Finance and the Financial Manager Chapter 1. 1.1 What is a Corporation? 1.2 The Role of the...

Finance and the Financial Manager

Chapter 1

1.1 What is a Corporation?

1.2 The Role of the Financial Manager

Two Basic Questions1 Investment Decision

2 Financing Decision

1.3 Who is the Financial Manager

Financial

ManagerFirm's

Operations

Financial

Markets

(1)(2)

(3)

(4a)

(4b)

1.4 Goal of the Firm ?

1.5 Agency Problem

Monitoring by board of directors1

Compensation package2

Active outside takeover market5

Efficient outside managerial labor market4

Monitoring by outside large blockholders

(Bank, insurance Co., pension, mutual fund)

3

B. How to solve agency problem?

A. Separation between Ownership and Management

Present Value and The Opportunity Cost of Capital

Chapter 2

C. PV and Rate of Return

B. Risk and Present Value

PV = C / (1+r)

2.1 Introduction

A. Present Value

NPV = PV - C0

r:

D. The Opportunity Cost of Capital

1 From your Investment

C0 : $ 100,000

Slump : $ 80,000

Boom : $ 140,000 Normal : $ 110,000

C1 :

E(C1)

From Stock Market2

Find stock X which has same risk as your project :

P0 : $ 95.65

Slump : $ 80

Boom : $ 140Normal : $ 110

P1 :

E(P1) = 1/3 (80 + 110 + 140) = 110

E(R) = = 0.15 15% k110 - 95.6595.65

Q : What is the Present Value of your project?

PV of project =

NPV =

How to Calculate Present Values

Chapter 3

3.1 Cash Flows in Several Periods (*)

3.2 Perpetuities and Annuities (*)

3.3 Growing Perpetuities (*)

3.4 Compounding Interest (*)

3.5 Nominal and Real Interest

A. Real CF = Nominal CF

(1+inflation rate)

B. (1+Real Rate) = (1+ Nominal rate)(1+inflation rate)

3.6 Bond Valuation

PVbond =C

1+rC

(1+r)2

C+F(1+r)n+ + … ... +

= C PVAF + F PVF

(Ex) Coupon rate: 10%, r=5%, face value=$1,000 N=7years

PVbond = 100 5.786 + 1100 0.711 = $1360.7

The Value of Common Stocks

Chapter 4

• NYSE• AMEX• OTC (NASDAQ)

B. Secondary Market

A. Primary Market

4.1 How Common Stocks are Traded?

(Ex) P0 = $100 , P1 = $110 , DIV = $5

r =

= Holding Period Return = E(R)

E(R) = (P1 - P0 + DIV) / P0 = r

r: market capitalization rate

4.2 Stock Valuation

A. Today’s Price

P1 - P0

P0

DIVP0

+=

Q: What happen if P0 is different from $100 ?

$ 100 ; equilibrium price if 15% is an appropriate discount rate

P0 = (P1 + DIV) / (1+r) = (110 + 5 ) / 1.15 = 100

B. What determines next year’s price ?

P0 = [D0 • (1 + g)] / (r - g) = D1 / (r - g)

Assume: Dividend grows at a constant rate; g

P0 = (P1 + D1) / (1 + r), P1 = (P2 + D2) / (1 + r)

P0 = D1 / (1 + r) + (P2 + D2) / (1 + r)2

= D1 / (1 + r ) + D2 / (1+r)2

+ D3 / (1 + r)3 + ………

Valuation Model

=

t=1Dt / (1 + r)t

D1 / P0 : Dividend Yield

g : Dividend Growth

r = D1 / P0 + g

4.3 Simple Way to Estimate r

EX : Pinacle West Corp (p 69)P0 = $41, Div1 = $1.27, g = 5.7%

r =

g = Plowback ratio * ROE =

ROE = EPS / Book Equity per Share = 0.1

Plowback Ratio = 1- Payout ratio = 0.53

Payout ratio = DIV1 / EPS = 0.47

Alternative Approach:

r = 0.031 + 0.053 = 0.084 or 8.4%

Some Warnings about Constant-Growth Formulas

1. Individual stock’s r is subject to estimation errorsPortfolio approach

2. Growth rate can rarely sustained indefinitelyEx. Growth-tech

DIV1=$0.05, P0=$50, Plowback Ratio=80%, ROE=25%

g =

r =

YEAR1 YEAR2 YEAR3 YEAR4

Book equity

Earning pershare, EPS

Return on Equity, ROE

Payout ratio

Dividends pershare, DIV

Growth rateof dividends

10.00 12.00 14.40 15.50

2.50 3.00 2.30 2.49

.25

.20

.25 .16 .16

.20 .50 .50

.50 .60 1.15 1.24

- .20 .92 .08

Ex: at t=3 and thereafter ROE =16% Firm responds by plowing back 50% of earnings

g =

Table 4.2

• General DCF formula to find the capitalization rate r:

DIV1

1+rP0 =DIV2

(1+r)2+ +DIV3 + P3

(1+r)3

P3 =

P0 =

50 =

4.4 The link between stock price and earning per Share

Growth stock vs Income stock

A. Income Stock

No Growth Perpetuity Model

P0 =EPS1

r = rDIV1

(EX) Expected Return = Dividend Yield = 10/100 =.10 = r

Price = DIV1 / r = EPS1 / r =

B. Growth Stock (r=10%)

NPV =

$ 1 (each year)

Invest $10 into project with permanent return of 10%

at t = 1: (once & for all)

This investment contributes “0” to value.

(EX) Return on project is higher or lower than 10%;

NPV? (go to table 4-3)

Table 4-3Effect on stock price investing an additional $10 in year 1 at different rates of return.Notice that the earnings-price ratio overestimates r when the project has negative NPVand underestimates it when the project has positive NPV.

Project's impact Project Rate Incremental Project NPV on Share Price Share Price EPS1

of Return Cash Flow, C in Year 1ain Year 0 b

in Year 0, P0

P0 r

.05 $ .50 - $ 5.00 - $ 4.55 $ 95.45 .105 .10

.10 1.00 0 0 100.00 .10 .10

.15 1.50 + 5.00 + 4.55 104.55 .096 .10

.20 2.00 + 10.00 + 9.09 109.09 .092 .10

.25 2.50 + 15.00 + 13.64 113.64 .088 .10

a Project costs $ 10.00 (EPS1). NPV = - 10 + C / r, where r = .10

b NPV is calculated at year 1. To find the impact on P0, discount for 1 year at r = .10

In general :

P0 = PVGOEPS1

r +

PVGO : Present Value of Grow Opportunity

Sum of all NPVs (per share)

EPS1

rCapitalized value of average earning under a no-growth policy

:

P0 = PVGOEPS1

r +

Divide each side by EPS

P/E = 1r

PVGOE

+

Q : Japanese firm : P/E 50U.S. firm : P/E 17

Is Japanese firm growing fast?

Determinants of P/E Ratio

1. Cost of Capital(r): “-” 2. Conservative accounting procedure(EPS): “-”3. Growth opportunities(PVGO): “+”

If EPS1 = $ 8.33, Payout ratio = D1 / EPS1 = 5 / 8.33 = 0.6

If ROE = .25, g =

P0 = D1 / (r - g) =

r = 15 % , D1 = $ 5

P0 =

EX : Fledgling Electronics Case (p73)

Analyze: $ 44.44Plowback Ratio = .4, 8.33 * .4 = $ 3.33 Invest: $ 3.33 at 25% (ROE) .25 * 3.33 = $ .83

at t = 1; NPV1 = -3.33 + .83 / .15 = 2.22 at t = 2; Invest 3.33 * 1.1 = 3.69 (g = 10%)

NPV2 = -3.33 * 1.1 + (.83 * 1.1) / .15 = 2.44

PVGO = NPV1 / (r - g) = 2.22 / (.15 - .1) = $ 44.44

This is growth stock, not because g = 10%, but because

Table 4-4 Estimated PVGOs (p.76)

Market PVGO, Stock Capitalization PVGO Percent of

Stock Price, P0 EPS* Rate, r** =P0 - EPS/r Stock Price P / EIncome Stocks: AT & T $52.00 $2.85 .094 $21.70 41.7 18.2

Conagra 26.00 1.33 .106 13.50 51.7 19.5

Duke Power 60.00 3.58 .094 21.90 36.5 16.8 Exxon 64.00 2.89 .099 34.70 54.3 22.1

Growth Stocks:

Compaq 30.00 0.69 .123 24.40 81.3 43.5 Merck 120.00 4.43 .118 82.50 68.7 27.1 Microsoft 101.00 2.08 .165 85.10 84.2 48.6

Wal-Mart 60.00 0.73 .094 52.20 87.1 82.2

* EPS defined as the average earnings under a no-growth policy. As an estimate of EPS, we use the forecasted earnings per share for the 12 months ending March31, 1999. Source: Value Line.* The market capitalization rate was estimated using the capital asset pricing model. We describe this model and how to use it in Section 8.2 and 9.2. EX: market risk premium = 6%

C. Some Example of Growth Opportunities

Why NPV leads to better

Investment Decisions

than Other Criteria

Why Net Present Value Leads to Better Investment Decisions than Other Criteria

Chapter 5

5.1 Review of Basics

1 Forecast Cash Flow

2 Determine appropriate Cost of Capital

3 Discount with Cost of Capital

Q : Why NPV ?

• All cash flows are considered

• Time Value of Money

• NPV is not affected by manager’s taste, accounting method, profitability of existing business, and profitability of other independent business

CASH FLOWS, DOLLARSPayback NPV at

Project C0 C1 C2 C3 Period, Years 10 Percent

B - 2,000 + 500 + 500 + 5,000 3 2,642

C - 2,000 500 +1,800 + 5,000 2 -58

D - 2,000 + 1,800 + 500 + 0 2 +50

5.2 Payback Period

• Number of years it takes before cumulative cash flow recovers initial investment

5.3 Book Rate of Return

Book Rate of Return Book incomeBook assets

=

Cash flow vs. Book Income

Problems :

Computing the average book rate of return on an investment of $9000 in project A CASH FLOWS, DOLLARS

Project A Year 1 Year 2 Year 3

Revenue 12,000 10,000 8,000

Out-of-Pocket cost 6,000 5,000 4,000

Cash flow 6,000 5,000 4,000

Depreciation 3,000 3,000 3,000

Net income 3,000 2,000 1,000

Average book rate of return = average annual income

= 2,000

= .44average annual investment 4,500

Year 0 Year 1 Year 2 Year 3

Gross book value of investment $ 9,000 $ 9,000 $ 9,000 $ 9,000

Accumulated depreciation 0 3,000 6,000 9,000

Net book value of investment $ 9,000 $ 6,000 $ 3,000 $ 0

Average net book value = $ 4,500

Example

(Rule) Accept IRR>k NPV>0

Reject IRR<k NPV<0

C0 = - 4,000 k: cost of capitalC1 = 2,000 C2 = 4,000

5-3 Internal Rate of Return: IRR Discount rate that makes NPV = 0

NPV = -4,000 + (1+IRR)

2,000+

4,000

(1+IRR)2= 0

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

10Discount rate (%)

Net Present Value, dollars

IRR=28%

20 30 50 60 80 90 1007040

Pitfall 1. Lending vs. Borrowing?

