Capital Structure
Basic concepts: no taxes
Chapter 15 Capital Structure:
Basic Concepts
 Capital-structure
 No-arbitrage
 Example:
and pie theory
pricing.
shares for debt
 Value
 Required
return on the levered firm.
Financial Leverage, EPS, and
ROE
Assets
Debt
Equity
Debt/Equity
Interest rate
Shares
Share price
Current
$20,000
$0
$20,000
0.00
n/a
400
$50
Proposed
$20,000
$8,000
$12,000
0.67
8%
240
$50
Comments
 Straight
swap of equity for debt
 Market prices unchanged
 Real asset unchanged
Financial leverage and risk
 Three
states: bust, normal, boom.
 Probabilities not explicit.
 Look at each state separately.
EPS, ROE, Current Structure
Shares Outstanding = 400
Bust
Normal
EBIT
$1,000 $2,000
Interest
0
0
Net income $1,000 $2,000
EPS
$2.50
$5.00
ROA
5%
10%
ROE
5%
10%
Boom
$3,000
0
$3,000
$7.50
15%
15%
EPS and ROE under
Proposed Capital Structure
Shares Outstanding = 240
Bust Normal
EBIT
$1,000 $2,000
Interest
640
640
Net income
$360 $1,360
EPS
$1.50
$5.67
ROA
5%
10%
ROE
3%
11%
Boom
$3,000
640
$2,360
$9.83
15%
20%
Financial and operating leverage
 Find
the point of equal EPS
 Let x = EBIT
 Solve x/400 = (x - 640)/240
 Solution x = 1600.
 EPS = 4 per share, in either structure
12.00
Debt
10.00
Break-even
Point
EPS
8.00
6.00
4.00
No Debt
2.00
0.00
EBIT
1,000
(2.00)
2,000
3,000
Modigliani-Miller (MM) Model
 Perpetual
Cash Flows (convenient)
 Firms and investors can borrow and
lend at the same rate (convenient)
 No transaction costs (convenient)
 No taxes
Homemade leverage
 Instead
of the firm leveraging or
unleveraging,
 the investor does it herself, by
borrowing or lending,
 leveraging or unleveraging her portfolio.
Borrow $8000, buy the
unlevered firm for $20,000
Earnings
Interest at 8%
Net Profits
ROE (on $12K)
Bust Normal Boom
$1000 $2000 $3000
$640 $640 $640
$360 $1360 $2360
3% 11%
20%
Same as owning the levered firm
Okay, don’t buy the whole firm
 Buy
10%, forty shares for $2000.
 Borrow $800.
 Total cost $1200
 Same as having 10% of the levered
firm, that is, 24 shares at $50 per share.
Homemade annihilation of
leverage
 Idea.
Form a portfolio.
 Part lending…
 part the levered firm.
 Portfolio has the action of the unlevered
firm.
 A levered firm is a portfolio.
Buy the levered firm (240
shares) and lend 8000
Cost of Portfolio = 12000 + 8000 = 20000
Bust Normal
Boom
EPS
$1.50 $5.67
$9.83
Earnings
$360 $1360 $2360
Interest at (8%)
$640
$640
$640
Net cash flow
$1000 $2000 $3000
ROE
5%
10%
15%
(Net cash flow / $2,000)
The firm is a veil
 A way
for shareholders to hold a
portfolio.
Proposition I of MM (No
Taxes)
 P1:
Value is unaffected by leverage
 P1: VL = VU ; or SL + B = SU
 Pie theory
Proposition II of M-M (no taxes)
 rB
is the interest rate
 rs is the return on (levered) equity r0 is
the return on unlevered equity
 B is value of debt
 SL is value of levered equity
 rs = r0 + (B / SL) (r0 - rB)
Quick derivation of MM II
 Uses
MM I. Value unchanged.
 Uses cash flow constraint.
For instance, capital structure
Value
Shares
SL
Random cash
flow
sL
Bonds
B
b
Unlevered firm SU
sU = s L + b
Conclusion: SU= SL + B
Cash flows
sU  sL  b
E ( sU )  E ( sL )  b
E ( sU )
E ( sL )
b
r0
 rs
 rb
r0
rs
rb
r0 SU  rs S L  rb B
MM I
SU  S L  B
MM I SU  S L  B
Expected
r
S

r
S

r
B
S L
B
cash flows 0 U
(*)
r0 ( S L  B)  rS S L  rB B
rS S L  r0 ( S L  B)  rB B
rS S L  r0 ( S L  B)  rB B
rS S L  r0 S L  (r0  rB ) B
B
rS  r0  (r0  rB )
SL
Weighted average cost of capital
 Go
back to equation (*) in the
derivation, divide by SL + B
 Result: rWACC = r0
MM Proposition II no tax
Cost of
capital: r
(%)
r0
.
B
rS  r0  (r0  rB )
SL
rS
rWACC
rB
Debt-toequity
ratio (B/S)
What is the weighted average
cost of capital ?
 Give
the definitions and the formula.
 rWACC = S/(S+B))rS + (B/(S+B))(1-TC)rB
 rWACC is the market rate at which the
physical asset of the firm is discounted.
 rWACC is the market rate for project
whose risk profile is like that of the
physical asset of the firm.
Conclusion
 Weighted
average cost of capital
doesn’t change because the physical
asset of the firm doesn’t change.