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In: Finance

Your firm is operating in a world where the only imperfection is that corporations must pay...

Your firm is operating in a world where the only imperfection is that corporations must pay tax. The company is currently all equity financed. Your company has 2,900,000 shares outstanding. Your firm expects to generate earnings before interest and taxes of $3,450,000 per year in perpetuity. The company is planning on borrowing $9,000,000 and using the proceeds of the loan to repurchase some of its outstanding shares. The unlevered cost of equity is 11.20%. The company's cost of debt before taxes is 5.60%. The tax rate is 35.00%.

What will be the required rate of return on the equity after the recapitalization (borrow the money and repurchase shares) is completed?

Solutions

Expert Solution

Value of Unlevered Firm = EBIT * (1 - Tax Rate) / Unlevered Cost of Equity
Value of Unlevered Firm = $3,450,000 * (1 - 0.35) / 0.1120
Value of Unlevered Firm = $2,242,500 / 0.1120
Value of Unlevered Firm = $20,022,321.43

Value of Levered Firm = Value of Unlevered Firm + Tax Rate * Value of Debt
Value of Levered Firm = $20,022,321.43 + 0.35 * $9,000,000
Value of Levered Firm = $23,172,321.43

Value of Equity = Value of Levered Firm - Value of Debt
Value of Equity = $23,172,321.43 - $9,000,000
Value of Equity = $14,172,321.43

Debt-Equity Ratio = Value of Debt / Value of Equity
Debt-Equity Ratio = $9,000,000 / $14,172,321.43
Debt-Equity Ratio = 0.6350

Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt) * (1 - Tax Rate) * Debt-Equity Ratio
Levered Cost of Equity = 0.1120 + (0.1120 - 0.0560) * (1 - 0.35) * 0.6350
Levered Cost of Equity = 0.1120 + 0.0231
Levered Cost of Equity = 0.1351 or 13.51%

Therefore, the required rate of return on the equity after the recapitalization is 13.51%

jeff jeffy answered 1 year ago
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