Question

Two mutually exclusive projects are being considered which have the following projected cash flows:

                                Year                       Project A               Project B

                                   0                           ($50,000)              ($50,000)

                                   1                           $15,625                                $         0

                                   2                           $16,000                                $         0

                                   3                           $15,000                                $         0

                                   4                           $16,000                                $         0

                                   5                           $15,500                                $99,500

a. Calculate the NPV for each of these projects using a 10% rate of return. Also, indicate which project should be chosen based on the NPV calculation. b.Calculate the payback periods for each of the above projects. Also, indicate whether either of the projects would be chosen by a company which requires a payback period of 4 years. c.Briefly explain in your own words why the two analyses yield differing results. d.Calculate the profitability index for each of the above potential projects.

Answer 1

a. NPV : Project A : $ 9,249.80 ; NPV: Project B : $ 11,781.54

Period	Cash Flows	PV factor at 10% discount rate
0	( 50,000)	1.00000	(50,000)
1	15,625	0.90909	14,204.53
2	16,000	0.82645	13,223.20
3	15,000	0.75131	11,269.65
4	16,000	0.68301	10,928.16
5	15,500	0.62092	9,624.26
		NPV	9,249.80

NPV for Project B = $ 99,500 x 0.62092 - $ 50,000 = $ 11,781.54

b. Payback Period : Project A : 3.21 years

Payback Period: Project B : 4.50 years

Project A should be chosen if the company requires a payback period of 4 years.

c. The two analyses yield differing results because, the payback period method ignores cash flows occurring beyond the payback / cutoff period, whereas the NPV method considers all discounted cash flows occurring over the entire life of the project.

d. Profitability Index: Present Value of Cash Inflows / Initial Investment

Project A : $ 59,249.80 / $ 50,000 = 1.1850

Project B : $ 61,781.54 / $ 50,000 = 1.2356