Risk-adjusted discount ratesBasic Country Wallpapers is considering investing in one of three

QUESTION

Risk-adjusted discount ratesBasic Country Wallpapers is considering investing in one of three mutually exclusive projects, E, F, and G. The firms cost of capital, r, is 15%, and the risk-free rate, RF, is 10%. The firm has gathered the basic cash flow and risk index data for each project, as shown in the following table.Initial investment (CF0)Project (j)EFG$15,000$11,000$19,000Year (t)Cash inflows (CFt)1234Risk index (RIj)$6,000 6,0006,0006,0001.80$6,0004,0005,0002,0001.00$4,0006,0008,00012,0000.60a. Find the net present value (NPV) of each project using the firms cost of capital. Which project is preferred in this situation?b. The firm uses the following equation to determine the risk-adjusted discount rate, RADRj, for each project j:RADRj = RF + [RIj+ (r RF)] where RF = risk-free rate of return RIj = risk index for project j r = cost of capitalSubstitute each projects risk index into this equation to determine its RADR.c. Use the RADR for each project to determine its risk-adjusted NPV. Which project is preferable in this situation?d. Compare and discuss your findings in parts a and c. Which project do you recommend that the firm accept?
Given Risk free rate, Rf 10% Cost of capital, r 15% Cashflows Discounted Cashflows @ r Year Project E Project F Project G Project E Project F Project G 0 -15000 -11000 -19000 -15000 -11000 -19000 1 6000 6000 4000 5217 5217 3478 2 6000 4000 6000 4537 3025 4537 3 6000 5000 8000 3945 3288 5260 4 6000 2000 12000 3431 1144 6861 a. Sum of discounted cash flows (NPV) 2130 1673 1136 NPV of project E is highest hence project E is preferred. Risk-adjusted discount rate, RADRj = RF + [RIj+ (r RF)] where RF = risk-free rate of return RIj = risk index for project j r = cost of capital Project E Project F Project G Risk index 1.8 1 0.6 Rf 10% 10% 10% r 15% 15% 15% b. RADRj 19.0% 15.0% 13.0% Cashflows Discounted Cashflows @ RADRj Year Project E Project F Project G Project E Project F Project G 0 -15000 -11000

00 -15000 -11000 -19000 1 6000 6000 4000 5042 5217 3540 2 6000 4000 6000 4237 3025 4699 3 6000 5000 8000 3560 3288 5544 4 6000 2000 12000 2992 1144 7360 c. Sum of discounted cash flows (NPV) 832 1673 2143 NPV of project E is highest hence project G is preferred. d. The NPV of these projects undergo drastic change when discounted with the normal discount rate and risk-adjusted cost of capital In both the cases, the NPV of project F is same as it does not have variable risk. Hence it is advisable to go for a stable project i.e.project F.

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