Question
A small firm has a capital structure consisting of $300,000 in debt and $300,000 in equity. The company's debt carries a 5% coupon and is selling at par. The firm's tax rate is 30%. A publicly-traded competitor has a capital structure of $300,000,000 debt and $500,000,000 of common stock. Their effective tax rate is 25%. The large firm's stock has a beta of 0.90. Estimate the smaller firm's cost of equity if the expected market return is 12%, treasury security are yielding 4% and the firm's stock has a standard deviation of returns equal to 18%.
Explanation / Answer
For the smaller firm, out of the total investment $600,000 , debt constitutes 50% ($300,000) and equity constitutes 50% ($300,000). Weight of debt = 50% Weight of equity = 50% The pre-tax cost of debt for the small firm is same as that of the coupon rate because the debt is issued at par value. When the debt is issued at par value, the coupon rate and the yield to maturity will be always the same. Pre-tax cost of debt = 5% After-tax cost of debt = Pre-tax cost of debt (1-Tax rate) = 5% (1 - 0.30) = 0.035 or 3.5% Computing the Cost of equity using CAPM for the smaller firm: Re = Rf + Beta [E(Rm) - Rf] = 0.04 + 0.9 [ 0.12 - 0.04] = 0.04 + 0.9 [ 0.08] = 0.04 + 0.072 = 0.112 or 11.2% Therefore, the cost of equity is 11.2% for the smaller firm.