CASH FLOWS, DOLLARS

NPV atProject C0 C1 IRR, Percent 10 Percent

A - 1,000 + 1,500 + 50B + 1,000 - 1,500 + 50

CASH FLOWS, DOLLARSNPV at

Project C0 C1 C2 C3 IRR, Percent 10 PercentC + 1,000 - 3,600 + 4,320 - 1,728 + 20 - .75

-20

0

20

40

60

10

Discount rate (%)

Net Present Value, dollars

20 30 50 60 80 90 1007040

Pitfall 2. Multiple Rates or Return

Pretax

Tax

Net

1 42 53 60

-1,000 300 300 300 300 300 300

+500 -150 -150 -150 -150 -150

-1,000 800 150 150 150 150 -150

CASH FLOWS, DOLLARSNPV at

Project C0 C1 C2 IRR, Percent 10 Percent

D + 1,000 - 3,000 + 2,500 none + 339

1000

NPV

500

0

-500

-1000

Discount Rate

IRR=15.2%

IRR=-50%

Pitfall 3. Mutually Exclusive Projects

3.1 Different scale

CASH FLOWS, DOLLARS NPV at

Project C0 C1 IRR, Percent 10 Percent

E - 10,000 + 20,000 100F - 20,000 + 35,000 75

CASH FLOWS, DOLLARS NPV at

Project C0 C1 IRR, Percent 10 Percent

F-E - 10,000 + 15,000 50 + 3,636

CASH FLOWS, DOLLARS IRR, NPV at

Project C0 C1 C2 C3 C4 C5 Etc. Percent 10 Percent

G - 9,000 +6,000 +5,000 +4,000 0 0 … 33 3,592

H - 9,000 +1,800 +1,800 +1,800 +1,800 +1,800 … 20 9,000

I -6,000 +1,200 +1,200 +1,200 +1,200 … 20 6,000

3.2 Different pattern of cash flow over time

10,000

NPV, dollars

0

-5000

Discount Rate,

percent

33.3

15.6

+5,000+6,000

10 20 30 40 50Project G

Project H

(generally)

IRR vs. r1

r2 ?

r3

NPV = - C0 + C1 / (1+r1) + C2 / (1+r2)2 + …

Pitfall 4. What happens if term structure is not flat?

CASH FLOWS, MILLIONS OF DOLLARS NPV at

Project C0 C1 C2 10 Percent

A - 10 + 30 + 5 21

B - 5 + 5 + 20 16

C - 5 + 5 + 15 12

5.5 Limited Resource (Capital Rationing)

<$10> t=0

CASH FLOWS, MILLIONS OF DOLLARS NPV at Profitability

Project C0 C1 C2 10 Percent Index

A - 10 + 30 + 5 21 2.1

B - 5 + 5 + 20 16 3.2

C - 5 + 5 + 15 12 2.4

D 0 - 40 + 60 13 0.4

<$10> t=0, t=1

• More Elaborate Capital Rationing Models We

accept proportion A of project A.

NPV of accepting A of A

Previous Example

NPV =

Constraint: (Costs)

at t = 0, 10 A + 5 B + 5 C + 0 D 10

at t = 1, 40 D 30A + 5 B + 5 C + 10

0 A , B , C , D 1

Maximize: 21 A + 16 B + 12 C + 13 D

Subject to : 10 A + 5 B + 5 C + 0 D 10

-30 A - 5 B - 5 C + 40 D 10

0 A , B , C , D 1

Making Investment Decisions with the Net Present Value Rule

Chapter 6

• How to apply the rule to practical investment problems?

• Question

What should be discounted?

CF: relevance, completeness, consistency, accuracy

How NPV rule should be used when there are

project interactions?

• Estimate Cash Flow on an Incremental Basis

Average vs. incremental

Include all incidental effects

Do not forget NWC requirement

Forget sunk cost

Include opportunity costs

Beware of allocated overhead costs

Consider spillover effect “erosion”

• Treat Inflation consistently. – Real CF : discount with real rate – Nominal CF: discount with nominal rate

(Ex) C0 C1 C2 C3

Real CF -100 + 35 +50 +30 rN = 15%, I = 10%

NPV =

NPV =

6.2 Example - IMFC Project

• Initial investment: $ 10 mil

• Salvage value at year 7: $ 1 mil (sold)

• Depreciation: 6 year straight line with arbitrary

salvage of : $ 500,000

annual depreciation = = $ 1.583

mil

9.5 mil

6

Table 6 - 1 Nominal Cashflow

Ex: forecast of inflation: 10%

IM&C's guano project - revised projections reflecting (figures in thousands of dollars)

PERIOD

0 1 2 3 4 5 6 71. Capital investment 10,000 -1,949*

2. Accumulated

depreciation 1,583 3,167 4,750 6,333 7,917 9,500 0

3. Year-end book value 10,000 8,417 6,833 5,250 3,667 2,083 500 0

4. Working capital 550 1,289 3,261 4,890 3,583 2,002 0

5. Total book value

(3 + 4) 10,000 8,967 8,122 8,511 8,557 5,666 2,502 0

6. Sales 523 12,877 32,610 48,901 35,834 19,717

7. Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830

8. Other costs ** 4,000 2,200 1,210 1,331 1,464 1,611 1,772

9. Depreciation 1,583 1,583 1,583 1,583 1,583 1,583

10. Pretax profit

(6 - 7 - 8 - 9) -4,000 -4,097 2,365 10,144 16,509 11,148 4,532 1,449**

11. Tax at 35% -1,400 -1,434 828 3,550 5,778 3,902 1,586 507

12. Profit after tax -2,600 -2,663 1,537 6,594 10,731 7,246 2,946 942* Salvage value.

** The difference between the salvage value and the ending book value of $ 500 is a taxable profit

0 1 2 3 4 5 6 7

1. Sales

2. Cost of goods and sold

3. Other costs

4. Tax on operations

5. Cash flow from operation6. Change in working capital7. Capital investment and Disposal8. Net cash flow9. Present value at 20%

Net present value = +3,519(sum of 9)

4,000

-1,400-2,600

-10,000

-12,600

-12,600

523

837

2,200

-1,434-1,080

-550

-1,630

-1,358

12,887

7,729

1,210

828

3,120

-739

2,381

1,654

32,610

19,552

1,331

3,550

8,177

-1,972

6,205

3,591

48,901

29,3451,464

5,778

12,314

-1,629

10,685

5,153

35,834

21,492

1,611

3,902

8,829

1,307

10,136

4,074

19,717

11,830

1,772

1,586

4,529

1,581

6,1102,046

2,002

1,442

3,444961

Period

IM&G’s guano project-cash-flow analysis(thousand)

• Cash flow = Sales - CGS - Other costs - Taxes

• Net cash flow = Cash flow from operation

Networking capital

[- Initial Investment + Recovery of Salvage Value]

• NPV =

6.3 Project Interacting

Choosing between Long & Short Equipment

C1C0 C3C2PV

at 6%

A

B

+15 +5 +5 +5

+10 +6 +6

28.37

21.00

Equivalent Annual Cost

C1C0 C3C2PV

at 6%

Machine A

EACA

+15 +5 +5 +5

+10 +6 +6

28.37

21.00Machine B

EACB

x x x

y y

28.37

21.00

Risk, Return & opportunity

Cost of Capital

Risk and Return & Opportunity Cost of Capital

Chapter 7&8

7.1 Seventy-Two year of Capital Market

0.1

10

1000

1925 1933 1941 1949 1957 1965 1973 1981 1989 1997

1,828 S&P

5,520 Small Cap

55.38 Corporate Bonds

39.07Government Bonds14.25 Treasury Bills

Dollars

0.1

10

1000

1925 1933 1941 1949 1957 1965 1973 1981 1989 1997

613.5 Small firms

203.2 S&P 500

6.16 Corporate bonds4.34 Government bonds

1.58 Treasury bills

Dollars

PORTFOLIO

AVERAGE ANNUALRATE OR RETURN

NOMINAL REAL

AVERAGE RISK PREMIUM(EXTRA RETURN VS.

TRESURY BILLS)

Treasury bills

Government bonds

Corporate bonds

Common stocks (S&P 500)

Small firmcommon stock

3.8

5.6

6.1

13.0

17.7

.7

2.6

3.0

9.7

14.2

0

1.8

2.3

9.2

13.9

Average rate of return on Treasury bills, Government bonds, Corporate bonds, and common stocks, 1926-1997

(Percent per year)

7.2 Measuring Portfolio Risk

• Variance (Standard Deviation)

• Expected = Ri * Pi = E (R) = R

• Variance = (Ri - R)2 * Pi = 2 = V

• Risk

Systematic Risk: market risk

macro-economic variables

Unsystematic Risk: firm unique or specific risk

PORTFOLIO

Treasury billsLong-term government bondsCorporate bondsCommon stock (S&P 500) Small-firm common stocks

3.2

STANDARD DEVIATION() VARIANCE(2)

9.28.7

20.333.9

10.284.675.7

412.11149.2

PERIOD

1926-1929

MARKET SD()

1930-19391940-19491950-19591960-19691970-19791980-19891990-1997

23.9%41.617.514.113.117.119.414.3

STOCK

AT&TBristol-Myers SquibbCoca-ColaCompaq Exxon

22.6

STANDARD DEVIATION() STOCK

STANDARD DEVIATION()

17.1

19.7

42.0

13.7

General ElectricMcDonald’sMicrosoftReebok Xerox

18.820.8

29.4

35.4

24.3

Stock

BPDeutscheBank

FiatHudsonBay

16.3

SD()

23.2

35.2

26.3

30.1KLM

MARKET

UKGermany

Italy

Canada

Netherlands

12.2

11.3

24.5

11.7

14.2

SD() Stock SD() MARKET SD()

LVMHNestle

Sony

TelefoniadeArgentina

25.818.9

27.5

52.2

FranceSwitzerland

Japan

Argentina

16.6

14.6

17.4

28.6

0

5 10 15

Number of Securities

Por

tfol

io s

tand

ard

devi

atio

n

Market risk

Uniquerisk

n = 2

7.3 Calculating Portfolio Risk

Itself Variance; 2(,)

Between A, B Covariance; 2(,)

A B

A

B

A

B

Weights; A , B , A + B = 1

A

B

A

B

2A

AB

BA 2B

Portfolio Risk =

Example;

Bristol-Myers :

McDonald’s :

0.55

0.45

0.171

0.208

BM = 0.15

2p =

n=3

Variance:

Covariance:

n=4

Variance:

Covariance:

lim VP N

VP = 2P =

2P = VP =

(Ex) mutual fund

Limits to Diversification

N * (1/N)2 2 + (N2 - N) * (1/N2) cov

2 : average variancecov : average covariance

(1/N) 2 + (1 - 1/N) cov

= 1

2P = X1

2 12 + X2

2 22 + 2X1X2 1 2 * 1

= (X1 1 + X2 2 )2

( a b)2 a2 + b2 2ab

P = X1 1 + X2 2 , when = 1

There is:• no diversification• no risk reduction

* Portfolio risk is simply weighted average of individual risk; linear combination !

