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The Capital Structure

Some classic arguments

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Today’s plan

The capital structure without corporate taxes Valuing risky corporate bonds Capital structure with corporate taxes Two theories for the optimal capital structure

in the real world.

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Look at the both sides of a balance sheet

Asset Liabilities and equity

Market value of the asset

V

Market value of equityE

Market value of debt

D

V=E+D

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Capital structure

Capital structure refers to the mix of debt and equity of a firm.

Capital structure has two related questions: • Does the capital structure affect the value of a

firm? Or does the amount of debt a firm has affect its value?

• What is the optimal amount of debt a firm should have?

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Capital structure

Does the size of a pizza have nothing to do with how it is sliced?

Is the value of a firm also independent of how the firm mixes debt and equity?

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Does capital structure affect the firm value?

Equity DebtEquity

Equity

DebtDebt

Govt.Govt.

Slicing the pie doesn’t affect the total amount

available to debt holders and equity holders

Slicing the pie can affect the size of the slice

going to government

Slicing the pie can affect the size of the

wasted slice

wasted

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Capital structure without corporate taxes

If there is no corporate tax, we will have the following two famous results• M&M propositions 1 and 2

Pay attention to the condition for these propositions to be valid

Why do we consider such simple, unrealistic situations?

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MM’s proposition 1 (without tax)

Modigliani & Miller• If the investment opportunity is fixed, there

are no taxes, and capital markets function well, the market value of a company does not depend on its capital structure.

What is the intuition for this result? Can we use different ways to prove this?

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MM’s proposition 2 (without tax)

Modigliani & Miller• If the investment opportunity is fixed, there

are no taxes, and capital markets function well, 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 WACC is a constant.

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Example - River Cruises - All Equity Financed

17.5%12.5%7.5% shares on Return

1.751.25$.75shareper Earnings

175,000125,000$75,000Income Operating

BoomExpectedSlump

Economy theof State Outcome

million 1 $Shares of ValueMarket

$10shareper Price

100,000shares ofNumber

Data

M&M (Debt Policy Doesn’t Matter)

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Example

cont.

50% debt

25%15%5% shares on Return

2.501.50$.50shareper Earnings

125,00075,000$25,000earningsEquity

50,00050,000$50,000Interest

175,000125,000$75,000Income Operating

BoomExpectedSlump

Economy theof State Outcome

500,000 $debt of ueMarket val

500,000 $Shares of ValueMarket

$10shareper Price

50,000shares ofNumber

Data

M&M (Debt Policy Doesn’t Matter)

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r

DV

rD

rE

WACC

WACC without taxes in MM’s view

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Valuing risky debt

So far, we have learned how to value a risk-free debt. By risk-free debt, we mean that bond investors always get paid for what they are promised when they lend money to firms or governments.

In reality, corporate bonds are not risk-free. When firms borrow money from the bond holders, they may not have enough cash to pay the bond holders in the future.

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Valuing risky debt

To illustrate how to value a risky debt, we focus on a simple situation: • Firms have a zero-coupon bond.

More specific, suppose that a firm has issued $K million zero-coupon bonds maturing at time T. Let the market value of the firm asset at time T be V(T).

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Valuing risky corporate debts

Using the put-call parity, we have

Where P(K,T) is the value of a European put option with the strike price K and the maturity date T

Please try to derive this formula and understand this situation?

),( TKPKeDTr f

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Problem: On march 4, 1994, Chrysler was the eighth largest U.S. firm according to Fortune magazine. It issued 20-years zero-coupon debt with book value of $36.994 billion. The book value of the asset is $43.83 billion and the market value of equity is $21.0468 billions. The risk free rate was 8% and the volatility of the asset return is 30%.

• What is the market value of the debt?

• What is the interest rate charged on Chrysler’s debt?

Example

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Solution

The market value of the debt is $5.98 million

The interest rate charge on Chrysler’s debt is 9.11%.

The market value of the asset is $27.03 million

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Capital structure with taxes

If there is corporate tax, we also have two famous results:• M&M propositions 1 and 2

Remember that to make the two propositions valid, we still have to assume that the investment opportunity is fixed and the financial market functions very well.

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MM’s propositions withtax

MM’s proposition 1• firm value = value of all equity firm + PV (tax

shield)

• PV(tax shield)=TcD

MM’s proposition 2 • The weighted average cost of capital is decreasing

with the ratio of D/E, and the cost of equity is increasing with D/E.

• Can you prove and understand these results?

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WACC Graph

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Optimal Capital structure with tax

So according to M&M proposition 1 with tax, the optimal capital structure is that firms issue all the debt.

In the real world, very few firms issue all the debt to raise money

What is wrong with M&M propositions?

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Capital structure with financial distress cost

Costs of Financial Distress - Costs arising from bankruptcy or distorted business decisions before bankruptcy.

Market Value = Value if all Equity Financed

+ PV Tax Shield

- PV Costs of Financial Distress

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Optimal Capital structure

Trade-off Theory - Theory that capital structure is based on a trade-off between tax savings and distress costs of debt.

Pecking Order Theory - Theory stating that firms prefer to issue debt rather than equity if internal finance is insufficient.

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Financial Distress

Debt

Mar

ket V

alue

of

The

Fir

m

Value ofunlevered

firm

PV of interesttax shields

Costs offinancial distress

Value of levered firm

Optimal amount of debt

Maximum value of firm