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 10 percent, and that the maximum allowable payback and discounted payback statistic for the projects are 2 and 3 years, respectively.

Project A Cashflow: Year 0: $-32,000.00 Year 1: $22,000.00 Year 2: $42,000.00 Year 3: $13,000.00

Project B Cashflow: Year 0: $-42,000.00 Year 1: $22,000.00 Year 2: $8,000.00 Year 3: $62,000.00

Use the payback decision rule to evaluate these projects; which one(s) should it be accepted or rejected?

Answer 1

Period	Project A	Cumulative Cash flow			Period	Project A	Discounted cash flow	Cumulative Cash flow
Year 0	-32,000.00	-32,000.00			Year 0	-32,000.00	-32,000.00	-32,000.00
Year 1	22,000.00	-10,000.00			Year 1	22,000.00	22000/(1.1)^1 = 20,000	-12,000.00
Year 2	42,000.00	32,000.00			Year 2	42,000.00	42000/(1.1)^2 = 34,710.74	22,710.74
Year 3	13,000.00	45,000.00			Year 3	13,000.00	13000/(1.1)^3 = 9,767.09	32,477.84
1+(10000/42000) = 1.2381 years					1+(12000/34710.74) = 1.3457 years
Period	Project B	Cumulative Cash flow			Period	Project B	Discounted cash flow	Cumulative Cash flow
Year 0	-42,000.00	-42,000.00			Year 0	-42,000.00	-42,000.00	-42,000.00
Year 1	22,000.00	-20,000.00			Year 1	22,000.00	22,000/(1.1)^1 = 20,000	-22,000.00
Year 2	8,000.00	-12,000.00			Year 2	8,000.00	8,000/(1.1)^2 = 6,611.57	-15,388.43
Year 3	62,000.00	50,000.00			Year 3	62,000.00	62,000/(1.1)^3 = 46,581.52	31,193.09
2+(12000/62000) = 2.1935 years					2+(15388.43/46,581.52) = 2.3304 years
Payback Period = X + ( Y / Z)
Where,
X is the last period number with a negative cumulative cash flow;
Y is the absolute value cumulative net cash flow at the end of the period X
Z is the cash inflow during the period following period X

Project A should be  accepted as Both the projects payback periods are under the allowable period but they are mutually exclusive Project A payback period is lower than project B it means the project A will paying back earlier than project B.