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 12 percent, and that the maximum allowable payback and discounted payback statistic for the project are two and two and a half years, respectively. $$\begin{array} { | l | c | c | c | c | c | c | }
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000 \
\hline
\end{array}$$
A)1.77 years, reject
B)1.94 years, accept
C)2.06 years, accept
D)3.00 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 12 percent, and that the maximum allowable payback and discounted payback statistic for the project are two and two and a half years, respectively. $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000 \
\hline
\end{array}$$
A)1.77 years, reject
B)1.94 years, accept
C)2.06 years, accept
D)3.00 years, reject

Quizplus · Accepted Answer

To determine whether or not to invest in this project, we will calculate the payback period, discounted payback period, and net present value (NPV).
Payback Period: 
We will start by finding the cumulative cash flows for the project. 
$$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000 \
\hline \text{Cumulative Cash Flow} & -125,000 & -60,000 & 18,000 & 123,000 & 228,000 & 253,000 \
\hline 
\end{array}$$
The payback period is the amount of time it takes for the cumulative cash flows to equal the initial investment. In this case, the payback period is between year 3 and year 4. 
Payback = 3 + (125,000 - 18,000)/105,000 = 3.81 years 
Since the payback period is longer than the maximum allowable payback period of 2 years, we reject this project.
Discounted Payback Period: To calculate the discounted payback period, we will discount the cash flows using a 12% discount rate, and then find the cumulative discounted cash flows. 
$$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000 \
\hline \text{Discounted Cash Flow} & -125,000 & 58,036 & 62,640 & 74,054 & 62,585 & 13,093 \
\hline \text{Cumulative Discounted Cash Flow} & -125,000 & -66,964 & -4,324 & 69,731 & 132,316 & 145,409 \
\hline
\end{array}$$
The discounted payback period is the amount of time it takes for the cumulative discounted cash flows to equal the initial investment. In this case, the discounted payback period is between year 4 and year 5.
Discounted Payback = 4 + (125,000 - 132,316)/62,585 = 4.89 years
Since the discounted payback period is longer than the maximum allowable discounted payback period of 2.5 years, we reject this project.

Net Present Value: 
To determine the NPV of the project, we need to discount each cash flow and then sum them up. 
$$NPV = -125,000 + \frac{65,000}{1.12} + \frac{78,000}{(1.12)^2} + \frac{105,000}{(1.12)^3} + \frac{105,000}{(1.12)^4} + \frac{25,000}{(1.12)^5}$$
$$NPV = -125,000 + 58,036 + 57,741 + 71,616 + 59,245 + 10,196$$
$$NPV = $31,834$$
Since the NPV is positive, we accept this project.

Based on the results of our analysis, we can see that the payback period and discounted payback period are both longer than the maximum allowable periods, but the NPV is positive, indicating that this project will add value to the firm. Therefore, we should accept this project. The best choice is option C) 2.06 years, accept.

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