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

Nature’s move,plus the contestant’sguess.

pr =

2/3

guess w

rong

guess right

pr = 1/3

switch and winor

stay and lose

switch and loseorstay 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 = 74

S = 80, call = 4

S = 70, call = 0Pr. = .5

Pr. = .5

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 impliesput 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 11

0 P

Pr

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 contribution balance0 3.25473 3.254731 3.25473 6.7047442 3.25473 10.36176… …15 3.25473 83.557116 3.25473 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

CFCF

r

CF

r

CF

rT

T01 2

21 1 10

( ). . .

( )

That is, IRR is the r such that

IRR’s at r=1 and r=2.

NPV

r

100% 200%

Scale problems in IRR

Time 0 1 IRR NPV(r=.1)

Littledam

-100 200 1 81.8181...

Bigdam

-1000 1500 .5 363.63...

Decision Tree for Stewart Pharmaceutical

Do not test

Test

Failure

Success

Do not invest

Invest

Invest

The firm has two decisions to make:To test or not to test.To invest or not to invest.

0$NPV

NPV = $3.4 B

NPV = $0

NPV = –$91.46 m

The Option to Abandon: Example

The firm has two decisions to make: drill or not, abandon or stay.

Do not drill

Drill

0$NPV

Failure

Success: PV = $575

Sell the rig; salvage value

= $250

Sit on rig; stare at empty hole:

PV = $0.

Traditional NPV analysis overlooks the option to abandon.

- $300

Beta measures risk

How much risk is added depends on the relation of AM and

Define beta

2M

AMA

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.

Rf

E[RM] Security

marke

t line

1

Rate of returnexpected by the market

E[Rj]

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)

Sources of Cash Flow (100%)

Internal cash flow (retained earnings plus depreciation)

97%

Long-term debt and

equity 3%

Uses of Cash Flow (100%)

Capital spending

98%

Net working capital

plus other uses 2%

Internal cash flow

External cash flow

Financial deficit

Event Studies: Dividend Omissions

Cumulative Abnormal Returns for Companies Announcing Dividend Omissions

0.146 0.108

-0.72

0.032-0.244

-0.483

-3.619

-5.015-5.411-5.183

-4.898-4.563-4.747-4.685-4.49

-6

-5

-4

-3

-2

-1

0

1

-8 -6 -4 -2 0 2 4 6 8

Days relative to announcement of dividend omission

Cum

ulat

ive

abno

rmal

ret

urns

(%

)

Efficient market response to “bad news”

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 informationrelevant to a stock

publicly availableinformation

past prices

EPS and ROE under Proposed Capital Structure

Shares Outstanding = 240

Bust Normal Boom

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%

MM Proposition II no tax

Debt-to-equityratio (B/S)

Cost of capital: r

(%)

.r0

rS

rWACC

rB

LBS S

Brrrr )( 00

MM II and WACC

Debt-to-equityratio (B/S)

Cost of capital: r

(%)

.r0

rS

rB.. rWACC

.

Channels$ of operatingcash flows

TC

Corporatetaxes

1-TB (1-TC)(1-TS)

TB TS

Personaltaxes

Debtchannel

Equitychannel

Value asequity

Value asdebt

Operating C.F.’s ofthe whole economy

...

tax cut

increasedequity

Summary: APV, FTE, and WACC

APV WACC FTE

Initial Investment All All Equity Portion

Cash Flows UCF UCF LCF

Discount Rates r0 rWACC rS

PV of financing Yes No No

Which is best?Use WACC and FTE when the debt ratio is constantUse 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

jfMfj RRERRE ][)(

T-bill rate is known.Market premium is known, approximately 8.5%.Estimate beta as in the project

Security Market LineExpected returnon security (%)

Beta ofsecurity

Rm

Rf

1

M.

0.8

S.

T. Security market line (SML)

S is overvalued.Its price falls

T is undervalued.Its price rises

.. .

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

Debt-to-equityratio (B/S)

Cost of capital: r(%)

.r0

rS

rWACC

rB

LBS S

Brrrr )( 00

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

Debt-to-equityratio (B/S)

Cost of capital: r(%)

.r0

rS

rB.0.200=

0.100

. rWACC

.0.2351

200370

Optimal Debt and Value

Debt (B)

Value of firm (V)

0

Present value of taxshield on debt

Present value offinancial distress costs

Value of firm underMM with corporatetaxes and debt

VL=VU+TCB=

V=Actual value of firm

VU=Value of firm with no debt

B*

Maximumfirm value

Optimal amount of debt

ChannelsOperating CashFlows = $1

Debtchannel

Equitychannel

TC

(1-TC)(1-TS)

TB

1 - TB

TS

Value asequity

Value asdebt

Operating C.F.’s ofthe whole economy

D of Institutions D of rich investors

V* = 1/RB V* = 1/RS

asdebt

as equity

Miller: Tax-class clienteles

Value asequity

Value asdebt

Operating C.F.’s ofthe whole economy

tax reform

increaseddebt

...

Separation theorem interpreted for dividends (Figure 18.4)

C1

C0

s lo p e = - (1 + r)

L o w -d iv id e n d firm

H ig h -d iv id e n dfirm

w

F u tu rere tu rno r

d iv id e n d n o

Dividend equilibrium

$ of operatingcash flows

HiDivvalueper $1

LoDivvalueper $1

mq ili riuo iv

EL

mEquilibriuHiD iv

u bD

V*=1/Rh V*=1/RL

...

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.