A company earns $200m on 100m shares and trades at $40. It borrows $400m at 5% pre-tax and buys back stock, with a 25% tax rate. What share price makes the buyback neutral to earnings per share, and what is the rule behind it?

A company earns $200m on 100m shares and trades at $40. It borrows $400m at 5% pre-tax and buys back stock, with a 25% tax rate. What share price makes the buyback neutral to earnings per share, and what is the rule behind it?

Approach: Set the after-tax cost of the borrowing equal to the earnings yield of the shares retired, solve for the price, then confirm it by recomputing earnings per share at that level.

$53.33. A debt-funded buyback is neutral when the earnings yield of the retired shares equals the after-tax cost of debt, which is 5% * 0.75, or 3.75%. With earnings per share of $2.00 the neutral price is 2.00/0.0375. Check it: at $53.33 the company retires 400/53.33, or 7.5m shares, leaving 92.5m, and after-tax interest of 400 * 0.05 * 0.75, or $15m, leaves earnings of $185m, so earnings per share is 185/92.5, which is exactly $2.00. At the actual price of $40 the earnings yield is 5%, comfortably above 3.75%, so the buyback lifts earnings per share to 185/90, or $2.06, a rise of 2.8%. Accretion at a 5% earnings yield says nothing about whether $40 sits below intrinsic value, and that second question decides whether value was created.

Follow-up: The company's cost of equity is 9%. At what share price does the buyback create value rather than only lift earnings per share?

Key concepts: share buyback, earnings yield, after-tax cost of debt, earnings per share.