Question

Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project. The company currently has a target debt-equity ratio of .35, but the industry target debt-equity ratio is .30. The industry average beta is 1.20. The market risk premium is 6.3 percent and the risk-free rate is 4.5 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 23 percent. The project requires an initial outlay of $875,000 and is expected to result in a $111,000 cash inflow at the end of the first year. The project will be financed at the company’s target debt-equity ratio. Annual cash flows from the project will grow at a constant rate of 6 percent until the end of the fifth year and remain constant forever thereafter. calculate the NPV of the project

Answer 1

Solution:

The risk-free rate = 4.5%

Beta for the industry average is = 1.2. We need to calculate the beta for Blue Angel by deleveraging this beta and then leveraging with the company's debt-equity ratio.

Levered Beta = Unlevered Beta * [1+ D/E * (1-tax)]

1.2 = Unlevered beta * [1+ 0.3 * (1-0.23)]  

1.2 = Unlevered beta * 1.231

Unlevered beta = 1.2/1.231 =0.9748

Levered Beta = Unlevered Beta * [1+ D/E * (1-tax)]  

Levered Beta = 0.9748 * [1+ 0.35 * (1-0.23)] = 1.24

Market risk premium = 6.3%

Using CAPM formula,

The cost of equity = Risk free rate + Beta * Market Risk Premium

The cost of equity = 4.5% + 1.24 * 6.3% = 12.31%

The after tax cost of debt = 4.5% * ( 1-tax) = 4.5%* (1-0.23) = 3.47%

Weight of equity = 1 / (1+D/E) = 1 / 1.35 = 0.74

Weight of debt = 1-0.74 = 0.26

WACC = 12.31% * 0.74 + 3.47% * 0.26 = 10%

The NPV of the project is = $464,289.23