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 8 percent, and that the maximum allowable payback and discounted payback statistics for the project are 3.5 and 4.5 years, respectively. Time: 0 1 2 3 4 5 6 Cash flow: ?$5,000 $1,200 $2,400 $1,600 $1,600 $1,400 $1,200 Use the discounted payback decision rule to evaluate this project.

Answer 1

• Evaluating this project on the basis of Payback Period.

Payback period is the time in which initial cash outflow is expected to be recovered from the cash inflows generated by project. The projects having Payback period earlier than Payback Period allowed will be accepted.

Computation of Payback Period in case of uneven cash flows.

Year	Cash Flow	Cumulative Cash Flow
0	($5,000)	($5,000)
1	$1,200	($3,800)
2	$2,400	($1,400)
3	$1,600	$200

Now Payback Period through Interpolation will be :-

Since this Project's Payback Period is lesser than Payback period allowed, this Project will be accepted.

• Evaluating this project on the basis of Discounted Payback Period.

Discounted Payback Period refers to the period within which the present values of cash inflows completely recover present value of cash outflows. It has plugged the deficiency of Payback Period of ignoring time value of money. It is computed by calculating cumulative present value of cash inflows till it becomes equal to present value of cash outflows. Projects having Discounted Payback Period lesser than Discounted Payback Period allowed will be accepted.

Computation of Discounted Payback Period

Year	Cash Flow	Present Value Factor	Discounted Cash Flow	Cumulative Discounted Cash Flow
0	($5,000)	1.0000	($5,000)	($5,000)
1	$1,200	0.9259	$1,111.08	($3,888.92)
2	$2,400	0.8573	$2,057.52	($1,831.4)
3	$1,600	0.7938	$1,270.08	($561.32)
4	$1,600	0.7350	$1,176	$614.68

Now Discounted Payback Period through Interpolation will be :-

Since this Project's Discounted Payback Period is lesser than Payback period allowed, this Project will be accepted.