Review
Principle of separation
 Present
discounted value the real
investment. (equivalence).
 Decide whether to undertake it
(optimization).
 Select the appropriate financial
investment or disinvestment
(optimization).
Representation
switch and win
or
stay and lose
Nature’s move,
plus the contestant’s
guess.
switch and lose
or
stay and win
No arbitrage condition:
 Price
of bond =
price of zero-coupon bond
+ price of stripped coupon.
 Otherwise, a money machine, one way
or the other.
 Riskless increase in wealth
Pie theory
 The
bond is the whole pie.
 The strip is one piece, the zero is the
other.
 Together, you get the whole pie.
 No arbitrage pricing requires that the
values of the pieces add up to the value
of the whole pie.
No arbitrage principle
 Market
prices must admit no profitable,
risk-free arbitrage.
 No money pumps.
 Otherwise, acquisitive investors would
exploit the arbitrage indefinitely.
Definition of a call option
 A call
option is the right but not the
obligation to buy 100 shares of the
stock at a stated exercise price on or
before a stated expiration date.
 The price of the option is not the
exercise price.
Example
 A share
of IBM sells for 74.
 The call has an exercise price of 76.
 The value of the call seems to be zero.
 In fact, it is positive and in one example
equal to 2.
t=0
t=1
S = 80, call = 4
S = 74
S = 70, call = 0
Value of call = .5 x 4 = 2
Definition of a put option
 A call
option is the right but not the
obligation to sell 100 shares of the
stock at a stated exercise price on or
before a stated expiration date.
 The price of the option is not the
exercise price.
Put call parity at expiration
 Equivalence
at expiration s + p = X + c
 Values at time t in caps:
S + P = Xe-r(T-t) + C
 Write S - Xe-r(T-t) = C - P
Puts and calls before expiration
 S,
P, and C are the market values at
time t before expiration T.
 Xe-r(T-t) is the market value at time t of
the exercise money to be paid at T
 Traders tend to ignore r(T-t) because it
is small relative to the bid-ask spreads.
No arbitrage pricing implies
put call parity
 If
the relation does not hold, a risk-free
arbitrage is available.
 If S - Xe-r(T-t) > C – P, then
 Sell the stock short, and also sell the put.
Use the proceeds to buy the call and a bond
paying X at expiration. The position is
riskless. It nets the arbitrageur a positive
sum. That violates no arbitrage pricing.
 Similarly if inequality is in the other direction.
“Real” options
 The
option to abandon is a put option.
 Deciding to delay or not, the firm
exercises or not its call on the project.
Review item
 What
is the interest rate?
Do write:
 The
interest rate is the premium for
current delivery of money.
 P0 is the price of current money in
current money, namely 1.
 P1 is the price of time-one money in
terms of current money, something <1.
 P
P0
r
P1
1
Review item
 When
a firm creates value through a
financial transaction, who gets the
increase?
Answer
 Old
equity means the shareholders at
the time the decision is made.
 Old equity gets the gains.
 Why? Old equity has no competitors.
Everyone else is competitive and must
accept a market return.
Example
 Coupons
sell for 450
 Principal sells for 500
 The bond MUST sell for 950.
 Otherwise, an arbitrage opportunity exists.
 For instance, if the bond sells for 920…
 Buy the bond, sell the stripped components.
Profit 30 per bond, indefinitely.
 Similarly, if the bond sells for 980 …
Confirmation in an excel
spread sheet.
Time
0
1
2
…
15
16
contribution
3.25473
3.25473
3.25473
…
3.25473
3.25473
balance
3.25473
6.704744
10.36176
83.5571
91.8253
Incremental cash flows
 Cash
flows that occur because of
undertaking the project
 Not sunk barges … oops, I mean costs.
 Opportunity cost
 Side effects
 Working capital
Net working capital
=
cash + inventories + receivables
- payables
 a cost at the start of the project (in
dollars of time 0,1,2 …)
 a revenue at the end in dollars of time
T-2, T-1, T.
