Question

Country Wallpapers is considering investing in one of three mutually exclusive​ projects, E,​ F, and G. The​ firm's cost of​ capital, r ​,is 14.8 %​, and the​ risk-free rate, Upper R Subscript Upper F​, is 9.7 %. The firm has gathered the following basic cash flow and risk index data for each project

		Project
	E	F	G
Initial Investment (CF0)	15700	11000	19900
Year		Cash Flows
1	6300	5600	4200
2	6300	3800	5700
3	6300	4900	9000
4	6300	1800	12700
Risk index (RI)	1.83	0.96	0.58

a. Find the net present value (NPV​) 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 Subscript j​, for each project nbsp j ​: RADR Subscript j equals Upper R Subscript Upper F plus RI Subscript j times left parenthesis r minus Upper R Subscript Upper F right parenthesis where Upper R Subscript Upper F = risk-free rate of​ return, RI Subscript j ​= risk index for project nbsp j ​, and r ​= cost of capital.Substitute each​ project's 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?

Answer 1

a)
Project E=-15700+6300/14.8%*(1-1/1.148^4)=2359.37512601096

Project F=-11000+5600/1.148+3800/1.148^2+4900/1.148^3+1800/1.148^4=1036.45924096477

Project G=-19900+4200/1.148+5700/1.148^2+9000/1.148^3+12700/1.148^4=1344.21429126822

Choose Project E

b)
Project E
=9.7%+1.83*(14.8%-9.7%)=19.033%

Project F
=9.7%+0.96*(14.8%-9.7%)=14.596%

Project G
=9.7%+0.58*(14.8%-9.7%)=12.658%

c)
Project E=-15700+6300/19.033%*(1-1/1.19033^4)=912.5637897

Project F=-11000+5600/1.14596+3800/1.14596^2+4900/1.14596^3+1800/1.14596^4=1080.1441474

Project G=-19900+4200/1.12658+5700/1.12658^2+9000/1.12658^3+12700/1.12658^4=2497.7697968

Choose Project G as it has highest NPV