Corporate nance
BY JONATHAN B. BERK AND PETER DEMARZO
14. Capital structure in a perfect market
14.1 EQUITY VS. DEBT FINANCING
The relative proportions of debt, equity and other securities that a rm has outstanding constitute
its capital structure. Suppose an entrepreneur invests 800 and can either generate a cash ow of
1400 or 900, depending on whether the economy is strong or weak, both have a 50% change.
Investors depend a risk premium, since the economy obtains a market risk. The risk-free interest
rate is 5% and the market risk of the investment is at 10%. The risk free interest rate of 5 plus the
risk premium of 10 combined results in the cost of capital for the project of 15%. The expected
cash ow in the year is ½*1400 + ½*900 = 1150
NPV of the investment opportunity: -800 + 1150/1.15 = -800 + 1000 = 200
There is a positive NPV, the entrepreneur will proceed with the investment. 200 is the value to the
rm, created by the project.
If there is no arbitrage, the price of a security equals the present value of its cash ows.
Market value of the rm’s equity: PV(equity cash ows) = .15 = 1000
Equity in a rm with no debt is called unlevered equity. The cash ows on t=0 are equal to those
of the project. Shareholders’ returns are either 40% or -10%. The changes of a weak and strong
economy are still 50-50, so the expected return on the unlevered equity is ½*40% + ½*-10% =
15%. The risk of unlevered equity equals the risk of the project, both are 15%. Shareholders are
earning an appropriate return for the risk the are taking.
The entrepreneur can also partially nance the investment using debt. The entrepreneur borrows
500. Since the cash ows of both 900 and 1400 will always be su cient to pay back the loan, the
debt is risk free. The rm can borrow at a risk-free interest rate of 5%, and it will owe the debt
holders 500 * 1.05 = 525 in one year. Equity in a rm that also has debt outstanding is called
levered equity. Payments to debt holders have a priority over equity holders. Given the economy
is strong, with the debt payment, the equity holders will receive 1400-525 = 875, and is the
economy is weak, they will receive 900 - 525 = 375.
Modigliani and Miller argued that with perfect capital markets, the total value of a rm should not
depend on its capital structure. The reasoning behind this is that the rm’s total cash ows still
equal the cash ows of the project, and therefore have the same present value of 1000. Because
the cash ows of debt and equity sum to the cash ows of the project, by the Law of One Price
the combined values of debt and equity must be equal to the same present value of 1000. If the
value of debt is 500, the value of the levered equity must be E = 1000 - 500 = 500.
The cash ows of levered equity are smaller than those of unlevered equity, but that does not
mean that the entrepreneur is o worse. He will still raise a total of 1000 and therefore will be
indi erent between the choices for the rm’s capital structure.
We can evaluate the relationship between risk and return more formally by computing the
sensitivity of each security’s return to the systematic risk of the economy. Because the debt’s
return bears no systematic risk, its risk premium is zero. In our case however, levered equity has
twice the systematic risk of unlevered equity. As a result, levered equity holders will receive twice
the risk premium.
To summarise: If the rm consist of 100% equity, the equity holders will require a 15% expected
return. If the rm consists of 50% debt and 50% equity, the debt holders will receive a lower
return of 5%, wile the levered equity holders will receive a higher expected return of 25%,
because of the increased risk. Considering both sources of capital together, the rm’s average
cost of capital with leverage is ½*5% + ½*25% = 15%, which is the same as for the unlevered
rm.
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, 14.2 MODIGLIANI-MILLER I: LEVERAGE, ARBITRAGE, AND FIRM VALUE
Leverage does not a ect the total value of the rm. Instead, it merely changes the allocation of
cash ows between debt and equity, without altering the total cash ows of the rm. Modigliani
and Miller (from now on MM), showed that this result holds more generally onder a set of
conditions referred to as perfect capital markets:
- Investors and rm can trade the same set of securities at competitive market prices equal to
the present value of their future cash ows
- There a no taxes, transaction costs, or issuance costs associated with security trading
- A rm’s nancing decisions do not change the cash ows generated by its investments, not do
they reveal new information about them.
