Chapter: 04(5)Risk

&Return

1

• Risk can be defined as the chance of financial loss or more formally, the variability of returns associated with a given asset.

• Return can be defined as the total gain or loss experienced on an investment over a given period of time.

2

Defining Risk & Return

• Firm-Specific Risks1. Business Risk: The chance that firm will be unable to

cover its operating costs.2. Financial Risk: The chance that firm will be unable to

cover its financial obligations.• Shareholders’-Specific Risks

1. Interest Rate Risk: The chance that the changes of interest rates will adversely affect the value of an investment.

2. Liquidity Risk: The chance that an investment cannot be easily liquidated at a reasonable price.

3. Market Risk: The chance that the value of an investment will decline because of market factors that are independent of the investment. (ex: economic, political, social)

3

Sources of Risk

• Firm & Shareholder Risks1. Event Risk: The chance that a totally unexpected event

will have a significant effect on the value of the firm or a specific investment.

2. Exchange Rate Risk: The exposure of future expected cash flows to fluctuations in the currency exchange rate.

3. Purchasing Power Risk: The chance that changing price levels caused by inflation or deflation in the economy will adversely affect the firm’s or investment’s cash flows & value.

4. Tax Risk: The chance that the unfavorable changes in tax laws will occur.

4

Sources of Risk…contd.

1. Risk- Indifferent: The attitude toward risk in which no change in return would be required for an increase in risk.

2. Risk-Averse: The attitude toward risk in which an increased return would be required for an increase in risk.

3. Risk-Seeking: The attitude toward risk in which a decreased return would be accepted for an increase in risk.

5

Risk Preferences Behavior

Risk-Averse

Risk-Indifferent

Risk-Seeking

x1 x2

seeking

indifferent

averse

Risk

Return

• Martin Products and U. S. Electric

6

Risk Measurement

Martin Products U.S. Electric

Boom 0.2 110% 20%Normal 0.5 22% 16%Recession 0.3 -60% 10%

1.0

Probability of This State Occurring

State of the Economy

Rate of Return on Stock if This State Occurs

• The rate of return expected to be realized from an investment

• The mean value of the probability distribution of possible returns

• The weighted average of the outcomes, where the weights are the probabilities

7

Expected Rate of Return

8

Expected Rate of Return

^ ^

(1) (2) (3) = (4)Boom 0.2 110% 22%Normal 0.5 22% 11%Recession 0.3 -60% -18%

1.0 km = 15%

State of the Economy

Martin ProductsProbability of This State

Occurring (Pr i)

Return if This State

Occurs (ki)Product: (2) x (3)

9

Expected Rate of Return

^ ^

(1) (2) (3) = (4)Boom 0.2 20% 4%Normal 0.5 16% 8%Recession 0.3 10% 3%

1.0 km= 15%

State of the Economy

U. S. Electric

Return if This

State Occurs (ki)Product: (2) x (3)

Probability of This State

Occurring (Pr i)

10

Expected Rate of Return

n

iii

nn2211

k

kkkk̂

1

Pr

PrPrPr

• Discrete probability distribution– the number of possible outcomes is limited, or

finite

11

Continuous versus Discrete Probability Distributions

12

Discrete Probability Distributions

-10 -5 0 5 10 16 20 25 Rate of Return (%)

Expected Rate of Return (15%)

b. U. S. ElectricProbability of Occurrence

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -

-60 -45 -30 -15 0 15 22 30 45 60 75 90 110Rate of

Return (%)Expected Rate

of Return (15%)

a. Martin ProductsProbability of Occurrence

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -

• Continuous probability distribution– the number of possible outcomes is unlimited, or

infinite

13

Continuous versus Discrete Probability Distributions

14

Continuous Probability Distributions

-60 0 15 110Rate of Return

(%)Expected Rate of

Return

Martin Products

Probability Density

U. S. Electric

• Calculating Martin Products’ Standard Deviation

15

Measuring Risk: The Standard Deviation

(1) (2) (1) - (2) = (3) (4) (5) (4) x (5) = (6)110% 15% 95 9,025 0.2 1,805.0 22% 15% 7 49 0.5 24.5 -60% 15% -75 5,625 0.3 1,687.5

