Rocky Top Car Wash is considering a new project whose data are shown below.The equipment that would be used has a 3-year tax life,would be depreciated by the straight-line method over the project's 3-year life,and would have zero salvage value.No new working capital would be required.Revenues and other operating costs are expected to be constant over the project's 3-year life.This is just one project for the firm,so any losses can be used to offset gains on other firm projects.If the number of cars washed declined by 50% from the expected level,by how much would the project's NPV change? (Hint: Cash flows are constant in Years 1 to 3.) $\begin{array}{lr}
\text { WACC } & 10.0 \% \
\text { Net capital investment cost } & \$ 60,000 \
\text { Number of cars washed } & 2,800 \
\text { Average price per car } & \$ 25.00 \
\text { Fixed cash operating cost } & \$ 10,000 \
\text { Variable op. costiunit (i.e., per car washed) } & \$ 5.357 \
\text { Annual capital cost allowance } & \$ 20,000 \
\text { Tax rate } & 35.0 \%
\end{array}$
A)$38,113
B)$40,119
C)$42,230
D)$44,453

Question

Quizplus · Accepted Answer

The NPV change due to a 50% decline in the number of cars washed can be calculated by first determining the original and new cash flows and then finding the difference in their NPVs. The original cash flow is based on 2,800 cars, and the new cash flow is based on 1,400 cars (50% of 2,800). The calculation involves determining revenues, costs, depreciation, taxable income, taxes, and net cash flows for both scenarios, then discounting these cash flows at the WACC to find the NPVs. The difference in NPVs reflects the impact of the decline in the number of cars washed.

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