Question

7. 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 12 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	-1,100	80	520	720	720	320	720

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

• 3.22 years, reject

• 3.29 years, reject

• 2.78 years, accept

• 2.69 years, accept

Answer 1

Discounted Payback Period for the Project

Year	Cash Flows ($)	Present Value Factor at 12%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-1,100.00	1.00000	-1,100.00	-1,100.00
1	80.00	0.89286	71.43	-1,028.57
2	520.00	0.79719	414.54	-614.03
3	720.00	0.71178	512.48	-101.55
4	720.00	0.63552	457.57	356.02
5	320.00	0.56743	181.58	537.60
6	720.00	0.50663	364.77	902.38

Discounted Payback Period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 3.00 Years + ($101.55 / $457.57)

= 3.00 Years + 0.22 Years

= 3.22 Years

DECISION

-Using the Discounted payback decision rule, the Project should be accepted only if the Discounted Payback Period for the Project is less than the maximum allowable discounted payback period, else reject the project.

-Here, the Discounted Payback Period for the Project (3.22 Years) is higher than the maximum allowable discounted payback of 3.00 Years. Therefore, the firm should reject the Project.

-Hence, the answer would be “3.22 years, reject”.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.