Piper Co has 40 million shares outstanding, trading for $10 per share. In addition, the firm...

Piper Co has 40 million shares outstanding, trading for $10 per share. In addition, the firm has $106 million in outstanding debt. Suppose the equity cost of capital is 15%, its debt cost of capital is 8% and the tax rate is 40%:

a) What is the WACC?

b)If the risk free rate is 15% and the Rm is 9%, what are the leveraged and unleveraged betas?

Solutions

Expert Solution

a) WACC = Weight of debt * Pretax cost of debt * (1 - Tax rate) + Weight of equity * Cost of equity

Total Capital Market Value = Market value of debt + market value of equity = $106 mil + $400 mil = $506 mil

Weight of debt = Market Value of Debt/Total Market Value of Capital = 106/506 = 20.95%

Weight of equity = Market Value of Equity/Total Market Value of Capital = 400/506 = 79.05%

WACC = 20.95% * 8% * (1 - 40%) + 79.05% * 15% = 1.00% + 11.86% = 12.86%

b) This question has some misplaced data. Risk free rate should be 9% and market rate of return Rm should be 15%. If risk free rate were higher than market return, why would anyone invest in market. (Let me know if you agree with the same in comments).

In order to calculate the levered beta, we can first use the CAPM equation

Reqd return on stock = Risk free rate + Beta * (Rm - Risk free rate)

15% = 9% + Beta * (15% - 9%)

6% = Beta * 6%

Beta = 1.00 --> This is levered Beta

Now, in order to calculate unlevered beta, we would use the mathematical relation:

Debt/Equity = 106/400 = 0.265

Substituting these values,

Beta (unlevered) = 0.8628

jeff jeffy answered 1 year ago

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