Download Document

Capital Structure. Introduction
How are projects and firms financed? This
choice determines the capital structure
Capital structure is


mix of types of securities issued by the firm
mix of claims that investors have on the firm’s cash
flows
Why is it important?

Capital structure affects the cost of capital, i.e. the
discount rate which we use in valuation
What are the determinants of the optimal
(“target”) capital structure?

Optimal c.s. should minimize the cost of capital (i.e.
maximize the market value of the firm)
Modigliani and Miller proposition: in the absence of
taxes, costs of financial distress and capital market
imperfections capital structure is irrelevant!
Why does the irrelevance result not hold in the real
world? MM proposition is obtained under several strong
assumptions. Any of the following factors can kill the
irrelevance result:





Taxes (corporate and personal) – Modified MM theory
Costs of financial distress
Transaction costs
Agency costs
Asymmetric information
We will discuss them
Sources of Long Term finance
Internal financing (retained earnings)

But firms often spend more than they
generate internally. The deficit is financed by
new sales of debt & equity
Types of instruments



Equity
Debt
Leases
Equity
Can be publicly traded or not
Types:

Common Stock - claim on the share of profits (after
tax and payments to creditors)
may have different voting rights

Preferred Stock – paid after tax and payment to
creditors too, but is normally a fixed claim (similarity
to debt)
No voting rights in normal times
Dividend is paid before dividend on common stock

Warrants
Call options on a firm’s shares
Debt
Can be publicly traded or not
Fixed claim (not a share of profits!)
Interest payments occur before payments
to preferred and common stockholders
and before taxes, i.e. tax deductible
No control (voting) rights in normal times
Control rights in case of default
Can be convertible into stock upon
realization of some conditions
Debt differs by


Maturity
Liquidity
public bonds - liquid
bank loans or private placements - illiquid

Security (for bonds)
secured (by an asset)

Mortgage bonds, collateral bonds
unsecured ordinary

Debentures, notes (“backed” by the earning power of the
firm, no collateral)
unsecured subordinated

Subordinated debentures (Least protected. Holders of
such bonds are paid after all other creditors)
Leases
Borrowing an asset in exchange for future
fixed repayments (similar to debt)
Types of leases

Operating lease
Usually short term and the asset is returned

Capital (investment) lease
Usually lasts for the entire life of the asset and the
asset can sometimes be acquired at the end by the
lessee at low price
Financing patterns
In the US, on average, 60-80% of the investment
expenditures is financed with internal funds. In other
countries reliance on internal funds is generally lower but
still 40-60%.
New sales of debt strongly prevail over new equity
issues
Large variations between types of firms and industries
(e.g. for startups equity financing strongly prevails)
Capital structure: in the US, average market value debtequity ratio is 0.5 (very roughly). Large variations
between industries: from 0.08 in biotech to 3 in financial
sector.
Pie model of the firm
E
D
D
F
E
default
V
As long as D is fixed, maximizing E is equivalent
to maximizing the whole pie (i.e. the total firm
value). But D is not fixed if debt is risky
Modigliani – Miller without taxes
Irrelevance of capital structure (MM I)
Cost of levered equity as a function of
capital structure (MM II)
Financing a firm with equity
Entrepreneur has an investment opportunity
Investment needed: $800
The project cash flows:
Prob(strong)=Prob(weak)=1/2
Suppose:



