Economics - Appraising Project Profitability - Notes - Economics, Study notes of Economics

Download Economics - Appraising Project Profitability - Notes - Economics and more Study notes Economics in PDF only on Docsity! APPRAISING PROJECT PROFITABILITY Methods of appraising profitability For examining the various projects under consideration, we should know some basic information about the alternative project proposals like the initial investment, the economic life, the scrap value, if any, the annual earnings and the cash flow. Besides, we should consider the following factors for evaluating a project proposal. (i) The timing of the proceeds over the economic life of the investment proposal, and (ii) The duration of the proceeds: Larger the duration proceeds larger the benefit. However, the future stream of income should be discounted The various methods of evaluating the relative profitability of the alternative investment projects are: 1. Pay-back Method, 2. Accounting Rate of Return, 3. Internal Rate of Return and 4. Net Present Value Index Method. It may be noted that the pay-back period does not reveal anything about the rates of return of different projects. The accounting Method and the Internal Rate of return Method spells out relative rates of return of different projects. Besides, the former method does not consider the time value of money, and the latter consider the time value of money. Under the Net Present Value Index Method, we proceed with our cost of capital as the base for calculating the relative profitability of the projects. Further, the net present value method, we also consider the time value of money. The pay-back Method and the Accounting Method are considered as traditional methods of investment appraisal as they are very commonly used. The Discounted Cash Flow Method or the Internal Rate of Return and the Net Present Value Index Method are the modern techniques as the development and use of discounting methods is relatively new. For purposes of illustration, we assume that there are five alternative proposals under consideration. The details about the proposals are given in the following table. We will examine the proposals while discussing the criteria of project appraisal.. Proposals Initial Investment Annual Cash Flow Life in Year Rs. Rs. A 72,000 12,000 15 B 88,000 22,000 22 C 3,000 1,500 3 D 22,500 4,500 10 Cash Flow A 72,000/12,000 = 6 years 5 B 88,000/22,000 = 4 years 3 C 3,000 / 1,500 = 2 years 2 D 22,500 / 4,500 = 5 years 4 E 4,25,000/2,25,000 = 1.9 years 1 Depends upon the availability of investment and quick return, we can select the project. The project ranked based on the pay-back method is E, C, B, D and A. The pay-back method emphasizes the quick cash return flow. This concept is particularly useful on the condition that liquidity is an important consideration. Advantages: The main advantages of the pay-back method are: (i) Pay-back method is extremely simple to apply and easy to understand. (ii) The company can judge the length of time its funds will be tied up and the risk involved in the various projects. This method takes care of the conditions of high uncertainty in evaluating project. (iii) Pay-back method is especially useful in industries subject to rapid technological advances, where the plant becomes obsolete before the end of its physical life. (iv) In a period of tight money when funds are difficult to get, a quick pay-back project may be preferred to one which may yield a higher rate of return, yet commit funds for a longer period. (iii) Pay-back period acts as a hedge against a poor decision. VI Accounting Rate of Return. Accounting Rate of Return Method is also known as the Financial Statement Method. This method aims at providing us with an estimate of the rate of return. Under this method, capital employed and related income are determined by following the principles and practices employed in accounting. The formula for calculating the rate of return under this method is:- Estimated Net Profit X 100 ARR = ------------------------- Capital Employed However, there is a diversity of practice in measuring the amount of capital employed. Some firms compute this rate of return on the initial amount invested; others, on the average amount invested over the life of the project. The initial investment is simply the amount of cash outlay necessary at the outset in order to make the investment. The average investment may be calculated in this manner: Initial investment + Scrap value 2 Average investments assume regular periodic recovery of capital over the life projects under consideration. In our example, we have only the cash inflow. But for calculating the rate of return under the accounting method, we must know the net profits. This we can find by subtracting the annual depreciation from the annual cash flow. Proposal Initial Invest -ment Annual Cash Flows Life in Years Annual Depreci- - ation Net Profits Rate of Return Rs. Rs. Rs. Rs . % A 72,000 12,000 15 4,000 8,000 11.10 