Payoff

ki(ki - k)2Pr iProbability

Expected Return

kki - k (ki - k)2^

^^ ^

59.3% 3,517σσ Deviation Standard

3,517.0σ Variance

2MM

2

16

Measuring Risk: The Standard Deviation

n

1iii

2 k̂-k Variance Pr2

n

1iii

2 k̂-k deviation Standard Pr2

• Standardized measure of risk per unit of return

• Calculated as the standard deviation divided by the expected return

• Useful where investments differ in risk and expected returns

17

Measuring Risk: Coefficient of Variation

k̂Return

Risk CV variation oft Coefficien

• Portfolio– A collection of investment securities. The main

purpose of building portfolio is to diversify/minimize risk. The expected return of portfolio is calculated as:

18

Portfolio Risk & Return

N

1jjj

NN2211p

k̂w

k̂wk̂wk̂wk̂

• Correlation coefficient, r– a measure of the degree of relationship between

two variables– positively correlated stocks rates of return move

together in the same direction– negatively correlated stocks have rates of return

than move in opposite directions

19

Portfolio Risk

• Risk reduction– combining stocks that are not perfectly positively

correlated will reduce the portfolio risk by diversification

– the riskiness of a portfolio is reduced as the number of stocks in the portfolio increases

– the smaller the positive correlation, the lower the risk

20

Portfolio Risk

• Beta coefficient, – a measure of the extent to which the returns

on a given stock move with the stock market– = 0.5: stock is only half as volatile, or risky,

as the average stock– = 1.0: stock is of average risk– = 2.0: stock is twice as risky as the average

stock

21

The Concept of Beta

• The beta of any set of securities is the weighted average of the individual securities’ betas

22

Portfolio Beta Coefficients

N

1jjj

NN2211p

βw

βwβwβwβ

– A model based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium, where risk reflects diversification

23

Capital Asset Pricing Model (CAPM)

jRFMRF

jMRFj

β kk k

β RP k k

24

The Relationship between Risk and Rates of Return

stock j the on premium risk βk-k RP

premium riskmarket k-k RP

return of rate k

stock j the on return of rate k

stock j the on return of rate k̂

thjRFMj

RFMM

RF

thj

thj

freerisk

required

expected

– The line that shows the relationship between risk as measured by beta and the required rate of return for individual securities

25

Security Market Line (SML)

26

Security Market LineRequired Rate of Return (%)

Risk-Free Rate: 6%

0 0.5 1.0 2.0 Risk, j

khigh = 22

kM = kA = 14

kLow = 10

kRF = 6

Safe Stock: Risk Premium: 4%

Market (Average Stock): Risk Premium: 8%

jRFMRFj β kk k k:SML

Relatively Risky Stock: Risk Premium = 16%

• kRF is the price of money to a riskless borrower

• The nominal rate consists of – a real (inflation-free) rate of return, k*– an inflation premium (IP)

• An increase in expected inflation would increase the risk-free rate, kRF

27

The Impact of Inflation

• The slope of the SML reflects the extent to which investors are averse to risk

• An increase in risk aversion increases the risk premium, which increases the slope

28

Changes in Risk Aversion

• The risk of a stock is affected by– composition of its assets– use of debt financing– increased competition– expiration of patents

• Any change in the required return (from change in or in expected inflation) affects the stock price

29

Changes in a Stock’s Beta Coefficient

• The condition under which the expected return on a security is just equal to its required return

• Actual market price equals its intrinsic value as estimated by the marginal investor, leading to price stability

30

Stock Market Equilibrium

jj k k̂

• Stock prices are not constant due to changes in:– risk-free rate, kRF

– Market risk premium, kM - kRF

– Stock X’s beta coefficient, x

– Stock X’s expected growth rate, gX

– Changes in expected dividends, D0(1+g)

31

Changes in Equilibrium Stock Prices

Chapter: 06Interest Rates

&Bond Valuation

3220/11/2009

• Interest Rate: The compensation paid by the borrower of funds to the lender; from the borrower points of view, the cost of borrowing funds.

• Required Return: The cost of funds obtained by selling an ownership interest; it reflects the funds supplier’s level of expected return.

• Real Rate of Interest: The rate that creates an equilibrium between the supply of savings & the demand for investment funds in a perfect world, without inflation, where funds suppliers & demanders are indifferent to the term of loans or investments & have no liquidity preference, where all outcomes are certain.

