A project costs $7 million and is expected to produce cash flows of $2 million per year for 10 years. The opportunity cost of capital is 16 percent. If the firm has to issue stock to undertake the project and issue costs are $0.5 million, what is the project's APV?

Question

Quizplus · Accepted Answer

The Adjusted Present Value (APV) approach values a project by considering the base-case NPV (net present value) and the NPV of the financing effects. Here, the base-case NPV is calculated by discounting the project's cash flows at the opportunity cost of capital, and then the net effect of financing (here, the cost of issuing stock) is added or subtracted.1. Calculate the base-case NPV:   - The cash flows are $2 million per year for 10 years. Using the formula for the present value of an annuity: $PV = C \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $C$ is the annual cash flow, $r$ is the discount rate (16% or 0.16), and $n$ is the number of periods (10 years).   - $PV = 2 \times \left[\frac{1 - (1 + 0.16)^{-10}}{0.16}\right] = 2 \times 4.833 = 9.666$ million.   - Subtract the initial project cost: $9.666 - 7 = 2.666$ million.2. Adjust for the financing effect:   - Subtract the cost of issuing stock: $2.666 - 0.5 = 2.166$ million.Therefore, the APV is approximately $2.17 million, making choice B the correct answer.

A Project Costs $7 Million and Is Expected to Produce