14.2How an Individual InvestorCan “Undo” a Firm’s Capital

Structure Choice

The proof of the Modigliani-Miller Theorem described in the last section implicitly

assumes that firms with identical cash flows but different capital structures exist. An

alternative interpretation of the Modigliani-Miller Theorem is that, under its assump-

tions, a firm’s shareholders are indifferent to a change in its capital structure. This is

illustrated in Example 14.2.

²Chapters 16-19 examine how the financing mix affects a firm’s investment choices and the

efficiency of its operations.

³This tracking does not have to be perfect. For example, if the CAPM holds, the Modigliani-Miller

Theorem still applies. The key is that investors cannot be made better off by the issuance of a new

security.

Grinblatt1025Titman: Financial	IV. Capital Structure	14. How Taxes Affect	© The McGraw1025Hill
Markets and Corporate		Financing Choices	Companies, 2002
Strategy, Second Edition

506Part IVCapital Structure

Example 14.2:Undoing Elco’s Capital Structure Change

Elco is considering a change in its capital structure.Before the change, the firm’s stock sells

for $100 per share, and the firm has 1,000 shares outstanding.The firm also is financed

with riskless zero-coupon debt maturing in one year, and having a current market value of

D$10,000.

Stanley Kowalski currently owns 100 shares of Elco stock (10 percent of its equity).In

the absence of a capital structure change, Stanley’s payoff next year will equal

.1[˜(1 r)$10,000].1X˜(1 r)$1,000

X

DD

Here Xis the firm’s cash flows and ris the risk-free interest rate to be paid to debt hold-

D

ers, so that the firm’s future debt service obligation is (1 r)$10,000.The firm plans to

D

repurchase 500 shares of its outstanding stock for $50,000 and will finance the equity repur-

chase by issuing $50,000 in risk-free debt.

First, show what Stanley’s payoff will be if he does nothing to counteract the firm’s actions.

Then show how he, as an individual investor, can alter his personal portfolio to undo the

effect of any change in the firm’s leverage, so that he attains the same cash flows he would

have received without the leverage change.

Answer:If Stanley chooses not to alter his portfolio, his share of Elco’s cash flow next

period will be

.2[˜(1 r)$60,000]

X

D

because he would own 20 percent ( 100/500) of the firm’s outstanding shares if half the

shares were repurchased.He would then have a riskier investment than he held previously,

which he may or may not prefer.

However, if Stanley sells 50 shares of his stock, using the proceeds to buy $5,000 in

bonds, he will once again own 10 percent ( 50/500) of the firm’s shares and will realize

a return equal to

.1[˜(1 r)$60,000] (1 r)$5,000.1X˜(1 r)$1,000

X

DDD

Example 14.2 illustrates how shareholders can undo the effect of a change in a

firm’s capital structure by making offsetting changes to their own portfolio. The share-

holder can achieve the same cash flow pattern and continue to control the same per-

cent of the firm’s shares. Thus, without transaction costs, the shareholder is indifferent

to changes in the firm’s capital structure.