Century Roofing is thinking of opening a new warehouse, and the key data are shown below.The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse.The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value.No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life.What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.) $\begin{array}{lr}
\text { Project cost of capital (r) } & 10.0 \% \
\text { Opportunity cost } & \$ 100,000 \
\text { Net equipment cost (depreciable basis) } & \$ 65,000 \
\text { Straight-line deprec. rate for equipment } & 33.333 \% \
\text { Sal es revenues, each year } & \$ 123,000 \
\text { Operating costs (excl. deprec.), each year } & \$ 25,000 \
\text { Tax rate } & 25 \%
\end{array}$

Question

Quizplus · Accepted Answer

The NPV of the project can be calculated by first determining the annual cash flows and then discounting them back to present value using the project's cost of capital. 1. Calculate the annual depreciation:   - Depreciation = $65,000 / 3 = $21,667 per year2. Calculate the annual operating cash flow (OCF):   - OCF = (Sales - Operating costs - Depreciation) * (1 - Tax rate) + Depreciation   - OCF = ($123,000 - $25,000 - $21,667) * (1 - 0.25) + $21,667   - OCF = $76,333 * 0.75 + $21,667   - OCF = $57,250 + $21,667   - OCF = $78,917 per year3. Calculate the NPV:   - NPV = -Opportunity cost + OCF * [1 - (1 + r)^-n] / r   - NPV = -$100,000 + $78,917 * [1 - (1 + 0.10)^-3] / 0.10   - NPV = -$100,000 + $78,917 * 2.4869   - NPV = -$100,000 + $196,254   - NPV = $96,254However, the calculation above contains a mistake in the NPV formula application. The correct NPV calculation should consider the opportunity cost as an initial outflow and then discount the constant annual cash flows back to the present value using the formula for an annuity since the cash flows are constant over the project's life. The correct approach is:NPV = -Opportunity cost + (OCF * [1 - (1 + r)^-n] / r)Given the options provided and the mistake in the initial calculation, it seems there was a misunderstanding in the calculation process. The correct calculation involves determining the net operating cash flow correctly and then applying the NPV formula with the given project cost of capital. The options provided do not match the miscalculated NPV, suggesting a need to re-evaluate the calculation steps, especially focusing on the correct application of tax effects, depreciation, and the annuity formula for NPV calculation. Without the exact cash flows derived from the given data, the correct answer cannot be determined from the provided calculation steps.

Century Roofing Is Thinking of Opening a New Warehouse, and the Key