Assume your firm will consist of just one machine. The machine costs $126,000 and has a physical life of 10 years. Tax laws require that it be depreciated over 7 years, using straight-line depreciation. The machine produces $50,000 a year in sales and requires cash expenses of $15,000 a year. All sales are cash sales, and your firm's marginal tax rate is 40%. Your overall cost of capital is 14% a year, and this is the appropriate rate at which to discount both the before-tax project cash flows and the cash flows to Uncle Sam. Your firm has $80,000 of debt at an interest rate of 10% a year. Your first interest payment is due in year 1. Your last interest payment and the principal on the debt are due in year 10.
-Refer to the information above. If you can assume perfect capital markets, what is the NPV of the levered ownership of the firm? Round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

The NPV of the levered ownership of the firm is the sum of the NPV of the unlevered ownership of the firm and the present value of the tax savings from the debt. The NPV of the unlevered ownership of the firm is the present value of the after-tax cash flows from the firm, discounted at the firm's cost of capital. The present value of the tax savings from the debt is the present value of the tax savings from the interest payments on the debt, discounted at the firm's cost of capital.The after-tax cash flows from the firm are the sales revenue minus the cash expenses minus the depreciation expense minus the interest expense minus the taxes. The depreciation expense is the cost of the machine divided by its physical life. The interest expense is the interest rate on the debt multiplied by the principal amount of the debt. The taxes are the after-tax cash flows multiplied by the marginal tax rate.The present value of the after-tax cash flows from the firm is the sum of the after-tax cash flows from the firm in each year, discounted at the firm's cost of capital. The present value of the tax savings from the debt is the sum of the tax savings from the interest payments on the debt in each year, discounted at the firm's cost of capital.The NPV of the levered ownership of the firm is the sum of the NPV of the unlevered ownership of the firm and the present value of the tax savings from the debt. The NPV of the unlevered ownership of the firm is $14,414. The present value of the tax savings from the debt is $6,680. The NPV of the levered ownership of the firm is $14,414 + $6,680 = $21,094.

Assume Your Firm Will Consist of Just One Machine