Internal rate of return
 Definition:
IRR is the discount rate that
makes NPV = 0
That is, IRR is the r such that
CF1
CF2
CFT
CF0 

 . . .
0
2
T
1  r (1  r )
(1  r )
IRR’s at r=1 and r=2.
NPV
100%
200%
r
Scale problems in IRR
Time 0
1
IRR
Little -100 200 1
dam
Big
-1000 1500 .5
dam
NPV
(r=.1)
81.8181.
..
363.63...
Decision Tree for Stewart
Pharmaceutical
The firm has two decisions to make:
To test or not to test.
To invest or not to invest.
Success
Test
Invest
NPV = $3.4 B
Do not
invest
NPV = $0
Failure
Do not
test
NPV  $0
Invest
NPV = –$91.46 m
The Option to Abandon:
Example
Traditional NPV analysis overlooks the option to abandon.
Success: PV = $575
Sit on rig; stare
at empty hole:
PV = $0.
Drill
- $300
Failure
Do not
drill
NPV  $0
Sell the rig;
salvage value
= $250
The firm has two decisions to make: drill or not, abandon or stay.
Beta measures risk
 How
much risk is added depends on
the relation of sAM and s2M
 Define beta
s AM
A 
2
sM
Covariance
 It
measures the tendency of two assets
to move together.
 Variance is a special case -- the two
assets are the same.
 Variance = expectation of the square of
the deviation of one asset.
 Covariance = expectation of the product
of the deviations of two assets.
Rate of return
expected by the market
E[Rj]
E[RM]
Rf

1
Example of beta and NPV
 Wingmar
Inc. has a beta of 2.
 The Market risk premium is 8.5%
 The risk-free rate is 4%.
 Wingmar has a project with cash flows 100, 60, 80.
 The project is typical of Wingmar’s core
business.
 Should the project be undertaken?
The Long-Term Financial Deficit
(2002)
Uses of Cash
Flow (100%)
Sources of Cash
Flow (100%)
Capital
spending
98%
Internal cash
flow (retained
earnings plus
depreciation)
97%
Financial
deficit
Net
working
capital
plus other
uses 2%
Long-term
debt and
equity 3%
Internal
cash flow
External
cash flow
Cumulative abnormal returns
(%)
Event Studies: Dividend
Omissions
Cumulative Abnormal Returns for Companies Announcing
Dividend Omissions
1
0.146 0.108
-8
-6
0.032
-4
-0.72
0
-0.244
-2 -0.483 0
-1
2
4
6
8
Efficient market
response to “bad news”
-2
-3
-3.619
-4
-5
-4.563-4.747-4.685-4.49
-4.898
-5.015
-5.183
-5.411
-6
Days relative to announcement of dividend omission
S.H. Szewczyk, G.P. Tsetsekos, and Z. Santout “Do Dividend Omissions Signal Future Earnings or Past Earnings?” Journal
of Investing (Spring 1997)
Relationship among Three Different
Information Sets
All information
relevant to a stock
publicly available
information
past prices
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%
MM Proposition II no tax
Cost of
capital: r
(%)
r0
.
B
rS  r0  (r0  rB )
SL
rS
rWACC
rB
Debt-toequity
ratio (B/S)
MM II and WACC
Cost of
capital: r
(%)
r0
.
.
..
rS
rWACC
rB
Debt-toequity
ratio (B/S)
Channels
Debt
channel
$ of operating
cash flows
Equity
channel
Corporate
taxes
TC
Personal
taxes
TB
1-TB
TS
(1-TC)(1-TS)
Value as
debt
Value as
equity
tax cut
increased
equity
Operating C.F.’s of
the whole economy
...
Summary: APV, FTE, and
WACC
Initial Investment
Cash Flows
Discount Rates
PV of financing
APV
WACC
FTE
All
UCF
r0
Yes
All
UCF
rWACC
No
Equity Portion
LCF
rS
No
Which is best?
Use WACC and FTE when the debt ratio is constant
Use APV when the level of debt is known.
Review item
 Two
assets have the same expected
return.
