17
Does Debt Policy Matter?
INTR0DUCTION
This chapter describes the classic Modigliani and Miller (MM) propositions concerning the
capital structure of business firms under perfect market conditions. MM’s proposition I states
that the value of a firm is unaffected by the financing mix of debt and equity used by the firm.
Proposition II, which is the corollary of the first proposition, states that the required rate of return
on the equity increases with an increase in proportion to debt such that the weighted-average cost
of capital does not change. The implication of these two propositions is that the choice of debtequity mix or capital structure is irrelevant and has no effect on the value of the firm. Debt
policy does not matter and investment and financing decisions can be separated.
The chapter focuses on MM's arguments that debt policy does not matter, the conditions under
which their case is made, and the counter argument put forth by the traditional view that leverage
has some intrinsic advantage. MM views are clearly difficult to challenge, once the perfect
market conditions are accepted. Deviations from these conditions are considered in the
following chapter. The primary logic of the MM propositions are based on the view that the
firm’s value is based only on the stream of cash flows produced by its assets. The claims to this
cash flow can be packaged in different ways, but unless there are market imperfections, which
permit deviations from the perfect market conditions, arbitrage across these claims will ensure
that the value of the firm is unaffected by the capital structure changes.
In practice, capital structure matters because deviations from perfect market conditions are
present in the real world. These deviations are discussed in Chapter 18. The significance of the
MM propositions is not because they depict a realistic picture of the world, but a clear
understanding of the propositions enable you to understand why capital structure decisions are
important and why one capital structure may be better than another.
KEY CONCEPTS IN THE CHAPTER
Leverage and its Effects in Perfect Markets: Under perfect market conditions, financial
leverage can have no effect on the value of the firm. MM presents simple arguments to prove
this point. Imagine two firms [U (unlevered) and L (for unleveraged)] with identical operating
cash flows but with different capital structures. Owning one percent of firm U will be equivalent
in terms of claims to cash flows to owning one percent of both the debt and equity of firm, L.
Ownership of one percent of each firm gives claims to identical cash flows. Therefore, the
values of these claims should be identical. Hence, VU = VL. An alternate approach is to compare
ownership of one percent of the equity of the leveraged firm to ownership of one percent of the
unleveraged firm and finance it by borrowing an amount equal to one percent of the leveraged
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firm’s debt. Again, the claims are identical and it leads to the result - VU = VL. It follows that
under these conditions, debt policy is irrelevant. This is proposition I.
Proposition I is essentially a restatement of the value additvity principle (see chapter 7): PV
(A+B) = PV(A) + PV(B). Proposition I applies this in reverse. It can be called a law of
conservation of value. The value of an asset is based on the cash flows produced by the asset and
is not affected by the nature of claims against it.
MM’s arguments supporting proposition I assume that both firms and individuals can borrow at
the risk-free interest rate. This assumption is not crucial to the proposition. A fact, which might
appear to give corporate debt some advantage, is that corporate stockholders have limited
liability and thus can borrow with limited liability. Individuals cannot, on their own, have
limited liability. Thus, corporate debt might have some advantage over personal debt. However,
the advantage is unlikely to be of any significant value now since there are any number of
corporations that can and have issued limited liability debt. In other words, any demand for
limited liability debt would have been fully met by now.
Leverage and Returns: Proposition I leads to proposition II, which gives the relationship of
returns on the debt, equity, and the asset return. If proposition I is to hold, the asset return, rA is
unaffected by leverage. This means that when the firm borrows, the required rate of return
demanded by the shareholders increases as their risk increases. Proposition II states that the
expected return on equity increases in proportion to the debt-equity ratio, expressed in market
value. The rate of increase in return depends on the difference between the return on assets and
the return on debt. The relationship can be expressed as follows:
rA = [D/(D + E) X rD] + [E/(D + E) X rE].
Rearranging, rE is given by:
rE = rA + (D/E)(rA - rD)
The essential implication of proposition II is that the increased return given by the equity in a
leveraged firm reflects the increased risk. Therefore, the shareholders will demand a higher
required rate of return. Or, the higher expected rate of return for the equity is simply the
reflection of the higher risk involved and will be exactly matched by the higher required rate of
return by the stockholders. Thus, the higher return is not going to result in a higher value of the
stock.
