AFM 371 Winter 2008
Chapter 16 - Capital Structure: Basic Concepts
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Outline
Background
Capital Structure in Perfect Capital Markets
Examples
Leverage and Shareholder Returns
Corporate Taxes
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Background
Background
capital structure is the firm’s mix of financing instruments
we will consider a highly simplified context with only straight
debt and common shares
let B denote the market value of the firm’s debt and let S
denote the market value of the firm’s equity
firm value V = B + S
the pie:
B
S
two questions:
1. What happens to the cost of various sources of funds if the
firm changes its capital structure?
2. Is there an optimal capital structure?
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Cost of Capital Review
Background
the cost of equity rS is the expected return on the firm’s
common shares
in the CAPM rS = rf + β [E (rM ) − rf ]
note that this return can be in the form of dividends, capital
gains, or both
the cost of debt rB is the expected return on the firm’s debt,
i.e. the rate of interest paid
the weighted average cost of capital is given by
rWACC =
S
B
× rS +
× rB
B +S
B +S
note that we are ignoring (for now) the tax deductibility of
interest payments
read over chapters 11 and 13 to review these concepts
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The Objective of Management
since management is (in principle) controlled by the
shareholders, we normally assume that management seeks to
maximize the value of the firm’s equity
however, as long as there are no costs of bankruptcy,
maximizing equity value S is equivalent to maximizing firm
value V
example:
a firm has 10,000 shares; share price is $25
debt has a market value of $100,000
firm value V = B + S = $100,000 + $25 × $10,000 = $350,000
suppose the firm borrows another $50,000 and pays it
immediately as a special dividend
the value of debt increases to $150,000, but how are
shareholders affected?
Background
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The Objective of Management Cont’d
Background
consider three possible outcomes:
S
Dividend
Capital gain/loss
Net gain/loss
V ↑ $380,000
$230,000
$50,000
-$20,000
$30,000
V → $350,000
$200,000
$50,000
-$50,000
$0
V ↓ $320,000
$170,000
$50,000
-$80,000
-$30,000
the change in capital structure benefits the shareholders if and
only if the value of the firm increases
managers should choose the capital structure that they believe
will have the highest firm value (i.e. make the pie as big as
possible)
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Perfect Capital Markets
we will begin by assuming perfect capital markets:
information is free and available to everyone on an equal basis
no transaction costs
no taxes
no costs of bankruptcy
we will also assume (for simplicity) that all cash flows are
perpetuities (just to make the calculations easier)
two famous names: Modigliani and Miller (MM)
MM Proposition I (No Taxes): The market value of any firm
is independent of its capital structure
let VU be the value of an “unlevered” firm (i.e. all equity
financing) and let VL be the value of an otherwise identical
“levered” firm (i.e. some debt financing)
MM Proposition I (No Taxes) then simply says VU = VL
Capital Structure in Perfect Capital Markets
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Proof of MM Proposition I (No Taxes)
let X be the identical income stream generated by each firm
(i.e. U and L); VU = SU be the value of the unlevered firm;
and VL = SL + BL be the value of the levered firm
consider an investor who owns some fraction α (e.g. 5%) of
the shares of U:
α of U’s equity
Investment
αSU = αVU
Return
αX
this investor can get the same return by investing in L:
α of L’s equity
α of L’s bonds
Investment
αSL = α(VL − BL )
αBL
αVL
Return
α(X − rBL )
αrBL
αX
if VU > VL the investor would not buy any shares in U since
the same return is available on a smaller investment in L
Capital Structure in Perfect Capital Markets
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Proof of MM Proposition I (No Taxes) Cont’d
consider an investor who owns α of L’s equity:
α of L’s equity
Investment
αSL = α(VL − BL )
Return
α(X − rBL )
this investor can get the same return by investing in U and
borrowing on personal account:
α of U’s equity
Borrow αBL
Investment
αSU = αVU
-αBL
α(VU − BL )
Return
αX
-αrBL
α(X − rBL )
if VL > VU the investor would not buy any shares in L since
the same return is available on a smaller investment in U
we have shown that no-one would buy shares in U if VU > VL
and that no-one would buy shares in L if VL > VU
therefore VU = VL is the only solution consistent with market
equilibrium
Capital Structure in Perfect Capital Markets
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Some Observations
MM’s result is based on a no-arbitrage argument: if two
investments give the same future returns, they must cost the
same today
a key (implicit) assumption is that individuals can borrow as
cheaply as corporations
one way to do this is through buying stock on margin
with a margin purchase, the broker lends the investor a portion
of the cost (e.g. to buy $10,000 of stock on 40% margin, put
up $6,000 of your own money and borrow $4,000 from the
broker)
since the broker holds the stock as collateral, brokers generally
charge relatively low rates of interest
firms, on the other hand, often borrow using illiquid assets as
collateral (and get charged higher rates)
the same arguments apply to more complicated capital
structures
the same arguments apply if cash flows are not perpetuities
Capital Structure in Perfect Capital Markets
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Example #1
Examples
given VU = $100M, X = $10M, r = 5%, BL = $50M, then
MM Proposition I ⇒ SL = $50M
suppose SL = $40M:
suppose SL = $60M:
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Example #2
suppose a firm has the following all equity capital structure:
Original Capital Structure: All Equity
Number of shares
1,000
Share price
$10
Market value of shares
$10,000
operating income differs across economic states as follows:
State
Probability
Operating income
EPS
ROE
Examples
1
0.20
$500
$0.50
5%
2
0.20
$750
$0.75
7.5%
3
0.20
$1,500
$1.50
15%
4
0.20
$2,250
$2.25
22.5%
5
0.20
$2,500
$2.50
25%
Expected
Value
$1,500
$1.50
15%
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Example #2 Cont’d
Examples
consider an alternative capital structure with 50% debt
financing:
Alternative Capital Structure: 50% Debt
Number of shares
500
Share price
$10
Market value of shares
$5,000
Market value of debt
$5,000
assuming an interest rate of 10%:
State
Probability
Operating income
Interest
Equity earnings
EPS
ROE
1
0.20
$500
$500
$0
$0.00
0%
2
0.20
$750
$500
$250
$0.50
5%
3
0.20
$1,500
$500
$1,000
$2.00
20%
4
0.20
$2,250
$500
$1,750
$3.50
35%
5
0.20
$2,500
$500
$2,000
$4.00
40%
Expected
Value
$1,500
$500
$1,000
$2.00
20%
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Example #2 Cont’d
Examples
graphing EPS vs. operating income:
EPS
4.00
3.50
50% debt
2.50
2.25
2.00
All equity
1.50
0.75
0.50
0.00
0
500
750
1500
2250 2500
Operating income
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Example #2 Cont’d
Examples
since the expected ROE is higher under 50% debt, should the
firm switch to this capital structure?
