Capital Structure: Basic
Concepts
Chapter 16
16-0
Key Concepts and Skills
Understand the effect of financial leverage
(i.e., capital structure) on firm earnings
 Understand homemade leverage
 Understand capital structure theories with
and without taxes
 Be able to compute the value of the
unlevered and levered firm

16-1
16.1 Capital Structure and the Pie

The value of a firm is defined to be the sum of
the value of the firm’s debt and the firm’s equity.
V=B+S
• If the goal of the firm’s
management is to make the
firm as valuable as possible,
then the firm should pick the
debt-equity ratio that makes
the pie as big as possible.
S B
Value of the Firm
16-2
Stockholder Interests
There are two important questions:
1.Why
should the stockholders care about
maximizing firm value? Perhaps they should be
interested in strategies that maximize shareholder
value.
2.What is the ratio of debt-to-equity that maximizes
the shareholder’s value?
As it turns out, changes in capital structure
benefit the stockholders if and only if the
value of the firm increases.
16-3
16.3 Financial Leverage, EPS, and ROE
Consider an all-equity firm that is contemplating going
into debt. (Maybe some of the original shareholders want
to cash out.)
Current
Assets
$20,000
Debt
$0
Equity
$20,000
Debt/Equity ratio
0.00
Interest rate
n/a
Shares outstanding
400
Share price
$50
Proposed
$20,000
$8,000
$12,000
2/3
8%
240
$50
16-4
EPS and ROE Under Current Structure
Recession Expected Expansion
EBIT
$1,000
$2,000
$3,000
Interest
0
0
0
Net income
$1,000
$2,000
$3,000
EPS
$2.50
$5.00
$7.50
ROA
5%
10%
15%
ROE
5%
10%
15%
Current Shares Outstanding = 400 shares
16-5
EPS and ROE Under Proposed Structure
Recession Expected Expansion
EBIT
$1,000
$2,000
$3,000
Interest
640
640
640
Net income
$360
$1,360
$2,360
EPS
$1.50
$5.67
$9.83
ROA
1.8%
6.8%
11.8%
ROE
3.0%
11.3%
19.7%
Proposed Shares Outstanding = 240 shares
16-6
Financial Leverage and EPS
12.00
Debt
10.00
EPS
8.00
6.00
4.00
No Debt
Advantage
to debt
Break-even
point
2.00
0.00
1,000
(2.00)
Disadvantage
to debt
2,000
3,000
EBIT in dollars, no taxes
16-7
Assumptions of the M&M Model
Homogeneous Expectations
 Homogeneous Business Risk Classes
 Perpetual Cash Flows
 Perfect Capital Markets:

◦
◦
◦
◦
◦
Perfect competition
Firms and investors can borrow/lend at the same rate
Equal access to all relevant information
No transaction costs
No taxes
16-8
Homemade Leverage: An Example
Recession Expected Expansion
EPS of Unlevered Firm $2.50
$5.00
$7.50
Earnings for 40 shares
$100
$200
$300
Less interest on $800 (8%) $64
$64
$64
Net Profits
$36
$136
$236
ROE (Net Profits / $1,200) 3.0% 11.3%
19.7%
We are buying 40 shares of a $50 stock, using $800 in margin.
We get the same ROE as if we bought into a levered firm.
Our personal debt-equity ratio is: B
$800 2
=
=
3
S $1,200
16-9
Homemade (Un)Leverage: An Example
Recession Expected Expansion
EPS of Levered Firm
$1.50
$5.67
$9.83
Earnings for 24 shares
$36
$136
$236
Plus interest on $800 (8%) $64
$64
$64
Net Profits
$100
$200
$300
ROE (Net Profits / $2,000)
5%
10%
15%
Buying 24 shares of an otherwise identical levered firm along
with some of the firm’s debt gets us to the ROE of the unlevered
firm.
This is the fundamental insight of M&M
16-10
MM Proposition I (No Taxes)
We can create a levered or unlevered
position by adjusting the trading in our
own account.
 This homemade leverage suggests that
capital structure is irrelevant in
determining the value of the firm:

VL = VU
16-11
16.4 MM Proposition II (No Taxes)