Special Cases

= - 1

2P = X1

2 12 + X2

2 22 - 2X1X2 1 2

= (X1 1 - X2 2 )2

P = X1 1 - X2 2 , when = -1

• Risk may be completely eliminated by combining

X1, X2 (Ex)

• Portfolio Risk is (again) a linear combination of

individual risks.

A B

E(R) 10% 12%

2 9% 16%

AB = -1

Find the weights, A, B for Minimum Variance Portfolio. ( p = 0)

What is the risk & return of that portfolio?

* General case : -1

We need Calculus.

Example

• Efficient Frontier

Ep • B

A •

P

AB = 1

= -1 • BEp

P

= -1 A •

Generally 1

P

Ep • B

A •

09 11 13 15 17 19 21

10

12

14

16

18

20

22

0 P

E(RP)

P

Efficient Portfolio

E(RP)

2P = X1

2 12 + X2

2 22 + 2X1X2 1 2 12

(risk-free asset : 2 = 0 )

- Lending2

P = X12 1

2 P = X1 1 (linear combination)

EP = X1R1 + X2Rf

- Borrowing 2

P = ( X* + 1 )2 12 + ( -X* )2 2

2 + 2( 1+X* )( -X* ) 12

P = (1+X*) 1

EP = (1+X*) R1 - X* Rf

Portfolio Risk : Linear combination of individual risk

We Introduce Borrowing & Lending (p193)

Combination of Risky(A) and Risk Free Asset

Rf

A•

New Efficient Portfolio

Rf

A•

C

•

•

•

•Old EfficientPortfolio

B

T D

Rf

•T

EM

EP

PM

• Risk-return relationship for efficient portfolios

• Intercept: Rf price of time

• slope: (EM - Rf) / M price of risk Ep = Rf + [ (EM - Rf) / M ] x P

T is a market portfolio; MCapital Market Line CML

• Capital Asset Pricing Model: CAPM Apply Portfolio Theory to evaluate all risky assets

We can eliminate unsystematic risk by combining securities. (it cancels each other)

We can not eliminate systematic risk since it moveswith market as a whole

Systematic Risk vs. Unsystematic Risk

Therefore,

= Rf +

= Rf +

= Rf + amount of risk Price of risk

• Systematic Risk = Market risk = Covariance(iM)

Required Rate of Returnon Risky Asset

Risk-free Rate(Rf)

RiskPremium= +

= Rf +

STOCK


.65

BETA STOCK

.95

.98

1.13.73


1.29.95

1.26

.871.25

BETA

STOCK

.74

BETA STOCK

1.05

1.11

.51

1.13

1.001.01

1.03

BETA

BPDeutscheBank

FiatHudsonBayKLM

LVMHNestle

Sony

Telefonia deArgentina 1.31

STOCK


.65

BETA

.95

.981.13.73


1.29.95

1.26.87

1.25

EXPECTED RETURNrf+(rm - rf)

10.7%13.113.314.511.315.813.115.612.513.9

Summary

“”

1) Covariance risk (normalized) iM

2M

2) Sensitivity of stock i’s return with respect to

market

Ex:

Security Market Line: SML

1) CAPM Line2) Equilibrium Line; If asset is correctly priced (in its equilibrium), in terms of CAPM, it falls on this line.

Below this line : Above this line :

E(Ri)

i0 1

?

?

Rf

E(R)

0 1.0

rm

rf

• A

• B

• C

0.5 1.5

Market lineAvg Risk Premium 1931-91

Portfolio Beta1.0

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium

12

3

4

5 6 78

9

10

Avg Risk Premium 1931-65

Portfolio Beta1.0

Market Line30

20

10

0

Investors

Market Portfolio12

34 5 6

7 89

10

Avg Risk Premium 1966-91

Portfolio Beta1.0

30

20

10

0

Investor

Market Portfolio

Market Line

12 3 4 5

6 7 89

10

8.4 Some Alternative Theories

Arbitrary Pricing Theory

Assumes that each stock’s return depends partly on macroeconomic factors or noise (event that are unique to company)

Expected Premium

= r - rf = b1 (r1- rf ) + b2 (r2 - rf )

+ b3 (r3 - rf ) + … …

R = a + b1rf1 + b2rf2 + b3rf3 + … … noise

APT example1. Identify the Macroecnomic Factors

• Yield Spread• Interest Rate• Exchange Rate• Real GNP• Inflation

2. Estimate the Risk Premium for Each Factor

Factor Estimated risk premium(rfactor - rf)Yield spread

Interest rateExchange rateReal GNPInflationMarket

5.10%-.61-.59.49

-.836.63

3. Estimate the Factor Sensitivity

Factor risk

(b)

Estimated risk premium(rfactor - rf)

Yield spread

Interest rate

Exchange rate

Real GNP

Inflation

Market

5.10%

-.61

-.59

.49

-.83

6.63

Total

Factor Factor risk premium

[b(rfactor - rf)]

1.04

-2.25

.70

.17

-.18

.32

5.30%

1.37

-.41

.08

.15

2.04

8.53%

Capital Budgeting and Risk

Chapter 9

Firm Value = PV(AB) = PV(A) + PV(B) = sum of separate assets

PV(A), PV(B) are valued as if they were mini-firms

in which stockholders invest directly.

Each project should be evaluated at its own Cost of Capital

(implication of Value Additivity Principle)

Are the New Projects More Risky or Less Risky than its Existing Business?

r

rf

•A

• B

Cost of Capital

• True Cost of Capital

- depends on the use to which the capital is put

- Project beta ()

Expected Return = r = rf + (project beta) (rm - rf) • “” of project or division

- Look at an average of similar companies

(or industry beta) - Firm’s borrowing policy (leverage) affects its stock

beta

- Project beta shifts over time.

Industry Beta and Divisional Cost of Capital

Individual measurement error

Portfolio error cancelled out

If you consider across-the-board expansion,

such as new division,

What is the “” for new division?

Answer:

• Measuring Betas

– Using monthly stock return on IBM

– Using monthly market return

(Ex) 60 months

R1

IBM R1M

R2IBM R2

M

R60

IBM R60M

… …

… …

( = alpha)

Average rate of price appreciation or depreciation,

born by stock-holders when investors in the market

as a whole earn nothing.

R-squared R2

The proportion of variance of stock price change

that can be explained by market movement.

means systematic risk / total risk

= -0.65% ; -0.65 12 -7.8%

Alpha = -.65Change in market index

Beta = 1.30

Change in prices of DEC common stock

9.2 Capital Structure & Company Cost of Capital(COC)

Cost of Capital; hurdle rate minimum return required to make firm value unchanged.

Depends on

also depends on

* Financial leverage does not affect the risk or the

expected return on the firm’s assets.

But,

How Changing Capital Structure Affects Expected Return?

CompanyCost of Capital

(WACC) = r d r eD

D + E +

EE + D

= r Asset = r portfolio

(EX) B/S (market value)A 100 D 40

100 100

r d = 8% r e = 15%

r Asset =

60E

• (Now) : Issue 10 equity, Retire 10 debt

* The change in financial structure does not affect

rAssets =

B/S (market value)A 100 D 30

100 100

70E

does affect

(Ex) lower leverage: rD 7.3% (Given)

How does Changing Capital Structure Affect Beta?

Assets = Portfolio =DV

EV

D + E

V = D + E D = 0.2 E = 1.2

A =

After refinancing; D 0.1(Given)

Expected return (%)

rdebt=8

rassets=12.2

requity=15

20

0 .2debt=Beta

.8assets= equity=1.2

Before Refinancing

20

0

Expected return (%)

.1debt=

rdebt=7.3

rassets=12.2

requity=14.3

Beta .8assets= equity=1.1

After Refinancing

9.3 How to Estimate the company Cost of Capital

• Pinnacle West’s Common Stock

.15.51Average Portfolio

21.37.ResourcesL&PP

21.43.Corp.West Pinnacle

23.70. EnergyPECO

15.39. EnergyOGE

19.35.System ElectricNE

18.65.Inc. GPU

19.66.Associate UtilitiesEastern

17.56. EnergyDTE

20.65. EdisonConsolidated

18.30. HudsonCentral

19.60. ElectricBoston

ErrorStandard.Beta

requity = rf + equity [ rm - rf]

= 0.045 + 0.51 0.08 = 0.0858

8.6%

rd = 6.9%, re = 8.6%, = 0.43, = 0.57

WACC = Company Cost of Capital

= rd + re

DV

EV

DV

EV

9.4 Discount Rates for International Projects

• Foreign investments are not always riskier.

.47.1203.80Taiwan

.35.1472.36Kazakhstan

.62.1603.80Brazil

1.46.4163.52Argentina

Betacoefficient

Correlation Ratio

• Foreign Investment in the US

09 11 13 15 17 19 21

10

12

14

16

18

20

22

Taiwan Index

US Index

0 P

E(RP)

9-4 Setting Discount Rate when you can’t calculate

Think about the determinant of asset beta

Avoid fudge factors

Do not add fudge factors to the discount rate instead adjust cash flow forecasts

(Ex) dry hole, FDA approval, politica1 unstability in foreign country etc

(Ex)

Q: What are industries which are risky,

but have low ?