not only have expected returns increased, but so has risk
the MM argument is that is doesn’t matter, because investors
can effectively create the payoffs from the alternative capital
structure themselves (“homemade leverage”)
assume the firm stays with the original all equity capital
structure but a particular investor prefers the alternative
suppose the investor buys 10 shares (at a cost of $100), but
finances this by investing $50 and borrowing $50:
EPS
Earnings (10 shares)
Interest (10% on $50)
Dollar returns
Percentage returns
(on $50 invested)
$0.50
$5.00
-$5.00
$0.00
0%
$0.75
$7.50
-$5.00
$2.50
5%
$1.50
$15.00
-$5.00
$10.00
20%
$2.25
$22.50
-$5.00
$17.50
35%
$2.50
$25.00
-$5.00
$20.00
40%
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How Does Leverage Affect Shareholder Returns?
note that from the previous example that leverage increases
the expected returns and risk for equity, even if there is no
chance of bankruptcy
recall the weighted average cost of capital formula
rWACC =
B
S
× rS +
× rB
B +S
B +S
MM Proposition I implies that the weighted average cost of
capital is constant (i.e. independent of capital structure)
in the previous example:
Leverage and Shareholder Returns
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MM Proposition II (No Taxes)
define
r0 = cost of capital for all equity firm
expected earnings for all equity firm
=
value of equity
since r0 = rWACC , we have
r0 =
S
B
× rS +
× rB
B +S
B +S
this can be rearranged to yield MM Proposition II (No Taxes):
Leverage and Shareholder Returns
rS = r0 +
B
(r0 − rB )
S
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MM Proposition II (No Taxes) Cont’d
Cost of capital (%)
graphing MM Proposition II:
rS
rWACC
r0
Leverage and Shareholder Returns
rB
B/S
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Corporate Taxes
Corporate Taxes
so far we have ignored corporate taxes, but the tax
deductibility of interest payments gives a big advantage to
debt financing
let TC be the corporate tax rate, and recall from chapter 13
that
rWACC =
S
B
× rS +
× rB × (1 − TC )
B +S
B +S
a levered firm makes interest payments of rB × B, and
therefore has its corporate taxes reducted by rB × B × TC
(the tax shield from debt)
in an all equity firm, the after tax cash flow to the
shareholders is EBIT × (1 − TC )
in a levered firm, the total after tax cash flow to the
shareholders and bondholders is EBIT × (1 − TC ) + TC rB B
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MM Proposition I (Corporate Taxes)
Corporate Taxes
the value of an all equity (unlevered) firm is the present value
of the after tax cash flow to the shareholders
VU =
EBIT × (1 − TC )
r0
MM Proposition I (Corporate Taxes):
VL = VU + PV(debt tax shield)
assuming the amount borrowed is constant over time, we can
calculate the present value of the debt tax shield by
discounting the cash flow at the rate of interest to get:
EBIT × (1 − TC ) TC rB B
+
r0
rB
= VU + TC B
VL =
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Example #3
Corporate Taxes
an investment project costs $100,000 and produces EBIT of
$20,000 per year forever, TC = 36%.
financing choices: U: all equity; L: $40,000 debt, rB = 5%,
r0 = 10%
EBIT
Interest
EBT
Tax
Net income
Total cash paid to investors
U
$20,000
0
20,000
7,200
12,800
$12,800
L
$20,000
2,000
18,000
6,480
11,520
$13,520
suppose the firm chooses U and issues 10,000 shares. It would
have the following market value balance sheet:
Physical assets
$128,000
Equity $128,000
(10,000 shares)
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Example #3 Cont’d
Corporate Taxes
now the firm announces it will switch to L by issuing $40,000
of debt and repurchasing shares
in an efficient market, the stock price will react immediately
to this announcement
the firm value will rise by the present value of the tax shield,
so the market value balance sheet becomes
Physical assets
$128,000
Equity
(10,000 shares)
the firm then issues the debt and carries out the repurchase:
Physical assets
$128,000
Debt
Equity
$40,000
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MM Proposition II (Corporate Taxes)
Corporate Taxes
how does leverage affect rS and rWACC ?
MM Proposition II (Corporate Taxes):
rS = r0 +
B
× (1 − TC ) × (r0 − rB )
S
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MM Proposition II (Corporate Taxes) Cont’d
Cost of capital (%)
graphing MM Proposition II:
r0
Corporate Taxes
rS = r0 + (B/S)(r0 − rB )
rS − r0 + (B/S)(1 − TC )(r0 − rB )
rWACC = (S/V )rS + (B/V )(1 − TC )rB
rB
B/S
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