Proposition II
◦ Leverage increases the risk and return to stockholders
Rs = R0 + (B / SL) (R0 - RB)
RB is the interest rate (cost of debt)
Rs is the return on (levered) equity (cost of equity)
R0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity
16-12
MM Proposition II (No Taxes)
The derivation is straightforward:
RW ACC =
B
S
× RB +
× RS
B+S
B+S
B
S
× RB +
× RS = R0
B+S
B+S
T
h
e
n
s
e
t
RW ACC = R
0
B+S
multiply both sides by
S
B+S
B
B+S
S
B+S
×
× RB +
×
× RS =
R0
S
B+S
S
B+S
S
B
B+S
× RB + RS =
R0
S
S
B
B
× RB + RS = R0 + R0
S
S
B
RS = R0 + ( R0 − RB )
S
16-13
Cost of capital: R (%)
MM Proposition II (No Taxes)
R0
RS = R0 +
RW ACC =
B
× ( R0 − RB )
SL
S
B
× RB +
× RS
B+S
B+S
RB
RB
Debt-to-equity Ratio B
S
16-14
What do we learn from MM I&II
without tax

You use OPERATIONAL CASH FLOWS
to evaluate the Projects

The value of the Firm is the Present Value
of those Cash Flows

The Cash Flows are independent of the
Capital Structure the Firm chooses.
16-15

So, in different Capital Structures you are
discounting the same Cash Flows and
getting the same Present Value of Cash
Flows, this means that:

the discount you are using is the same for
different capital structures which is
WACC!
16-16

What is happening is the following:
◦ When you increase Debt in the Firm, Equity
becomes more expensive
◦ But, you are using less of the more expensive
capital (Equity) and more of the more cheap
capital (Debt)
◦ In the end, they compensate exactly, leaving
the WACC constant.
16-17

The second Modigliani-Miller Proposition
tells us what is the cost of Equity for
different Capital Structures

We know two facts:
◦ The Cost of Equity increases with more Debt
◦ The WACC remains constant
16-18
16.5 MM Propositions I & II (With Taxes)

Proposition I (with Corporate Taxes)
◦ Firm value increases with leverage
VL = VU + TC B

Proposition II (with Corporate Taxes)
◦ Some of the increase in equity risk and return
is offset by the interest tax shield
RS = R0 + (B/S)
16-19
MM Proposition I (With Taxes)
The total cash flow to all stakeholde rs is
( EBIT − RB B ) × (1 − TC ) + RB B
The present value of this stream of cash flows is VL
Clearly ( EBIT − RB B) × (1 − TC ) + RB B =
= EBIT × (1 − TC ) − RB B × (1 − TC ) + RB B
= EBIT × (1 − TC ) − RB B + RB BTC + RB B
The present value of the first term is VU
The present value of the second term is TCB
∴VL = VU + TC B
16-20
MM Proposition II (With Taxes)
Start with M&M Proposition I with taxes:
Since
VL = VU + TC B
VL = S + B ⇒ S + B = VU + TC B
VU = S + B (1 − TC )
The cash flows from each side of the balance sheet must equal:
SRS + BR B = VU R0 + TC BR B
SRS + BR B = [ S + B (1 − TC )]R0 + TC RB B
Divide both sides by S
B
B
B
RS + RB = [1 + (1 − TC )]R0 + TC RB
S
S
S
B
Which quickly reduces to RS = R0 + × (1 − TC ) × ( R0 − RB )
16-21
S
The Effect of Financial Leverage
Cost of capital: R
(%)
RS = R0 +
RS = R0 +
B
× ( R0 − RB )
SL
B
× (1 − TC ) × ( R0 − RB )
SL
R0
RW ACC =
SL
B
× RB × (1 − TC ) +
× RS
B+SL
B + SL
RB
Debt-to-equity
ratio (B/S)
16-22
All Equity
Total Cash Flow to Investors
EBIT
Interest
EBT
Taxes (Tc = 35%)
Levered
Total Cash Flow to S/H
EBIT
Interest ($800 @ 8% )
EBT
Taxes (Tc = 35%)
Total Cash Flow
(to both S/H & B/H):
EBIT(1-Tc)+TCRBB
Recession
$1,000
0
$1,000
$350
Expected
$2,000
0
$2,000
$700
Expansion
$3,000
0
$3,000
$1,050
$650
$1,300
$1,950
Recession
$1,000
640
$360
$126
$234+640
$874
$650+$224
$874
Expected
$2,000
640
$1,360
$476
$884+$640
$1,524
$1,300+$224
$1,524
Expansion
$3,000
640
$2,360
$826
$1,534+$640
$2,174
$1,950+$224
$2,174
16-23
Total Cash Flow to Investors
All-equity firm
S
G
Levered firm
S
G
B
The levered firm pays less in taxes than does the all-equity firm.
Thus, the sum of the debt plus the equity of the levered firm is
greater than the equity of the unlevered firm.
This is how cutting the pie differently can make the pie “larger.”
-the government takes a smaller slice of the pie!
16-24
Summary: No Taxes