• Determinants of Asset Beta:

Operating Leverage

Cyclicality: Firms whose revenue depend on business cycle high

Commitment to fixed production charges

• High fixed cost ratio High operating leverage

High Asset Beta

Why ?

$

Q

Unit VariableCost

Break Even Point Analysis

FixedCost

TotalCost

Profit

Loss

FC

TC

TR

Low Fixed Cost(high Variable Cost) Low OL

BEF

FC

TC

TR

High Fixed Cost(Low Variable Cost) High OL

9-6 Another Look at Risk and Discounted Cash flow

Risk-adjusted:

t=1PV = [Ct / (1+r)t], r = rf + (rM - rf)

n

(Ex) r = 6 + 0.75 8 = 12% Year CF PV 1 100 89.3 2 100 79.7 3 100 71.2 240.2

x = 94.658 (x = certainty equivalent cash flow)

1001.12

100(1.12)2

= 89.3 =x

(1.06)2

x = 100 (1.06/1.12)2 = 89.57

• General Solution

Certainly equivalentCash Flow at time t

RiskyCash Flow at time t

1+rf

1+r

t

We call t =

=

1+rf

1+r

t

Certainty equivalent coefficient 1 = (1.06 / 1.12) = 0.946 2 = (1.06 / 1.12)2 = 0.896 3 = (1.06 / 1.12)3 = 0.848

Valuing CE cash flow

PV = CE(CF)(1 + rf)

CF1 + r

=

(Example) E(C) = -1,000,000 0.5 = -500,000

r = 25%

Convert into Certainty Equivalent cash flow:

5001.25

125(1.25)t

t=2NPV = -125 - +

= -125 or -$125,000?

NPV = -1000 + (250/0.1) = +1500 (50% chance)

NPV = 0 (50% chance)

E(NPV) = 1500 0.5 = 750 (if = 0.5)

NPV = -125 + = 225.5 or $225,000(750 0.5)

1.07

Success

Failure

Making Sure Managers Maximize NPV

Chapter 12

12.1 Incentives

A. Agency Problems in Capital Budgeting

• Reduced Effort

• Perquisites

• Empire Building

• Entrenchment

• Avoiding Risk

B. Monitoring

C. Compensation

6.120.11702,30347-Walt Disney

2.78.9420,13298UAL

5.87.15963,4335Safeway

5.121.20885,423,119 MorrisPhilip

8.111.47680,51,727Microsoft

5.1423.0219,221,688Merck

3.1321.8138,181,327Johnson & Johnson

8.117.867,4312,743-IBM

7.1515.224,18599-Packard-Hewlett

7.95.982,8873,527- MotorsGeneral

7.1217.753,5672,515 ElectricGeneral

1.912.158,2721,719 MotorFord

0.912.223,0246,81ChemicalDow

9.7%36.0%$10,814$2,442ColaCoca Capital

ofCost

Capital

on Return

Invested

CapitalEVA

Corporate Financing and Market Efficiency

Chapter 13

• So far, we assume ‘all equity’ financing.

Stockholders supply all the firm’s capital, bear all the business risks, and receive all the rewards.

<Questions>

How to spend $? How to raise $?

?

B/S

13.1 We always come back to NPV

(ex) Government offer: $100,000, 10yrs at 3%Market fair rate: 10%

NPV = Amount borrowed - PV of interest payments

- PV of loan payment

3,000(1.10)t= +100,000 -

t=1

10- 100,000

(1.10)10 = $43,200

Difference between Investment & Financing Decisions Easy reverse Abandonment value is O.K. Lose or make money is not easy

80

130

180

Month

Lev

el

80

130

180

230

Month

Lev

el

13.2 Efficient Market Hypothesis

• Definition

Stock price reflects information immediately and completely

• Level of Efficiency- Weak Form

Stock price reflects previous price movement immediately and completely

- Semi-Strong Formall publicly available information

- Strong Formall information (public, private, and insider)

• Test of Market Efficiency

- Weak form

- Semi-Strong form

- Strong form

• Market Anomaly

- Small firm Effect

- January Effect

- Weekend Effect

Q: Is market inefficient?

The Dividend Controversy

Chapter 16

Q1 : How company set dividend?

Q2 : How dividend affect stock price?

- So far:

independent

Investment Financing

If dividend affects firm value, attractiveness of new project depends on where the money is coming from.

DividendDecision Mixed with

FinancingInvestment

decision

Given capital budgeting & financing decision,what is the effect of change in dividend?

16.1 How dividends are paid? Board of directorsRecord date

Legal Limitation Companies are allowed to pay a dividend out of surplus

but they may not distribute legal capital (par value of all outstanding shares)

Share Repurchase ’80: Ford: $1.2 bil, Exxon: $15 bil, IBM, COCA etc.

Just after 1987 Crash: Citi Corp $6.2 bil

How to Repurchase? 1. Open market repurchase 2. Tender Offer 3. Direct negotiation

16.2 Information content of Dividend

Signaling Model

Other Signaling Tools

GreenmailTarget of a takeover attempt buys off the hostile bidder by repurchasing any shares that it has acquired with premium at the expense of existing shareholders.

16.3 Dividend Controversy

MM(1961) - Dividend irrelevance

In a world without taxes and transaction costs(efficient and perfect capital market)

(Ex) B/S (Market Value)Cash 1,000FA 9,000

0 D10,000+NPV E

10,000 + NPV 10,000 + NPV

Pay dividend by issuing new shares($1,000)We want to continue project w/t cash($1,000)

• Value of original shareholders’ shares (Ex Post)

= Value of company - Value of new shares = (10,000 + NPV) - 1,000 = $ 9,000 + NPV

$1,000 cash dividend = $1,000 capital loss

Investment and borrowing policies are unaffected by dividend[overall value 10,000 + NPV, is unchanged]

* Crucial Assumption New stock holders pay fair-price

Old stockholders have received $1,000 dividend and $1,000 capital loss

Dividend policy doesn’t matter.

(Ex)

N = 1,000 shares

NPV = $2,000

Vold* =

Vold =

Number of new sharessold

=

16.4 The Rightist

Trade a safe receipt with an uncertain future gain?

Sell it!

– Market Imperfection

• Transaction costs• Temporarily depressed price• Information asymmetry about future Earning

16.4 The Leftist

Tax Argument

Weakened after 1986 ‘Tax Reform Act’

16.6 Middle of the Roaders• Without tax and transaction cost (perfect & efficient market), company’s

value is not affected by dividend policy (irrelevant): MM (1961)

• Even if with tax and other imperfections,

Q: If company increase stock price by paying more or less dividend, why have not they already done so?

(perhaps)

– “Supply Effect”

Does Debt Policy Matter?

Chapter 17

B/S

AssetStructure

CapitalStructure

Mix of differentsecurities

“Maximize V”

MM Proposition IFirm can not change the total value of securities just bysplitting its cash flows into different streams. (RHS)Firm value is determined by its real assets. (LHS)

17.1 The Effect of Leverage in a Tax Free Economy

VU: Value of unlevered firm

EL = VL - DL

1) 1% of unlevered firm

$ investment $ return (NOI)

.01 VU .01 profit

2) 1% of equity & debt of levered firm (I: interest)

$ invest $ return Debt .01 DL .01 I

Equity

NI.01 EL

.01(DL + EL)

= .01 VL

same profit (NOI) VU = VL

.01 (profit -I).01 profit

same cost (same investment)

3) Buy 1% of equity of levered firm

$ investment $ return

.01 EL .01 (profit -I) = .01 (VL - DL)

4) Alternative way: Borrow .01 DL on your account Buy 1% of equity of unlevered firm

$ investment $ return

same cost (same investment)

-.01 DL -.01 I.01 VU .01 profit.01(VU - DL) .01 (profit - I)

Same profit

VU = VL

Borrowing Equity

Example of Proposition I (p.477)

All Equity

E(EPS) = $1.5, P = $10, E(R) = 1.5/10 = 15%

N = 1,000

P = $10

VU = $10,000

NOI($) 500 1,000 1,500 2,000

EPS($) .5 1.0 1.5 2.0

ROE(%) 5 10 15 20

A

Issue: debt $5000, k = 10%, repurchase: 500 shares

B

NOI($) 500 1,000 1,500 2,000

Interest 500 500 500 500

NI($) 0 500 1,000 1,500

EPS($)

ROE(%) 0 10 20 30

0 1 2 3

N = 500P = $10, k = 10%Market value of stock: $5,000Market value of debt : $5,000

.50

1.00

1.50

2.00

2.50

3.00

500 1000 1500 2000

Equal proportions debt and equity

All equity

Expected EPS with debt and equity

Expected EPS with all equity

Expectedoperatingincome

Personal LeverageC

Borrow $10, then invest $20 in two unlevered shares(Initially, I have $10)

Earnings on two shares($)

Interest($) at 10%

Net Earnings($)

Return on $10 investment

500 1,000 1,500 2,000NOI($)

1 2 3 4

-1 -1 -1 -1

0 1 2 3

0% 10% 20% 30%

17.2 How Leverage Affects Return

E(EPS)

P

E(ROE)

Current structureall equity

Proposed structure

$1.5 $2.0

$10 $10

15% 20%

V=10,000

D=5,000

E=5,000

NOI = $1,500

N =1,000

Kd = 10%

Leverage increases EPS, but not P.

The change in EPS is exactly offset by a change in the rate at which the earning are capitalized. 15% 20%

Expected return on asset(rA) Market value of all security

NOI=

• In a perfect market, borrowing decision does not affect operating income or total market value of its securities.

• Borrowing decision does not affect expected return on firm’s assets(rA).

Assumption:

rE rA= + DE

(rA - rD)

Expectedreturn onequity

Expected return on assets

rAD

D+E= rD

ED+E+ rE

Debt/EquityRatio

= +Expectedreturn onassets

Expectedreturn ondebt

-

• Proposition II (MM)

The expected return on equity (rE) of a levered firm increases in proportion to debt to equity ratio (D/E)

& the rate depends on the spread between rA and rD. (Ex)

rA = 15% D = 5,000

rD = 10% E = 5,000

rE =

• Figure 17-2

MM’s proposition II. The expected return on equity rE increases

linearly with the debt-equity ratio so long as debt is risk-free. But if leverage increases the risk of the debt, debtholders demand a higher return on the debt. This causes the rate of increase in rE to

slow down.

r

DE

rD

Risk free debt

Risky debt

rA Expected Return on Assets=

rE Expected Return on Equity=

rD Expected Return on Debt=

The Risk-Return Trade-off

AD

D+E= D +

ED+E

E

E A +DE

(A D)-=

Investors (stock-holders) require higher returns on levered equity

17.3 The Traditional Position

Moderate degree of financial leverage

may increase rE although not to the degreepredicted by MM proposition II

Excessive debt raise rE faster

rA (=WACC) decline & later rise.

