Technico has determined that its optimal capital structure is 40% debt, at which point its weighted cost of capital, k_a, is 13.7%. Due to financial problems, the firm has decided to raise the proportion of debt to 50%, which will increase its weighted cost of capital to 14.4%. What is the effect on the stock price of Technico? The current dividend is $1.60 and the long-term growth rate of dividends is expected to be 8.5%. A) Decrease $3.65 B) Decrease $3.96 C) Increase $3.65 D) Increase $3.96

Question

Quizplus · Accepted Answer

To find the effect on the stock price, we need to use the following formula: k_a = kD(1-T)(D/S) + kS(1-T)(E/S) where k_a = weighted average cost of capital (WACC) at 40% debt kS = cost of equity kD = cost of debt T = corporate tax rate D/S = debt-to-equity ratio E/S = equity-to-total value ratio We can solve for kS: kS = [k_a - kD(1-T)(D/S)]/[1-T(E/S)] At 40% debt, D/S = 0.4/0.6 = 0.67 E/S = 0.6/0.6 = 1 Substituting the values, we get: kS = (13.7% - kD(1-0.35)(0.67))/(1-0.35) At 50% debt, D/S = 0.5/0.5 = 1 E/S = 0.5/0.5 = 1 We can solve for kS: 14.4% = kD(1-0.35)(1) + kS(1-0.35)(1) kS = (14.4% - kD(0.65))/0.65 We can equate the two equations for kS and solve for kD: (13.7% - kD(1-0.35)(0.67))/(1-0.35) = (14.4% - kD(0.65))/0.65 kD = 8.83% Now we can find the new WACC at 50% debt: WACC = kD(1-T)(D/S) + kS(1-T)(E/S) WACC = 8.83%(1-0.35)(1) + kS(1-0.35)(1) 14.4% = 5.74% + kS(0.65) kS = 14.62% Using the constant growth model, we can find the stock price change: P0 = D1/(kS-g) At 40% debt, D1 = $1.60(1+8.5%) = $1.736 kS = 13.7% g = 8.5% P0 = $1.736/(13.7%-8.5%) = $34.72 At 50% debt, D1 = $1.60(1+8.5%) = $1.736 kS = 14.62% g = 8.5% P0 = $1.736/(14.62%-8.5%) = $30.76 The change in stock price is: $30.76 - $34.72 = -$3.96 Therefore, the correct answer is B) Decrease $3.96.

Technico Has Determined That Its Optimal Capital Structure Is 40