# share repurchases

in a leveraged recap, a company incurs in debt to repurchase stock. how does this raise the stock price?

Because of the arbitrage spread between the offer and the current price. Arbritragers and incumbent investors appreciate the instant premium, so market demand pushes up the stock in the interim. Also, a lower stock count by means of buybacks, means higher EPS so quant funds and other funds that track EPS for various companies are trigerred to buy the stock, thus the surge in price.

Simple Example: Earnings = \$1000 S/O = 1000 EPS = 1 P/E multiple = 10 stock price = \$10 Now lets say they raise some debt and repurchase 100 shares. Earnings = 1000 - say of \$6 after tax interest = 994 (that would be a roughly 9% yeild before tax). S/O = 900 EPS = \$1.10 Assuming the P/E multiple doesn’t change with the increase in debt, you have a higher stock price.

strikershank Wrote: ------------------------------------------------------- > Simple Example: > > Earnings = \$1000 > S/O = 1000 > EPS = 1 > > P/E multiple = 10 > stock price = \$10 > > Now lets say they raise some debt and repurchase > 100 shares. > > Earnings = 1000 - say of \$6 after tax interest = > 994 (that would be a roughly 9% yeild before > tax). > > S/O = 900 > EPS = \$1.10 > Assuming the P/E multiple doesn’t change with the > increase in debt, you have a higher stock price. I think your after-tax interest calculation is incorrect. 100 shares x \$10 stock price = \$1,000 of new debt to finance repurchase. 9% pre-tax cost of debt = 5.85% after-tax assuming 35% tax rate. After-tax interest expense would be \$58.50 NOT \$6.00. New net income would be \$1,000 - 58.50 = \$941.50. With 900 S/0, EPS would \$1.046. Assuming the 10x multiple, implied stock price = \$10.46. Your pro-forma stock price is higher because you are repurchasing relatively cheap stock (10x) vs. your cost of financing of 9%. The pro-forma stock price would be LOWER if you repurchased stock when it was trading at a 20x multiple.

I remember something about if the earnings yield is equal to the after-tax cost of debt, the stock price stays the same. So if after tax cost of debt is 6%, then a PE of 1/0.06 or approx 16.6 is where there would be no effect on stock price. If the PE is more like 20, then the marginal cost of the debt (6%) is more expensive than the marginal return on stock (1/20 = 5%), so the inefficiency of capital use ends up lowering the stock price.

Happysappy, you’re right - i made a calculation mistake (that’swhat happens when you rush and don’t double check). But the message remains the same and you summarized it nicely. Thanks.