Question

Question #5: Shortcliff Co.’s uses the Payback Period method for evaluating its projects. The Payback Period cut-off rule is 3 years. Shortcliff is considering the following project:        

	Cash Flow for
Year	Project A
0	-$75,000
1	$33,000
2	$36,000
3	$19,000
4	$9,000

                                   

                       

Required:

1. Should Shortcliff accept or reject Project A?
2. Why or why not?

Answer 1

Solution:

Payback period for uneven cash flows is calculated by first finding out the cumulative cash flows, finding the last year of negative cumulative cash flow, taking that year and adding it to a period of the next year which is arrived at by interpolation. The process is explained below:

(To find cumulative cash flows starting with the first cash flow at point 0, keep adding each cash flow to previous cumulative cash flow to get subsequent cumulative cash flow value doing this till the end)

Year	Cash Flows	Cumulative cash flows
0	-75,000	-75,000
1	33,000	-42,000
2	36,000	-6,000
3	19,000	13,000
4	9,000	22,000

We see that the cumulative cash flows are negative upto end of year 2. This means that the initial investment has not yet been recovered till the end of year 2 and $6,000 is still to be recovered which will be done in year 3. In year 3 it turns positive, which means that the initial investment is recovered in year 3.

The point in time in which it is recovered in year 3 is found out by interpolation i.e. dividing the last negative cumulative cash flow by the next year cash flow and multiplying by the days in the year i.e. 365. The assumption in interpolation is that the cash flow for a year accrues evenly over the year thereby daily cash flow accrues at a constant rate.

So we have (6000 / 19000) x 365 = 115.26 days

So the payback period is 2 years (last negative cumulative cash flow) and 115.26 days (in years and months, it is just under 2 years 4 months)

The Payback Period cut-off rule is 3 years which means Shortcliff will accept the project so long as it recovers its initial investment in the first 3 years. Since it recovers the investment in approximately within 2 years and 4 months, Shortcliff should accept the project based on this internal criteria set by its management.