33

Interest Rate Fundamentals

Nominal Rate of Interest: The actual rate of interest charged by the suppliers of funds & paid by the demander.

Nominal rate of interest = real rate of interest + inflation premium + risk premium.

Risk free rate of interest = real rate of interest + inflation premium

Term Structure of Interest Rates = The relationship between interest rate or rate of return & the time to maturity.

Yield to Maturity (YTM): Annual rate of return earned on a debt security purchased on a given day & held to maturity.

34

Interest Rate Fundamentals…contd.

• Yield Curve: A graph of the relationship between the debt’s remaining time to maturity & its YTM.

• Inverted Yield Curve: A downward slopping yield curve that indicates generally cheaper long term borrowing costs than short-term borrowing costs.

• Normal Yield Curve: An up-ward slopping yield curve that indicates generally cheaper short-term borrowing costs than long-term borrowing costs.

• Flat Yield Curve: A yield curve that reflects relatively similar borrowing costs for both short-term & long-term loans.

35

Interest Rate Fundamentals…contd.

Expectations Theory: The theory that the yield curve reflects investor expectations about future interest rates; an increasing inflation expectation results in an upward-slopping yield curve & a decreasing inflation expectations results in a downward-slopping yield curve.

Liquidity Preference Theory: Theory suggesting that for any given issuer, long-term interest rates tend to be higher than short-term rates because:

1. Lower liquidity & higher responsiveness to general interest rate movements of longer-term securities exists, &

2. Borrower willingness to pay a higher interest rate for long-term financing; causes the yield curve to be upward slopping.

36

Theories of Term Structure

• Market Segmentation Theory:Theory suggesting that the market for loans is segmented on the basis of maturity & that the supply of & demand for loans within each segment determine its prevailing interest rate; the slope of the yield curve is determined by the general relationship between the prevailing rates in each segment.

37

Theories of Term Structure…contd.

1. Default Risk: The possibility that the issuer will not pay the contractual interest or principal as scheduled.

2. Maturity Risk: The fact that the longer the maturity, the more the value of security will change in response to a given change in interest rates.

3. Contractual Provision Risk: Conditions that are often included in a debt agreement or a stock issue.

38

Debt-specific issuer & issue-related Risk

• A bond is a long-term debt instruments/obligations that promises to pay the bondholder a predetermined, fixed amount of interest each year until maturity. At maturity, the principal will be paid to the bondholder.

• In the case of a firm's insolvency, a bondholder has a priority of claim to the firm's assets before the preferred and common stockholders. Also, bondholders must be paid interest due them before dividends can be distributed to the stockholders.

39

Corporate Bond

• An indenture (or trust deed) is the legal agreement between the firm issuing the bonds and the bond trustee who represents the bondholders. It provides the specific terms of the bond agreement such as the rights and responsibilities of both parties. The bond indenture includes:1. Descriptions of the amount & timing of all interest &

principal payments,2. Standard provisions,3. Restrictive covenants,4. Sinking-fund requirements, 5. Security interest provisions.

40

Bond Indenture

1. Maintain satisfactory accounting record in accordance with GAAP.

2. Periodically supply audited financial statements.

3. Pay taxes & other liabilities when due, &

4. Maintain all facilities in good working order.

41

1) Standard Provisions

a) Require a minimum level of liquidity, to ensure against loan default.

b) Prohibit the sale of accounts receivable to generate cash.

c) Impose fixed-asset restrictions.d) Constrain subsequent borrowing.e) limit the firm’s annual cash dividend

payments to a specified percentage or amount.

42

2) Restrictive Covenants

• A restrictive provision often included in a bond indenture, providing for the systematic retirement of bonds prior to their maturity. To carry out this requirement, the corporation makes semiannual or annual payments that are used to retire bonds by purchasing them in the market place.

43

3) Sinking-Fund Requirements

• The bond indenture identifies any collateral pledged against the bond & specifies how it is to be maintained. The protection of bond collateral is crucial to guarantee the safety of a bond issue.

44

4) Security Interest

• A paid individual, corporation or commercial bank trust department that acts as the third party to a bond indenture & can take specified actions on behalf of the indenture are violated.

45

Trustee

• Rate of interest paid by the bond issuer,• Bond’s Maturity,• Size of the offering,• Issuer’s Risk, &• Basic cost of money.

