CHAPTER 12. (i) Determination of expected CFAT (Amount in lakh of rupees) Year 1 Year 2 Year 3 CFAT P j. Cash flow CFAT P j

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1 CHAPTER 12 Solved Problems P Skylark Airways is planning to acquire a light commercial aircraft for flying class clients at an investment of Rs 50,00,000. The expected cash flow after tax for the next three years is as follows: (Amount in Rs lakh) Year 1 Year 2 Year 3 CFAT Probability CFAT Probability CFAT Probability The Company wishes to take into consideration all possible risk factors relating to an airline operations. The Company wants to know: (i) The expected NPV of this venture assuming independent probability distribution with 6 per cent risk free rate of interest. (ii) The possible deviation in expected value (iii) How would standard deviation of the present value distribution help in capital budgeting decisions. (i) Determination of expected CFAT (Amount in lakh of rupees) Year 1 Year 2 Year 3 CFAT P j Cash flow CFAT P j Cash flow CF P j Cash flow (CF P j ) (CF P j ) (CF P j ) Rs Rs Rs Mean Determination of expected NPV CFAT PV factor (0.06) Total PV Total PV of CFAT Less: Cash outflows NPV (ii) Determination of standard deviation for each year (x) P j1 P j1 Year x x x x σ (x) P j2 P j2 Year x x

2 7.29 x x σ (x) P j3 P j3 Year x x x x σ Standard deviation about the expected value σ (iii) Standard deviation enables to make use of the normal probability distribution to have more insight about the element of risk in capital budgeting. The use of the normal probability distribution will enable the decision-maker to have an idea of the probability of different expected values of NPV, that is the probability of having the value of zero or less; greater than zero and within the range of two values. The formula is Z (Expected value NPV)/σ. If the probability of having NPV of zero or less is considerably low, say 0.005, it implies that the risk in the project is negligible and the project is worth accepting. P A company is evaluating three proposed projects. You are required to rank the projects with respect to both risk and returns. The relevant data are given as follows: A B C NPV Probability NPV Probability NPV Probability Rs (3,500) 0.05 (Rs 2,000) 0.01 Rs (4,500) 0.03 (1,000) (1,500) , , , , , , , , , , , , , Expected NPV Project A Project B Project C NPV P i ) NPV P i ) NPV P i ) Rs (3,500) 0.05 Rs (175) Rs (2,000) 0.01 Rs (20) Rs (4,500) 0.03 Rs (135) (1,000) 0.10 (100) (1,500) 0.07 (105) , , , ,500 4, ,000 2, , ,000 6, , , , , , , Expected 3,255 Expected 1,785 Expected 2,510 Project A Determination of standard deviation about the expected NPV ( ( Rs (3,500) Rs 3,255 Rs (6,755) Rs 4,56,30,025 Rs 0.15 Rs 22,81,501

3 (1,000) 3,255 (4,255) 1,81,05, ,81, ,255 (3,255) 1,05,95, ,89,254 2,000 3,255 (1,255) 15,75, ,15,005 4,000 3, ,55, ,38,756 6,000 3,255 2,745 75,35, ,30,254 11,000 3,255 7,745 59,98, ,98,602 17,500 3,255 14,245 20,29,20, ,58,400 Σ( 144,92,823 Project B ( ( Rs (2,000) Rs 1,785 Rs (3,785) Rs 1,43,26, Rs 1,43, ,785 (1,785) 31,86, ,27, ,785 (1,285) 16,51, ,47,684 1,500 1,785 (285) 81, ,245 2,000 1, , ,867 2,500 1, ,11, , ,000 1,785 1,215 14,76, ,85,735 3,750 1,785 1,965 38,61, ,54,449 Σ( 16,90,936 Project C Rs (4,500) Rs 2,510 Rs (7,010) Rs 4,91,40, Rs 14,74,203 (1,500) 2,510 (4,010) 1,60,80, ,25, ,510 (2,510) 63,00, ,30,010 3,000 2, ,40, ,20,050 4,000 2,510 1,490 22,20, ,55,025 5,000 2,510 2,490 62,00, ,10,005 Σ( 42,14,900 Determination of coefficient of variation (V) V A V B V C 3,833 1,300 2,053 Ranking of projects Project Return Risk A 1 3 B 3 1 C 2 2 P What would be the risk-adjusted rates of discount for projects, A, B and C in P.12.6 if the company has gathered the following data to determine the risk-return trade-offs: Coefficient of variation Market discount rate Coefficient of variation Market discount rate Project Coefficient of variation Market discount rate (%)

4 A B C Review Questions The probability distributions of two projects NPV are given below: Project X Project Y NPV Probability NPV Probability Rs 5, , Rs 7, , , Calculate the expected value, the standard deviation, and the coefficient of variation for each project. Which of these mutually exclusive projects do you prefer and why? Determine the risk-adjusted net present value of the following projects: Net cash outlays (Rs) 1,00,000 1,20,000 2,10,000 Project life (years) Annual cash inflow (Rs) 30,000 42,000 70,000 Coefficient of variation The company selects the risk-adjusted rate of discount on the basis of the coefficient of variation: Coefficient of variation Risk-adjusted rate of discount More than A company is considering two mutually exclusive projects X and Y. Project X costs Rs 30,000 and Project Y Rs 36,000. You have been given below the net present value probability distribution for each project: Answers Project X Project Y NPV estimate Probability NPV estimate Probability Rs 3, Rs 3, , , , , , , (a) Compute the expected net present value of projects X and Y. (b) Compute the risk attached to each project that is, standard deviation of each probability distribution. (c) Which project do you consider more risky and why? (d) Compute the profitability index of each project Expected NPV x Rs 7,250; Expected NPV y Rs 8,250. σ x 1,346, σ y 4,039. V x 0.185, V y Therefore, project X is preferable Project A Rs 8,150; B Rs 24,186; C Rs 19, (a) Expected NPV of X Rs 9,000; Expected NPV of Y Rs9,000. (b) σ x 3,795; σ y 4,450.

5 (c) Project Y is riskier (V x 0.421; V y 0.494). (d) PI x 1.3; PI y 1.25.

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