Apex Corp. is planning to buy a production machine costing $\$ 120,000$. This machine's expected useful life is five years, with no residual value. Apex uses a discount rate of $8 \%$ and has calculated the following data pertaining to the purchase and operation of this machine:
$\begin{array}{|l|r|}
\hline \text { Year } & \text { Estimated Annual Net Cash Inflow } \
\hline 1 & \$ 50,000 \
\hline 2 & \$ 40,000 \
\hline 3 & \$ 20,000 \
\hline 4 & \$ 20,000 \
\hline 5 & \$ 20,000 \
\hline
\end{array}$
(Ignore income taxes in this problem.)
-What is the payback period for this investment?
A) 3.50 years.
B) 2.75 years.
C) 3.00 years.
D) 5.00 years.

Question

Quizplus · Accepted Answer

The payback period is the time it takes for the investment to generate cash flows sufficient to recover the initial investment. Here, the cumulative cash flows are \$50,000 in Year 1, \$90,000 by Year 2 (\$50,000 + \$40,000), and \$110,000 by Year 3 (\$90,000 + \$20,000). The initial investment is \$120,000. By the end of Year 3, the investment has not been fully recovered. In Year 4, the cash inflow is \$20,000, making the total \$130,000, which exceeds the initial investment. To find the exact payback period, calculate the portion of the year needed to recover the remaining \$10,000 in Year 3. Since the cash inflow in Year 3 is \$20,000, half a year (\$10,000/\$20,000) is needed to recover the full investment. Therefore, the payback period is 3 years plus 0.5 year = 3.5 years.

Apex Corp Is Planning to Buy a Production Machine Costing $120,000\$ 120,000$120,000

Apex Corp Is Planning to Buy a Production Machine Costing $\$ 120,000$