B 88,000 22,000 22 6,000 16,000 18.80 C 3,000 1,500 3 500 1,000 33.33 D 22,500 4,500 10 2,000 2,500 11.10 E 4,25,000 2,25,000 20 25,000 2,00,000 47.10 Here, higher the rate of return higher the viability of a project. Hence, in the above example the projects are selected in the order of E, C, B, A and D. Limitations: The main limitations of the accounting method are: (i) It does not take into account the time value of money. It gives the same weight to the money received now and the money to be receipts in the first year. (ii) The expected profit is unlikely to be the same every year. The use of profit in a typical year or of the average profit per year is likely to be misleading because both ignore the year- by-year pattern of profits. (iii) No specific account is taken of the earning life of the project. VII Internal Rate of Return or Discounted Cash Flow Method. The basic assumption of Discounted Cash Flow Method is that the same amount of money received today is more valuable than the one received after a year and so on. The B 76,000 20,000 10 3.8 Between 25 and 30% (23.56%) C 1,400 1,000 4 1.4 Over 40% (52.50%) D 46,000 10,000 8 4.6 Between 15 and 20% (18.64%) E 1,90,000 1,00,000 20 1.9 Over 40% (53.00%) An example as to how to arrive at the rate of interest may be given here. For proposal A, the life is 15 years. Reading against 15 years, to locate the P Ratio, we find that the required P Ratio, of5.00 lies between 15 per cent (5.938) and 20 per cent (4.7509). The rate can be interpolated but it would be nearer 20than 15. The interpolation will be done by the following formula: p – p2 r = r2 – ------- x (r2 – r1) p1 – p2 p1 - p or r = r1 + --------- x (r2 – r1) p1 – p2 where p = rate of return to be determined by interpolation, r1 = lower rate of return, r2 = higher rate of return, p1 = the P ratio at the low rate of return, p2 = the P ratio at the higher rate of return, and v = The P ratio for which r is to be interpolated Applying the formula, we get 5 – 4.7509 r = 20 - ------------------- x (20 – 15) 5.9638 – 4.7509 Year Annual rate Present value Present value factor: 15% 1 30,000 0.9286 27,858 2 40,000 0.7993 31,972 3 60,000 0.6879 41,274 4 50,000 0.5921 29,605 5 40,000 0.5096 20,384 1,51,093 Let us now try with an interest rate of 14 per cent. It will be seen that the present value of all cash flows comes to Rs.1,54,740 which is approximation equal to our investment. Thus we can say that the rate of return is slightly lower than 14 per cent. Year Annual Cash Present value Present value flow factor: 15% 1 30,000 0.9332 27,996 2 40,000 0.8112 32,449 3 60,000 0.7050 42,318 4 50,000 0.6131 30,652 5 40,000 0.5330 21,320 1,54,737 The main merits of the internal rate of return method are: (i) It considers the time value of money. (ii) It considers the cash flows over the entire life of the project. (iii) The calculation of the cost of capital is not a pre-condition for the use of this method. One of the limitations of this method is that it is difficult to understand and use in practice as its computation is complicated. VIII Net present Value Index Method. The net present value of an investment proposal is the difference between the total of present values of the estimated annual cash flows over the life of the project and the initial investment of the project. If the net present value is positive, the investment is profitable. If the net present value is negative, investment is not feasible. The investment proposal that simply breaks even will have a net present value of zero. The annual cash flows are discounted to find out the present value with an interest rate which is equal to the average cost of capital of the company or the lending rate, whichever is higher. The method of computation of Net Present Value index is:- Total Present Value of All Cash Flows Net Present Value Index = ----------------------------------------------- Initial Investment The higher the index, the more profitable the project is. We can then rank the various proposals according to their net present value index. If the projects have a salvage value, we can find out the present value of the scrap value at the same rate of interest and add it to the total present value of all cash flows. Let us now apply this formula to find out the relative profitability of the five proposals which are given below: Proposal Initial Annual Life in PV PV NPVI Rank Invest- Cash years factor - ment Rs. flow Rs. 10% Rs There are a number of other considerations which have to be taken into account in addition to profitability. Some of these considerations are explained below:- (i) Type of decision being made. The management may decide to make a tactical decision to provide funds to a division which is making a low return to preserve its earning power and maintain its existing market share. (ii) Type of investment. A firm would accept a lower return on a cost reduction programme (with relatively certain results) as against a project with a higher but uncertain