Leverage and Beta: The effect of leverage on beta is similar to the effect on expected return.
The relationship can be stated as follows:
Beta of the firm's assets:
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A = [D/(D+E) X D] + [E/(D+E) X E]
Rearrange to obtain the beta of the equity of a leveraged firm.
E = A + D/E(A - D)
This is an alternative explanation of why equity investors require higher returns as debt increases.
Proposition II is consistent with CAPM.
The Traditional View: Prior to MM’s work, the traditional wisdom was that some leverage was
beneficial and by leveraging, a firm increased the return on equity. The traditional position used
the weighted-average cost of capital, which is the expected return on the portfolio of all the
company's securities. Weighted-average cost of capital is used to compute net present values of
project cash flows when the project being evaluated does not differ from the firm's business risk.
If leverage lowers the weighted-average cost of capital, then (assuming that the leverage does not
lower cash flows correspondingly) the value of the firm will increase.
rA = (D/V x rD) + (E/V x rE)
The traditional position held that increasing leverage resulted in lower weighted-average cost of
capital because an increase in the cost of equity, if at all, is not proportionate to the increase in
leverage. The traditional view, if correct, has the following implications:
-
Proposition II does not hold or the expected return on equity does not increase as a firm
borrows more.
-
The weighted-average cost of capital declines at first as the debt-equity ratio increases
and then rises.
-
There is an optimal D/E ratio that exists, that is, where the cost of capital is lowest.
A word of caution is in order. The firm should try to maximize the value of the firm. This is not
always equivalent to having the lowest cost of capital. The two goals will be equivalent only if
the operating income is not affected by the change in leverage.
Beware of the managers who make the simplistic argument that they can enhance the firm’s
value by lowering the cost of capital, by borrowing more as the cost of debt is lower than the cost
of equity. This argument ignores proposition II.
The traditional view made two arguments to support their claim. The first one essentially said
that the shareholders did not increase their required rate of return in proportion to the rise in
leverage. This argument implied some irrationality on the part of the shareholders. If some debt
is good, more debt must be even better, and the optimal leverage would be one hundred percent
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debt. The second argument used possible imperfections in the market and the advantage for
corporate debt over personal debt suggesting that individuals could not borrow at the same rate as
corporations. It is true that some individuals face higher borrowing cost on account of
transaction costs (lack of economies of scale). Such individuals might find it advantageous to
borrow through a corporation. However, any such demand for corporate debt must be fully
satisfied now. In other words, trying to make money by leveraging now is like trying to make
money selling automobiles or personal computers. You are late by a few decades.
Essentially, borrowing costs should be a function of the risk of the borrower or more specifically,
the use to which the borrowed money is put (or to be more exact, how the loan is backed or
secured). Most individuals can get mortgage loans or margin loans from their broker at very
competitive rates.
To sum up, the traditional view lacks support and it is not backed by valid arguments. One has
to look elsewhere for weaknesses in MM’s position. If you can find deviations from the perfect
market framework used by MM, you can find situations where their propositions will not hold.
Many of these deviations are created by government regulations. Chapter 18 focuses on the
practical implications of the market imperfections for corporate debt policy.
It is possible that there may be unsatisfied clienteles demanding specially designed securities
with unique features. If a firm can design and structure a package of securities that exploits these
needs, it can profit from it and you will find an exception to MM’s proposition I. Of course,
investment bankers are trying to do this all the time and it is very unlikely that there is any
unsatisfied demand for the garden-variety or plain vanilla debt security. The next several
chapters describe different type of securities invented by investment bankers and companies. It
is however, hard to see that a firm’s value can be increased greatly by these innovations in the
absence of some government created imperfection.
WORKED EXAMPLES
1. Grey Bird Corp. operates in perfect capital markets with no corporate or personal taxes. The
company has 25 percent debt and 75 percent equity in its capital structure. The expected
return on debt is 12 percent and the rate of return on equity is 16 percent. Calculate its
expected return on assets.
