Question

EQUATION 9.6 - beta of equity = beta of asset * (1 + (1-T) debt-equity ratio)

The asset beta for a particular industry is 0.75. Use Equation 9.6 to estimate the equity betas for the following three firms based on their respective debt ratios and tax rates. Then calculate each firm's cost of equity assuming an expected market premium of 6% and a risk-free rate of 4%.

Firm A: 75% debt ratio and 35% tax rate

Firm B: 20% debt ratio and 38% tax rate

Firm C: 80% debt ratio and 45% tax rate

Answer 1

Firm A:

Debt Ratio = 75%

Debt-equity Ratio = Debt Ratio / (100% - Debt Ratio)
Debt-equity Ratio = 75% / (100% - 75%)
Debt-equity Ratio = 3

Beta of Equity = Beta of Assets * [1 + (1 - tax) * Debt-equity Ratio]
Beta of Equity = 0.75 * [1 + (1 - 0.35) * 3]
Beta of Equity = 0.75 * 2.95
Beta of Equity = 2.2125

Cost of Equity = Risk-free Rate + Beta of Equity * Market Premium
Cost of Equity = 4% + 2.2125 * 6%
Cost of Equity = 17.28%

Firm B:

Debt Ratio = 20%

Debt-equity Ratio = Debt Ratio / (100% - Debt Ratio)
Debt-equity Ratio = 20% / (100% - 20%)
Debt-equity Ratio = 0.25

Beta of Equity = Beta of Assets * [1 + (1 - tax) * Debt-equity Ratio]
Beta of Equity = 0.75 * [1 + (1 - 0.38) * 0.25]
Beta of Equity = 0.75 * 1.155
Beta of Equity = 0.86625

Cost of Equity = Risk-free Rate + Beta of Equity * Market Premium
Cost of Equity = 4% + 8.6625 * 6%
Cost of Equity = 9.20%

Firm C:

Debt Ratio = 80%

Debt-equity Ratio = Debt Ratio / (100% - Debt Ratio)
Debt-equity Ratio = 80% / (100% - 20%)
Debt-equity Ratio = 4

Beta of Equity = Beta of Assets * [1 + (1 - tax) * Debt-equity Ratio]
Beta of Equity = 0.75 * [1 + (1 - 0.45) * 4]
Beta of Equity = 0.75 * 3.20
Beta of Equity = 2.40

Cost of Equity = Risk-free Rate + Beta of Equity * Market Premium
Cost of Equity = 4% + 2.40 * 6%
Cost of Equity = 18.40%