Question

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 13 percent, and that the maximum allowable payback and discounted payback statistic for the project are 2 and 3 years, respectively.

Use the payback decision rule to evaluate this project; should it be accepted or rejected?

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 13 percent, and that the maximum allowable payback and discounted payback statistic for the project are 2 and 3 years, respectively. Time Cash Flow 0 -110 1 70 2 530 3 730 4 730 5 330 6 730 0 0 Use the payback decision rule to evaluate this project should it be accepted or rejected? Multiple Choice 270 years,rejea Ο γιος, κοι 400 years, rect

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 (n)	Cash Flow	Cumulative Cash Flow
0	-$1,110	-$1,110
1	$70.0	-$1,040
2	$530.0	-$510
3	$730.0	$220
4	$730.0	$950
5	$330.0	$1,280
6	$730.0	$2,010

We can see from above table that at the end of year 2 the initial investment is not recovered, so the payback period is greater than 2 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)

= 2 + ($510/ $730) = 2 + 0.70 = 2.70 years

The payback period is 2.70 years. Therefore reject it because as per payback decision rule it should not be more than 2 years.

Therefore correct answer is option: 2.70 years, reject

Discounted Payback Period calculation takes money value of money into consideration and gives us an idea that how long it will take for a project to recover the initial investment.

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

Year (n)	Cash Flow	Discounted Cash Flow [Cash Flow/(1+13%)^n]	Cumulative discounted Cash Flow
0	-$1,110	-$1,110.00	-$1,110.00
1	$70.0	$61.95	-$1,048.05
2	$530.0	$415.07	-$632.99
3	$730.0	$505.93	-$127.06
4	$730.0	$447.72	$320.66
5	$330.0	$179.11	$499.77
6	$730.0	$350.63	$1,229.77

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

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

= 3 + ($127.06/ $447.72) = 3 + 0.28 = 3.28 years

The discounted payback period is 3.28 years. Therefore reject it because as per discounted payback decision rule it should not be more than 3 years.