two alternatives should be preferred. The following are the details: Old New Machine Machine Purchase price 40,000 60,000 Estimated life of machine 10 years 10 years Machine running hours per annum 2,000 2,000 Units per hour 24 36 Wages per running hour 3 5.25 Power per annum 2,000 4,500 Consumable stores per annum 6,000 7,500 All other charges per annum 8,000 9,000 Material cost per unit 0.50 0.50 Selling price per unit 1.25 1.25

You may assume that the above information regarding sales and cost of sales will hold good throughout the economic life of each of the machines. Depreciation has to be charged according to straight-line method.

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Solution: PROFITABILITY STATEMENT

Cost of the Machine (Rs.) Life of Machine Output Sales Value Less: Cost of Sales: Direct Material Wages Power Consumable stores Other charges Depredation Profit before tax Tax at 50% Profit after tax

(yrs.) (Units) (Rs.) 24,000 6,000 2,000 6,000 8,000 4,000

Old Machine 40,000 10 48,000 60,000

New Machine 60,000 10 72,000 90,000 36,000 10,500 4,500 7,500 9,000

50,000 10,000 5,000 5,000

6,000

73,500 16,500 8,250 8,250

Accounting Rate of return Old Machine Average Net Earnings X 100 (i) Original Investment = 5,000/40,000 x 100 = 12.5%

New Machine 8,250 x 100 60,000 = 13.75%

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Average Net Earnings X 100 (ii) Average Investment = 5,000/20,000 x 100 = 25%

8,250 x 100 30,000 = 27.50%

Incremental Earnings X 100 (iii) Incremental Investment 3,250 X 100 = Rs.60,000 - Rs,20,000 3,250 X 100 = 8%(approx) = 40,000 Thus, replacement of the old machine by a new machine (ignoring interest) is profitable. Illustration 17: Determine the average rate of return form the following data of two machines A and B. Original Cost Addl. Investment in net working capital Estimated life in years Estimated salvage value Average Income-tax rate Annual estimated income after depr. and tax: 1st year 2nd year 3rd year 4th year 5th year

Machine A Rs. 56,125 5,000 5 3,000 55% 3,375 5,375 7,375 9,375 11,375 36,875

Machine B Rs. 56,125 6,000 5 3,000 55% 11,375 9,375 7,375 5,375 3,375 36,875

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Depreciation has been charged on straight line basis. Solution Average Earnings X 100 ARR = Average Investment Total Income Average Income = Number of years Machine A = Machine B =

Rs. 36,875 5 Rs.36,875 5

=

Rs. 7,375

= Rs. 7,375

Original investment-Scrap value Average Investment = 2 Add.Net + Working Capital

+

Scrap Value

56,125-3,000 + Rs. 5,000 + Rs. 3,000 Machine A = 2 = 26,562.50 + 8,000 = Rs.34,562.50 Machine B

56,125-3,000 + Rs. 6,000 + Rs. 3,000 = 2 = 26,562.50 + 9,000 = Rs.35,562,50

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ARR for Machine A = =

Rs.7,375 X 100 34,562,50 21.34%

ARR for Machine B = =

Rs.7,375 X 100 35,562.50 20.74%

Illustration 18: M/s Bharat Industries Limited purchased a machine five years ago. A proposal is under consideration to replace it by a new machine. The life of the machine is estimated to be 10 years. The existing machine can be sold at its written-down value. As the cost accountant of the Company, you are required to submit your recommendations based on the following information: Existing New Machine Machine Initial cost Rs. 25,000 Rs. 50,000 Machine hours per annum 2,000 2,000 Wages per running hour 1.25 1.25 Power per hour 0.50 2.00 Indirect material per annum 3,000 5,000 Other expenses per annum 12,000 15,000 Cost of materials per unit 1 1 Number of units produced per hour 12 18 Selling price per unit 2 2 Interest to be paid at 10% on fresh capital invested.

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Solution STATEMENT OF PROFIT

Production per annum (Units) Selling price per unit Cost of Sales: Materials Wages Power Indirect Materials Other Expenses Depreciation Interest Total profit Cost per unit Profit per unit

Existing Machine 24,000 Rs. 2 Rs. 48,000 Rs. 24,000 2,500 1,000 3,000 12,000 2,500 -45,000 Rs.3,000 Re. 1.87 Re. 0.13

New Machine 36,000 Rs. 2 Rs. 72,000 Rs. 36,000 2,500 4,000 5,000 15,000 5,000 3,750 71,250 Rs. 750 Re. 1.98 Re. 0.02

The above analysis shows that it will be better to continue with the existing machine than replacing it by a new machine. On the basis of accounting rate of return also, it will be better to continue with the existing machine. This has been shown as under:

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Profit on installation of new machine before charging interest = Rs. 750 + 3,750 = Rs, 4,500 Incremental profit = Rs.4,500 - Rs. 3,000 = Rs. 1,500 Incremental Investment = Rs.37,500 Rs. 1,500 X 100 Rate of Return = 37,500 = 4% Working Notes: Interest has been calculated as follows: Investment in New Machine Less: Sale value of the old machine (Rs. 25,000 -Dep. Rs. 12,500 on fixed instalment basis) Interest at 10% p.a. on Rs. 37,500 = Rs.3,750

Rs.50,000 Rs. 12,500 Rs. 37,500

In case the rate of return is calculated on average investment (i.e, ½ of Rs.37,500) the rate of return will be 8%. This is not even sufficient to pay interest at 10% on additional investment required. Thus, it will be advisable to continue with the existing machine. Illustration 19: Balrampur Engineering Works manufactures a part A which is used in the air-coolers which it sells. The quantity required is 7,000 units per year. The direct cost of manufacturing this part is Rs.4

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per unit. It has received a proposal from a Cuttack firm offering to meet the entire heeds @ Rs.5 per unit. If the Balrampur Works discontinues making this part, it can expand its existing facilities for manufacturing a new product for sale which would involve the following: Investment on new machine (Life of Rs.40,000 40,000 hrs) Material Cost Rs. 3 per unit Direct Labour Rs. 2 per unit Indirect Expenses (other than depreciation) for 8,000 hours Rs. 12,000 Estimated volume of sales 8,000 units at Rs. 9 per State whether the proposal of the Cuttak firm should be accepted or not if: (i) The current cut-offrate is 25%. (ii) The current cut-off rate is 30%.

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Solution PROTABILITY OF NEW PRODUCT Sales (8,000 units x Rs.9) Rs.72,000 Less: Cost of Production; Rs. Materials Cost (8,000 x Rs.3) 24,000 Direct Labour (8,000 x Rs.2) 16,000 Indirect Expenses 12,000 Depreciation (8,000 hrs. x Re.l) 8,000 60,000 12,000 Extra cost for Part 'A' payable to Cuttak Firm 7,000 5,000 Average investment in the new project 20,000 Rate of return at 25% cut-off rate 5,000 Rate of return at 30% cut-off rate 6,000 The proposal may be accepted at cut-off rate of 25%. However, it is not acceptable at cut-off rate at 30%. Advantages The following are the advantages of this method: (i) The method takes into account savings over the entire economic life of the asset. Hence, it provides a better comparison of the projects as compared to the pay-back method, (ii) The method embodies the concept of 'net earnings' while evaluation capital investment projects which is absent in case of all other methods.

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Disadvantages The method suffers from the following disadvantages: (i) The method does not take into account the time value of money. Thus, it has the same fundamental defect as that of the pay-back method. (ii) There are different methods for calculating the Accounting Rate of Return due to diverse concepts of the investments as well as earnings. Each method gives different results, This reduces the reliability of the method. On account of the above disadvantages, the Accounting Rate of Return Method is not much in use of these days, REPLACEMENT OF EXISTING ASSET It has already been explained, that capital budgeting decisions have to be taken because the assets require constant replacements. In the illustrations discussed so far we have assumed that the assets are replaced only at the end of their useful lives. However, it is not always so in practice. An equipment or asset may have to be replaced before its useful life because a more economic alternative is available in view of the constant technological developments. This helps in reducing the costs and increasing the operational efficiency. In such a case, it will be necessary to determine the most

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opportune time for replacement of the asset. This can be understood with the following illustrations: Illustration 20: A machine used on a production line must be replace at least every four years, The costs incurred in running the machine according to its age are:

0 Rs. 3,000

Purchase price Maintenance Repairs Net realisable value

Age of machine (years) 1 2 3 Rs. Rs. Rs. 800 1,600

900 200 1,200

1,000 400 800

4 Rs. 1,000 800 400

Future replacement will be identical machines with the same costs. Revenue is unaffected by the age of the machine. Assume there is no inflation of the machine. The cost of capital is 15%, Determine the optimum replacement cycle. Present value factors at 15% for years 1,2,3 and 4 are 0.8696, 0.7591, 0.6575 and 0.5718 respectively. Present value of annuity at 15% for years 1, 2, 3 and 4 are 0.8696, 1.6257, 2.2832 and 2.8550 respectively.

