fin 819 capital structure some classic results and arguments

FIN 819

Capital Structure

Some classic results and arguments

FIN 819

Today’s plan Review of the key ideas in option pricing Investment Decision vs. Financing Decision Advantages and shortcomings of debt Optimal capital structure

• The capital structure without corporate taxes• Capital structure with corporate taxes

Two theories for the optimal capital structure in the real financial world.

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Key ideas in option pricing There are two important ideas in option pricing

• No arbitrage argument• Replicating portfolios

These two ideas have a lot of applications.• Get the PV of a piece of uncertain cash flow in the future• Used to show or derive a lot of important results in modern

finance (two famous examples)• Black-Sholes formula• Capital structure irrelevancy in the case of no corporate tax

• The no arbitrage condition is a much weaker condition than the equilibrium one, and thus has been widely applied in finance.

Financial management: lecture 10

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

The choice of financing

As shown in the previous slide, there are two ways for a firm to raise capital or money.

The first is debt. The debt makes fixed payments in the future . If firms fail to make promised payments, firms will go bankrupt.

The other is equity. With equity, share holders get residual cash flows after the payment to debt holders.

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Capital structure

Capital structure• Capital structure refers to the mix of debt and

equity of a firm. Measure of capital structure

• Ratio of D/E

• Ratio of D/V, V= E+D, the firm’s value or asset value

Capital structure (continues)

The question we will examine in capital structure is to examine what is the optimal amount of debt a firm should have to maximize a firm’s value?

Or what is the optimal mix of Debt (D) and Equity or the ratio of D/E or D/V?

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How much debt? To understand how much debt is optimal, we have to

understand the benefits and cost of issuing debt. Benefits of debt

• Tax shield

• management discipline

• a strong signal to investors Costs of debt

• Bankruptcy costs

• Agency costs

• Loss of future flexibility

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Tax Benefits of Debt When firms borrow money, interest payments are deductible from the

income to calculate pro-tax income. This will reduce firms’ tax payment. When firms use equity, firms are not allowed to deduct payments such as dividends to calculate taxable income. This will not help reduce firms’ tax payment.

The tax reduction for each interest payment in any period is:• Tax reduction = Interest payment * Tax rate

Observation 1: The higher the tax rate, the more debt a firm will tend to have .

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The benefit of debt

Consider the debt ratios for the following two companies: A real estate company, which pays the corporate tax rate, and a real estate investment trust, which doesn’t pay tax, but is required to pay 95% of its earnings as dividends to its stockholders.

Which company tends to have a higher debt ratio?

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Discipline to management When firms have no debt and produce a lot of cash flows,

financial managers in these firms may become too confident. This tends to result in inefficiency and investment in NPV negative projects. But financial managers are not held responsible for these bad investment decisions.

The debt a firm has may help reduce financial managers’ “over-confidence.” When a firm has debt, the managers have to ensure that they work hard to produce enough cash flows to make interest or principal payment. In addition, they have to invest in projects that will earn at least enough return to cover the interest expenses. The cost of not doing so is bankruptcy and the possibility of losing the job.

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The benefit of debt Based on the above discussion, Which company will benefit most

from issuing more debt? A company with very little debt and privately owned business A publicly traded company with very little debt and its stocks held by

millions of investors, none of whom hold a large percent of the stock. A publicly traded company with very little debt and an activist and

primarily institutional holding.

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May send a positive signal to investors

Investors understand that to reduce the possibility of default and thus the job loss, financial managers tend to issue less debt.

If financial managers issue a lot of debt to raise capital, this may mean that financial managers are confident about the financial health of the firm, a possible positive signal sent to investors. This is also a positive aspect of having more debt.

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Bankruptcy Cost The expected bankruptcy cost is determined by

• the probability of bankruptcy, which will depend on the risk of future

cash flows

• the cost of going bankrupt

– direct costs: Legal and other Costs

– indirect costs: Costs arising because people perceive you to

be in financial trouble Observation 2: Firms with more volatile earnings and cash flows will have

higher probabilities of bankruptcy at any given level of debt and for any given level of earnings.

Observation 3: Other things being equal, the greater the indirect bankruptcy cost, the less debt the firm can afford to use for any given level of debt.