SOLUTION
rA 
ExpectedOperatingIncome
MarketValueofAllSecurities
= (proportion in debt X expected return on debt) + (proportion in equity X
expected return on equity)
= (weight of debt X cost of debt) + (weight of equity X cost of equity)
= WDrD + WErE
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I
= [D/(D + E) X rD] + [E/(D + E) X rE]
= (0.25 X 0.12) + (0.75 X 0.16)
= 0.03 + 0.12
= 0.15 = l5 percent
2. Tricky Dick Inc. has an operating income is $9,000, and the market value of all its all-equityfinanced securities is $50,000. If the company decides to sell $15,000 of debt and retire an
equal amount of equity, how will the rate of return for equity change? Assume that it
operates in perfect capital markets with no corporate or personal taxes, and that the expected
return on debt is 12 percent.
SOLUTION
The return on assets is give by:
rA = expected operating income/market value of all securities
= $9,000/$50,000
= 0.18 = 18 percent
In an all-equity-financed firm, the return on equity rE is equal to the return on assets; so
rE = rA = 18 percent
While borrowing changes the return on equity, it will not change the return on assets. This will
remain the same because the value of the firm does not change and the expected operating
income does not change. Therefore, the return on equity is:
rE = rA + (D/E)(rA - rD)
= 0.18 + ($15,000/$35,000)(0.18 - 0.12)
= 0.18 + 0.4286(0.06)
= 0.18 + 0.0257
= 0.2057 = 20.57 percent
3. Use the information given in problem 2 and assume that the beta of the firm is 1.2 before the
debt financing and the beta of the debt is 0.5. What is the beta of the equity with the debt
financing given in problem 2? What will the beta of the equity be if the debt-equity ratio
were 30, 50, 60, and 70 percent?
SOLUTION
The beta of the equity without any debt financing is the same as the beta of the firm because no
other securities are outstanding. After the financing, the beta of the equity changes as follows:
E = A + (D/E)(A - D)
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= 1.2 + 0.4286(1.2 - 0.5)
= 1.2 + 0.3 = 1.5
For the other debt proportions, E is given in the table below.
D/E (%)
30
50
60
70
E
1.41
1.55
1.62
1.69
4. If beta of equity with no debt is 1.2. Calculate the equity betas for different debt levels for
the following values of beta for debt: 0, 1.2 and 0.5. Compare these results with those of
problem 3.
SOLUTION
The values for E for different debt/equity ratios and different D are given in the table below.
D/E (%)
0
5
10
20
40
60
80
100
E for different value of D
D = 0
D = 1.2
D = 0.5
1.20
1.20
1.20
1.26
1.20
1.24
1.32
1.20
1.27
1.44
1.20
1.34
1.68
1.20
1.48
1.92
1.20
1.62
2.16
1.20
1.76
2.40
1.20
1.90
While the data above are somewhat contrived, several interesting results emerge. You can
clearly see that the increase in the risk or beta of the equity with increased debt levels is a
function of the beta or risk of the debt itself. First, when the beta of the debt is equal to the beta
of the firm, when it is all-equity-financed, for all practical purposes, the company has issued
another dose of equity and not debt. Consequently, the beta of the equity does not change. If the
company were able to issue debt at the zero-beta level, the risk-free rate, the betas of the equity
would tend to increase substantially with additional debt. In practice and in most cases, the beta
of corporate debt is greater than zero but less than the beta of the all-equity-financed firm.
5. Jane Black, the financial manager of Leverage Unlimited thinks she can increase shareholder
value by increasing the leverage of the company. The company is currently all equity
financed and is earning 20 percent. The company can borrow at 10 percent and the beta of
the debt is at 0.4. The beta of equity before borrowing is 1.2. There are 10,000 shares
outstanding and the price-earnings ratio of the common shares is 5 on an operating income of
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$25,000. The company can be expected to continue to generate that amount of operating
income after the debt financing. Ms. Black feels that the leverage will substantially raise the
value of the firm and wants to buy back half the shares of the company. Formulate a
response to Ms. Black assuming operation in perfect capital markets with no corporate or
personal taxes.
SOLUTION
First, estimate the value of the firm before the debt financing. The operating earnings are
capitalized at 20 percent, so the value of the firm when it is all-equity-financed is $125,000
($25,000/0.20). The value per share is $12.50; earnings per share are $2.50 ($25,000/10,000
shares); with the price-earnings ratio being 5.0 times ($12.50/$2.50).
Next, determine the earnings per share after the debt financing. The company must sell $62,500
of debt at the going market rate of 10 percent in order to repurchase an equivalent amount of
equity ($125,000/2). Remember, because the operating income remains unchanged, the firm's
total value remains unchanged at $125,000.
