Question

The Mosco Manufacture is attempting to select the best of three mutually exclusive projects: X,Y, and Z. Although all the projects have 5-year lives, they possess differing degrees of risk. Project X is in class, V, the highest risk class; project Y is in class II, the below-average-risk class; project Z is in class III, the average-risk class.

The basic cash flow data for each project and the risk classes and risk-adjusted discount rate (RADR) used by the firm are shown in the following tables:

Project	X	Y	Z
Initial Investment	-180,000	-$235,000	-$310,000
Year (t)	Cash flows	Cash flows	Cash flows
1	80,000	50,000	90,000
2	70,000	60,000	90,000
3	60,000	70,000	90,000
4	60,000	80,000	90,000
5	60,000	90,000	90,000

Risk Classes	Description	RADR
I	Lowest Risk	10%
II	Below-average Risk	13%
III	Average Risk	15%
IV	Above-average Risk	19%
V	Highest Risk	22%

a) Find the risk-adjusted NPV for each project (X,Y,Z).

b.) Which project, if any, would you recommend that the firm undertake?

Answer 1

a. Project X:

Year	Cash Flows	PV factor at 22 %	Present Values
0	$ ( 180,000)	1.0000	$ ( 180,000)
1	80,000	0.8197	65,576
2	70,000	0.6719	47,033
3	60,000	0.5507	33,042
4	60,000	0.4514	27,084
5	60,000	0.3700	22,200
		NPV	$ 14,935

Project Y :

Year	Cash Flows	PV factor at 13 %	Present Values
0	$ ( 235,000)	1.0000	$ ( 235,000)
1	50,000	0.8850	44,250
2	60,000	0.7831	46,986
3	70,000	0.6931	48,517
4	80,000	0.6133	49,064
5	90,000	0.5428	48,852
		NPV	$ 2,669

Project Z :

NPV = $ 90,000 x [ { 1 - ( 1 / 1.15 ) ⁵ } / 0.15 ] - $ 310,000 = $ 90,000 x 3.3522 - $ 310,000 = $ ( 8,302 )

b. It is recommended that the firm should undertake Project X, as its NPV is the highest.