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ASSESSING RISK RELATED TO CB We assess the future expected cash flows from projects that we expect to invest. Future cash flows are uncertain, and we use forecasts of uncertain cash flows in capital budgeting decisions Thus, risk is inherent in Capital Budgeting Decisions 9/2/2021 2 Traditional Methods of Risk Analysis ◦Payback Period ◦Risk Adjusted Discount Rate ◦Certainty Equivalent Cash Flow 9/2/2021 3 Payback Period ◦Managers tend to choose projects with the least pay back period with the intention of avoiding risk of being unable to recover the invested funds. 9/2/2021 4 Risk Adjusted Discount Rate The discount rate is decided taking into consideration the risk of each project. In deciding the discount rate two factors are considered ◦ Time preference ◦ Risk Preference The adjustment for time preference comes with the risk free interest rate. 9/2/2021 Risk adjustment is effected through the β coefficient of the project which is used in measuring risk. 5 β coefficient In the Capital Asset Pricing Model (CAPM) the premium for risk is determined by multiplying the β coefficient by the difference between the return for the Market portfolio and the risk free rate. β(Rm -Rf) β =Cov(rs, rm)/σ2m by changing the value of the β coefficient relevant to each project the proportion for risk preference can be calculated. A higher β value will be selected for high risk projects and a low β value will be selected for low risk projects. Higher β values will give a higher discount rate and lower β values will give a lower discount rate example ER= RF + β(Rm -Rf) Market return is 15 % , risk free rate is 6%, and β is .8 what will be the expected rate of return? what would it be if β =1.2 ? Or β = .73 ? 9/2/2021 7 The Ramakrishna Ltd., in considering the purchase of a new investment. Two alternative investments are available (X and Y) each costing Rs. 150000. Cash inflows are expected to be as follows: ◦ The company has a target return on capital of 10%. Risk premium rate are 2% and 8% respectively for investment X and Y. ◦ Which investment should be preferred? 9/2/2021 year X Y 1 60,000 65,000 2 45,000 55,000 3 35,000 40,000 4 30,000 40,000 8 solution year DF X 12% CF X DCFX CFY 1 60,000 65,000 2 45,000 55,000 3 35,000 40,000 4 30,000 40,000 DFY 18% DCFY Investment X Net present value = 133415 – 150000 = – Rs. 16585 Investment Y Net present value = 156485 – 150000 = Rs. 6485 9/2/2021 9 Certainty Equivalent Cash Flow This is another method of analyzing risk of projects. What we do here is reduce the estimated cash flows to some conservative level . For this purpose we use a “Risk Adjustment Factor” or “ Certainty Equivalent Coefficient” which is called “α” α = Certainty Equivalent CF/ Risky CF This will take a value between 0-1 . Depending on the riskiness of the cash flow this α value will change. In order to convert the cash flows to the certainty equivalent values we can multiply the estimated risky cash flows by the α coefficient. In converting these to the PV we must use a risk free rate to discount the cash flows 9/2/2021 10 Example Following are details of a project year CF α 1 50,000 0.7 2 60,000 0.6 3 40,000 0.8 4 30,000 0.5 Initial investment is Rs 90,000and the risk free rate is 12% 9/2/2021 11 year CF α CE CF 1 50,000 0.7 35,000 2 60,000 0.6 36,000 3 40,000 0.8 32,000 4 30,000 0.5 15,000 We can discount the certainty Equivalent CF’s by the risk free discount rate. NPV=-90,000 +92,260.80=2260.80 9/2/2021 12 exercise ◦ There are two projects A and B. Each involves an investment of Rs. 50,000. The expected cash inflows and the certainly co-efficient are as under: year CF A CE A CF B CE B 1 35,000 .8 25000 .9 2 30,000 .7 35000 .8 3 25,000 .9 20000 .7 Risk-free cutoff rate is 10%. Suggest which of the two projects. Should be preferred 9/2/2021 13 solution First calculate the adjusted cf’s and then discount them by the risk free rate ◦ Project A ◦ Net present value = Rs. 56,316 – 50,000= Rs. 6,316 Project B Net present value = 54,095 – 50,000= Rs. 4,095 As the net present value of project A in more than that of project B. Project A should be preferred: 9/2/2021 14 Non Traditional Methods Statistical Techniques ◦Scenario Analysis ◦Sensitivity Analysis ◦ 9/2/2021 15 Statistical Techniques ◦ We concentrate on two factors Uncertainty Probability Future is uncertain . The Environment changes . It is difficult to forecast cashflows under uncertainty. First we try and forecast the possible economic conditions with their probability . Then we would forecast the possible cashflows under each economic condition. 