Chapter 17 – Corporate Capital Structure – Foundations (Sections 17.1 and 17.2. Skim section 17.3.)
The primary focus of the next two chapters will be to examine the debt/equity choice by firms. In particular, we will
discuss possible advantages and disadvantages to debt versus equity financing. In Chapter 17, we will:
1) Learn the perfect capital market assumptions (needed to demonstrate capital structure irrelevance).
2) Learn the arbitrage proof for capital structure irrelevance.
3) Learn how investors can manipulate capital structure of any firm to suit their own tastes.
4) Review the effect of leverage changes on the return on equity, return on debt, return on assets, and WACC (Chapter 9
stuff).
The purpose of the discussion of this chapter is to lay the foundations for a higher level (real world) discussion in
Chapter 18.
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Capital Structure Analysis in a Nutshell
•
If the firm is all equity, the firm's stockholders are the owners of 100% of the firm's cash flows. Cash flows can be:
Paid to stockholders as a dividend (or stock repurchase), or
Reinvested by the corporation in projects, or
Put in a bank checking account or invested in securities
•
If there is debt and equity (and perhaps other types of securities such as preferred stock, convertible debt, etc.) on
the right-hand-side of its balance sheet, then the firm's cash flows must be split among the various claimants.
•
Capital structure analysis attempts to find the particular combination of debt and equity (and other types of
securities) that maximizes firm value (and stockholder value).
•
Based on a certain set of assumptions discussed below, a firm's capital structure decision is irrelevant. In other
words, a firm cannot increase or decrease its value by making changes to the right-hand-side of its balance sheet.
•
Starting with the foundation of capital structure irrelevance, Chapter 18 will incorporate ‘real world’ assumptions
and examine the effects of these ‘real world’ assumptions on the firm's capital structure decision.
Chapter 17 "Perfect Capital Market" Assumptions:
1.
No income taxes. (Therefore, no income tax deduction for interest payments.)
2.
No bankruptcy costs. (No attorney/accountant/trustee fees or other costs from going bankrupt.)
3.
No transaction costs. (The is no cost to the corporation for issuing and repurchasing securities. Investors can also
buy and sell securities for free.)
4.
Unlimited borrowing and lending at the risk-free interest rate for corporations and investors.
5.
No asymmetric information. (Outside investors know as much as corporate insiders.)
6.
Managers and firm employees work to maximize stockholder wealth. Also, managers and employees of the firm are
not affected by the amount of debt versus equity in a firm. (For instance, managers and employees do not let the
amount of leverage affect the criteria they use to select projects, how they manage the firm’s assets, etc.)
1
Modigliani and Miller (1958) Proposition 1: With the above assumptions, the value of the firm (in equilibrium) is
independent of the proportion of debt and equity in the firm's capital structure.
Stating the proposition in another way: If two firms (Firm A and Firm B) have identical assets, then with perfect capital
markets: DA + EA = DB + EB
If not identical, it is possible to earn a risk-free, zero cash investment, arbitrage profit. More specifically, if the
market values of these two firms are not identical, then it is possible to make a series of investments in the firm’s
securities that require no net cash outlay and have no risk, but pays the investor a positive cash flow.
Four examples of an arbitrage profit (all cash flows are risk free):
0
$0
$1
$0
$1
1
$1
$0
$1
$0
2
3
4
5
6
→
$1
$0
$1
$0
$1
$0
$1
$0
$1
$0
→
→
Earning money because you make a cash investment, or take on some risk, is consistent with market equilibrium.
However, in equilibrium, a risk-free investment that requires no cash outlay should not pay a positive cash flow
to the investor.
If the market is out of equilibrium (and arbitrage profits are available), then investors taking advantage of the
arbitrage opportunity would quickly force prices back into equilibrium (and eliminate the arbitrage opportunity).
A simple example of an (almost) risk-free, zero-cash investment, arbitrage profit.
Gold purchaser on 42nd Street in New York says that he will buy gold at $301 per ounce.
Gold seller on 43rd Street in New York says that she will sell gold at $300 per ounce
•
What can you do to earn a $1 profit per ounce of gold? Does this meet our definition of a risk-free, zero cash
investment, arbitrage profit?
