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

Time	0	1	2	3	4	5	6
Cash Flow	-1,000	200	400	600	600	200	600

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

Multiple Choice

• 2.83 years, accept

• 3.09 years, reject

• 3.10 years, reject

• 2.91 years, accept

Answer 1

Answer: 3.09 years, reject

Discounted payback period measures the amount of time it takes for the cumulative discounted cash inflows to equal the outflows.

Here, Discounted payback period = 3.09 years

Discounted payback statistic for the project = 3 years

Decision rule for discounted payback period is to accept project if its discounted payback period is less than the statistic. Since, 3.09 years > 3 years, the project should be rejected.

Time	Cash Flow	Discount factor (1/((1+0.1)^n)	Present Value Cash Flow*Discount Factor	Cumulative value
0	-1,000	1.00000	-1000.00
1	200	0.90909	181.82	181.82
2	400	0.82645	330.58	512.40
3	600	0.75131	450.79	963.19
4	600	0.68301	409.81	1372.99
5	200	0.62092	124.18
6	600	0.56447	338.68

Discounted Payback Period for the project is between 3 and 4 years. Number of months beyond 3 years can be found by interpolating =(1000-963.19)/(1372.99-963.19) = 0.089 months. Thus, Discounted Payback Period for the project is 3.09 years.