A

r

DE

rD

Traditionalist believe there is an optimal debt-equity ratio that minimizes rA

rA (MM)=

rE (MM)=

rD

rE (traditional)=

rA (traditional)=

debtequity=

Transaction Costs

Imperfections may allow firms that borrow

to provide valuable service.

(Ex. Economies of scale in borrowing)

Levered Shares might trade at premium compared to their theoretical valuein perfect market

Smart financial engineer already recognize this and shift capital structure to satisfy this client.

B

How Much Should a Firm Borrow?

Chapter 18

Question: Why do we worry about debt policy?

Evidence:

1. D/E ratio are different across the industry.

2. Imperfections:

• Tax• Bankruptcy Costs (T.C.)• Cost associated with financial distress• Potential conflicts of interests between security holders• Interactions of investment and financing decision

18.1 Corporate Taxes

Income statement

of Firm UIncome statement

of Firm L

Earnings before interest and taxesInterest paid to bondholders

Pretax income

Tax at 35%

Net income to stockholders

Total income to bothbondholders and stockholders

Interest tax shield (.35interest)

$1,000 $1,000

0 80

1,000 920

350 322

$650 $598

$0 + 650 = $650 $80 + 598 = $678

0 28

Interest Payment D=

PV(Tax shield) =

rD

(rDTC D)•

rD

TC D=

PV(Tax shield) =0.35 0.08 1000

$350=0.08

Normal Balance Sheet(Market Values)

Asset value (present valueof after-tax cash flows)

DebtEquity

Total assets Total value

Expanded Balance Sheet(Market Values)

Pretax asset value (present

value of pretax cash flows)

Debt

Government ‘s claim(present value of futuretaxes)

Total pretax assets Total value

Equity

Book ValuesNet working capital

Total assets

Market Values


$2,64417,599Long-term assets

$20,243

Long-term debtOther long-term

liabilitiesEquity

$1,3476,282

12,614

$20,243

Net working capitalMarket value of long-term assets

$134,156

$2,644

131,512

$134,156

Long-term debt

Other long-term liabilities

Equity

$1,347

6,282

126,527

Table 18.3(a)

Book Values

Net working capital

Total assets

Market Values


$2,64417,599Long-term assets

$20,243

Long-term debtOther long-term

liabilitiesEquity

6,282

11,614

$20,243

Net working capitalMarket value of long-term assets

$2,644

131,512

Long-term debt

Other long-term liabilities

Equity

6,282

Additional tax shields

Table 18.3(b)

MM & Taxes: MM Prop I with corporate tax.

VL = VU + PV (Tax Shield)

100% debt?

18.2 Corporate and Personal Taxes

Operating income$1.00

Corporate tax

Income aftercorporate tax

Personal tax

Income after all taxes

Corporate Borrowing is better If (1 - TP) > (1- TPE) * (1 - Tc)

Relative Tax Advantage of Debt =

Special Cases:

1. TPE = TP, RTAD =

MM’s original

2. (1 - TP) = (1 - TPE) * (1 - Tc) RTAD = 1.0 Debt policy is irrelevant! This case happen when Tc < TP & TPE is small.

(1 - TP)(1 - TPE) • (1 - Tc)

1(1 - TC)

(Ex) Tc = 35%, TP = 39.6% What TPE makes debt policy irrelevant?

18.3 Cost of Financial Distress

Value of firm(levered)

Value of allequity PV(tax shield)

PV (costs of financial distress)

= +

-

Debt

Mar

ket V

alue

of

The

Fir

m

Bankruptcy Costs

Payoff

Payoff tobondholders

ACE LIMITED(limited liability)

1,000

500

Assetvalue1,000500

Payoff

Payoff tobondholders

ACE LIMITED(unlimited liability)

1,000

500

Assetvalue1,000500

Assetvalue

PayoffPayoff tostockholders

1,000

01,000500

-1,000

Assetvalue

Payoff

Payoff tostockholders

1,000

01,000500

-1,000

Direct: legal fee, court fee, etc.Indirect: difficult to measure

SHARE PRICE

FRIDAYAPR 10, 1987

MONDAYAPR 13, 1987 CHANGE

NUMBER OF SHARES

(MILLIONS)

CHANGE IN VALUE

(MILLIONS)

Texaco

Pennzoil

Total

$31.875 $28.50 -$3.375 242 -$ 817

-62892.125 77.00 -15.125 41.5

-$1,445

Table 18.4

• Financial Distress without BankruptcyWhen firms get into trouble, stockholders’ & bondholders’ interests conflict. reduce value of firm

Circular File company (Book Values)

Net working capital $ 20

Fixed assets 80

Total assets $100

$ 50

50

$100

Bonds outstandingCommon stock

Total value

Circular File company (Market Values)

Net working capital $20

Fixed assets 10

Total assets $30

$25

5

$30


Total value

Risk Shift: The First Game

C0 C1

-$10$120

$ 0

(p=10%)

(p=90%)

If r=50%,

NPV = -10 +1200.1+0

1.5= -$2

Circular File company (Market Values)


Fixed assets 18

Total assets $28

$20

8

$28


Total value

(Ex1)

High Risk Project

Good (p=0.5) Bad (p=0.5)

VD

S

S =

2,000 300

D =

V =

(Ex2): Amount of Debt = $600

Low Risk Project

Good (p=0.5) Bad (p=0.5)

V

D

S

S =

1,400 1,000

D =

V =

Refusing to contribute equity capital: The second game

Good project with NPV= + $5 by investing $10


Fixed assets 25

Total assets $45

$33

12

$45

Bonds Common stock

Total value

Firm value increase by $15Bond value increase by $8Stock value increase by $7

Cost of Distress Vary with Type of Asset

Firms with intangibles having value only as a part of going concern, high technology, investment opportunities, human capital, lose more in the financial distress.

Trade off Theory of Capital Structure

Trade-off between interest tax shield and the costsof financial distress

• Company with safe, tangible asset and plenty of taxable income High debt ratio

• Unprofitable company with risky, intangible assets

Equity finance• Trade-off theory explains what kinds of companies “go private in LBO”

• Trade-off theory cannot explain why some most successful companies thrive with little debt.

18.4 The Pecking Order of Financing Choice, Information Asymmetry

Asymmetric information affects the choice between internal and external financing andbetween new issues of debt and equity securities

Pecking order: internal fund, new issue of debt,finally new issue of equity

(Exception) Firm with already excessive debt High-tech, high-growth company

Implication of Pecking Order1. Firms prefer internal financing2. Firms adopt target payout ratio & try to avoid sudden changes in dividend3. Sticky dividend policy

4. If external finance is required, debt, convertible bond, then equity

Financial Slack: Cash, marketable securities, readily saleable real assets, & ready access to the debt marketor to bank financing

More valuable to firm with plenty of positive-NPVgrowth opportunity

Interactions of Investment and Financing Decisions

Chapter 19

Introduction

• So far, all equity financing All financing decisions are irrelevant

• In this chapter,we consider capital budgeting decision when investment and financing decision interact and can not be separated

APV = BaseNPV

NPV offinancing decisionscaused by project acceptance

+

(value additivity principle)

19.1 After-tax WACC

WACC = rDDV

rEEV

+

WACC = rD (1-Tc) DV

rEEV

+

Sangria Corporation

(Book Values, millions)

Asset $100

Total assets $100

$50

50

$100

DebtEquity

Total value

(Market Values, millions)

Asset $125

Total assets $125

$50

75

$125

DebtEquity

Total value

WACC =?

rD =0.08 rE =0.146 TC=0.35

DV = E

V =

WACC =

Invest: $12.5 million

Pretax cashflow: $2.085 (perpetual)

Tax: 35%

$ 7.5 million (Equity)$ 5 million (Debt)

After-tax cashflow: $1.355 million

NPV =

Return on Investment =

Return on Equity:

NOI

I

Earning After tax

-Tax

2.085-0.4 (=0.085)

1.685

1.095

Expected return on Equity 1.0957.5= = 0.146

E(RE) = rE NPV=0

-0.59 (=1.6850.35)

19.2 Using WACC - Some tricks of the trade

Current Assets, Current liabilities, including cash, inventory, including accounts payable and accounts receivable and short-term debtPlant and equipment Long-term debt (D) Preferred stock (P)Growth opportunities Equity (E)

Firm value (V)

Total capitalization (V)

Industry Cost of Capital

Cost of capital of new subsidiaryCompany’s WACC vs. a weighted-average costof capital of for a portfolio of industry

An Application of the Railroad IndustryAggregate industry capital structure in 1979

DebtEquity

$24,383 bil$57,651 bil

29.7%70.3%

rd=7.2%, g=11.5%, D/P= 2.3%, TC = 35%

WACC =

rE =

Valuing Companies:

WACC vs. Flow-to-Equity Method

WACC• Debt ratio is expected to be constant

• Calculate tax as if firm is all equity-financed

• Usually forecast to a median-time horizon and add a terminal value to the cashflow in the horizon year• Discount at WACC evaluation of the assets and operation of the firm

Flow-to Equity Method

• Evaluation of equity

• Discount the cashflow to equity, after interest and taxes, at the cost of equity• Leverage change cost of equity change two methods give different answer

rE=rA + (rA-rD)(1-TC)DE

19.3 Adjusting WACC when debt ratios or business risks change

Rate of return

r

Debt-Equity Ratio

WACC

Opportunity cost of capital (r)

Cost of Equity(rE)

Cost of Debt(rD)

(Ex) DV = 0.4

DV = 0.2

Step1: unlevering the WACC

Calculate opportunity cost of capital

rDDV

rEEV

+r =

Step2: Estimate rD at 20% debt ratio, & Calculate new rE

rADE

+=rE (rA- rD)

* If taxes are left out, WACC equals the r and is independent of leverage

Step3: Recalculate the WACC at the new financing weight

Step1: current = 0.4DV

r =

Step2: rd = 8%, when = 0.2

rE=

Step3:

WACC=

DV

Rate of return, percent

Debt-Equity Ratio(D/E)

WACC

Opportunity cost of capital (r)

Cost of Equity(rE)

Cost of Debt(rD)8

10

12

14

.25

8.0

11.410.84

13.0

14.6

.67(D/V = .2) (D/V = .4)

Unlevering and Relevering

- Unlevering

asset = debt ( ) + equity( )DV

EV

- Relevering

equity = asset + (asset - debt)DE

or (1+ ) asset , if debt = “0” DE

*. Underlying assumption: Rebalancing Maintain the same market-value debt ratio

19.4 The Adjusted Present Value Rule

Base-NPV

NPV = -10 + [1.8 / (1.12)t ] = $0.17 mil • Issue costs. 5% of gross proceeds of issue

APV = base NPV - issue cost = .17 mil - 526,000 = -356,000 Reject it!