Have you invested any cash (for even a short period of time)? Does this investment have any risk?
•
Since this doesn’t exactly meet our definition, what would you have to do to make a $1 risk-free, zero cash
investment, arbitrage profit?
•
Assuming you can structure your purchases and sales of gold to earn a risk-free, zero cash investment,
arbitrage profit, what should happen to the market price of gold on 42nd and 43rd streets?
In equilibrium, if an investment requires no cash outlay (for even a short period of time) and no risk, then you
should not expect to make money! If the market is out of equilibrium and an arbitrage profit opportunity existed, then
prices should quickly move back to equilibrium so that the arbitrage opportunity is eliminated.
Application of perfect capital markets and a ‘no arbitrage’ condition to corporate capital structure policy
An example
1.
Two identical firms, except one firm has perpetual debt (U is the unlevered firm and L is the levered firm).
2.
The required rate of return for Firm L’s perpetual debt = 5% (5% = rD = rf).
2
3.
The investment policy common to each firm generates a perpetual stream of the following yearly cash flows from
the firm’s assets
1/3 probability of a $30 cash flow (pessimistic outcome)
1/3 probability of a $45 cash flow (middle outcome)
1/3 probability of a $225 cash flow (optimistic outcome)
The expected cash flow is $100 per year (in perpetuity)
4.
Cash flows from assets are first used to pay interest to the owners of debt (if any). The residual is paid as a dividend
to stockholders.
Notation
DL is the market value of the debt (bonds) in the levered firm.
EL is the market value of the equity (stock) in the levered firm.
DL + EL = VL is the market value of the levered firm.
EU = VU = the market value of the stock in the unlevered firm (and the market value of the unlevered firm).
With the perfect capital market assumptions given above, the equilibrium pricing relationship is:
VU = EU = DL + EL = VL
What happens if this relationship doesn't hold exactly? (That is, what happens if (1) VU > VL or (2) VU < VL)
Case 1: VU > VL
VU = EU = $1000
EL = $300, DL = $600, VL = DL + EL = $900
Cash flow to owners of Firm U: All of the $100 expected cash flow is paid as a dividend to stockholders
Owners of Firm L: $100 expected cash flow split between stockholders and bondholders
Bondholders: rD x DL = 5% x $600 = $30 (risk free)
Stockholders: $100 - $30 = $70 (expected cash flow)
1/3 probability of ______.
1/3 probability of ______.
1/3 probability of ______.
How can you earn a risk-free, zero cash investment, arbitrage profit?
1. Buy (at time 0)
2. Sell (at time 0)
3. Collect and Deliver (at time 1, 2, 3, etc.)
Net cash flow from the three-step procedure (at time 0) =
Net cash flow from the three-step procedure (at time 1, 2, 3, etc.) =
3
Is any cash investment required? Is there any risk?
Investors taking advantage of this (risk-free, zero cash investment) arbitrage profit opportunity will cause:
•
•
The price of firm L's stock to increase.
The price of firm U's stock to decrease.
The price movement will continue until VU = VL.
Case 2: VU < VL
Same assumptions as Case 1 except EL = $500.
How can you earn a risk-free, zero cash investment, arbitrage profit?
1. Buy (at time 0)
2. Sell (at time 0)
3. Collect and Deliver (at time 1, 2, 3, etc.)
Net cash flow from the three-step procedure (at time 0) =
Net cash flow from the three-step procedure (at time 1, 2, 3, etc.) =
Investors taking advantage of this (risk-free, zero cash investment) arbitrage profit opportunity will cause:
•
•
The price of firm U's stock to increase
The price of firm L's stock to decrease
The price movement will continue until VU = VL.
In equilibrium, there should be no arbitrage profits available, so VU cannot be greater than VL and VU cannot be less
than VL. Therefore, VU must equal VL.
This means that with perfect capital markets, the equilibrium value of a firm is independent of its capital
structure. That is, the proportion of debt and equity on its balance sheet does not affect firm value. Therefore:
•
•
Financing a project with debt is equivalent to financing a project with equity
Capital structure changes (i.e., issuing debt to buy back equity, or vice versa) will not affect firm value
Another reason that capital structure does not affect firm value: With perfect capital markets (and assuming
market equilibrium) investors can buy levered or unlevered firms and manipulate the cash flows to suit their particular
capital structure tastes. Example:
1.
