Question

Suppose that XYZ Corp is considering financing a project with only equity. The project’s unlevered cost of capital is 10%. The project will require a $1000 initial investment today and pay incremental free-cash-flows of $100 in perpetuity starting the end of the next year. If the firm were to finance the project with debt so that its D/E ratio is 0.50 how will the NPV of the project change? Assume the interest rate on the new debt will be 3%, and the firm faces a 21% tax rate. Round your answer to two decimals.

Answer 1

Initially, the firm is all-equity financed and the unlevered cost of capital is 10%. The unlevered cost of capital is the discount rate in this case.

Initial Investment = $ 1000 and Perpetual Project Cash Flow = $ 100

NPV = (100/0.1) - 1000 = $ 0

Post levering, the firm has a D/E ratio of 0.5 and the leverage changes the cost of equity of the firm.

Cost of Debt = 3 % and Tax Rate = 21 %

Let the levered cost of equity be Re

Therefore, Re = 10 + (0.5) x (1-0.21) x (10-3) = 12.765 %

Debt Proportion = 1/3 and Equity Proportion = 2/3

Weighted Average Cost of Capital (WACC) = (1/3) x (1-0.21) x 3 + (2/3) x 12.765 = 9.3 %

Project NPV = (100/WACC) - 1000 = $ 75.27

As is observable. the Project's NPV goes up post levering the project as the WACC of the project (the discount rate) goes down. This happens owing to the benefits of the interest tax shield accruing to the firm owing to the introduction of debt in the capital structure.