• Additions to the Firm’s debt capacity APV = base NPV + PV tax-shield

t=1

10

Table 19-1 Calculating the present value of interest tax shields on debt supported bythe solar heater project (dollar figures in thousands)

Debt Outstanding Interest Present Value Year at Start of Year Interest Tax Shield of Tax Shield

1 $ 5,000 $400 $140 $129.62 4,500 360 126 108.03 4,000 320 112 88.94 3,500 280 98 72.05 3,000 240 84 57.2

6 2,500 200 70 44.17 2,000 160 56 32.68 1,500 120 42 22.79 1,000 80 28 14.010 500 40 14 6.5

Total: $576

Assumptions:1. Marginal tax rate = Tc = .35; tax shield = .35 x interest.2. Debt principal repaid at end of year in ten $500,000 installments.3. Interest rate on debt is 8 percent.4. Present value calculated at the 8 percent borrowing rate. The assumption here is that the tax shields are just as risky as the interest payments generating them.

• APV = 170,000 + 576,000 = $746,000

• The value of interest Tax Shield (ITS).– We treat the interest tax shield as safe cash-inflow

& discount at 8%.– We assume firm can capture interest tax shields of

35cents on every dollar of interest.

• You can’t use interest tax shield unless you pay taxes.

• Corporate tax favors debt. Personal tax favors equity.

• A project’s debt capacity depends on how well it does.

APV for the Perpetual Crusher projectBase case NPV = - 10 + 1.355/0.12 = $1.29 mil

Financing Rule 1: Debt fixedFinancing Rule 2: Debt rebalanced

Under rule 1 PV (tax shield) = [0.350.08 5] ÷ 0.08 = $1.75 mil APV = 1.29 + 1.75 = $3.04 mil

Under rule 2 Debt is rebalanced to 40% of actual project value.

debt levels are not known & depend on the project’s actual performance. cost if capital is 12%

PV(tax shield) = (0.35 0.08 5) 0.12 = $1.17 mil APV = 1.29 + 1.17 = $2.36 mil

A. Technical Point on Financing Rule 2

• Discount at opportunity cost of capital

• Multiply the resulting PV by (1+r) and

divide by (1+rD)

PV(approx) =0.140.12 = 1.17

PV(exact) = 1.17 1.121.08

= 1.21

APV = 1.29 + 1.21 = $2.5 mil

APV and hurdle Rates

APV tells whether a project makes a net contribution

to the value of the firm

It tells break-even cashflow

APV = - Investment + PVTaxShield

CFr

(Ex) APV = - 10 + PVCF

0.12TaxShield

APV = - 10 + 0.97 = 0CF

0.12

CF = 1.084 IRR = 10.84%

General Definition of Adjusted Cost of Capital

• The Opportunity Cost of Capital (r)

• The Adjusted Cost of Capital (r*)

The expected rate of return offered in capital markets

by equivalent-risk assets.

This depends on the risk of the project’s cash flows.

Adjusted opportunity cost or hurdle rate that reflectsthe financing side effects of an investment project

Spotting and Valuing Options

Chapter 20

20.1 Call vs. Put

Call: Right to buy underlying asset at a specified price

Put: Right to sell underlying asset at a specified price

American: Exercise anytime

European: Exercise only at an expiration date

Exercise Date Exercise Price

Price of Call Options

Price of Put Options

October 1998

January 1999

January 1999

$80

80

85

$8.875

11.375

8.625

$3.25

4.75

6.875

Share Price

Value of Call

85

85

(a)Share Price

Value of Put

85

85

(b)

Value of Share

85

85

(c)

Share Price

Selling Calls, Puts, and Shares

(c)

Share Price

Value of Call Seller’s Position

-85

(a)

085

Share Price

Value of Put Seller’s Position

-85

(a)

085

085

-85

Value of Stock Seller’s Position

Share Price

Buy Share

Value of Share

$85 Future Stock Price

Sell call

Your Payoff


Your Payoff


+ =

Buy Share

Value of Share


Buy Put

Your Payoff


Your Payoff


+ =

Bank deposit paying $85

Value of Share

$85

Buy Call

Your Payoff

$85 FutureStockPrice

Your Payoff

$85 FutureStockPrice

+ =$85

FutureStockPrice

Put - Call Parity

C + PV (Ex) = P + S

Today

V1=C+PV(EX)

V2=P+S

Expiration Date

S* EX S* < EX

The Difference between Safe & Risky Bonds

Bond holder: Effectively acquire a firm

Stock holder: Effectively purchase a call optionon the assets of firm(PB=promised payment to bondholders)

Asset value $30 Bond: Asset - Call$25

$30

5

$30

Stock: CallFirm: Asset

Circular File Co. (MV)

S

Ex= $500 V (Promised Payment to Bondholders)

Stockholders’ PositionV<50 S =

V50 S =

B

Ex= $500 V (Promised Payment to Bondholders)

Bondholders’ PositionV<50 B =

V50 B =

PB: Promised Payment to Bondholders (safe)

V : Firm value (asset)

S : Stock value

B : Risky bond value

C+ PV(EX) = P + S

S+ PV(PB) = P + V

S+ B = V

B = V - S = PV(PB) - P

Value of risky debt =

Value of risklessdebt

“p”-

?

Asset value $30 Bond value =$25

$30

5

$30

Circular File Co. (Market Value)

present value of promised

payment - value of put

Stock value = asset value - present value

of promised payment +

value of put

Spotting the Option

(Ex) Incentive program:

Paid bonus of $50,000 for every $ that

price of stock exceeds $120. Maximum

bonus is set at $2 millionPay off

1200 Stock Price

$40

160

Pay off

1200 Stock Price160

Buy call with exercise price of $120 and Sell call with exercise price of $160

* Any set of contingent payoffs can be valued as a mixture of simple options on that assets

Share PriceExercise price

Valueof call

A

C

BUpper bound:Value of callequals shareprice

Lower bound:Value of callequals payoffif exercisedimmediately

20.3 What determines option values?

Payoff to call option on firm

Y’s shares

Probabilitydistribution of future price of firm Y’s shares

Payoff tooption on Y

Exercise price

Probabilitydistribution of future price of firm X’s shares

Payoff tooption on X

Exercise price

Payoff to call option on firm

X’s shares

Share PriceExercise price

Value of callson shares of firms X and Y

X

Upper bound

Lower boundY

What the price of a call options depends on

1. Increase in variables:If there is an increase in:

Stock price (P)Exercise price(EX)Interest rate (rf)Time to expiration(t)Volatility of stock price ()

Positive NegativePositivePositivePositive

The changes in the calloption price are:

2. Other properties:a. Upper bound. The option price is less than the stock priceb. Lower bound. The option price never falls below the payoff to immediate exercise (P-EX or zero, whichever is larger)c. If the stock is worthless, the option is worthlessd. As the stock price becomes very large, the option price approaches the stock price less the present value of the exercise price

20.4 An Option-Valuation Model

Constructing Option Equivalents fromcommon stocks & borrowing

Stock PriceToday

$85

Stock Price6 months later Call

$68

$106.25

rf =2.5%

Exercise price = $85

• Hedge ratio (Option delta):

Number of shares that are needed to replicate on call

Optiondelta = Spread of share prices

Spread of option prices

=

• How much to borrow?Present value of the different between the payoff fromthe option and the payoff from the option delta numberof shares

PV(37.78) = $36.86 Amount of borrowing

Option Equivalents:

Buy shares and borrow $36.86 today59

Today

Buy shares

Borrow $36.36

6 month later S* = $68 S* = $106.25

Value of call today= value of shares - $36.86 bank loan

=

59

Arbitrage Opportunity

EX 1: If call is priced at $12 : overpriced

Strategy: Sell a call option Buy 5/9 share & borrow 36.86 today

Today

+12

-47.22

6 month later S* = $68 S* = $106.25

+36.86

+ $ 1.64

EX 2: If call is priced at $9 : underpriced

Strategy: Buy a call option Sell 5/9 share of stock short & lend(deposit) $36.86 today

Today

- 9

+47.22

6 month later S* = $68 S* = $106.25

-36.86

+ $ 1.36

Risk-Neutral Valuation: All investors are indifferent about risk

Expected Return on any risky assets = rf =

E(R) = Pu Ru + Pd Rd

where, Pu + Pd = 1 Pu = probability of stock price increase in the hypothetical risk-neutral world Pu =

at t=1

at t=0

E(C1) =

C0 =

E(R) = Pu ( ) + Pd ( ) =

Ru =106.25-85

85 =

Rd =68-85

85 =

Pd =

Valuing the Intel Put Option

t=0

$85

S P

$68

$106.25

shares Intel share &

Lend $46.07 How is it computed?

Optiondelta = Spread of share prices

Spread of option prices

= =

EX=$85

Today

Sell shares

Lend $46.07

6 month later S* = $68 S* = $106.25

49

Value of put = - of share + $46.07 bank loan

=

49

20.5 The Black -Scholes Formula

Construct a situation where the stock price ischanging continuously and generate a continuumof possible six month prices

Replicate a call option by a levered investment in the stock by adjusting the degree of leverage continuously

Value of call = (delta Share price) - (bank loan)

[N(d1) P] [N(d2) PV(EX)]

where

d1

Log[P/PV(EX)] t

+2

t=

d2 t= d1 -

N(d) = cumulative normal probability density function

EX = exercise price of option; PV(EX) is calculated by discounting at the risk-free interest rate, rf

t = number of periods to exercise date

P = price of stock now = standard deviation per period of (continuously compounded) rate of return on stock

Value of call=[N(d1) P] + [N(d2) PV(EX)]

Real Options

Chapter 21

Option to make follow-on investment if the immediate investment project succeeds.

