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. $$\begin{array} { l l l l l l l }
\text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000
\end{array}$$ Use the discounted payback decision rule to evaluate this project; should it be accepted or rejected?
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. $$\begin{array} { l l l l l l l } 
\text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000
\end{array}$$ Use the discounted payback decision rule to evaluate this project; should it be accepted or rejected?
A)1.77 years, reject
B)1.94 years, accept
C)2.06 years, accept
D)3.00 years, reject

Quizplus · Accepted Answer

To calculate discounted payback, we need to first calculate the present value of each cash flow. Using a required rate of return of 12 percent, we get the following present values:

$$\begin{array} { l l l l l l l } 
\text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\text { Cash Flow } & - 125,000 & 65,000 & 78,000 & 105,000 & 105,000 & 25,000 \
\text { PV factor } & 1.0000 & 0.8929 & 0.7972 & 0.7118 & 0.6355 & 0.5674 \
\text { PV of cash flow } & - 125,000 & 58,036 & 62,244 & 74,904 & 67,130 & 14,184 \
\end{array}$$

We then calculate the cumulative present value of cash flows at each time period:

$$\begin{array} { l l l l l l l } 
\text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\text { Cumulative PV } & - 125,000 & - 66,964 & - 4,720 & 70,184 & 137,314 & 151,498 \
\end{array}$$

The discounted payback period is the time at which the cumulative present value of cash flows equals zero. Looking at the table above, we can see that this occurs between years 2 and 3. To be more precise, we can calculate the exact year by noting that the cumulative PV at the end of year 2 is negative while the cumulative PV at the end of year 3 is positive:

$$\text { Discounted payback period } = 2 + \frac{4,720}{70,184 - (-4,720)} = 2.06 \text{ years}$$

Since this is less than the maximum allowable discounted payback period of 2.5 years, the project should be accepted. Therefore, the answer is C)2.06 years, accept.

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