return. (iii) Degree of certainty about cash flow. The degree of uncertainty in relation to the estimated cash flows is an important consideration be kept in view. Hence projects with relatively assured cash flows over with lower rates of return are to be preferred to projects with uncertain cash flows despite high rates of return. (iv) Intangible factors. Very often, intangible factors such as the effect of a course of action on company’s prestige and image. These factors cannot be ignored and some projects may have to be accepted whether they are profitable or not. (v) Overall profitability. If we strictly follow the rate of return criterion, we may be persuaded to choose a smaller investment proposal with a higher rate of return over a large investment proposal with a lower rate of return. (vi) Urgency of the project. Sometime, the firm may have no choice but to make the investment irrespective of its rate of return, i.e., a roof blown by; the cyclone should be replaced at once. Here the main point to be considered is the cost of not doing so, i.e., the damage to merchandise and equipment which is imminent if the roof is not immediately replaced. IX Probability approach for Project Appraisal We will arrive at two types of conclusions, If an experiment is repeated under essentially homogeneous and similar conditions,. They are: - the results are unique and the outcome can be predictable and result is not unique but may be one of the several possible outcomes. In this context, it is better to understand various terms pertaining to probability before examining the probability theory pertaining to project evaluation. The main terms are explained as follows:- (i) Random experiment: An experiment which can be repeated under the same conditions and the outcome cannot be predicted under any circumstances is known as random experiment. For example: An unbiased coin is tossed. Here we are not in a position to predict head or tail is going to occur. Hence, this type of experiment is known as random experiment. (ii) Sample Space A set of possible outcomes of a random experiment is known as sample space. For example in the case of tossing an unbiased coin twice, the possible outcomes are HH, HT, TH and TT. This can be represented as S= ( HH, HT, TH, TT ). (iii) An event Any possible outcomes of a random experiment are known as an event. In the case of tossing of an unbiased coin twice, HH is an event. An event can be classified into two. They are: (a) Simple events, (ii) compound event. Simple event is an event which has only one sample point in the sample space. Compound event is an event which has more than one sample point in the sample space. In the case of tossing of an unbiased coin twice HH is a simple event and TH and TT are the compound events. (iv) Complementary event A and A’ are the complementary event if A’ consists of all those sample point which is not included in A. For instance, an unbiased dice is thrown once. The probability of an odd number turns up are complementary to an even number Let X is discrete random variable which takes the values of x1, x2, ……….. xn and the corresponding probabilities will be p1, p2, ……….pn. Then, X follows the probability distribution. The two main properties of probability distribution are :- (i) P(Xi) is always greater than or equal to zero and less than or equal to one, and (ii) the summation of probability distribution is always equal to one. For example tossing of an unbiased coin thrice (something needs to be added). Then the probability of distribution is: X ( probability of obtaining head): 0 1 2 3 P(Xi) : 1/8 3/8 3/8 1/8 Expectation of probability Let X is discrete random variable which takes the value of x1, x2, ………… xn then the respective probability is p1, p2, ………… pn, Then the expectation of probability distribution is p1x1 + p2x2 + ………….. + pnxn. In the above example, the expectation of probability distribution is 0(1/8) + 1(3/8) + 2(3/8) + 3(1/8) = 12/8 = 1.5 This indicates that on an average the probability obtaining head is 1.5 times. Probability theory approach A more rational method for taking into account the varying risks associated with different investment projects is based on the probability theory. Under this method one has to find out a range of possible cash flows, from the most optimistic to the most pessimistic for each pertinent year, and assign probabilities to each of the possible outcomes. The various methods of appraisal may then be applied to each of the cash flows. Of course, the assignment of probabilities would be subjective; depending upon each individual executive’s beliefs and opinions. However, objectivity can be achieved by a consensus among a team of executives or by taking an average of the probabilities assigned by different executives to each outcome. The application of this method is illustrated in following table TABLE – Probability Calculation of Cash Flows First year Second year Third year Cash flows Proba- expec Probability Expectation Proba- Expec-