Corporate Finance
BA (H) Sem 6
HRC - Neha Arya

Capital Structure
 A major choice facing a firm is the mix of different
securities (debt and equity) it should choose, to meet
its financing needs.
 This mix of different securities is known as the firm’s
Capital Structure.
 The choice of capital structure is mainly a marketing
problem for firms because it is subject to the
maximization of its overall market value.

Leverage
 The firm’s problem is to find that combination of
securities which maximizes its market value.
 Before dealing with this marketing problem though,
we need to ensure that a policy which maximizes firm
value also maximizes the shareholders’ wealth.
 Let D and E denote the market values of the
outstanding debt and equity of the Wapshot Mining
Company.

 Each of Wapshot’s 1,000 shares sells for $50
 Thus:
E = 1,000 * 50 = $50,000
 Wapshot has also borrowed $25,000, and so V, the
aggregate market value of all its outstanding securities,
is
 V = D + E = $75,000

 Wapshot’s stock is known as levered equity.
 Q. How does this financial leverage (or gearing) affect
Wapshot’s shareholders?
 A. Say Wapshot “levers up” more by borrowing $10,000
more and paying the proceeds to shareholders as a
special dividend of $10 per share.

 This results in substitution of debt for equity leaving
Wapshot’s assets unchanged.
 If V is unchanged at $75,000 then
 E = V – D = 75000 – 35000 = $40,000
 This implies that the stockholders have suffered a
capital loss (= $50000-40000) which exactly offsets the
$10,000 special dividend.

 But if V increases to $80000 due to change in the
capital structure, then
 E = $45000 and stockholders gain $5000 in all
 So in general, increase or decrease in V caused by
change in capital structure accrues to the firm’s
stockholders.
 Conclusion: A policy that maximizes market value of
the firm is also best for its shareholders

 The assumptions that support this conclusion are:
 1. Wapshot can ignore dividend policy
 2. The old and the new debt is worth $35000 after the
change in capital structure.

Modigliani and Miller
 If indeed the firm’s aims to find the combination of
securities that maximizes its value, how can this be
achieved?
 MM give an answer by saying that in perfect capital
markets, any combination of securities is as good as
another.
 Hence, choice of capital structure has no effect on
the firm’s value.
 MM’s Proposition I states: “The market value of
any firm is independent of its capital structure.”

 Example:
 Consider 2 firms that differ only in their capital structure.
 Firm U is unlevered. Hence, total value of its equity EU is
the same as the total value of the firm.
 Firm, L, on the other hand, is levered. The value of its stock
is, therefore, equal to value of the firm less the value of the
debt:
 EL = VL – DL
 Strategy 1:
 Say, you don’t want to take much risk, so you buy common
stock in the unlevered firm U. If you buy 1% of firm U’s
shares, your investment = 0.01 VU and you are entitled to
1% of the gross profits.

 Strategy 2:
 Say, you wanted to buy same fraction of both the debt
and equity of firm L. So, investment in Debt = .01DL
and in Equity = .01 EL
 Total investment = 0.01 (DL + EL) = .01 VL
 Payoff again is 1% of the firm’s profits.
 In perfect markets, both these strategies giving same
payoffs must have same cost.

 Hence .01VU must = .01VL meaning that Value of
Unlevered firm must equal value of levered firm.
 Strategy 3:
 You want to take a bit more risk and buy 1% of the
levered firm’s shares.
 You invest .01EL = .01 (VL-DL) and expect return = .01
(Profits-Interests)

 However, an alternative strategy would be to borrow
.01DL on your own account and buy 1% of the stock of
the unlevered firm.
 Your investment = .01 (VU-DL) and expected return =
.01(Profits – Interests)
 Since, both these strategies offer same payoff again
they must have same cost. So, it must be that .01 (VU-
DL) = .01 (VL-DL)
 So, VU must = VL

 This example shows that if investors can borrow or
lend on their own account and on terms same as the
firm, they can “undo” the effect of any changes in the
firm’s capital structure.
 This is the basis for MM’s first proposition, stated
earlier. (see the example from the text)

Law of conservation of value
 In the context of our discussion on the capital
structure of firms, the law of conservation of value
implies that we can split a cash flow into as many parts
as we like, the values of the parts will always sum back
to the value of the original cash flow stream.
 Thus, the value of an asset is preserved regardless of
the nature of the claims against it.

 Applying the law to the choice between issuing
preferred stock, common stock or a combination of
both, we can say that the choice is irrelevant.
 It is contingent on the condition of perfect capital
markets, and that the choice does not affect the firm’s
investment, borrowing and operating policies.

