Question

A private firm has equity of 4000 and debt of 1000 (book values) and a FCFF of 100. The risk premium is 6%, the risk-free rate 3% and the corporate tax rate 30%. Cost of debt is 4% and the expected growth rate of FCFF is 2% forever. The firm operates in a sector with an unlevered beta of 0.5. Assume that the book and market values of debt are the same. Find the “market” value of equity that produces consistency in the D/E ratio, beta levered, and the WACC.

Answer #1

Debt = 1000

Market value = Book Value Equity = 4000

Book Value D/E = 1/4 = 0.25

Weight of Debt (Wd) = 1000 / 5000 = 0.20

Weight of equity (We) = 4000 / 5000 = 0.80

Beta levered = Beta unlevered * (1 + (1-t) * D/E

= 0.50 * (1+ (1-0.30)*0.25

= 0.2125

Cost of equity = Risk free return + beta * Market risk premium

= 3% + 0.2125 * 6%

= 4.275%

After tax Cost of debt = 4% * (1-0.30) = 2.8%

WACC = Weight of equity * Cost of equity + Weight of debt * cost of debt

= 0.80 * 4.275 + 0.20 * 2.8

= 3.98 %

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