Question

Alpha Industries is considering a project with an initial cost of $8.8 million. The project will produce cash inflows of $1.68 million per year for 8 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.85 percent and a cost of equity of 11.43 percent. The debt–equity ratio is .68 and the tax rate is 40 percent. What is the net present value of the project?

Answer 1

The net present value (NPV) of the project is $102 million.

Step-by-step explanation:

The net present value (NPV) is a financial metric used to evaluate the profitability of an investment project. To calculate the NPV, we need to discount the future cash inflows to their present value and subtract the initial cost of the project. The formula for NPV is:

NPV = -initial cost + (cash inflow / (1 + cost of capital)^year)

In this case, the initial cost is $8.8 million. The cash inflow per year is $1.68 million, and the project will last for 8 years. The cost of capital is calculated as the weighted average cost of debt and equity, weighted by the debt-equity ratio. The cost of debt is 5.85% and the cost of equity is 11.43%. The debt-equity ratio is 0.68. The tax rate is 40%.

Using these values, we can calculate the NPV of the project as follows:

NPV = -8.8 + (1.68 / (1 + (0.68 * 0.05) * 0.4))^year

Substituting the values, we get:

NPV = -8.8 + (1.68 / (1 + (0.68 * 0.05) * 0.4))^year = $102 million

Therefore, the net present value of the project is $102 million.