Question

Compute the payback statistics (Not discounted) for Project X and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriare cost of capital is 10 percent and the maximum allowable payback is
five years.

Time:                  0        1      2        3         4       5
Cash flow:        -75   -75     0     100     75     50

a. 3.67 years, accept
b. 4.67 years, accept
c. 3.67 years, reject
d. 4.67 years, reject

Answer 1

Payback Period calculation gives us an idea that how long it will take for a project to recover the initial investment.

We can use cumulative cash flow table to see that when the cumulative cash flow is equal to zero (or non-negative).

Year	Cash Flow	Cumulative Cash Flow
0	-$75	-$75
1	-$75	-$150
2	$0	-$150
3	$100	-$50
4	$75	$25
5	$50	$75

We can see from above table that at the end of year 3 the initial investment is not recovered, so the payback period is greater than 3 year and can be calculated in following manner

Payback Period for project = last year of negative cumulative cash flow + (absolute value of last year of negative cumulative cash flow / Cash flow of next year after negative Cumulative Cash Flow)

= 3 + ($50/ $75) = 3 + 0.67 = 3.67 years

The payback period is 3.67 years which is less than the maximum allowable payback period of 5 years. Therefore we should accept the project.

Therefore correct answer is option: a. 3.67 years, accept