46

Factors Affecting the Cost of Bonds to Issuer

• Bond ratings are simply judgments about the future risk potential of the bond in question. Bond ratings are extremely important in that a firm’s bond rating tells much about the cost of funds and the firm’s access to the debt market.Three primary rating agencies exist—Moody’s, Standard & Poor’s, and Fitch Investor Services in the United States.

47

Bond Ratings

48

Bond Ratings…contd.

49

Types of Bonds

Unsecured Bonds Secured Bonds

1. Debenture.2. Subordinated

debenture.3. Income Bonds.

1. Mortgage Bonds.2. Collateral trust

bonds.3. Equipment Trust

certificates.

Zero-Coupon Bonds.Junk Bonds.Floating-rate bonds.Extendible notes.Putable bonds.

50

Contemporary Types of Bonds

Bond value

51

Valuation of Bonds

Nd

N

1t

td

Nd

Nd

2d

1d

d

k1

M

k1

INT

k1

M

k1

INT

k1

INT

k1

INTV

kd = required rate of return on a debt instrument

N = number of years before the bond maturesINT = dollars of interest paid each year (Coupon rate Par value)M = par or face, value of the bond to be paid off at maturity

• Genesco 15%, 15year, $1,000 bonds valued at 15% required rated of return

52

Valuation of Bonds

• Numerical solution:

53

Valuation of Financial Assets - Bonds

Vd = $150 (5.8474) + $1,000 (0.1229)

= $877.11 + $122.89 = $1,000

15

15

0001150151

11

1501.15

1,$

.

.$Bond

value

• If the market rate associated with a bond (kd) equals the coupon rate of interest, the bond will sell at its par value

• If interest rates in the economy fall after the bonds are issued, kd is below the coupon rate. The interest payments and maturity payoff stay the same, causing the bond’s value to increase (investors demand lower returns, so they are willing to pay higher prices for bonds).

54

Changes in Bond Values over Time

• Current yield is the annual interest payment on a bond divided by its current market value

55

Changes in Bond Values over Time..contd.

Begind,

Begind,Endd,

d

V

VV

value bondBeginning

value bondBeginning

value bondEnding

V

INT

Current yield

Capital gains yield

•Discount bondA bond that sells below its par value, which occurs whenever the going rate of interest rises above the coupon rate

•Premium bondA bond that sells above its par value, which occurs whenever the going rate of interest falls below the coupon rate

56

Changes in Bond Values over Time…contd.

• An increase in interest rates will cause the price of an outstanding bond to fall

• A decrease in interest rates will cause the price to rise

• The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt

57

Changes in Bond Values over Time…contd.

• Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20%

58

Changes in Bond Values over Time..contd.

$0

$250

$500

$750

$1,000

$1,250

$1,500

1 3 5 7 9 11 13 15

Kd = Coupon Rate

Kd < Coupon Rate

Kd > Coupon Rate

Years

Bond Value

• YTM is the average rate of return earned on a bond if it is held to maturity

59

Yield to Maturity

Approximate yield to maturity

3

M V 2

N

V-M INT

bond of value Average

gains capital interest d Accrue

Annual

d

d

60

Bond Values with Semiannual Compounding

2N

d

2N

1tt

d

d

2

k1

M

k1

2

INT

V

2

• Interest Rate Price Risk - the risk of changes in bond prices to which investors are exposed due to changing interest rates

• Interest Rate Reinvestment Rate Risk - the risk that income from a bond portfolio will vary because cash flows have to be reinvested at current market rates

61

Interest Rate Risk on a Bond

62

Value of Long and Short-Term15% Annual Coupon Rate Bonds

Current Market Interest Rate, kd

1-Year Bond

14-Year Bond

5% 1,095.24$ 1,989.86$ 10% 1,045.45$ 1,368.33$ 15% 1,000.00$ 1,000.00$ 20% 958.33$ 769.47$ 25% 920.00$ 617.59$

Value of

63

Value of Long and Short-Term15% Annual Coupon Rate Bonds

Interest Rate, kd (%)

BondValue

($) 2,000

1,500

1,000

500

0 5 10 15 20 25

14-Year Bond

1-Year Bond

Stability in revenue & earnings exists.There is a satisfactory profit margin.There is a good liquidity & cash flow position.The debt-equity ratio is low. Stock prices are currently depressed.Control considerations are a primary factor. Inflation is expected.Bond indenture restrictions are not burdensome.

