Risk-adjusted discount rates: Basic Country Wallpapers is considering investing

Question

Risk-adjusted discount rates: Basic Country Wallpapers is considering investing in one of three mutually exclusive projects, E, F, and G. The firm?s 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. a. Find the net present value (NP V) of each project using the firm?s cost of capital. Which project is preferred in this situation? b. The firm uses the following equation to determine the risk-adjusted discount rate, RADR,, for each project ,: where Rr = risk-free rate of return RIi = risk index for project j r = cost of capital Substitute each project?s risk index into this equation to determine its RADR. c. Use the RAI)R 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?

Explanation / Answer

Project E would be prefered because it has the highest NPV of 2130.

PV of cash flow is equal to cash flow/(1+i)^n where i the cost of capital and n is the number of period

B)

RADR = Rf + ( RI* ( r - Rf)

here Rf is 10% and r is 15%

RI for Project E is 1.8, RI for Project F is 1.0 , RI for Project G is 0.6

For projct E

RADR = 0.1 + (1.8* ( .15-0.1)) = 0.19

For project F

RADR = 0.1 + (1.0* ( .15-0.1)) = 0.15

For project G

RADR = 0.1 + (0.6 * ( .15-0.1)) = 0.13

Using the above rates NPV is as follows

So according to this Project G has the highest NPV, so G should be preferred.

The decision change from Project E to G because project G has the lowest risk index

Year E PV of cash flows F PV of cash flows G PV of cash flows 0         (15,000)         (15,000)         (11,000)         (11,000)         (19,000)         (19,000) 1              6,000              5,217              6,000              5,217              4,000              3,478 2              6,000              4,537              4,000              3,025              6,000              4,537 3              6,000              3,945              5,000              3,288              8,000              5,260 4              6,000              3,431              2,000              1,144           12,000              6,861 sum of cash flow              2,130              1,673              1,136

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