Question

Risk classes and RADR   Moses Manufacturing is attempting to select the best of three mutually exclusive​ projects, X,​ Y, and Z. Although all the projects have

55​-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; and 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 rates​ (RADRs) used by the firm are shown in the following tables

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.

a. Find the ​risk-adjusted NPV for each project.

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

Project X	Project Y	Project Z
Initial investment ​(CF 0CF0​)	​$177 comma 000177,000	​$239 comma 000239,000	​$305 comma 000305,000
Year ​(tt ​)	Cash inflows ​(CF Subscript tCFt​)
1	​$85 comma 00085,000	​$59 comma 00059,000	​$92 comma 00092,000
2	67 comma 00067,000	65 comma 00065,000	92 comma 00092,000
3	61 comma 00061,000	76 comma 00076,000	92 comma 00092,000
4	63 comma 00063,000	83 comma 00083,000	92 comma 00092,000
5	58 comma 00058,000	91 comma 00091,000	92 comma 00092,000

Risk Classes and RADRs
Risk Class	Description	Risk adjusted discount rate​ (RADR)
I	Lowest risk	10.7 %
II	​Below-average risk	13.8
III	Average risk	15.7
IV	​Above-average risk	19.6
V	Highest risk	22.7

Answer 1

1-
Project X
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r = 22.7%	present value of cash flow = cash flow/(1+r)^n r = 22.7%
0	-177000	-177000/(1.227)^0	-177000
1	85000	85000/1.227^1	69274.65363
2	67000	67000/1.227^2	44502.62997
3	61000	61000/1.227^3	33021.45055
4	63000	C44/1.227^4	27794.71969
5	58000	58000/1.227^5	20854.75921
Net present value = sum of present value of cash flow			18448.21306
Project Y
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r = 22.7%	present value of cash flow = cash flow/(1+r)^n r = 22.7%
0	-239000	-239000/1.138^0	-239000
1	59000	59000/1.138^1	51845.34271
2	65000	65000/1.138^2	50191.34485
3	76000	76000/1.138^3	51568.77394
4	83000	83000/1.138^4	49489.04169
5	91000	91000/1.138^5	47679.3232
Net present value = sum of present value of cash flow			11773.82638
Project Z
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r = 22.7%	present value of cash flow = cash flow/(1+r)^n r = 22.7%
0	-305000	-305000/1.157^0	-305000
1	92000	92000/1.157^1	79515.98963
2	92000	92000/1.157^2	68726.00659
3	92000	92000/1.157^3	59400.17856
4	92000	92000/1.157^4	51339.82589
5	92000	92000/1.157^5	44373.22895
Net present value = sum of present value of cash flow			-1644.77038
2- As all the projects are mutually exclusive in this case project X would be selected as Its NPV is greater than Project Y while Project Z is having negative NPV