The equity earnings change, however, as follows:
Operating income
less interest
Equity earnings
$25,000
6,250
$18,750
With 5,000 shares now outstanding, earnings per share increase to $3.75 ($18,750/5000 shares).
Ms. Black assumes that she can still get the same price-earnings ratio of 5. Then, the shares have
a market price of $18.75 (5 x $3.75). But going into debt entails additional risk to the
shareholders. The beta will increase substantially. Using the formula:
E = A + D/E(A - D)
Before borrowing:
 = 1.2 + 0.0(1.2 - 0) = 1.2
After borrowing:
 = 1.2 + 1.0(1.2 - 0.4) = 1.2 + 0.8 = 2.0
Risk increases by two-thirds. With increased risk, the required rate of return on equity increases
too. Assuming that the return on asset stays same, we can calculate the required return as
follows:
rE = rA + (D/E)(rA - rD)
= 0.20 + 1.0(0.20 - 0.10)
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= 0.20 + 0.10
= 0.30 or 30 percent
The value of the shares will then be: $3.75/0.30 = $12.50
Thus, there is no change in the value of the stock and leverage does not increase the value of the
stock. Any increase in earnings is fully neutralized by the corresponding increase in risk and
required rate of return. The price-earnings ratio will go down and the market price of the shares
will remain the same.
SUMMARY
This chapter presents the well-known Modigliani-Miller propositions on debt policy under
perfect market conditions. Proposition I states that a firm’s value is unaffected by changes in
leverage. Proposition II states that the risk of equity increases in proportion to the debt-equity
ratio. This will cause an increase in the required rate of return demanded by investors.
Essentially, under perfect market conditions, debt policy is irrelevant and the firm’s value is not
affected by changes in leverage. The value of a firm depends only on the cash flows produced by
its assets. While financial leverage tends to magnify returns to common stockholders, their risk
is increased too. Therefore, they require higher returns on their shares; thus, the value of a share
remains unchanged.
Proposition I is very general and applies to all types of securities (short-term debt vs. long term
debt, equity vs. preferred stock, etc.) and one can say that no combination of securities is better
than any other. The MM propositions have replaced the traditional view that the cost of capital
will tend to decrease initially as debt is added to the capital structure but that it will increase only
after a market-determined intolerable-threshold level of risk is passed. At that point, the cost of
equity and the cost of debt increase significantly. The traditional view cannot be supported
unless one is willing to accept irrational behavior on the part of investors or the presence of
market imperfections.
MM’s propositions cannot be refuted once the perfect market conditions are accepted. Any
violation of MM's propositions can only be found in market imperfections. These market
imperfections are often created by government regulations (differential tax treatment of income
streams, for example) and can create profitable opportunities for firms. It is also possible that
there are clienteles for specific types of securities such as money market mutual funds and
floating-rate notes. However, the demands by clienteles are often quickly met by an adequate
supply of these securities and a firm getting into these markets now is unlikely to benefit.
LIST OF TERMS
Capital structure
Financial leverage
Gearing
Proposition II
Separation of investment and financing
Value additivity
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Law of conservation of value
Proposition I
Weighted-average cost of capital
EXERCISES
Fill-in Questions
1. _________ is another term used to describe financial leverage.
2. ________________ is the term used to describe the mix of debt and equity used by a firm.
3. __________________ states that the value of the firm is not changed by the mix of debt and
equity.
4. A firm that borrows is said to engage in ___________________.
5. The _____________________ states that the value of an asset is preserved regardless of the
nature of the claim on it.
6. The ___________________ is the sum of the returns on debt and equity each weighted by its
percentage in the capital structure.
7. __________________ states that the expected return on the common stock of a financially
leveraged firm increases in proportion to the debt ratio.
8. Proposition I of Modigliani and Miller permits ________________ decisions.
9. Proposition I is a restatement of the _______________ principle learned in Chapter 7.
Problems
1. JMH Corp. is operating in perfect market conditions with no corporate or personal taxes.
The company’s debt has an expected return of 11 percent and the return on equity is 16
percent. The debt to assets ratio is 40 percent. Calculate the return on assets.
2. Use the information given in problem 1. How will the return on equity change if the debt is
increased to 60 percent?
