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.
FIN 819
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.
FIN 819
Look at the both sides of a
balance sheet
Asset
Liabilities and equity
Market value of equity
E
Market value of the asset
V
Market value of debt
D
V=E+D
Financial management: lecture 10
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.
FIN 819
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
FIN 819
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?
FIN 819
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
FIN 819
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 .
FIN 819
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?
FIN 819
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.
FIN 819
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.
FIN 819
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.
FIN 819
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.
FIN 819
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
FIN 819
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.
FIN 819
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
FIN 819
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.
FIN 819
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

FIN 819
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.
FIN 819
WACC without taxes in MM’s view
r
rE
WACC
rD
D
V
Financial management: lecture 10
M&M (Debt Policy Doesn’t Matter)
Example - River Cruises - All Equity Financed
Data
Number of shares
100,000
Price per share
$10
Market Value of Shares
$ 1 million
Outcome
State of the Economy
Slump
Expected
Boom
Operating Income
$75,000 125,000
175,000
Earnings per share
$.75
1.25
1.75
Return on shares
7.5%
12.5%
17.5%
FIN 819
M&M (Debt Policy Doesn’t Matter)
Example
cont. 50% debt
Data
Number of shares
50,000
Price per share
$10
Market Value of Shares
$ 500,000
Market val ue of debt
$ 500,000
Outcome
State of the Economy
Slump
Expected
Boom
Operating Income
$75,000 125,000
175,000
Interest
$50,000 50,000
50,000
Equity earnings
$25,000 75,000
125,000
Earnings per share
$.50
2.50
1.50
Capital structure and Corporate
Taxes

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.
Financial management: lecture 10
River Cruise’s “Value Pie”
FIN 819
Valuing risky debt


So far, we have learned how to value a riskfree 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.
FIN 819
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).
FIN 819
Valuing risky corporate debts

Using the put-call parity, we have
D  Ke


r f T
 P( K , T )
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?
FIN 819
Example

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?
FIN 819
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
FIN 819
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.
FIN 819
WACC Graph
Financial management: lecture 10
An example on Tax shield
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?
Financial management: lecture 10
C.S. & Corporate Taxes
All Equity
EBIT
Interest Pmt
1/2 Debt
1,000
0
Pretax Income
1,000
Taxes @ 40%
400
Net Cash Flow
$600
Financial management: lecture 10
C.S. & Corporate Taxes
All Equity
1/2 Debt
1,000
1,000
0
100
Pretax Income
1,000
900
Taxes @ 40%
400
360
$600
$540
EBIT
Interest Pmt
Net Cash Flow
Financial management: lecture 10
Capital Structure and Corporate
Taxes
All Equity
1/2 Debt
1,000
1,000
0
100
Pretax Income
1,000
900
Taxes @ 40%
400
360
Net Cash Flow
$600
$540
EBIT
Interest Pmt
Total Cash Flow
All Equity = 600
*1/2 Debt = 640
(540 + 100)
Financial management: lecture 10
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
Financial management: lecture 10
Average Book Debt Ratios
Industry
Internet information
Biotech
Communications equipment
Semiconductors
Oil exploration
Aerospace defense
Beverages (alcohol)
Consumer appiances
Hotels and motels
Gas utilities
Airlines
Debt Ratio
0.07
0.12
0.19
0.21
0.29
0.32
0.36
0.40
0.53
0.53
0.73
FIN 819
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?
FIN 819
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
FIN 819
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.
FIN 819
Financial Distress
Market Value of The Firm
Maximum value of firm
Costs of
financial distress
PV of interest
tax shields
Value of levered firm
Value of
unlevered
firm
Optimal amount
of debt
Debt
FIN 819