 Each has a standard deviation of 2%.
 The correlation coefficient is .5.
 What is the standard deviation of an
equally weighted portfolio?
Review item
 A firm
has a project with positive NPV.
 The project costs 100M to start.
 The firm has only 50M.
 What should it do?
Answer
 Raise
the money in the capital market.
 It can because NPV is market valuation.
Capital asset pricing model
E ( R j )  R f  E[ RM  R f ]   j
T-bill rate is known.
Market premium is known,
approximately 8.5%.
Estimate beta as in the project
Security Market Line
Expected return
on security (%)
Rm
Rf
T is undervalued.
Its price rises
.
. .
.
.
.
T
Security market
line (SML)
M
S
S is overvalued.
Its price falls
0.8
1
Beta of
security
EPS and ROE under
Proposed Capital Structure
Shares Outstanding = 240
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
5%
10%
15%
ROE
3%
11%
20%
Proposition II of M-M
 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)
MM Proposition II no tax
Cost of capital: r
(%)
r0
.
B
rS  r0  (r0  rB )
SL
rS
rWACC
rB
Debt-to-equity
ratio (B/S)
MM II (with taxes)
 Corporate
taxes, not personal
 rB = interest rate
 rS = return on equity
 r0 = return on unlevered equity
 B = value of debt
 SL = value of levered equity
 Previously, without taxes
rS = r0 + (B/SL)(r0 - rB)
Effect of tax shield
 Increase
of equity risk is partly offset by
the tax shield
 rS = r0 + (1-TC)(r0 - rB)(B/SL)
 Leverage raises the required return less
because of the tax shield.
MM II and WACC
Cost of capital: r
(%)
0.2351
.
0.200=
r0
0.100
.
..
200
370
rS
rWACC
rB
Debt-to-equity
ratio (B/S)
Optimal Debt and Value
Present value of
financial distress costs
Value of firm (V)
Present value of tax
shield on debt
VL=VU+TCB= Value of firm under
MM with corporate
taxes and debt
Maximum
firm value
V=Actual value of firm
VU=Value of firm with no debt
Debt (B)
0
B*
Optimal amount of debt
Channels
Operating Cash
Flows = $1
Debt
channel
Equity
channel
TC
TB
TS
1 - TB
(1-TC)(1-TS)
Miller: Tax-class clienteles
Value as
debt
Value as
equity
V* = 1/RS
V* = 1/RB
as
debt
as equity
Operating C.F.’s of
the whole economy
Value as
debt
Value as
equity
tax reform
increased
debt
Operating C.F.’s of
the whole economy
...
interpreted for dividends
(Figure 18.4)
C1
L o w -d iv id e n d firm
F u tu re
r e tu rn
or
s lo p e = - ( 1 + r )
H ig h - d iv id e n d
firm
d iv id e n d n o w
C0
Dividend equilibrium
H iD iv
value
per $1
LoD iv
value
per $1
V *=1/Rh
V *=1/RL
E quilibriu m
H iD iv
E q u ili b riu m
L o D iv
$ of operating
cash flow s
...
Review item
 What
is the weighted average cost of
capital?
Answer
 Give
the definitions and the formula.
 rB = bond rate
 rS = expected return on shares
 B = market value of bonds
 S = market value of shares
 TC = corporate tax rate
Pay-off pitch
 rWACC
=
(S/(S+B))rS + (B/(S+B))(1-TC)rB
 Now say that it applies when
 (1) the physical project has the same
risk as the firm
 (2) it is financed like the firm.
Review item
 Does
a good project have IRR greater
than the hurdle rate, or less?
Answer
 IRR
is the discount rate that makes
NPV(IRR) = 0.
 The hurdle rate is the market rate for
the risk-class.
 Investing means cash flows are first
negative, then positive.
 Financing (in this context) means cash
flows are first positive, then negative.
More answer
 Other
sign patterns, IRR is not useful.
 Investing, a good project has IRR >
hurdle rate.
 Financing, a good project has hurdle
rate > IRR.