Kaylea Co. Ltd. has perpetual debt with a face value of $20 million at 5% and a market value of $18 million. It has no preferred shares. Ten million common shares were issued at $12.50 and are now trading for $15.00 each from a high three years ago of $24.00. Common shareholders are demanding a 9% return from companies of equal risk. The company has a tax rate of 35%. It wishes to repurchase four million common shares to reduce the threat of a hostile take-over. Kaylea Co. will use all of its retained earnings of $32 million and fund the balance with perpetual debt at 7% where the market value will equal face value. Assume the cost of Kaylea's old debt will remain unchanged and that share price remains the same. If the repurchase goes through, in absolute terms, what will be the change in the company's cost of capital?

Question

Quizplus · Accepted Answer

First, we need to calculate Kaylea Co.'s current cost of capital. We can do this by using the following formula:
Weighted Average Cost of Capital (WACC) = (Cost of Equity x % Equity) + (Cost of Debt x % Debt x (1 - Tax Rate))

% Equity = (10,000,000 shares / 14,000,000 total shares outstanding) = 71.4%
% Debt = (4,000,000 shares x $15.00 per share) + $10,000,000 face value of debt = $70,000,000 total debt
% Debt = ($70,000,000 / $88,000,000 total capital) = 79.5%

Cost of Equity = 9.0% (as given in the problem)
Cost of Debt = 5.0%

WACC = (0.090 x 0.714) + (0.050 x 0.795 x (1 - 0.35)) = 7.38%

Next, we need to calculate Kaylea Co.'s new cost of capital after the share repurchase. We can do this by assuming that the cost of debt will increase to 7.0%. This is because Kaylea Co. will be issuing new debt at a higher rate to fund the share repurchase. Additionally, the % Equity and % Debt will change as follows:

% Equity = (6,000,000 shares / 10,000,000 total shares outstanding) = 60.0%
% Debt = ($70,000,000 face value of debt + $2,000,000 new debt) = $72,000,000 total debt
% Debt = ($72,000,000 / $92,000,000 total capital) = 78.3%

Using the same formula as before, we can calculate the new WACC:

WACC = (0.090 x 0.6) + (0.070 x 0.783 x (1 - 0.35)) = 6.27%

Finally, we can calculate the change in the company's WACC:

Change in WACC = Current WACC - New WACC
Change in WACC = 7.38% - 6.27% = 1.11%
Therefore, the answer is choice C, which indicates that the company's cost of capital will be lower by 1.1%.

Kaylea Co Ltd