MM proposition I: In a perfect capital market, the total value of a rm’s securities is equal to the
market value of the total cash ows, generated by its assets and is not a ected by its choice of
capital structure.
In the absence of taxes or other transactional costs, the total cash ows paid out to all of the
rm’s security holders is equal to the total cash ow generated by the rm’s assets. By the Law of
One Price , the rm’s securities and its assets must have the same total market value. If securities
are fairly prices, then buying or selling securities has an NPV of zero, and therefore should not
change the value of a rm. There is no net gain or loss from using leverage, and the value of the
rm is determined by the present value of the cash ows from its current and future investments.
When investors use leverage in their own portfolios to adjust the leverage choice made by the
rm, we say that they are using homemade leverage. This can be the case when an investors
would prefer an alternative capital structure to the one the rm has chosen. As long as investors
can borrow at the same interest rate as the rm, homemade leverage is a perfect substitute for
the use of leverage by the rm.
One application of MM I is the market value balance sheet of the rm. A market value balace
sheet is similar to an accounting balance sheet, with two important distinctions. First, all assets
and liabilities of the rm are included, so even intangible assets as reputation. Second, all values
are current market values rather than historical costs. The market value balance sheet captures
the idea that value is created b y a rm’s choice of assets and investments . By choosing projects
with a positive NPV, a rm van increase its value. The value of the rm cannot be altered by the
choice of capital structure. Market value of equity = Market value of assets - Market value of debt
and other liabilities
When a rm repurchases a signi cant percentage of its outstanding shares, the transaction is
called a leveraged recapitalisation. We will look at an example where an all equity rm with 50
million outstanding share, which are trading for 4 dollar per share, borrows 80 million, used to
repurchase 20 million of its outstanding shares. After borrowing, the liability of the rm grows by
80 million, which is also equal to the amount of cash the rm has raised. The assets and liabilities
increase by the same amount, so the market value of the equity remains the same. There is no
change is the value per share.
14.3 MODIGLIANI-MILLER II: LEVERAGE, RISK, AND THE COST OF CAPITAL
We can use Modigliani and Miller’s rst proposition to derive an explicit relationship between
leverage and the equity cost of capital.
MM I: E + D = U = A E = Market value of equity
D = Market value of debt
U = Market value of equity if the rm is unlevered
A = Market value of the rms assets.
The total market value of the rm’s securities is equal to the market value of its assets, whether
the rm is unlevered or levered. The return of the portfolio of a rm’s equity and debt is equal to
the weighted average of the returns of the securities in it, this equality implies the following
relationship between the returns of levered equity (RE), debt (RD), and unlevered equity (RU):
This is also the unlevered cost of capital (Preta WACC)
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, We can rewrite the above formula into a function of RE:
This is the formula of the cost of capital of levered equity.
This equation reveals the e ect of leverage on the return of the levered equity. When the rm does
well, RU > RD and when the rm does poorly RU < RD.
MM proposition II: The cost of capital of levered equity increases with the rm’s market value
debt-equity ratio.
We measure the rm’s leverage in terms of its debt-to-value ratio, D/ (E+D), which is the fraction
of the rm’s total value that corresponds to debt. With no debt, the WACC is equal to the
unlevered equity costs of capital. With 100% debt, the debt would be as risky as the assets
themselves. Although debt has a lower cost of capital than equity, according to MM I, leverage
does not lower a rm’s WACC. As a result, the value of the rm’s free cash ow evaluated using
the WACC does not change, and so the enterprise value of the rm does not depend on its
nancing choices.
Till so far we calculated the rm’s unlevered cost of capital and WACC assuming that the rm only
has equity or debt, but a capital structure can be more complex. Then RU and RWACC are
calculated by computing the weighted average cost of capital of all of the rm’s securities.