9/2/2021 16 Example year Economic Condition Probability NCF 1.0 -10,000 growth 0.2 7,000 normal 0.6 5,000 recession 0.2 3,000 growth 0.2 10,000 normal 0.7 8,000 recession 0.1 3,000 growth 0.1 9,000 normal 0.6 7,000 recession 0.3 4,000 0 1 2 3 9/2/2021 17 If the relevant discount rate is 12% , find the NCF for this project year EC CF P ACF 1 growth 7,000 0.2 1400 normal 5,000 0.6 3000 recession 3,000 0.2 600 growth 10,000 0.2 2000 normal 8,000 0.7 5600 recession 3,000 0.1 300 growth 9,000 0.1 900 normal 7,000 0.6 4200 recession 4,000 0.3 1200 2 3 9/2/2021 AACF 5000 7900 6300 18 year DF 0 -10,000 1 4464 2 6297 3 4487 NPV 9/2/2021 DCF 5248 19 Variance and Standard Deviation By looking at variance of the real cash flows from the estimated cash flows would give us a better picture about the risk of a project. We can calculate the variance and the standard deviation of the cash flows. given are the cash flows for two projects P and Q 9/2/2021 20 event CF P Prob. P CF Q Prob.Q 1 8,000 .10 5,000 .10 2 7,000 .20 10,000 .30 3 10,000 .40 8,000 .20 4 6,000 .20 7,000 .10 5 9,000 .10 12,000 .30 Calculate the variance and the standard deviation and comment about the risk of these projects. 9/2/2021 event CF P Prob CF*P (Ecf-Ecf)^2*P 1 8,000 .10 800 (8000-8300)^2*.1 2 7,000 .20 1400 (7000-8300)^2*.2 3 10,000 .40 4000 (100008300)^2*.4 4 6,000 .20 1200 (6000-8300)^2*.2 5 9,000 .10 900 (9000-8300)^2*.1 (EcfEcf)^2*prob 1615.55 21 event CF Q Prob CFQ*P 1 5,000 .10 500 (5000-9400)^2 *.10 2 10,000 .30 3000 (100009400)^2*.3 3 8,000 .20 1600 (80009400)^2*.2 4 7,000 .10 700 (70009400)^2*.1 5 12,000 .30 3600 (120009400)^2*.3 9400 9/2/2021 2245 22 conclusion ◦ As the SD of Q is higher than the SD of P project Q is riskier than project P 9/2/2021 23 Coefficient of Variation P 1615.55/8300*100= 19.46 Q 2245/9400*100=23.88 the investment decision depends on the investors risk preference. If an investor is risk averse s/he will select the project with lower risk . If an investor prefers risk he will choose the project that gives a higher return at higher risk 9/2/2021 24 X 1957.2 Y 1544.8 CV X31.31%,Y29.52% As the co-efficient of variation of project ‘X’ is more than that of ‘Y’ project X is more riskier. Hence, project Y should be selected. 9/2/2021 25 exercise From the following information, ascertain which project should be selected on the basis of standard deviation. 9/2/2021 CF X Prob.X CF Y Prob Y 3200 .2 32000 .1 5500 .3 5500 .4 7400 .3 7400 .4 8900 .2 8900 .1 Evaluate the projects on standard deviation and coefficient of variation 26 Scenario Analysis 9/2/2021 ◦ When cash inflows are sensitive under different circumstances more than one forecast of the future cash inflows may be made. These inflows may be regarded as ‘Optimistic’, ‘most likely’ and ‘pessimistic’. Further cash inflows may be discounted to find out the net present values under these three different situations. If the net present values under the three situations differ widely it implies that there is a great risk in the project and the investor’s decision to accept or reject a project will depend upon his risk bearing abilities. 27 ◦Mr. Silva is considering two mutually exclusive projects ‘X’ and ‘Y’. You are required to advise him about the acceptability of the projects from the following information. ◦discount rate of 15%. 9/2/2021 28 Cost of the investment Forecast cash inflows per annum for 5 years Optimistic Most likely Pessimistic 9/2/2021 X Y 1,00,000 1,00,000 60,000 35,000 20000 55,000 30,000 20000 29 9/2/2021 X ACF 15% PV NPV Optimistic 60,000 3.3522 2,01,132 1,01,132 Most likely 35,000 3.3522 1,17,327 17,327 Pessimistic 20,000 3.3522 67,105 (32,895) Y ACF 15% PV NPV Optimistic 55000 3.3522 1,84,371 84,371 Most likely 30000 3.3522 1,00,566 566 Pessimistic 20000 3.3522 67,105 (32,895) 30 The acceptability of the project will depend upon Mr. Silva’s attitude towards risk. 9/2/2021 31 Scenario Analysis There can be three basic levels that are considered in scenario Analysis. ◦ Expected level or the Base level ◦ Upper bound or the Optimistic level ◦ Lower bound or the Pessimistic level Upper bound Analysis We expect the