All equity firm with 100 shares outstanding.
2.
The firm’s assets earn one of the three possible cash flows each year (in perpetuity)
1/3 probability of a $30 cash flow (pessimistic outcome)
1/3 probability of a $45 cash flow (middle outcome)
1/3 probability of a $225 cash flow (optimistic outcome)
4
Expected yearly cash flow (in perpetuity) = $100
3.
Cash flows from assets are first used to pay interest to the owners of debt (if any). The residual is paid as a dividend
to stockholders.
4.
rf = 5%, MRP = 8.4%, beta of equity = 0.595238
The required rate of return for the firm's equity using the CAPM is 10%. (Obviously, there is a lot of stand-alone
risk with these cash flows. Why is the beta and discount rate so low?)
What is the market value of the firm's stock (per share)?
5.
The value of the firm = outstanding shares x price per share =
6.
What are the dividends per share and return on investment across the three economic states:
State
Cash flow from assets (total dividend)
DPS
ROI
Pessimistic
$30
Middle
$45
Optimistic
$225
Expected
$100
Assume the firm changes its capital structure by issuing $600 of default risk-free perpetual debt (rD = 5%). The firm
uses the $600 of cash to repurchase $600 (60 shares) of stock. The firm is now 60% debt and 40% equity: DL = $600
and SL = $400.
State
Cash flow from assets
Interest
Total dividend
DPS
ROI
Pessimistic
$30
Middle
$45
Are stockholders better off with debt in the firm's capital structure?
1.
Expected return on the equity investment
Expected ROI (100% equity) =
Expected ROI (40% equity) =
2.
Equity beta
Equity beta (100% equity) =
Equity beta (40% equity) =
3.
Required rate of return for the stock (using CAPM)
Required return (100% equity) =
Required return (40% equity) =
4.
Market Value of the Stock
Price per share (100% equity) =
Price per share (40% equity) =
5
Optimistic
$225
Expected
$100
Conclusion: How did the change in capital structure affect the stockholders of the firm?
•
•
•
Expected return increased, but
Beta risk and required return also increased
End result - no change in stockholder’s wealth.
Before change in capital structure, stockholder wealth =
After change in capital structure, stockholder wealth =
However, should a firm lever up if its stockholders prefer high expected return / high-risk cash flows?
No, because the stockholders of the firm can create these same risky cash flows using "homemade leverage."
Assume an investor has $16 to invest, but can purchase stock on margin at 5% interest (perpetual debt). With $24
of borrowed funds, the investor can purchase four shares ($40) of the unlevered firm.
State
DPS
Dividends for 4 shares
Less Interest
Net Income
ROI
Pessimistic
$0.30
$1.20
-$1.20
$0.00
0%
Middle
$0.45
$1.80
-$1.20
$0.60
3.75%
Optimistic
$2.25
$9.00
-$1.20
$7.80
48.75%
Expected
$1.00
$4.00
-$1.20
$2.80
17.5%
Therefore, purchasing stock on margin in the unlevered firm can make the ROI (and risk) the same as from ownership
of stock in the levered firm.
A similar procedure can be used to "unlever" a levered firm. For example, take your $16 of cash and buy $6.40 of stock
(0.64 shares) of the levered firm and lend $9.60 (5% perpetual debt).
State
Debt Income
Stock Income
Net Income
ROI
Pessimistic
$0.48
$0.00
$0.48
3%
Middle
$0.48
$0.24
$0.72
4.5%
Optimistic
$0.48
$3.12
$3.60
22.5%
Expected
$0.48
$1.12
$1.60
10%
Implications
1.
Investors can take unlevered stock and create levered stock cash flows by buying stock on margin.
2.
Investors can buy levered stock and debt and create unlevered stock cash flows.
3.
In fact, anything the firm can do, investors can do.
Lesson - Since a firm's capital structure decision does not affect investors’ cash flow opportunities, capital structure is
irrelevant.