Risk free interest rate = 5%
The appropriate risk premium for this investment = 10%
Hence, the cost of capital (return investors require) is 15%
NPV = -800 + (½*1400 + ½*900)/1.15 = $200 > 0
Imagine, in order to finance the project entrepreneur
sells 100% of shares of this project to outside investors –
the project will be all-equity financed
How much would he raise?
Fair price for 100% of shares is
(½*1400 + ½*900)/1.15 = 1000
He would invest 800 and keep 200. Hence, his gain is
exactly NPV
In fact he could sell 80% of shares and keep 20% for
himself. Then investors would provide 800 and he would
get 0.2*1000 = 200, i.e. the same
Imagine, entrepreneur had invested 400 from his
own money and had raised only 400 as outside
equity.
He had to sell exactly 40% to outside investors
and would keep 60%. His payoff would be
0.6*1000 – 400 = 200, e.g. as before
Hence, observation: in a perfect market (no
transaction cost, asymmetric info problems,
moral hazard) it does not matter whether to
finance a firm internally or by raising external
funds
Adding Debt
Suppose entrepreneur decides to finance the project partially
through debt. He sells bonds for $500. If they are risk free, the
required return is 5%, hence he will pay $525 in a year. Since 525 <
900, debt is indeed risk-free.
He wants to sell then 100% of equity (now it would be levered
equity). How much would investors pay for it now?
Modigliani – Miller: E = $500
Modigliani – Miller Proposition I
In a perfect capital market a firm’s total market value is
equal to the market value of the total cash flows
generated by its assets and is independent of its capital
structure:
U=A=E+D

A – market value of assets, U – market value of unlevered equity,
E – market value of levered equity, D – market value of debt.
Perfect capital market:






No taxes
No costs of financial distress
No transaction and issuance costs
No asymmetric information
The firms' financing and operating decisions are independent. In
particular, no agency costs (managers maximize firm value)
Individuals can undertake the same financial transactions as the
firms and at the same prices (e.g. borrow at the same interest
rate)
Intuition
If the way we divide cash flows from an asset
among different claims (securities) does not
affect these cash flows, the total market value of
these claims must be independent of the way we
divide the cash flows

(We need some more for this result to hold: any
division is costless, all investors know the same as
insiders, i.e. do not treat a particular division as any
signal of firm value, investors can freely trade at the
same terms as firms)
MM I holds not only for a split into debt and
equity, but for any combination of any securities
Proof by arbitrage argument
Consider firm 1 and firm 2.
At t=1,2,...., both firms generate the same (random)
earnings (EBIT) X > 0.
But they differ in their cap. structure:


Firm 1 has equity and debt (risk free and perpetual for simplicity)
Firm 2 has no debt
Firm 1 pays annual interest rf, which is equal to the
return on safe debt in the market
market value of firm i's debt: Di
market value of firm i's equity: Ei
total market value of firm i: Ui = Ei + Di
Hence, at t:



firm 1's debtholders receive: rf D1
firm 1's equityholders receive: X- rf D1
firm 2's equityholders receive: X
Step 1: It cannot be that U₂>U₁.
Proof:
Suppose U₂>U₁ and consider an investor
holding a fraction α of firm 2's shares. At t, he
would receive αX. Instead, he could:



Sell the shares for αU₂
Buy in a fraction αU₂/U₁ of firm 1's debt and equity as:
αU₂ = (αU₂/U₁)⋅D₁+(αU₂/U₁)⋅E₁
At t, the investor would receive:
(αU₂/U₁) rf D1 + (αU₂/U₁)⋅(X- rf D1) = (αU₂/U₁)X > αX
for all X
Hence, there is an arbitrage opportunity. Intuition:
Arbitrageurs can "undo firm 1's leverage" by buying
its debt and equity in proportions such that interest
paid and received cancel.
Step 2: It cannot be that U₁>U₂.
Proof:
Suppose U₁>U₂ and consider an investor
holding a fraction α of firm 1's shares. At t, he
would receive X- rfD1. Instead, he could:




Sell the shares for αE1
Borrow αD1
Invest the total in a fraction α(U₁/U₂) of firm 2's
shares: αE₁+αD₁ = α(U₁/U₂)U₂
At t, the investor would get α(U₁/U₂)X and pay
interests rfD1: α(U₁/U₂)X - rfD1 > α(X- rf D1) for all X.
Hence, there is an arbitrage opportunity. Intuition:
Arbitrageurs can "lever up" firm 2 by borrowing on
individual accounts (homemade leverage).
Example: arbitrage for our firm
Changing a capital structure does
not change stock price
Example: leveraged recapitalization






