Question

Suppose your firm is considering two mutually exclusive, required projects with the cash flows shown below. The required rate of return on projects of both of their risk class is 9 percent, and that the maximum allowable payback and discounted payback statistic for the projects are 2 and 3 years, respectively. Time: 0 1 2 3 Project A Cash Flow -36,000 26,000 46,000 17,000 Project B Cash Flow -46,000 26,000 36,000 66,000 Use the discounted payback decision rule to evaluate these projects; which one(s) should be accepted or rejected?  accept neither A nor B  accept both A and B  accept A, reject B  reject A, accept B

Answer 1

Calculation of Cumulative PV -

	Project A					Project B
Year	Project A	Discounting @ 9%	PV	Cum. PV		Project B	Discounting @ 9%	PV	Cum. PV
0	-36000	1.0000	-36000			-46000	1.0000	-46000
1	26000	0.9174	23853.21	23853.21		26000	0.9174	23853.21	23853.21
2	46000	0.8417	38717.28	62570.49		36000	0.8417	30300.48	54153.69
3	17000	0.7722	13127.12	75697.61		66000	0.7722	50964.11	105117.8

Discounted Payback for project A = 1year + (36000-23853.21)/(38717.28) * 12

= 1 + 12146.8/38717.28*12

= 1 + 0.31373*12

= 1 + 3.76 months

Discounted payback for proejct B -

1 + (46000-23853.21) /30300.48*12

= 1+ 22146.8/30300.48*12

= 1 + 0.73091*12

= 1 + 8.77

so 1 year and 8.77 months

conclusion - both projects are acceptable as its DCF (Discounted cash flow ) are less than 2 & 3 years specified in question.

but as they are mutually exclusive means can choose singlr project so i would go with project 1 as it has shorter payback.

so option (c) accept A and reject B.

Please comment in case of any clarification.