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, R_F, is 10%. The firm has gathered the basic cash flow and risk index data for each project as shown in the following table.

	Project (j)
	E	F	G
Initial investment (CF0)	−$15,000−$15,000	−$11,000−$11,000	−$19,000−$19,000
Year (t)	Cash inflows (CFt)
1	$6,000	$6,000	$  4,000
2	6,000	4,000	6,000
3	6,000	5,000	8,000
4	6,000	2,000	12,000
Risk index (RIj)	1.80	1.00	0.60

1. Find the net present value (NPV) of each project, using the firm’s cost of capital. Which project is preferred in this situation?

2. The firm uses the following equation to determine the risk-adjusted discount rate, RADR_j, for each project j:

   RADRj=RF+[RIj×(r−RF)]RADRj=RF+[RIj×(r−RF)]

   where

   RFRIjr===risk-free rate of returnrisk index for project jcost of capitalRF=risk-free rate of returnRIj=risk index for project jr=cost of capital

   Substitute each project’s risk index into this equation to determine its RADR.

3. Use the RADR for each project to determine its risk-adjusted NPV. Which project is preferable in this situation?

4. Compare and discuss your findings in parts a and c. Which project do you recommend that the firm accept?

Answer 1

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