The Sawyer Company has $\$ 80,000$ to invest and is considering two different projects: $\mathrm { X }$ and $\mathrm { Y }$. The following data are available on the projects:
$\begin{array}{|l|r|r|}
\hline & \text { Project X } & \text { Project Y } \
\hline \text { Cost of equipment needed now } & \$ 80,000 & --- \
\hline \text { Working capital requirement } & -- & \$ 80,000 \
\hline \text { Annual cash operating inflows } & \$ 23,000 & \$ 18,000 \
\hline \text { Salvage value in five years } & \$ 6,000 & -- \
\hline
\end{array}$
Both projects will have a useful life of five years; at the end of five years, the working capital will be released for use elsewhere. Sawyer's discount rate is $12 \%$. (Ignore income taxes in this problem.)
- What is the net present value of project X? (Do not round your intermediate calculations and round your final answer to the nearest whole number.)
A) ($11,708).
B) $2,910.
C) $5,283.
D) $6,314.

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV) of Project X, we use the formula for NPV which is the sum of the present value of cash inflows minus the initial investment. The cash inflows are the annual operating inflows and the salvage value at the end of the project's life, both discounted back to their present value using the discount rate of 12%.1. Calculate the present value of the annual cash inflows:$$PV = \frac{C}{r} \times (1 - (1 + r)^{-n})$$Where $C = \$23,000$, $r = 0.12$, and $n = 5$.$$PV = \frac{\$23,000}{0.12} \times (1 - (1 + 0.12)^{-5}) = \$23,000 \times 3.60478 = \$82,909.94$$2. Calculate the present value of the salvage value:$$PV = \frac{F}{(1 + r)^n}$$Where $F = \$6,000$, $r = 0.12$, and $n = 5$.$$PV = \frac{\$6,000}{(1 + 0.12)^5} = \$6,000 \times 0.56743 = \$3,404.58$$3. Calculate the NPV:$$NPV = PV_{inflows} + PV_{salvage} - Initial\,Investment$$$$NPV = \$82,909.94 + \$3,404.58 - \$80,000 = \$6,314.52$$Rounded to the nearest whole number, the NPV of Project X is approximately \$6,314.

The Sawyer Company Has $80,000\$ 80,000$80,000 To Invest and Is Considering Two Different Projects

The Sawyer Company Has $\$ 80,000$ To Invest and Is Considering Two Different Projects