Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted payback statistic for the project are three and three and a half years, respectively. $$\begin{array} { | l | c | c | c | c | c | c | }
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 100,000 & 30,000 & 45,000 & 55,000 & 30,000 & 10,000 \
\hline
\end{array}$$
A)2.45 years, accept
B)2.83 years, accept
C)3.45 years, accept
D)3.83 years, reject

Question

Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted payback statistic for the project are three and three and a half years, respectively. $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 100,000 & 30,000 & 45,000 & 55,000 & 30,000 & 10,000 \
\hline
\end{array}$$
A)2.45 years, accept
B)2.83 years, accept
C)3.45 years, accept
D)3.83 years, reject

Quizplus · Accepted Answer

To determine whether to accept or reject the project, we need to calculate both the payback period and the discounted payback period.

1) Payback Period: 
We start by calculating the cumulative cash flows each year:

Year 0: -$100,000 
Year 1: -$70,000 
Year 2: -$25,000 
Year 3: $30,000 
Year 4: $60,000 
Year 5: $70,000

The payback period is the time it takes for the cumulative cash flows to reach the initial investment of -$100,000. In this case, it takes 2 years and $25,000 to reach the initial investment. Therefore, the payback period is 2 + $25,000/$55,000 = 2.45 years.

Since the maximum allowable payback period is 3 years, the project is acceptable based on the payback criterion.

2) Discounted Payback Period:

To calculate the discounted payback period, we need to discount each cash flow to its present value using the required rate of return of 8 percent.

Year 0: -$100,000 
Year 1: $27,778 
Year 2: $37,561 
Year 3: $41,064 
Year 4: $20,707 
Year 5: $6,481

The present value of the cash flows after three years is $68,253, which means that the discounted payback period is 3 + ($31,747/$41,064) = 3.77 years. Since the maximum allowable discounted payback period is 3.5 years, the project is not acceptable based on the discounted payback criterion.

Therefore, the project is acceptable based on the payback criterion, but not acceptable based on the discounted payback criterion. The best choice would be to accept the project since the payback period is below the maximum allowable payback period.

Suppose Your Firm Is Considering Investing in a Project with the Cash