Option to abandon a project

Option to wait before investing

Option to vary the firm’s output or its production methods

Real Option

21.1 The value of follow-on investment

Table 21-1 Summary of cash flows and financial analysis of the Mark I microcomputer

(millions of dollars)

Year1982 1983 1984 1985 1986 1987

After-tax operating

cash flow (1) * -200 +110 +159 +295 +185 0

Capital Investment (2) 250 0 0 0 0 0Increase in working

capital (3)0 50 100 100 -125 -125

Net Cash Flow

(1) - (2) - (3)-450 +60 +59 +195 +310 +125

NPV at 20% = - $46.45, or about -$46 million

• Table 21-2. Valuing the option to invest in the Mark II microcomputer.

Assumptions1. The decision to invest in the Mark II must be made after

3 years, in 1985.

2. The Mark II investment is double the scale of the Mark I (note the expected rapid growth of the industry). Investment required is $900 million (the exercise price), which is taken as fixed.

3. Forecasted cash inflows of the MarkII are also double those of the MarkI, which present value of about $800 million in 1985 and 800/(1.2)3 = $463 million in 1982.

4. The future value of the Mark II cash flows is highly uncertain. This value evolves as a stock price does with a standard deviation of 35 percent per year.(Many high-technology stocks have standard deviation higher than 35%.)

5. The annual interest rate is 10 percent.

• Interpretation

The opportunity to invest in the Mark II is a 3-year call option on asset worth $463 million with a $900 million exercise price.

• Valuation

PV(EX) = 900(1.1)3 = 676

Call value = N(d1)P - N(d2) • PV(EX)

d1 = log[0.685] / 0.606 + 0.606 /2 = -0.3216d2 = d1 - 0.606 = -0.9279

N(d1) = 0.3739 N(d2) = 0.1767

Call value = 0.3739463 - 0.1767676 = $53.59 mil

21.2 The Option to Abandon

Good Demand

Bad Demand

Tech A Tech B

$18.5 $18

8.5 8

If we bail out Tech B for $10 mil when bad demand Exercise option to sell assets

Value of Tech B = DCF + Value of the abandonment Put

(Value of Flexibility)

Valuing the Abandonment Putt=1 Pr Payoff Put

Good DemandBad Demand

0.5 $ 18

0.5 $ 8

EX = $10, r = 8.3%, rf = 5%

PV=

E(R) = Pu ( ) + Pd ( ) = = rf

Pu = Pd =

E(P) = 0.46 + 0.54 =

P =1+rf

E(P)=

Value of project =

21.3 The Timing Option: rf = 5%

t = 0

If invest $180,project worth $200

GoodDemand

BadDemand

Project Value

Cash flow

Value of Call

$250 $25

$160 $16

t = 1

If undertake project today,

capture either $25, or $16 at t=1

If delay, miss out on this cashflow at t=1, but will have more information on how the project is lively to work out

Project NPV0

Value of option

to invest

Investment nowor never

Investment canbe postponed

RG=

RB=

E(R) = PG ( ) + PB ( ) = = rf

PG = PB =

t=1, E(C) =

t=0, Value of call =

Q: Do you undertake project now?

Warrants and Convertibles

Chapter 22

22.1 What is warrant?

Value of warrant

Exercise price = $15

Actual warrant value prior to expiration

Theoretical value (lower limit on warrant value)

Stock price

• Two Complications: Dividends and Dilution• Example: Valuing United Glue’s Warrants

Number of shares outstanding (N) Current stock price (P)

Number of warrants issued per share outstanding (q)

Total number of warrants issued (Nq)

Exercise price of warrants (EX)

Time to expiration of warrants (t) Annual standard deviation of stock price changes

Rate of interest (r): United stock pays no dividends.

()

1 million

$12

.10

100,000

$10

4 years

.40

10%

……………………..…………..

…………..

……….

……………

……………

……………

…………………………..

United Glue’s market value balance sheet (in $ millions)

Before the Issue

Existing assets

Total

$16

$16

$ 4 Existing loans

Common stock (1 million shares at $12 a share)

12

$16

After the Issue

Existing assets Existing loans$16 $ 4New assets financedby debt and warrants 2

New loan without warrants

1.5

Total

Total debt5.5.5 Warrants

12 Common stockTotal $18 $18 Total

United Glue has just issued a $ 2million package of debt and warrant

Suppose

$ 1.5 mil: value of debt without warrants

$ 0.5 mil: value of warrants

Each warrant costs investors =

Value of warrant from Black-Scholes formula

=

• Dilution Effect

Nq =

Nq EX =

V: value of equity

V = Total asset - debt

Share price afterexercise =

Warrant valueat maturity = Max (P - EX, 0)

= Max V + Nq•EXN + Nq

- EX, 0

Max V/N + EX1 + q

, 0=

Max VN

, 0=1

1 + q - EX

$ 12.5 mil: Current equity value of alternative firm (=18 mil - 5.5 mil) Current share priceof alternative firm = V

N= 12.5

1 mil= $12.5

Suppose of alternative firm: = 0.41

Black-Sholes value of call:

Value of warrant = 1

1 + q Value of call on

alternative firm

=

deal for United

22.2 What is a Convertible Bond

• Difference between convertible bond vs. bond-warrant package

Bond value:

Conversion value:

• The price of convertible bond depends on its bond value and its conversion value

0

1

2

3

1 2 3 4 5Value of firm ($ million)

Bon

d va

lue,

$th

ousa

nd

0

1

2

3


Con

vers

ion

valu

e, $

thou

sand

0

1

2

3


Val

ue o

f co

nver

tible

,$

thou

sand

ConvertBond paid

in full

Default

• Value at Maturity

Default

Bond paid in full

0

1

2

3


Bon

d va

lue,

$th

ousa

nd

0

1

2

3


Low

er li

mit

on C

onve

rtib

le,

$th

ousa

nd

Bond Value

Conversion Value

0

1

2

3


Val

ue o

f co

nver

tible

,$

thou

sand

Lower limit on value

Value of convertible

• Value before Maturity

A B CStock price

Value of Convertible

Bond Value

Conversion Value

Call price

Forcing Conversion

Value of convertible

bond

Value of straight

bondConversion

optionRedemption

option= + -

22.3 Difference between Warrants and Convertibles

1. Warrants are usually issued privately

2. Warrants can be deleted

3. Warrants may be issued on their own

4. Warrants are exercised for cash

5. A package of bond & warrants may be taxed differently

22.4 Why do companies issue

Warrants and Convertibles?

Valuing Debt

Chapter 23

• Present Value of Bond

Q: What determines the discount rates?

PV C(1+r1)

=C

(1+r2)2C

(1+r3)3+ + + … (1000+C)(1+rn)n+

r1 , r2 , r3 , …. rn : discount rates for cashflows to be received by the bond holders in periods 1, 2, …,n.

(Ex) Same security offers different yields at a different time.

Bonds maturing at different dates offer different rate of interestBorrowing rate of government is lower than your borrowing rate

23.1 Real and Nominal Rates of Interest

Real Rate: compensation for time value of money

Nominal Rate = Real Rate + Perspective Rate of Inflation

How Real Rate is determined?

Supply of capital: time preference for today’s consumption over future consumption

Demand of capital: Availability for profitable investment opportunities ( Positive NPV Projects)

S

D

rr1

S

D

rr2

23.2 Term Structure and Yield to Maturity

PV = C1+r1

PV =C

1+r1

C(1+r2)2

r1, r2 : Spot rate

The series of spot rates r1, r2 … Term structure of interest rates

+

• Yield to MaturityRate of return to bondholders if he/ she keeps the bonduntil maturity

Price of Bond =C

(1+y)C

(1+y)2+ + … C+F(1+y)n+

PRESENT VALUE CACULATIONS5s of ‘08 10s of ‘08

PERIOD INTEREST RATE Ct PV AT rtCt PV AT rt

t = 1

t = 2

t = 3

t = 4

t = 5

r1 = .05

r2 = .06

r3 = .07

r4 = .08

r5 = .09 Totals

$ 50

50

50

50

1,050$1,250

$ 47.62

44.50

40.81

36.75

682.43$852.11

$ 100

100

100

100

1,100$1,500

$ 95.24

89.00

81.63

73.50

714.92$1,054.29

YIELD TO MATURITYBond Price Percent (IRR)

5s of ‘0810s of ‘08

85.21%105.43

8.78%8.62

23.3 Duration and Volatility

Duration: Average time to each payment

D =1 PV(C1)

V+ … +

2 PV(C2)V

…

YEAR CtPV(Ct) AT 5.5%

1

2

3

4

5

6

137.5

137.5

137.5

137.5

137.5

1137.5

PROPORTION OF TOTAL VALUE

[PVt/V]PROPORTION OF TOTAL

VALUE TIME

130.33

123.54

117.10

110.99

105.21

824.97

.092

.087

.083

.079

.075

.584

.092

.175

.249

.314

.373

3.505

V = 1,412.13 1.000 Duration = 4.708 years

(A) 13 ¾s of 2004 (B) 7 ¼s of 2004

VB =

DB = 5.115 years

vs.