best ◦ Highest prices adopted in the case of Income ◦ Lowest prices adopted in the case of expenditure ◦ Expectation for a higher sales volume 9/2/2021 32 Lower Bound Analysis We expect the worst in all aspects ◦ Lowest prices adopted in the case of Income ◦ Highest prices adopted in the case of expenditure ◦ Expectation for a lower sales volume We first take the base level and then adjust it to suit the upper bound level and the lower bound level Example: a company is planning to spend Rs 200,000 for capital expenditure, of which the life time is 5 years. Cost of capital is estimated to be 12% Following are relevant estimates for the firm 9/2/2021 33 Base level Upper bound Lower bound Sales units 6000 6500 5500 Unit price 80 85 75 Variable cost 60 62 58 Fixed cost 50,000 55,000 45,000 Tax is 34% at all levels. Let us re arrange according to the basic principles. 9/2/2021 Base level Upper bound Lower bound Sales units 6000 6500 5500 Unit price 80 85 75 Variable cost 60 58 62 Fixed cost 50,000 45,000 55,000 34 BL 9/2/2021 OP L PML sales 6000*80 480,000 6500*85 552500 5500*75 412,500 vc 6000*60 (360,000 ) 6500*58 (377,000) 5500*72 (341,000) contributio n 120000 175500 71500 fc (50,000) (45,000) (55,000) 70,000 130,500 16,500 depn (40,000) (40,000) (40,000) PBIT 30,000 90,500 (23,500) 34% (10,200) (30,770) (7,990) PAT 19,800 59,730 (15,510) +depn 40,000 40,000 40,000 ACF 59,800 99,730 24,490 PVIFA 3.6048 3.6048 3.6048 PVOA 215,567 359,507 88,280 (200,000) (200,000) (200,000) 15,567 159,507 (11,718) 35 IRR 15.1% 40.9% -14.4% Scenario analysis provides a basic idea about the cash flows NPV and IRR which will help identifying risky Areas, but it will not give a clear indication as to which projects to be selected. 9/2/2021 36 Sensitivity Analysis A sensitivity analysis is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions. Most important point here is to identify most important variable that would make an influence on the NPV. Once Identified we would change only that , and calculate NPV keeping other variables at the base level . By looking at the relationship between the NPV and this critical variable the management may be able to take measures to control the risk imposed by that variable let us take the same example 9/2/2021 37 Base level Upper bound Lower bound Sales units 6000 6500 5500 Unit price 80 85 75 Variable cost 60 62 58 Fixed cost 50,000 55,000 45,000 Tax is 34% at all levels. Let us re arrange according to the basic principles. 9/2/2021 38 BL 9/2/2021 OP L PML sales 6000*80 480,000 6500*80 520,000 5500*80 440,000 vc 6000*60 (360,000 ) 6500*60 (390,000) 5500*60 (330,000) contributio n 120,000 130,000 110,000 fc (50,000) (50,000) (50,000) 70,000 80,000 60,000 depn (40,000) (40,000) (40,000) PBIT 30,000 40,000 20,000 34% (10,200) (13,600) (6,800) PAT 19,800 26,400 13,200 +depn 40,000 40,000 40,000 ACF 59,800 66,400 53,200 PVIFA 3.6048 3.6048 3.6048 PVOA 215,567 239,353 191,775 (200,000) (200,000) (200,000) 15,567 39,349 (8,225) 39 50 40 30 NPV 20 npv Линейная (npv) 10 0 430 440 450 460 470 480 490 500 510 520 530 -10 -20 9/2/2021 sales 40 Slope of this line indicates the sensitivity of NPV to sales. ◦ Higher slope indicates high sensitivity of sales on NPV ◦ Lower slope indicates low sensitivity of sales on NPV Sensitivity analysis using different variables and comparing the slopes we can have an understanding about the variables with high sensitivity and low sensitivity. The High sensitivity variables may be controlled in order to manage the risk let us take another variable ; fc 9/2/2021 41 BL 9/2/2021 OP L PML sales 6000*80 480,000 6000*80 480,000 6000*80 480,000 vc 6000*60 (360,000 ) 6000*60 (360,000) 6000*60 (360,000) contributio n 120,000 120,000 120,000 fc (50,000) (45,000) (55,000) 70,000 75,000 65,000 depn (40,000) (40,000) (40,000) PBIT 30,000 35,000 25,000 34% (10,200) (11,900) (8,500) PAT 19,800 23,100 16,500 +depn 40,000 40,000 40,000 ACF 59,800 63,100 56,500 PVIFA 3.6048 3.6048 3.6048 PVOA 215,567 227,463 203,671 (200,000) (200,000) (200,000) 15,567 27,463 3671 42 30 25 NPV 20 15 npv Линейная (npv) 10 5 0 0 10 20 30 40 50 60 FC 9/2/2021 43 The slope of this line will give us the sensitivity of NPV on FC We can see that the slope of this line is smaller to the slope of the line using sales This implies that NPV is more sensitive to change of sales than for a change of FC 9/2/2021 44