3. What is the expected return on assets for a firm that is 60 percent debt-financed and pays an
expected return on debt of 9 percent and has a required return on equity of 20 percent?
Assume the firm operates in perfect capital markets with no corporate or personal income
taxes.
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4. Your firm's expected operating income is $5,000, and the market value of its outstanding
securities is $25,000 when it is all-equity-financed. Assuming that the firm operates in
perfect capital markets with no corporate or personal taxes, calculate the required return on
equity when the firm sells enough debt to repurchase half of the outstanding equity for each
of the following rates of return on debt: (a) 8 percent, (b) 10 percent, and (c) 12 percent.
5. Using the data in problem 4 above, a beta for the firm of 1.4, and a beta for the debt of 0.5,
what is the beta of the equity after the financing?
6. The financial manager of Jumping Jack, Inc. estimates that she will increase the earnings per
share of her presently all-equity-financed firm if she borrows at the going market rate of 8
percent. She estimates the debt's beta to be 0.3 and the beta of the all-equity firm is 0.8. A
return of 12.5 percent is expected on the all-equity firm, the price-earnings ratio of 8 is
expected to persist, expected operating income is $300,000, and 100,000 shares are
outstanding. She plans to replace 40 percent of her equity with debt. How will the values of
the shares change?
Essay Questions
1. Explain the Modigliani and Miller's propositions I and II and their implications for financial
managers.
2. Discuss the following argument often heard in defense of leverage. “Cost of debt is definitely
less than the cost of equity. By using the cheaper source of funds, a firm can increase the
return available to its equity holders and thereby increase their value.”
3. "Modigliani and Miller propositions I and II have very little practical appeal as they assume
the so called perfect market conditions, which do not exist.” Give a detailed response to that
statement.
4. How may individual investors augment or undo the debt policy of firms in which they wish to
invest? Explain fully. Also explain why this concept is important to the Modigliani-Miller
position regarding debt policy.
5. Demonstrate how the beta of a firm is dependent on the beta of the capital structure
components.
ANSWERS TO EXERCISES
Fill-in Questions
1. Gearing
6. Weighted-average cost of capital
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2.
3.
4.
5.
Capital structure
Proposition I
Financial leverage
Law of conservation of value
7. Proposition II
8. Separation of financing and investment
9. Value additivity
Problems
1. (0.4 X 0.11) + (0.6 X 0.16) = 14 percent
2. rE = rA + D/E (rA - rD) = 0.14 + 1.5(0.14 – 0.11) = 18.5 percent
3. (0.6 X 0.09) + (0.4 X 0.2) = 13.4 percent
4. rA = $5,000/$25,000 = 20 percent. rE = rA + D/E(rA - rD).
a. When rD = 8 percent, rE = 0.20 + [(0.5/0.5)(0.20 - 0.08)] = 32
b. When rD =10 percent, rE = 30 percent
c. When rD =12 percent, rE = 28 percent.
5. E = A + D/E(A - D) = 1.5 + 1.0(1.5 - 0.6) = 2.40
6. The analysis is the same as that for problem 5 of the Worked Examples.
First, calculate the value of the all-equity firm:
Value = $300,000/12.5 percent = $2,400,000
Value per share = $2,400,000/100,000 shares = $24
Earnings per share = $300,000/100,000 = $3
Then, compute the effect of debt financing on earnings per share:
Amount of required debt: 0.4($2,400,000) = $960,000
Operating income
less interest (0.08 X $960,000)
Equity earnings
= $300,000
= 76,800
= $223,200
Earnings per share: $223,200/60,000= $3.72
Now, calculate the beta of equity after debt financing:
Before-debt financing: 0.8; after:
E = A + D/E(A - D)
= 0.8 + 0.4/0.6(0.8 - 0.3)
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= 1.133
Now, we can calculate the return on equity, after debt financing:
rE = rA + (D/E)(rA - rD)
= 0.125 + (0.4/0.6)(0.125 - 0.08)
= 15.5 percent
Market price of equity after debt financing can be calculated as below:
Market price per share = $3.72/0.155 = $24
Value of equity = market price per share X number of shares
= $24 X 60,000 = $1,440,000
Value of firm after debt financing = Debt + Equity
= $960,000 + 1,440,000
= $2,400,000
The value of the firm is unaffected by the leverage.
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