(EX) 1% changes in yield

13 ¾s of 2004 7 ¼s of 2004NEW PRICE CHANGE NEW PRICE CHANGE

Yield falls, 0.5%Yield rises, 0.5%

144.41138.11

Difference 6.30

+2.26%- 2.20

4.46%

111.42106.15

5.27

+2.46%- 2.39+4.85%

Volatility (%) Duration1+yield

VA =

DA = 4.708 years

• Hedging

By equalizing the duration of the asset and that of the liability,we can immunize against any change in interest rate

(EX) Aztec Learning has just purchased some equipment andArranged to rent it out for $ 2mil a year over eight years at 12%

Aztec finances by issuing a packaging of one year and six-year bond, each with 12% coupon to set up hedged position, find out proportion of one year and six year bond

Solution

PV of rental income =

Duration of Rental income =Duration of one year bond =Duration of 6-year bond =

Let : x is the proportion raised by 6-year bond1-x is the proportion raised by 1 year bond

Duration Package = x duration of6-year bond + (1-x) duration of

1 year bond3.9 years = x 4.6 years + (1-x) 1 years

23.4 Explaining the Term StructureTopic Why do we observe different shape of term- structure?

Ms. Long: invest $1,000 for 2 years 1,000

1,000

Forward Rate

The extra return that Ms. Long gets by lending for 2 years rather than 1 Implicit & guaranteed

(1+r2)2 = (1+ r1 ) (1+f2)

f2 =(1.105)2

1.1- 1 0.11 11%

=

=

Expected Payoff: L1 Certain Payoff: L2

1,000 (1+r1) [1+E(1r2)] vs.1,000 (1+r2)2

1,000 (1+ r1 )(1+f2)or

Strategy L1 gives higher-return if

Mr. Short: invest 1 year

Buy 1 year bond:

Buy 2 year bond & sell it after 1 year

PV of 2 year bond at year 1 =

Certain Payoff: S1 Expected Payoff: S2

1,000 (1+r1) vs. or

Strategy S2 is better if

1,000 (1+r2)2

1+E(1r2)

1,000 (1+ r1 )(1+f2)1+E(1r2)

• The Expectations Hypothesis

Ms.Long and Mr. Short try to maximize their expected return

If f2 > E(1r2) prefer 2yr. bond price bond of 2yr return of 2yr. Bond and f2

Equilibrium: f2 = E(1r2)

If f2 < E(1r2) prefer 1 yr. bond

The only reason for upward sloping term structure is investor expect the relationship such that

f2 = E(1r2)

f2 > r1 , E(1r2) > r1

• Consider “risk”

Long Case: horizon 2 yr.If Ms. Long buys 1 year bond: first year return is certain

but, uncertain “reinvestment rate” at the end of year 1

Ms. Long holds 1 year bond only if E(1r2) f2

Short Case: horizon: 1 yr.If Mr. Short buys 2 year bond: he has to sell it next year at an

“unknown price”. Mr. Short holds 2 year bond only if E(1r2) f2

Other things equal, Ms. Long will prefer to buy year bond & Mr. Short will prefer to buy year bond

The Liquidity Preference (Theory)

If more companies want to issue 2 year bond thanthere are Ms. Long to hold them,

They need to offer “Bonus” to attempt some of theMr. Short to buy 2 year bond.

Any bonus shows up as a difference between f2 & E(1r1) Liquidity Premium

In reality, there are shortage of long-term lender,liquidity premium is positive.

f2 = E(1r2) + Liquidity Premium ( = LP2)

f2 = E(2r3) + LP3

23.5 Allowing for the risk of Default

Q: Why do some borrowers have to pay a higher rateof interest than others?

Default risk premium

Expected yield

other risk premium

Rf

Promised yield y

Yield= Rf+ Risk Premium

(EX) Rf = 9% Payoff (t=1)$ 1,090

0

Probability0.80.2

Expected payoff ($) at t=1:

If default is totally unrelated to other event of economy,= default risk is wholly diversifiable

PV =

Promised yield = (expected yield = 9%)

Since default occurs in recession, ,

PV =

Promised yield = (expected yield = 11%)

say risk premium=2%

Bond Ratings“relative quality” of bond by

MOODY’S STANDARD AND POOR’SAaaAaABaa

BaBCaaCaC

AAAAAABBB

BBBCCCCCC

Investment grade

Junkbonds

PERCENTAGE DEFAULTING WITHINRATING ATTIME OF ISSUE

1 YEAR AFTER ISSUE

5 YEAR AFTER ISSUE

10 YEAR AFTER ISSUE

AAAAAABBBBBBCCC

.00 .00 .00 .03 .371.472.28

.06 .67 .22 1.64 8.3221.9535.42

.06 .74 .64 2.8016.3733.0147.46

Moody’sStandard & Poor’s

Leasing

Chapter 25

A rental agreement that extends for a year or moreand involves a series of fixed payments

What to lease?

LesseeLessor : Leasing industry

Equipment manufacturersBanksIndependent leasing company

Operating Lease

Capital Lease(financial/ full payment)

25.2 Why lease ? – Convenient (short-term)– Cancellation option – Maintenance provided– Tax-shield can be used.– Etc.

25.3 Operating lease.In real life, idle time is considered.

In operating lease, the lessor absorbs idle risk, not the lessee.

The discount rate must include a premium sufficient to compensate its shareholder for the risk of idling.

– For operating lease: Lease vs. Buy

– For financial lease : Lease vs. Borrow

Table 25-1 Calculating the zero-NPV rental rate (or equivalent annual cost) for EstablishmentIndustries' pearly white stretch limo (figures in thousands of dollars)

Year0 1 2 3 4 5 6

Initial cost -75

Maintenance, insurance, selling, and administrative costs -12 -12 -12 -12 -12 -12 -12

Tax Shield on costs +4.2 +4.2 +4.2 +4.2 +4.2 +4.2 +4.2

Depreciation tax shield +5.25 +8.40 +5.04 +3.02 +3.02 +1.51Total -82.80 -2.55 .60 -2.76 -4.78 -4.78 -6.29

NPV at 7% = -$98.15

Break-even rent (level) 26.18 26.18 26.18 26.18 26.18 26.18 26.18

Tax -9.16 -9.16 -9.16 -9.16 -9.16 -9.16 -9.16

Break-even after tax 17.02# 17.02 17.02 17.02 17.02 17.02 17.02

NPV at 7% = $98.15* no inflation; r = 7%; Tc = 35%` * Table 6-5: depreciation

* First payment: immediate # 17.02 = 65% of 26.18 7% PVA 7yrs = 5.389 5.389 * 1.07 = 5.766

25. 4 Financial LeaseTable 25-2 Cash-flow consequences of the lease contract offered to Greymare Bus Lines(figures in thousands of dollars; some columns do not add due to rounding)

NPV of 'Lease' relative to 'Buy'

Year0 1 2 3 4 5 6 7

Cost of new bus +100Lost depreciation tax shield -7.00 -11.20 -6.72 -4.03 -4.03 -2.02 0Lease payment -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9Tax shield of lease payment +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 +5.92Cash flow of lease +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98* 5 yr: depreciation (Table 6.4), 7yrs/8 times payment, Tc = 35%, rD = 10%

* After tax: rD * (1 - Tc) = 6.5%

NPV lease = +89.02 - 17.99 - 22.19 - 17.71 - 15.02 - 15.02 - 13 - 10.98

1.065 (1.065)2

(1.065)3

(1.065)4

(1.065)5

(1.065)6

(1.065)7

= -0.7 -$700

Year

0 1 2 3 4 5 6 7

Lease cash flows, thousands +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98

Table 25-3: Equivalent loan; exactly same debt service on lease.

Year

0 1 2 3 4 5 6 7

Amount borrowed at year-end 89.72 77.56 60.42 46.64 34.66 21.89 10.31 0

Interest paid at 10% -8.97 -7.76 -6.04 -4.66 -3.47 -2.19 -1.03Interest tax shield at 35% +3.14 +2.71 +2.11 +1.63 +1.21 +.77 +.36Interest paid after tax -5.83 -5.04 -3.93 -3.03 -2.25 -1.42 -0.67Principal repaid -12.15 -17.14 -13.78 -11.99 -12.76 -11.58 -10.31Net cash flow of equivalent loan 89.72 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98

How much can I borrow when I pay same cash as lease payment?

Creating Equivalent Loan

25.5 When Do Financial Leases Pay? The value of the lease to the bus manufacturer would be(Tc=35%)

Value of lease to lessor

-89.02 +17.99

+1.065

= +.70 Zero sum gameSuppose that Greymare paid no tax (Tc = 0).

Then the only cash flows of the bus lease would be:

Year0 1 2 3 4 5 6 7

Cost of new bus +100

Lease payment -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9

These flows would be discounted at 10 percent,because rD (1-Tc)= rD when Tc =0

+22.19

(1.065)2

17.71

(1.065)3+

15.02

(1.065)4+

15.02

(1.065)5

13

(1.065)6+ +

10.98

(1.065)7=

t=0

10

(1.1)t

16.9100 -Value of lease = = +100 - 99.18 = +.82 or $820

The potential gains to lessor and lessee are higher when:

The lessor’s tax rate is substantially higher than the lessee’s

The depreciation tax shield is received early in the lease period

The lease period is long and the lease payments are concentrated toward the end of the period

The interest rate rD is high - if it were zero, there would be no advantage in present value terms to postponing tax

Mergers

Chapter 33

Selling Company Acquiring Company Payment, billions of dollars

NYNEX Bell Atlantic 21.0McDonnell Douglas Boeing 13.4Digital Equipment Compaq Computer 9.1Schweizerischer Union Bank of Swiz. 23.0Energy Group PCC Texas Utilities 11.0Amoco Corp. British Petroleum 48.2Sun America American Intl. 18.0BankAmerica Corp. Nationsbank Corp. 61.6Chrysler Daimler-Benz 38.3Bankers Trust Corp. Deutsche Bank AG 9.7Netscape America Online 4.2Citicorp Travelers Group Inc. 83.0

33.2. Sensible Motives for Mergers Economies of Scale

Vertical Integration

Complementary Resources

Unused Tax Shields

Surplus Fund Free Cash Flow ?

Eliminating Inefficiencies

Diversification

Increasing Earning Per Share

Lower Financing Cost

33.3 Estimating Merger Gains and Costs

A: Buyer B: Seller

Synergy Gain = PVA+B - (PVA + PVB)

Cost = Cash paid - PVB

NPV = Gain - Cost = PVAB - (Cash-PVB)

(Ex)

PVA = 200, PVB = $50, PVA+B = $275

Gain = PVAB = + $25

Cash = $65

Firm A Firm BMarket priceper share

Number of share

Market value of firm

$ 200 $ 100

1,000,000 500,000

$ 200 mil $ 50 mil

Cost = Cash - PVB = Cash - MVB + (MVB - PBB)

= 65 -50 + (50 - 44) = $21 mil

Cash payment depends on the relative bargainingpower of the two participants

• Stock offer

N : shares received by seller

PAB: combined firm’s worth

Cost= N PAB - PVB(Ex) N = 325,000

A’s price before merger: $200PVB = $50 mil

Apparent cost =

If PVAB = $275mil (due to synergy gain)

New share price =

Cost = 0.325 -50 =

Takeover Defense Preoffer Defenses

• Shark-repellent Charter Amendments– Staggered Board– Super Majority– Fair price

• Dual class stock• Poison Pill, Poison put• ESOP

Postoffer Defenses • Litigation• Asset Restructuring• Liability Restructuring

Divestitures (sell offs) and Spin offs.

- Synergy Motivated

- Focus

- Complementary Resources

- More Efficient Contracting (Better Organization Structure)

- Raising Capital

Question:

What is the source of gain and where it is created?

Leveraged Buyouts

• Debt financed (junk-bond)

• Going private

• MBO

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