64

When is Bond Financing more appropriate?

Chapter: 06 (7)

Stock Valuation

65

66

Difference between Debt & Equity Capital

Investment Decisions Financing Decisions

Use of Funds Sources of Funds

Assets (A) = Liabilities(L) + Equity (E)

Working Capital Management

Current Assets

Current Liabilities

Working Capital Management

Capital Budgeting/ Investment decisions

Fixed Assets

Long-term liabilities

Stockholders’ Equity

Capital Structure

67

Differences between Debt & Equity Capital

Type of Capital

Characteristics Debt Equity

Voice in Management No Yes

Claims on Income & Assets Senior to Equity Subordinated to Debt

Maturity Stated None

Tax Treatment Interest deduction No deduction

• Types of security: Equity security denoting full ownership except in unusual circumstances.

• Privileges Claims

Residual claims on income - no guarantee of payment.

Residual claim on assets – in case of bankruptcy. a) Control

Voting rights on corporate charter & board of directors.

Preserve proportionate ownership by preemptive right.

68

Common Stock

• Retirement Provisions: No formal retirement provisions – no maturity date.

• Advantages to Issuer:• Not required to pay dividend.• No maturity date – no obligation to redeem.• Enhances equity base.

• Disadvantages to Issuer:• Potential dilution of control.• Potential dilution of earnings per share.• Highest explicit cost of capital.

69

Common Stock…contd.

Types of security: A hybrid security – technically an equity security, but has features of debt securities.

Prerogatives:a) Claims

Priority status : paid before common stockholders but after debt holders. In case of bankruptcy, comes ahead common but behind debt.

Fixed-income status: fixed dividends stated in dollars terms or as a percent of par.

Cumulative feature: all arrearages must be paid before common dividends can be paid.

Participation feature: although rare, allows preferred owners to share in unusual profits of firm.

b) Control Contingent voting rights: vest only when firm is in

arrears on preferred dividends by a specified amount.

70

Preferred Stock

• Retirement Provisions: Has no maturity date, but can be retired by:

• A conversion into common stock if the preferred is convertible.

• The call provision.• A sinking fund.

• Advantages to Issuer:• Leverage with no default risk.• Cash flow flexibility – dividends can be

omitted.• Preservation of stockholder control.

• Disadvantages to Issuer:• Dividends are not tax deductible.• More expensive than debt financing.

71

Preferred Stock…contd.

• The three primary types of public offerings are:1. Initial Public Offering (IPO) or General Cash

Offering (GCO).2. Privileged Subscriptions or Right Offerings.3. Private Placement,

72

Raising Capital

73

Issuer

Negotiated Offering

CompetitiveBid

Underwriting Best Effort

UnderwritingManager

Other InvestmentBanker

InvestmentBankers

Brokerage Firms

Buyer ofSecurities

or

or

syndicate

+

Selling group+

Investment Banking Process

• Investment banker is the financial intermediary that specializes in selling new security & advising firms with regard to major financial transactions. The investment banker usually performs three functions:

1. Advisory Functions,2. Underwriting Functions, & 3. Marketing Functions.

74

Investment Banker

• The advices typically covers all aspects of the issue:– Which securities to sell (bond, stocks)– The price of the new security.– The non-price features (in case of bond issue-:

maturity, coupon interest, provision for sinking fund)

– The issuing date.• The Negotiated Offering is an arrangement in which

the firm selects an investment banker or group of investment bankers at the beginning of the planning stage and negotiates and works with the banker to decide on all details of the planned issue.

• The Competitive Bid is an arrangement in which the firm decides before approaching any investment bankers the kind of securities it will issue and other associated details, and then ask investment banker as an advisor.

75

1) The Advisory Functions

• The firm has two basic choices:– Sell the issue to investment bankers – who

then resells the securities to investors. Investment bankers protect themselves by forming Syndicate, that is a group of investment bankers that handles a new issue of securities.

– Best Efforts basis – the investment bankers do not actually buy the new issue securities, but only agree to sell as many as they can at the agreed price.