A rm’s unloved or asset beta is the weighted average of its equity and debt beta:
When a rm changes its capital structure without changing its investments, its unlevered beta will
remain unaltered. However, its equity beta will change to re ect the e ect of the capital structure
change on its risk. ßE can be formulated as:
14.4 CAPITAL STRUCTURE FALLACIES
Leverage can increase a rm’s expected earnings per share. An argument sometimes made is that
by doing so, leverage should also increase the rm’s stock price. Consider an all equity rm who’s
expects to generate an EBIT of 10 million. The rm has 10 million outspend shares of 7.5 dollar
per share. The rm considers changing its capital structure by borrowing 15 million at an interest
rate of 8% and using the proceeds to repurchase 2 million shares, for $7.5 each.
Without debt, the rm pays no interest and so the earnings would be equal to the rm’s EBIT. The
earnings per share EPS = Earnings / number of shares. In our example, the EPS would be 10
million / 10 million = $1.
With debt, the rm pays 15 million * 8% interest rate = 1.2 million per year. The expected earnings
now consist of the EBIT - interest. = 10 million - 1.2 million = 8.8 million. The EPS = 8.8 million / 8
million = $1.1. The number of outstanding shares has fallen from 10 million to 8 million, because
of the share repurchase.
Comparing the options with and without debt, we see an increase in expected earnings per share
with leverage. It might appears as if shareholders are better o with leverage, but keep in mind the
MM I that states that as long as the securities are fairly prices, these nancial transactions have
an NPV of zero and o er no bene t to shareholders.
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, Another fallacy is that issuing equity will dilute existing shareholders’ ownership, so dept nancing
should be used instead. By dilution, the proponents of this facially mean that if the rm issues
new share, the cash ows generated by the rm must be divided among a larger number of
shares, thereby reducing the value of each individual share. The problem with this line of
reasoning is that it ignores the fact that the cash raised by issuing new share will increase the
rm’s assets. Because the expansion decision has already been announced, in perfect capital
markets this value incorporates the NPV associated with the expansion.
14.5 MM: BEYOND THE PROPOSITION
Modigliani and Miller’s work formalised a new way of thing about nancial markets that was rst
put forth by John Burr Williams in 1938, in his book the theory of investment value. Williams
argues that if the investment value of an enterprise is the present worth of all its future
distributions to security holders, whether on interest or dividend account, then this value is no
wise depends on that the company’s capitalisation is. The results in this chapter can be
interpreted more broadly as the conservation of value principle for nancial markets: With
perfect capital markets, nancial transactions neither add nor destroy value, but instead represent
a repackaging of risk (and therefore return).
15. Debt and Taxes
15.1 THE INTEREST TAX DEDUCTION
Interest expenses reduce the amount of corporate tax rms must pay. This creates an incentive
for rm’s to use debt. Imagine a company with an EBIT of 2.8 billion, interest expense of 400
million and the corporate tax rate of 35%.
The net income is lower with leverage than it would be without leverage. However, if we look at
the total available to all investors, we see it is bene cial foor investors to use leverage.
There is a di erence between 1960 and 1820 of 140. The interest expenses to the rm are 400,
with a tax percentage of 35%. 35% of 400 is 140. The gain to investors from the tax deductibility
of interest payments is referred to as the interest tax shield. The interest tax shield is the
additional amount that a rm would have paid in taxes if it did not have leverage.
Interest tax shield = Corporate tax rate * interest payments
15.2 VALUING THE INTEREST TAX SHIELD
When a rm uses debt, the interest tax shield provides a corporate tax bene t each year. To
determine the bene t of leverage for the value of the rm, we must compute the present value of
the stream of future interest tax shields the rm will receive. Each year a rm makes interest
payments, the cash ows it pays to investors will be higher than they would be without leverage
by the amount of interest tax shield.
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