 Similarly, applying the law to a mix of debt securities
issued by the firm (i.e long-term vs short-term,
secured vs unsecured, senior vs subordinated and
convertible vs nonconvertible), none of the choices
should affect the overall value of the firm. Of course,
the assumption is that both firms and individuals can
borrow/lend at the same risk-free rate.

How leverage affects returns
 Implications of proposition I for expected returns of a
firm’s stock:
 The expected return on Macbeth’s assets rA (in the
example given in the text) is equal to the expected
operating income divided by the total market value of
the firm’s securities:
 Expected return on assets = rA = (expected operating
income/market value of all securities)

 In perfect capital markets the company’s borrowing
decision does not affect either its operating income or
the total market value of its securities.
 Hence, its borrowing decision also does not affect the
expected return on the firm’s assets.

 Expected return on a portfolio consisting of all the
firm’s securities is
 Expected return on assets = (proportion in
debt*expected return on debt) +
(proportion in equity*expected return on equity)
 rA = {D/(D+E) * rD} + { E/(D+E) * rE}

 Rearranging terms, we get an expression for the
expected return on equity of a levered firm:
 Expected return on equity = expected return on assets
+ [debt-equity ratio *{expected return on assets –
expected return on debt}]
 rE = rA + D/E (rA – rD)

 MM’s Proposition II:
 States that the expected rate of return on the common
stock of a levered firm increases in proportion to the
debt-equity ratio (D/E), expressed in market values.
 The rate of increase depends on the spread between rA
(expected rate of return on a portfolio of all the firm’s
securities) and rD (expected return on debt)

 Continuing the Macbeth Spot Removers e.g
 Before the firm’s decision to borrow, rE = rA
 rE = rA = expected operating income/ market value of
all securities
rE = 1500/ 10000 = .15 = 15%
 If the firm decides to borrow, rA is still 15% and rE = rA
+ D/E (rA – rD)
= .15 + (5000/5000)*(.15 - .10)= .20 = 20%

 For implications of MM’s proposition II refer to the
figure in your texts (or the link of presentation shared)
 The figure assumes that the firm’s bonds are
essentially risk-free at low debt levels.
 Thus rD is independent of D/E, and rE increases
linearly as D/E increases. As the firm borrows more,
the risk of default increases and the firm is required to
pay higher rates of interest.
 Proposition II predicts that when this occurs the rate
of increase in rE slows down. The more debt the firm
has, the less sensitive is to further borrowing.

The Risk-Return Trade-off:
 Proposition I says that financial leverage has no effect
on shareholders’ wealth.
 Proposition II says that the rate of return they can
expect to receive on their shares increases as the firm’s
debt–equity ratio increases.
 Despite the 2nd proposition, shareholders are
indifferent to increased leverage.

 This is so because, any increase in expected return is
exactly offset by an increase in risk and therefore in
shareholders’ required rate of return.
 *refer to the example in the text*
 As you know, the beta of the firm’s assets equals the
weighted average of the betas of the individual
securities.

 Beta of assets = (proportion of debt*beta of debt) +
(proportion of equity*beta of equity)
 Rearranging,
 Beta of equity = beta of assets + debt/equity ratio *
(beta of assets – beta of debt)
 Clearly this shows that investors require higher returns
on levered equity to match the increased risk.

The traditional position
 In response to MM, a traditional position has emerged.
It requires a discussion on Weighted Average Cost of
Capital (WACC), i.e the expected return on a portfolio
of all the company’s securities.
 WACC = rA = [ D/V * rD ] + [ E/V * rE ]
 The WACC is used in capital budgeting decisions to
find the NPV of projects that would keep business risk
of firms unchanged.

 If MM’s proposition I holds, then firm’s objective to
“maximize overall market value” is equivalent to
“minimize the wacc”.
 If MM’s proposition I doesn’t hold, then the capital
structure that maximizes the value of the firm also
minimizes the weighted-average cost of capital,
provided that operating income is independent of
capital structure.

Two Warnings
Warning 1:
 Shareholders want management to increase the firm’s value.
They are more interested in being rich than in owning a firm
with a low weighted-average cost of capital.
Warning 2:
 Trying to minimize the WACC seems to encourage logical short
circuits like the following. Suppose that someone says,
“Shareholders demand—and deserve—higher expected rates of
return than bondholders do. Hence, debt is the cheaper capital
source. We can reduce the WACC by borrowing more.”
 But this doesn’t follow if the extra borrowing leads stockholders
to demand a still higher expected rate of return.
 According to MM’s proposition II the cost of equity capital
increases by just enough to keep the WACC constant.