 

76

2) The Underwriting Functions

Securities are usually sold through a Selling group established by the investment banking syndicate expressly for the purpose of the marketing the securities to investors. This group comprises the sales organization of the underwriters, as well as dealers who are specialists in marketing new securities.

Flotation Cost: Flotation Cost have two components: Underwriter’s Spread

The Spread includes all components for investment banking

services: advising, underwriting, and selling. Underwriter’s Spread = {Gross sales proceeds-Net Sales}/

Gross sales proceeds

Issue Expenses –: legal fees, printing costs, registration fees, & taxes.

77

3) The Marketing Functions

• Theory describing the behavior of an assumed “perfect” market in which:1. Securities are typically in equilibrium, which means that

they are fairly priced & their expected returns equal their required returns,

2. Security prices fully reflect all public information available & react swiftly to new information, &

3. Since stocks are fairly priced, investors need not waste time looking for mispriced securities.

• Levels of market efficiency– Weak-form efficiency– Semistrong-form efficiency– Strong-form efficiency

78

The Efficient Market Hypothesis (EMH)

• Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future.

• Evidence supports weak-form EMH, but “technical analysis” is still used.

79

Weak-form efficiency

• All publicly available information is reflected in stock prices, so it doesn’t pay to over analyze annual reports looking for undervalued stocks.

• Largely true, but superior analysts can still profit by finding and using new information

80

Semistrong-form efficiency

• All information, even inside information, is embedded in stock prices.

• Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.

81

Strong-form efficiency

• Empirical studies have been conducted to test the three forms of efficiency. Most of which suggest the stock market was:– Highly efficient in the weak form.– Reasonably efficient in the semistrong form.– Not efficient in the strong form. Insiders could

and did make abnormal (and sometimes illegal) profits.

• Behavioral finance – incorporates elements of cognitive psychology to better understand how individuals and markets respond to different situations.

82

Is the stock market efficient?

• Should management be equally concerned about employees, customers, suppliers, and “the public,” or just the stockholders?

• In an enterprise economy, management should work for stockholders subject to constraints (environmental, fair hiring, etc.) and competition.

83

Social/Ethical Question

• Dividend growth model• Corporate value model• Using the multiples of comparable firms

84

Different approaches for valuing common stock

Dividend growth model

• Value of a stock is the present value of the future dividends expected to be generated by the stock.

)k(1D

... )k(1

D

)k(1D

)k(1

D P

s3

s

32

s

21

s

10

^

85

Constant growth stock

• A stock whose dividends are expected to grow forever at a constant rate, g.

D1 = D0 (1+g)1

D2 = D0 (1+g)2

Dt = D0 (1+g)t

• If g is constant, the dividend growth formula converges to:

g -kD

g -kg)(1D

Ps

1

s

00

^

86

• If g > ks, the constant growth formula leads to a negative stock price, which does not make sense.

• The constant growth model can only be used if:– ks > g

– g is expected to be constant forever

87

What happens if g > ks?

• Use the SML to calculate the required rate of return (ks):

ks = kRF + (kM – kRF)β

= 7% + (12% - 7%)1.2= 13%

88

If kRF = 7%, kM = 12%, and β = 1.2, what is the required rate of return on the firm’s stock?

89

If D0 = $2 and g is a constant 6%, find the expected dividend stream for the next 3 years, and their PVs.

1.8761

1.7599

D0 = 2.00

1.6509

ks = 13%

g = 6%0 1

2.247

2

2.382

3

2.12

What is the stock’s market value?

• Using the constant growth model:

$30.29

0.07$2.12

0.06 - 0.13$2.12

g - k

D P

s0

1

90

What is the expected market price of the stock, one year from now?

• D1 will have been paid out already. So, P1 is the present value (as of year 1) of D2, D3, D4, etc.

• Could also find expected P1 as:$32.10

0.06 - 0.13$2.247

g - k

D P

s

2^

1

$32.10 (1.06) P P 0

^

1

91

• Dividend yield= D1 / P0 = $2.12 / $30.29 = 7.0%

• Capital gains yield= (P1 – P0) / P0 = ($32.10 - $30.29) / $30.29 = 6.0%

• Total return (ks)= Dividend Yield + Capital Gains Yield

= 7.0% + 6.0% = 13.0%

92

What is the expected dividend yield, capital gains yield, and total return during the first year?

• Can no longer use just the constant growth model to find stock value.

