case 26 An Introduction to Debt Policy and Value

4. What remains to be seen however, is whether shareholders are better or worse off with more leverage. Problem 2 does not tell us, because there we computed total value of equity, and shareholders care about value per share. Ordinarily, total value will be a good proxy for what is happening to the price per share, but in the case of a relevering firm, that may not be true. Implicitly we assumed that, as our firm in problems 1-3 levered up, it was repurchasing stock on the open market (you will note that EBIT did not change, so management was clearly not investing the proceeds from the loans in cash-generating assets). We held EBIT constant so that we could see clearly the effect of financial changes without getting them mixed up in the effects of investments. The point is that, as the firm borrows and repurchases shares, the total value of equity may decline, but the price per share may rise.
Now, solving for the price per share may seem impossible, because we are dealing with two unknowns—share price and change in the number of shares:
Share price = Total market value of equity (Original shares - Repurchased shares)

But by rewriting the equation, we can put it in a form that can be solved:
Share price = Total market value of equity + Cash paid out Number of original shares
Referring to the results of problem 2, let's assume that all the new debt is equal to the cash paid to repurchase shares. Please complete the following table: 0% Debt 25%Debt 50% Debt 100% Equity 75% Equity 50% Equity
Total market value of equity $ 10.000 $ 8.350 $ 6.700
Cash paid out $ - $ 2.500 $ 5.000
Number of original shares 1000 1000 1000
Total value per share $ 10,00 $ 10,85 $ 11,70