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Debt & Bankruptcy Cost

Rank the following companies on the magnitude of bankruptcy costs from most to least, taking into account both explicit and implicit costs:

A Grocery Store

An Airplane Manufacturer

High Technology company

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Agency cost An agency cost arises whenever you hire someone else to do something for you. It arises

because your interests(as the principal) may deviate from those of the person you hired

(as the agent).

When you lend money to a business, you are allowing the stockholders to use that

money in the course of running that business. Stockholders interests are different from

your interests, because

• You (as creditor) are interested in getting your money back

• Stockholders are interested in maximizing their wealth

In some cases, the clash of interests can lead to stockholders

• Investing in riskier projects than you would want them to

• Paying themselves large dividends when you would rather have them keep the

cash in the business.

Observation 4: Other things being equal, the greater the agency problems associated with

lending to a firm, the less debt the firm can afford to use.

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Agency cost

Assume that you are a bank. Which of the following businesses would you perceive the greatest agency costs?

• A Large technology firm

• A Large Regulated Electric Utility

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Loss of future financing flexibility

When a firm borrows up to its capacity, it loses the flexibility of financing future projects with debt.

Observation 5: Other things remaining equal, the more uncertain a firm is about its future financing requirements and projects, the less debt the firm will use for financing current projects.

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What is the optimal debt?

We will consider the optimal structure or optimal amount of debt for a firm in two cases:

Case 1: no corporate tax and no bankruptcy cost Case 2: there is corporate tax but no bankruptcy cost

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Case 1: the optimal structure

In the case of no corporate tax and no bankruptcy cost, any amount of debt is optimal. ( irrelevancy result, MM proposition 1)

In addition, in this case, we have the following results. • The firm’s cost of capital and firm’s value is a constant.

• When a firm has more and more debt, the risk of stock and

the thus the cost of stock will increase.


r

DV

rD

rE

WACC

WACC without taxes in MM’s view

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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)

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)


The use of debt has a lot of implications:• Financial risk- The use of debt will increase the risk to

share holders and thus Increase the variability of shareholder returns.

• Interest tax shield- The savings resulting from deductibility of interest payments.

Capital structure and Corporate Taxes

River Cruise’s “Value Pie”

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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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Case 2: the optimal structure

In the case of having corporate tax but no bankruptcy cost, the optimal amount of debt is all debt, no equity. ( irrelevancy result)

In addition, in this case, we have the following results.• The value of a firm with debt is the value of the firm without

debt plus the present value of tax savings

• The cost of capital (WACC) is decreasing over the ratio of D/V or the amount of debt

• When a firm issue more and more debt, the cost of equity will arise.


WACC Graph


You own all the equity of Space Babies Diaper Co.. The company has no debt. The company’s annual cash flow is $1,000, before interest and taxes. The corporate tax rate is 40%. You have the option to exchange some of your equity position for 10% bonds with a face value of $1,000.

Should you do this and why?

An example on Tax shield


All Equity 1/2 Debt

EBIT 1,000

Interest Pmt 0

Pretax Income 1,000

Taxes @ 40% 400

Net Cash Flow $600

C.S. & Corporate Taxes


All Equity 1/2 Debt

EBIT 1,000 1,000

Interest Pmt 0 100

Pretax Income 1,000 900

Taxes @ 40% 400 360

Net Cash Flow $600 $540

C.S. & Corporate Taxes


Capital Structure and Corporate Taxes

All Equity 1/2 Debt

EBIT 1,000 1,000

Interest Pmt 0 100

Pretax Income 1,000 900

Taxes @ 40% 400 360

Net Cash Flow $600 $540

Total Cash Flow

All Equity = 600

*1/2 Debt = 640*1/2 Debt = 640

(540 + 100)


Capital Structure and tax shield

PV of Tax Shield =

D x rD x Tc

rD

= D x Tc

Example:

Tax benefit = 1000 x (.10) x (.40) = $40

PV of 40 perpetuity = 40 / .10 = $400

PV Tax Shield = D x Tc = 1000 x .4 = $400

Average Book Debt Ratios

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Industry Debt RatioInternet information 0.07 Biotech 0.12 Communications equipment 0.19 Semiconductors 0.21 Oil exploration 0.29 Aerospace defense 0.32 Beverages (alcohol) 0.36 Consumer appiances 0.40 Hotels and motels 0.53 Gas utilities 0.53 Airlines 0.73

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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

fin 819 capital structure some classic results and arguments

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