Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all-equity firm that specializes in this business. Suppose Harburtin's equity beta is 0.84, the risk-free rate is 4 %, and the market risk premium is 5 %. a. If your firm's project is all-equity financed, estimate its cost of capital. After computing the project's cost of capital you decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second firm, Thurbinar Design, which is also engaged in a similar line of business. Thurbinar has a stock price of $ 19 per share, with 14 million shares outstanding. It also has $ 102 million in outstanding debt, with a yield on the debt of 4.3 %. Thurbinar's equity beta is 1.00. b. Assume Thurbinar's debt has a beta of zero. Estimate Thurbinar's unlevered beta. Use the unlevered beta and the CAPM to estimate Thurbinar's unlevered cost of capital. c. Estimate Thurbinar's equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield and using these results, estimate Thurbinar's unlevered cost of capital. d. Explain the difference between your estimate in part (b) and part (c).

a. Harburtin's cost of capital is 8.20%.

b. Unlevered Beta is 0.72 and unlevered cost of capital is 7.60%.

c. Equity cost of capital is 9% and unlevered cost of capital is 7.70%.

d. See the explanation in d below.

Explanation:

a. If your firm's project is all-equity financed, estimate its cost of capital.  

Using Capital Asset Pricing Model (CAPM), the cost of capital of an all equity firm can be calculated as follows:

Cost of capital = Risk free rate + (beta × market risk premium)

Cost of capital = 0.04 + (0.84 × 0.05) = 0.082 or 8.20%

Therefore, Harburtin's cost of capital is 8.20%.

b. Assume Thurbinar's debt has a beta of zero. Estimate Thurbinar's unlevered beta. Use the unlevered beta and the CAPM to estimate Thurbinar's unlevered cost of capital.

Step 1: Estimation of Thurbinar's unlevered beta

Equity = $19 × 14,000,000 = $266,000,000

Debt = $102,000,000

Equity and debt = $266,000,000 + $102,000,000 = $368,000,000

Unlevered Beta = [($266,000,000 ÷ $368,000,000) × 1.00] + [($102,000,000 ÷ $368,000,000) × 0]  = 0.72 + 0 = 0.72

Unlevered cost of capital = 0.04 + (0.72 × 0.05) = 0.076 or 7.60%

c. Estimate Thurbinar's equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield and using these results, estimate Thurbinar's unlevered cost of capital.  

Equity cost of capital = 0.04 + (1.0 × 0.05) = 0.0900 or 9%

Unlevered cost of capital = [0.09 × ($266,000,000 ÷ $368,000,000)] + [0.043 × ($102,000,000 ÷ $368,000,000)]

Unlevered cost of capital = 0.0651 + 0.0119 = 0.0770 or 7.70%

d. Explain the difference between your estimate in part (b) and part (c).

In part (b), an assumption is made that the beta of debt is equal to zero and the cost of debt was considered to be the riskless rate.

In part (c), the cost of debt is made to be equal to the yield on debt.

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