Columbia Gas Company's (CG) current capital structure is 35% debt and 65% equity. This year CG has earnings after tax of $5.31 million and is paying $1.6 million in dividends. To finance a transmission pipe line, CG can borrow $2 million at a cost of 10%, the same rate that CG is currently paying on a total of $15 million long-term debt. CG has 1,000,000 shares outstanding, and its current market price is $31. If CG's long-term growth rate of dividends is expected to be 8%, what is the weighted cost of capital for the firm? Assume a marginal tax rate of 40%.

Question

Quizplus · Accepted Answer

The weighted cost of capital (WACC) is calculated by weighting the cost of each component of capital (debt and equity) by its proportion in the firm's capital structure and then summing these weighted costs. For debt, the after-tax cost of debt = interest rate * (1 - tax rate) = 10% * (1 - 0.4) = 6%. Since the capital structure is 35% debt, the weighted cost of debt = 35% * 6% = 2.1%.For equity, using the dividend discount model (Gordon Growth Model) where the cost of equity (Ke) = (D1/P0) + g, where D1 is the dividend next year, P0 is the current price, and g is the growth rate. The dividend next year (D1) can be calculated as D0 * (1 + g) = $1.6 million * (1 + 0.08) / 1,000,000 shares = $1.728/share. So, Ke = ($1.728 / $31) + 0.08 = 0.05574 + 0.08 = 13.574%. The weighted cost of equity = 65% * 13.574% = 8.823%.Adding the weighted costs of debt and equity gives the WACC = 2.1% + 8.823% = 10.923%, which rounds to approximately 10.9%.

Columbia Gas Company's (CG) Current Capital Structure Is 35% Debt