IsFalse

Assume:

•	Company U is financed totally with equity and is worth $100 million.

•	An otherwise identical company L is financed with $40 million in equity plus $50million (market value) in riskless debt that offers a 10 percent interest rate.Thus,the bonds pay $55 million ($5 million in interest plus $50 million in principal) atthe end of the year.

•	If the economy is weak, cash flows for each company will be $80 million;if the economy is strong, cash flows for each company will be $200 million.

Show how a shrewd investor, able to purchase or short up to $10 million in any security,

would profit from this violation of the Modigliani-Miller Theorem.

Answer:The shrewd investor can profit by purchasing 10 percent of company L’s equity

($4 million) and 10 percent of its outstanding debt ($5 million) while selling short 10 percent

of the shares of company U.The investor would then realize an immediate cash inflow of

$1 million (.10 ($100 million $40 million $50 million).However, as the following table

shows, the investor would have no net obligations at the end of the year, so the initial $1

million inflow can be considered a risk-free profit.

Cash Flow to Investor (in $ millions) at

Beginning of YearEnd of Year

Weak EconomyStrong Economy

Short sale of U equity$10	($8.0)	($20.0)
Purchase of L equity(4)	2.5	14.5
Purchase of L debt(5)	5.5	5.5
Net cash inflow$1	$0.0	$0.0

The year-end equity figures for company L are, by definition, the total cash flows for com-

pany L less the principal and interest payments to debt holders.

Stating the Modigliani-MillerTheorem Explicitly.Example 14.1 illustrates how a

shrewd investor can realize arbitrage profits when the Modigliani-Miller Theorem is vio-

lated. Result 14.1 states explicitly the assumptions and the implications of this theorem.

Result 14.1

(The Modigliani-Miller Theorem.)Assume: (1) a firm’s total cash flows to its debt andequity holders are not affected by how it is financed, (2) there are no transaction costs, and(3) no arbitrage opportunities exist in the economy. Then the total market value of the firm,which is the same as the sum of the market values of the items on the right-hand side ofthe balance sheet (that is, its debt and equity), is not affected by how it is financed.

Assumptions of the Modigliani-Miller Theorem

Result 14.1 indicates that the capital structure irrelevance theorem holds only under

some restrictive assumptions. The Modigliani-Miller theorem is, however, important

because it provides a framework that allows managers to focus on those factors that

are important determinants of the optimal capital structure choice. Examining the

Grinblatt1023Titman: Financial	IV. Capital Structure	14. How Taxes Affect	© The McGraw1023Hill
Markets and Corporate		Financing Choices	Companies, 2002
Strategy, Second Edition

Chapter 14

How Taxes Affect Financing Choices

505

different assumptions of the theorem provides important insights into how the capital

structure decision affects firm values.

The Key Assumption.The first assumption of the Modigliani-Miller Theorem—that

the sum of all future cash flows distributed to the firm’s debt and equity investors is

unaffected by capital structure—is really the key, and it will be the focus of much of

the remainder of this text. In reality, capital structure can affect a firm’s cash flows for

a number of reasons. This chapter focuses on how capital structure can affect a firm’s

total cash flows by altering its tax liabilities.²

The Importance of Transaction Costs.The second assumption, no transaction costs,

was used throughout Parts II and III of the text. However, transaction costs play a spe-

cial role here that requires some additional discussion. In the absence of transaction

costs, the cash flows to investors from any new security that a firm issues can be tracked

by other securities that already exist in the market.³

This means that the issuing firm

is not really offering the investing public a pattern of returns that they could not oth-

erwise obtain. However, transaction costs limit the availability of return patterns that

can be obtained in the market and sometimes provide firms with an opportunity to

improve their value by issuing special securities that investors desire.

For example, in the early 1990s in Hong Kong, there was a strong demand for war-

rants because they provide investors with highly leveraged positions with limited down-

side risk. In the absence of transaction costs, warrants are not special securities because

they can be tracked with a dynamic strategy involving the underlying stock and the

risk-free asset (see Chapter 8). However, if transaction costs are high, tracking a war-

rant with a dynamic strategy may be impossible. As a result, Hong Kong firms were

able to take advantage of the demand for option-like payoffs by issuing warrants at

prices exceeding the theoretical Black/Scholes prices discussed in Chapter 8. For sim-

ilar reasons, a firm might be able, in some instances, to obtain relatively attractive

financing with a convertible bond.

The Absence of Arbitrage.The final Modigliani-Miller assumption, no arbitrage, is

made throughout the text. Analyzing any sort of decision that affects a corporation’s value

requires some framework for determining valuation. The Modigliani-Miller Theorem

isconsistent with all pricing models that satisfy the most basic assumption in asset

pricing: Equilibrium prices cannot provide opportunities for riskless arbitrage profits.