In summary, with perfect capital markets, the equilibrium value of a firm and investor cash flows opportunities are
independent of the firm’s capital structure choice. Therefore:
•
Capital structure changes (issue debt to buy back equity, or vice versa) will not affect firm value
•
Financing a project with debt is equivalent to financing a project with equity
6
Perfection, efficiency, equilibrium and financing projects
A project requires a time zero investment of $100 and produces an expected cash flow of $110 in one year. The
opportunity cost of capital is 7% and the project NPV is $2.80. The firm has two financing choices for raising the $100,
a one-year risk-free debt issue with a 5% interest rate or a common stock issue with a 15% required return to
stockholders. (Assume the risk free opportunity cost of capital is 5%.)
1.
Perfect (and in equilibrium) financial markets mean that the choice of debt versus equity financing has no effect on
firm value. Therefore:
NPV (debt financing) = NPV (equity financing) = $???
2.
Market efficiency implies that the current value of the firm’s securities reflect available and relevant information
about those securities. Available and relevant information about the debt security:
The debt security will pay $105 in one year (risk free)
The risk-free opportunity cost of capital is 5%.
PV of $105 time 1 cash flow =
This means that the NPV (debt financing) =
Therefore NPV of equity financing must also =
Conclusion:
Base case NPV = $2.80
Financing NPV = $0 (for both debt and equity financing)
Project NPV = $2.80 + $0 = $2.80
Complication - The Modigliani-Miller capital structure irrelevance proposition centers on the ability of individual
investors to replicate (or reverse) actions by firms. What if they can't? Examples:
1.
What if individual investors are limited to 50% margin, but firms can borrow a higher percentage of money (say
60%).
2.
What if firm's can borrow at a lower interest rate than individuals (perhaps due to economies of scale)?
In both examples, there is an advantage to firms borrowing money (rather than individuals borrowing money).
Therefore, stocks of levered firms should sell at a premium!
However:
1.
2.
3.
Investors can borrow money from other sources (besides the broker) to make stock investments.
Compare home mortgage interest rates with long-term corporate bond interest rates
It is likely that the supply of levered firms would rise to meet the demand, eliminating any premium.
How close does the MM theory fit the real world (or, is capital structure really irrelevant)?
Evidence against MM - The capital structure decisions of companies do not appear to be random.
In fact, companies in certain industries are primarily debt financed, and in other industries, they are primarily equity
financed.
7
The reason for this pattern may be:
Managers of successful companies set the standard in the industry for capital structure. Other firms mimic. Since
capital structure doesn't affect firm value, there is no real benefit / penalty. Or:
The assumptions used in the model are unreasonable (this is the primary topic of Chapter 18).
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Chapter 17 Review Questions
1.
Understand the perfect capital market assumptions used in the capital structure irrelevance proof.
2.
Understand the arbitrage proof for capital structure irrelevance. Be able to demonstrate the method of generating
arbitrage profits if market prices are out of equilibrium. (Remember that when investors take advantage of an
arbitrage opportunity, their actions quickly force prices back into equilibrium - - thereby eliminating the arbitrage
opportunity.)
3.
Understand how changes in leverage affect:
•
•
•
•
Expected equity return
Beta risk of the equity
Required return using the CAPM
Price per share and market value of a firm's stock
4.
Be able to show how an individual investor can take an unlevered firm's stock and create levered stock cash flows
by buying on margin. Be able to show how an individual investor can take a levered firm's stock and create
unlevered stock cash flows by buying stock and lending money. Understand the significance of being able to
manipulate capital structure with respect to the issue of capital structure irrelevance.
5.
Understand the implications of a financial market that is perfect, efficient, and in equilibrium with respect to
financing projects. (That is, understand that in such a market, the financing NPV = $0 for any financing choice.)
Chapter 17 Practice Problems
1.
Assume that the market value of the equity of Firm X is $800. (Firm X is an all equity firm.) Firm Y has the exact
same assets as Firm X, managed in exactly the same way that Firm X manages its assets. The only difference
between Firm X and Firm Y is that Firm Y has both debt and equity in its capital structure. (The market value of
Firm Y’s debt = $200.) Using the perfect capital market assumptions listed in Chapter 17 notes, which of the
following statements are correct?