• However, the growth does become constant after 3 years.

93

Supernormal growth:What if g = 30% for 3 years before achieving long-run

growth of 6%?

94

Valuing common stock with nonconstant growth

ks = 13%

g = 30% g = 30% g = 30% g = 6%

P 0.06

$66.543

4.658

0.13

2.301

2.647

3.045

46.114

54.107 = P0^

0 1 2 3 4

D0 = 2.00 2.600 3.380 4.394

...

4.658

• Dividend yield (first year)= $2.60 / $54.11 = 4.81%

• Capital gains yield (first year)= 13.00% - 4.81% = 8.19%

• During nonconstant growth, dividend yield and capital gains yield are not constant, and capital gains yield ≠ g.

• After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

95

Find expected dividend and capital gains yields during the first and fourth years.

96

Nonconstant growth:What if g = 0% for 3 years before long-run growth of

6%?

ks = 13%

g = 0% g = 0% g = 0% g = 6%

0.06 $30.29P3

2.12

0.13

1.77

1.57

1.39

20.99

25.72 = P0^

0 1 2 3 4

D0 = 2.00 2.00 2.00 2.00

...

2.12

• Dividend yield (first year)= $2.00 / $25.72 = 7.78%

• Capital gains yield (first year)= 13.00% - 7.78% = 5.22%

• After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

97

Find expected dividend and capital gains yields during the first and fourth years.

If the stock was expected to have negative growth (g = -6%), would anyone buy the stock, and what is its value?

• The firm still has earnings and pays dividends, even though they may be declining, they still have value.

$9.89 0.19$1.88

(-0.06) - 0.13(0.94) $2.00

g - k) g 1 (D

g - k

D P

s

0

s

1^

0

98

• Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows.

• Remember, free cash flow is the firm’s after-tax operating income less the net capital investment– FCF = NOPAT – Net capital investment

99

Corporate value model

• Find the market value (MV) of the firm.– Find PV of firm’s future FCFs

• Subtract MV of firm’s debt and preferred stock to get MV of common stock.– MV of = MV of – MV of debt and

common stock firm preferred• Divide MV of common stock by the number of shares

outstanding to get intrinsic stock price (value).– P0 = MV of common stock / # of shares

100

Applying the corporate value model

• Often preferred to the dividend growth model, especially when considering number of firms that don’t pay dividends or when dividends are hard to forecast.

• Similar to dividend growth model, assumes at some point free cash flow will grow at a constant rate.

• Terminal value (TVn) represents value of firm at the point that growth becomes constant.

101

Issues regarding the corporate value model

102

Given the long-run gFCF = 6%, and WACC of 10%, use the corporate value model to find the firm’s intrinsic

value.

g = 6%

k = 10%

21.20

0 1 2 3 4

-5 10 20

...

416.942

-4.5458.264

15.026398.197

21.20530 = = TV3

0.10 0.06-

• MV of equity = MV of firm – MV of debt= $416.94m - $40m= $376.94 million

• Value per share = MV of equity / # of shares= $376.94m / 10m= $37.69

103

If the firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per

share?

• Analysts often use the following multiples to value stocks.– P / E– P / CF– P / Sales

• EXAMPLE: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price.

104

Firm multiples method

What is market equilibrium?

• In equilibrium, stock prices are stable and there is no general tendency for people to buy versus to sell.

• In equilibrium, expected returns must equal required returns.

)k(k k k g PD k RFMRFs

0

1^

s

105

• Expected returns are obtained by estimating dividends and expected capital gains.

• Required returns are obtained by estimating risk and applying the CAPM.

106

Market Equilibrium

• If expected return exceeds required return …– The current price (P0) is “too low” and offers a

bargain.– Buy orders will be greater than sell orders.– P0 will be bid up until expected return equals

required return

107

How is market equilibrium established?

• Required return (ks) could change– Changing inflation could cause kRF to change

– Market risk premium or exposure to market risk (β) could change

• Growth rate (g) could change– Due to economic (market) conditions– Due to firm conditions

108

Factors that affect stock price

• Vp = D/ kp

• If preferred stock with an annual dividend of $5 sells for $50, what is the preferred stock’s expected return?

Vp = D / kp

$50 = $5 / kp

kp = $5 / $50

= 0.10 = 10%

109

Preferred Stock Valuation