Harrison Industries is currently all-equity with 50 mln
shares traded at $4 per share. Hence, its assets
market value = equity value = 200
Harrison plans to borrow $80 mln and use the money
to repurchase stock
How much would the stock cost after the transaction?
Imagine after the announcement the stock price
would be $x. The firm can repurchase 80 mln/x
shares. The stock price after the transaction must be
equal $x too (investors are forward looking)
50 mln – 80 mln/x has left. Their total value should be
assets market value – debt market value = 200 – 80
=120
x(50 – 80/x) = 120  x = 4 – did not change!
Market value balance sheet after each stage
of Harrison’s leveraged capitalization
Note: this was a zero-NPV transaction. Non-zero NPV
transaction would change the stock price, but choosing
whether to use debt or equity for financing does not
matter for the stock price
Returns to equity with and without
leverage
Levered equity has higher expected return than
levered. Why? Because it’s more risky.
Leverage increases both return and risk of
equity
Modigliani – Miller Proposition II
In fact, the following relationship is true:
Return (expected) on all firm’s assets rA = return on
unlevered equity rU = (E/(E+D))rE + (D/(D+E))rD

Here rE – return (expected) on equity in a levered firm, rD – return
(expected) on debt
Hence, MM II:
Firm’s return on equity (cost of equity) increases with
leverage
Cost of capital for a firm:
rWACC – weighted average cost of capital
(we will use it for valuation of projects and
firms)
As the fraction of the
firm financed with debt
increases, both the
equity and the debt
become riskier and
their cost of capital
rises. Yet, because
more weight is put on
the lower-cost debt, the
weighted average cost
of capital remains
constant.
Levered and Unlevered Betas
When debt is risk free
its beta = 0, and then
Since r  rf  β ( rm  rf ) , these formulas
are consistent with MM II
Cash, Net Debt and Enterprise
Value
Very often Enterprise Value is used as a market value of
a business
EV = Equity + Net Debt
Net Debt = Debt – Cash and Risk-Free Securities
EV – market value of assets excluding cash
MM I for EV: In a perfect capital market a firm’s EV is
equal to the market value of the total cash flows
generated by its assets excluding cash and is
independent of the combination of Equity, Debt and
Cash (or of the combination of Equity and Net Debt)
MM II is the same, but rU, rD and D have slightly different
meanings
Cash reduces market risk of equity (effect
opposite to the one of debt)
Note: here D is Net Debt and betaU is beta of
assets net of cash
Is the following statement true?:
Leverage can increase expected earnings per share. If it
does, it should increase stock price.
Wrong. Stock price does not change as we saw. Even if
EPS increase they become more volatile with leverage.
Example:




Levitron Industries (LVI) is currently all-equity. Its expected next
year EBIT = $10 mln.
It has 10 mln shares outstanding, traded at $7.50 per share
LVI wants to do leveraged recapitalization: borrowing $15 million
at interest rate 8% and using the proceeds to repurchase 2 mln
shares at $7.50 (we know such transaction should not change
the stock price)
Let’s show that EPS will become more volatile
Currently Net Income = EBIT = $10 mln

Hence EPS = $10 mln/10 mln = $1
With the debt, annual interest payment = $15
mln * 0.08 = $1.2 mln


Hence, NI = EBIT – i = $8.8 mln
Hence EPS = $8.8 mln/8 mln = $1.10 > $1
But $10 mln is expected EBIT. Imagine EBIT =
either $4 or $16 (each with prob. ½)


In an unlevered firm EPS would be either $0.4 or $1.6
In a levered firm EPS would be either $0.35 or $1.85.
More volatility (hence, more risk)
The sensitivity of
EPS to EBIT is
higher for a levered
firm than for an
unlevered firm. Thus,
given assets with the
same risk, the EPS
of a levered firm is
more volatile.