A. In equilibrium, the market value of Firm Y’s equity = $800
B. In equilibrium, the market value of Firm Y’s equity = $600 (correct answer)
The next five problems (#2 - #6) have a common set of assumptions.
2.
The assets of ABC Inc. produce a perpetual stream of $150 expected cash flows. The beta of these cash flows is
5/6. With a risk-free interest rate of 5% and a market-risk premium of 8.4%, the appropriate discount rate for these
cash flows (using the CAPM) is 12%. This implies that the assets of ABC Inc. are worth $1250. Since ABC Inc. is
all equity, then the beta for the equity is also 5/6, the required rate of return for the equity is 12%, and the market
value of the equity is $1250. XYZ Inc. has the exact same assets as ABC Inc., managed in exactly the same way as
ABC Inc. manages its assets. However, XYZ Inc. has $900 of perpetual, default risk-free debt (5% interest rate,
zero-beta) and stock with a current market value of $300. Both companies have a 100% dividend payout ratio.
Using the Chapter 17 assumptions, describe the steps necessary to earn a $50 arbitrage profit at time 0.
8
•
•
•
Step 1. At time 0, buy all of the stock of XYZ Inc. for $300. Invest $900 in default risk-free perpetual debt
(with a 5% interest rate).
Step 2. Simultaneous to step 1, Sell a $150 perpetual expected cash flow stream (with risk equivalent to the
dividend payments from ABC Inc. stock) at a market price of $1250.
Step 3. Expected dividends from the stock of XYZ Inc. are $105 per year. Cash flows from the perpetual
debt investment are $45 per year. Combined cash flows are expected to be $150 and these cash flows have
the exact same risk as the assets and equity of ABC Inc. Each year, deliver these cash flows to the
purchasing investor from step two.
3.
Repeat the analysis assuming that the market value of XYZ Inc. stock is $400 instead of $300. All other numbers
remain the same. Do on your own.
4.
Assume that the market is in equilibrium (i.e., no arbitrage profits are available) and we are in a Chapter 17 world.
Therefore when two firms (e.g., levered and unlevered) have the exact same assets, managed in exactly the same
way, the market values of the securities of a levered and unlevered firm are identical. Using the information from
problem 2, assume that ABC's stock has a market value of $1250 and the stock and debt of XYZ Inc. have market
values of $350 (instead of $300) and $900 respectively.
•
•
•
•
•
•
What are the expected dividend payments for ABC Inc. and XYZ Inc. stock? ABC Inc. = $150, XYZ Inc. =
$105.
What are the expected returns for the stocks of the two companies? ABC Inc. = 12.0%, XYZ Inc. = 30.0%.
What are the betas of the stocks of the two companies? ABC Inc. = 5/6 or 0.8333, XYZ Inc. = 2.9762. (Hint:
The beta risk for XYZ's debt is 0.0. Use this to solve for the stock beta risk.)
What are the required rates of return for the two stocks using CAPM? ABC Inc. = 12.0%, XYZ Inc. = 30.0%.
Using the expected dividend payments and required returns, what are the market values for the two stocks?
ABC Inc. = $150 / 0.12 = $1250. XYZ Inc. = $105 / 0.30 = $350.
What if the debt beta for XYZ's debt was 0.4 instead of 0.0? Keeping the asset beta at 5/6, what is XYZ's
stock beta? 1.9476. (For all of the remaining questions, assume that XYZ debt is risk free.)
5.
You have $60 and want the risk and return characteristics of XYZ stock. However, XYZ stock is not for sale (but
ABC stock is available). What can you do? Take your $60 of cash and borrow an additional $154.2857
(perpetual debt, 5% interest rate). Use the $214.2857 to buy 17.14286% ($214.2857 divided by $1250) of the
total outstanding stock of ABC. The annual expected return on this $60 investment is 30% and the beta risk is
2.9762.
6.
You have $60 and want the risk and return characteristics of ABC stock. However, ABC stock is not for sale (but
XYZ stock is available). What can you do? Take your $60 and buy $16.80 of XYZ stock. Take the remaining
$43.20 of cash and invest in default risk free perpetual debt with a 5% interest rate and a zero beta. The annual
expected return on this $60 investment is 12% and the beta risk is 5/6.
9