# Share Repurchase

Best way to tackle this problem? Calculate EPS after share repurchase.

Jeff Roth is a corporate finance manager at BLB Ltd. The company plans to pay back some of its excess cash to the shareholders. Jeff has recommended the share repurchase method for returning the cash to the shareholders. The current earnings per share are \$3.2. The stock is trading at a price of \$40 per share. The company doesn’t have enough cash to buy back the shares. It is planning to borrow debt for repurchasing of shares. The debt raised by the company is currently yielding 12%, and it can borrow more debt at the same rate. It will be using a mixture of cash and borrowing debt to repurchase the share. 40% of the total repurchase amount will be paid via cash of the company and rest 60% will be borrowed. The cash of the company is earning an after-tax yield of 6.4%.

\$40 * 40% = \$16 / share will be financed by cash which earns after-tax 6.4% * \$16 = \$1.024 this amount the company will forgo as a result of spending cash, not keeping and earning on it.

\$40 * 60% = \$24 / share will be financed by debt which costs 12% * \$24 = \$2.88 (assuming after-tax) this amount the company should spend to raise debt

overall effect on earnings for each purchased share = - \$1.024 - \$2.88 = - \$3.904

Assuming N shares outstanding, and x shares for repurchase, also the above effects will impact on the current EPS, we will have new EPS as follows: EPS after buyback = (Earnings - After-tax cost of funds - forgone interest to be earned on idle cash) / Shares outstanding after buyback = (3.2*N - 3.904*x) / (N - x)

Since we don’t have number of shares outstanding and of planned repurchase, exact dollar amount is not identifiable. However, we can find the direction of EPS change, whether it will increase or decrease.

Earnings yield = EPS / Stock price = 3.2 / 40 = 8% Cash has 6.4% yield, debt has 12% after-tax cost. Since 40% is financed by cash, and the rest by debt, weighted average cost of funds used for share repurchase is equal to = 6.4% * 40% + 12% * 60% = 9.76%. Since the earnings yield is less than the cost of funds for share repurchase, I expect reduction in EPS.

Correct me if I am wrong.

The book value per share of the company is \$32. The total number of shares outstanding is 20 million. The company wants to repurchase 4 million of shares at the current market price. The marginal tax rate for the company is 40%.

= (3.2*N - 3.904*x) / (N - x)

= (3.2 * 20mln - 3.904 * 4mln) / (20mln - 4mln) = 3.024

Correct me if this is a wrong answer.

That is an answer choice but is not correct. You havre to adjust the cost of debt to be after tax so .12(1-.4)=7.2%. Otherwise, the rest is right. Thanks!

Totally agree! Thank you as well.