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Solution The possible replacement of the machine could be after every one or two or three or four years. The annual equivalent cost of each of the replacement policies is as follows: Policy I: Replacement every year Beginning of At the end the year Rs. of 1st year Rs. Cost of Machine Rs. Maintenance Cost (3,000) Resale Value (800) ______ 1,600 Discounting Factor at 15% (3,000) 800 1.0 0.8696 (3,000) 696 Total PV of Costs = Rs. (2,304) Annual Equivalent Cost = (2,304) Rs.(2,649) (0.8696)

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Policy II: Replacement every year Beginni At the At the ng of the end of end of year Rs. 1st year 1st year Rs. Rs. Cost of Machine Maintenance Cost (3,000) Repairs (800) (900) Resale Value _______ 1,600 (200) (3,000) (800) 1,200 Discounting Factor at 15% 1.0 0.8696 100 (3,000) 696 0.7561 (3,620) 76 Total PV of Costs (3,620) Annual Equivalent Cost = 16,257 (2,227) In a similar manner: Policy III: Replacement every three years Annual Equivalent Cost is = Rs.(2,l 56) Policy IV: Replacement every four years Annual Equivalent Cost is = Rs.(2,189) The optimum replacement cycle is, therefore, three years. Comprehensive Illustrations

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Illustration 21: A Limited company is considering investing in a project requiring a capital outlay of Rs.2,00,000. Forecast for annual income after depreciation but before tax is as follows: Year 1 2 3 4 5

Rs. 1,00,000 1,00,000 80,000 80,000 40,000

Depreciation may be taken as 20% on original cost and taxation at 50% of net income. You are required to evaluate the project according to each of the following methods: (a) Pay-back method. (b) Rate of return on original investment method. (c) Rate of return on average investment method. (d) Discounted cash flow method taking cost of capital as 10%. (e) Net present value index method. (f) Internal rate of return method.

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Solution (a) Pay-back Method STATEMENT NET CASH INFLOW Year

Profit after depreciation

Tax Profit before depreciation but after tax 1 Rs. 1,00,000 Rs. 50,000 Rs. 90,000 2 1,00,000 50,000 90,000 3 80,000 40,000 80,000 4 80,000 40,000 80,000 5 40,000 20,000 60,000 Pay-back Period Rs. 1,80,000 is recovered in 2 years. The balance of Rs. 20,000 will be recovered in 20,000/80,000 or .25 year. Hence, pay-back period is 2.25 years. (b) Rate of Return on Original Investment Method Year Net Profit after tax and depreciation 1 Rs. 50,000 2 50,000 3 40,000 4 40,000 5 20,000 Total return 2,00,000 Average Annual Return 40,000

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40,000 Rate of return = 2,00,000 = 20%

X

100

(c) Rate of Return on Average Investment Method = 40,000/1,00,000x100 = 40% (d) Discounted Cash Flow Method COMPUTATION OF NPV Year

Net Profit before dep. But after tax

1 2 3 4 5

90,000 90,000 80,000 80,000 60,000 Present Value of Cash inflow Initial Investment Excess Cash Inflow (or NPV)

Discount Factor @ 10% 0.909 0.826 0.751 0.683 0.621

Present Value Rs. 81,810 74,340 60,080 54,640 37,260 3,08,130 2,00,000 1,08,130

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(e) Net Present Value Index Total present value of cash inflows Total present value of cash outflows =

3,08,130 2,00,000 =1.541 or 154%

(f) Internal Rate of Return Method Since the annual cash inflows are not uniform, the factor will have to be located for determining the approximate rate of return: I F = C where F = Factor to be located I = Initial Investment C = Average annual cash inflow F

=

2,00,000 80,000

= 2.5

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The present value at 28% rate: Year Cash inflow Discount Present Factor Value 1 Rs.90,000 0.781 Rs. 70,092 2 90,000 0.610 54,900 3 80,000 0.477 38,160 4 80,000 0.373 29,840 5 60,000 0.291 17,460 Total Present Value 2,10,650 Initial Investment 2,00,000 Excess Present Value 10,650 At 28% discounting rate, the present value is higher by Rs. 10,650. Hence, a higher discounting rate should be taken. Taking it at 30%. Year Cash inflow Discount Present Factor Value 1 Rs.90,000 0.769 69,210 2 90,000 0.592 53,280 3 80,000 0.455 36,400 4 80,000 0.350 28,000 5 60,000 0.269 16,140 Total Present Value 2,03,030 Initial Investment 2,00,000 Excess Present Value 3,030

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The present value at 30% is higher by Rs.3,030. The internal rate of return will, therefore, by slightly higher than 30%. Though exact interpolation can b? done, it would not affect much the management decision. Hence, the rate may be taken as 30%. Judging from all angles, the investment in the new project seems to be fairly attractive.