In a world of no taxes, the value of the firm is unaffected by
capital structure.
This is M&M Proposition I:
VL = VU
Proposition I holds because shareholders can achieve any
pattern of payouts they desire with homemade leverage.
In a world of no taxes, M&M Proposition II states that
leverage increases the risk and return to stockholders.
B
RS = R0 + × ( R0 − RB )
SL
16-25
Summary: Taxes




In a world of taxes, but no bankruptcy costs, the value of the
firm increases with leverage.
This is M&M Proposition I:
VL = VU + TC B
Proposition I holds because shareholders can achieve any
pattern of payouts they desire with homemade leverage.
In a world of taxes, M&M Proposition II states that leverage
increases the risk and return to stockholders.
B
RS = R0 + × (1 − TC ) × ( R0 − RB )
SL
16-26
Example
Green Manufacturing plans to announce that it
will issue $2m in perpetual debt and use the
proceeds to repurchase common stock. The bonds
will sell at par with a 6% annual coupon rate.
 Green is currently an all-equity firm, worth $10m
with 0.5m shares.
 After the sale of the bonds, Green will maintain
the new capital structure indefinitely.
 Green currently generates annual pretax earnings
of $1.5m. This is supposed to continue in
perpetuity and the tax rate is 40%

16-27
What is the expected return on Green’s equity
before the announcement?
b) What is Green’s market value balance sheet
before the announcement? What is the price per
share?
c) Construct Green’s market value balance sheet
after the announcement?
d) What is the price share after the
announcement?
a)
16-28
e) How many shares will Green repurchase?
f) Construct the market value balance sheet
after the announcement
g) What is the required return on equity after
the re-structuring?
16-29

You may think the new structure will be
Debt $2m and Equity $8m, but that will
not happen.

You may think that the proceeds from the
bond issue will buy 100,000 shares, but
that will not happen.
16-30
a)
In order to answer the question, we just
need to calculate the Cash Flow that the
stockholders will receive
The pretax earnings are $1.5m. After
taxes of 40% it becomes $900,000.
So the rate of return on equity is
$900,000 divided by $10,000,000. It’s
9%
16-31

b) The company is only equity. So the
balance sheet is simply
Assets
Total
$10,000,000
$10,000,000
Debt
$0
Equity
$10,000,000
Total
$10,000,000
The price per share is only $10m divided
by 0.5m shares. It is $20.
16-32

c) After the announcement of the issue of
the $2m bonds, the efficient market
hypothesis and the MM propositions tell
you that the tax shield of the debt will be
incorporated in the value of the firm.
Because, there is only equity in the firm,
the equity will absorb this gain in value.
16-33
The debt is perpetual. It is sold at par, with a
coupon rate of 6%.
This means the debt will pay a perpetual
coupon of 6% of $2m. Since it is at par, to
get the present value of the tax shield , we
discount it using 6% too.
As we saw in previous class this means the
present value of this tax shield is
t*B=40%*$2m=$0.8m
16-34

The balance sheet of Green will now look
like
Assets
$10,000,000
Debt
$0
PV tax shield
$800,000
Equity
$10,800,000
Total
$10,800,000
Total
$10,800,000
16-35
d) The new price will reflect this new value being
incorporated.
So, the Equity is worth $10.8m and there are still
0.5m shares. The price is $21.6
e) The number of shares repurchased is the quantity
of shares that, at the new price, add up to a value
of $2m.
This number is 92,593. There will the 407,407
shares left.
16-36

f) After the re-structuring, the value of the
equity is reduced by the amount it was
repurchased ($2m). The value of the firm will
not change, because any changes in value
coming from this operation is already
incorporated.
Assets
$10,000,000
Debt
$2,000,000
PV tax shield
$800,000
Equity
$8,800,000
Total
$10,800,000
Total
$10,800,000
16-37
Notice that 407,407*$21.6=$8,800,000
g) From part a) we know that R0 is 9%. We also
know RB is 6%, B is $2m and S is $8.8m. So,
we just need to apply MM Proposition II
B
RS = R0 +  (R0 − RB )(1 − t )
S
 $0.8m 
RS = 9% + 
(9% − 6% )(1 − 0.4 ) = 9.41%
 $2m 
16-38
Suggested problems (Chapter 16)

9, 12, 19, 20, 23, 24
16-39