Security Valuation FIN 461: Financial Cases & Modeling George W. Gallinger Associate Professor of...

Security ValuationFIN 461: Financial Cases & Modeling

George W. GallingerAssociate Professor of FinanceW. P. Carey School of Business

Arizona State University

W. P. Carey School of Business Slide 2

Valuation Fundamentals Value of any financial asset is the PV of

future cash flows Bonds: PV of promised interest & principal

payments Stocks: PV of all future dividends

Valuation is the process linking risk & return Output of process is asset’s expected market

price Key input is the expected return on an asset

Defined as the return an arms-length investor would require for an asset of equivalent risk

Debt securities: risk-free rate plus risk premium(s) Required return for stocks using CAPM or other asset

pricing model.


Basic Valuation Model

• P0 = Price of asset at time 0 (today)

• CFt = cash flow expected at time t

• r = discount rate (reflecting asset’s risk)• n = number of discounting periods (usually

years)

Model expresses the price of any asset at t = 0 mathematically.


Start with Bonds

Calculate price Calculate yields

Current Holding period Yield to maturity.


How to Value Bonds

Identify the size and timing of cash flows.

Discount at the correct discount rate. If you know the price of a bond and

the size and timing of cash flows, the yield to maturity is the discount rate.


Definition & Example of a Bond

Consider a U.S. government bond listed as 63/8% of December 2009

The par value of the bond = $1,000 Coupon payments are made semi-annually (June 30

and December 31 for this particular bond) Since the coupon rate is 63/8% the payment = $31.875 On January 1, 2002 the size and timing of cash flows

are:

02/1/1

875.31$

02/30/6

875.31$

02/31/12

875.31$

09/30/6

875.031,1$

09/31/12


Pure Discount BondsInformation needed for valuing pure discount

bonds: Time to maturity (T) = Maturity date - today’s date Face value (F) Discount rate (r)

Tr

FPV

)1(

Present value of a pure discount bond at time 0:

0

0$

1

0$

2

0$

1T

F$

T


Pure Discount Bonds: Example

Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.

11.174$)06.1(

000,1$

)1( 30

Tr

FPV

0

0$

1

0$

2

0$

29

000,1$

30

0

0$

1

0$

2

0$

29

000,1$

30


Level-Coupon BondsInformation needed to value level-coupon bonds:

Coupon payment dates and time to maturity (T) Coupon payment (C) per period and Face value (F) Discount rate

TT r

F

rr

CPV

)1()1(

11

Value of a level-coupon bond= PV of coupon payment annuity + PV of face value

0

C$

1

C$

2

C$

1T

FC $$

T


Level-Coupon Bonds: Example

Find the present value (as of January 1, 2002), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5%.

On January 1, 2002 the size and timing of cash flows are:

02/1/1

875.31$

02/30/6

875.31$

02/31/12

875.31$

09/30/6

875.031,1$

09/31/12

30.049,1$)025.1(

000,1$

)025.1(

11

205.

875.31$1616

PV


Current Yield


Holding Period Rate of Return


Importance & Calculation of Yield to Maturity

Yield to maturity (YTM) Rate of return investors earn if they buy the bond at P0 and hold it until

maturity

YTM on a bond selling at par (P0 = Par) = coupon rate When P0 Par, the YTM will differ from the coupon rate

YTM is the discount rate that equates the PV of a bond’s cash flows with its price

Use T-Bond with n=2 years, 2n=4, C/2=$20, P0=$992.43

432

21

020,1$

21

20$

21

20$

21

20$43.992$

rrrr


Price & Yield Relationships


Semi-Annual Bond Interest Payments

Most bonds pay interest semi-annually rather than annually Can easily modify basic valuation formula; divide both

coupon payment (C) and discount rate (r) by 2:

• C annual coupon payment; C/2 semi-annual payment • r annual required return; r/2 semi-annual discount rate • n number of years; 2n semi-annual payments.

nr

C

r

C

r

C

r

C

2321 )2

1(

000,12....

)2

1(

2

)2

1(

2

)2

1(

2Price


Semi-Annual Bond Interest Payments …

An example....

Value a T-Bond Par value = $1,000 Maturity = 2 yearsCoupon pay = 4% r = 4.4% per year

= $992.43


Characteristics of Bonds

Important factors can be stated using 5 bond theorems.


Bond Theorem 1

Market rate > coupon rate

Bond's price is less than its face value of $1000

Market rate < coupon rate

Bond's price exceeds its face value

Market rate = coupon rate

Bond's price = face value.


Bond Theorem 2

The longer the maturity, the greater the price change.


Bond Theorem 3


Bond Theorem 4

Maturity has no effect on bond value, and thus gains or losses, when the coupon rate = market rate

If the market rate < coupon rate, the bond's capital gains--the price minus the face value of $1000--become smaller as maturity shortens

If the market rate > coupon rate, the bond's capital losses become smaller as maturity shortens.


Bond Theorem 5

Maturity has no affect if coupon rate equals market rate.


Bond Risk PremiumsFebruary 97-November 98Bond Risk PremiumsFebruary 97-November 98

0

100

200

300

400

500

600

High-yield BondYields less yieldon 10-yearTreasurys inbasis points

9897


Term Structure of Rates Term structure of interest rates compares YTMs of comparable risky

securities and maturities at a point in time Provides info about market's forecast of rates and inflation


Some Historical Perspective

2

4

6

8

10

12

14

16

5 10 15 20 30

Years to Maturity

Inte

res

t R

ate

%

August 1996

October 1993

May 1981

January 1995

1 3


Shapes & Levels of Treasury Yield CurveOctober 1998

3.7

3.9

4.1

4.3

4.5

4.7

4.9

5.1

5 10 30

Maturity in Years

Yie

ld %

October 9

October 8

October 2

1


YTM & Forward Rates


Bond Duration

Coupon rate = 8%;

market rate = 8%


Factors Influencing Duration

Duration increases with maturity Decreases with higher yield, higher coupon rates, and higher payment

frequency.


Discuss Common Stocks


Valuation of Stocks

Value a function of expected future cash flows Capital gains Dividends

Growth prospects Zero Constant Differential.


Dividend Fundamentals Relevant dates for dividend payments

Announcement, ex dividend, record and payment dates Stock price should drop by about dividend amount on ex

date Legal factors affecting dividend policy

Capital impairment constraint: Cannot pay out “legal capital”

Cannot accumulate earnings to escape taxes Contractual constraints on dividend payments

Loan covenants restrict, but don’t prevent, dividend payments

Establish a “pool” of earnings that can be paid out Liquidity and ownership constraints

Must have cash on hand (cannot used borrowed funds) High payout leads to potential dilution Investment opportunity sets of investors.


Types of Dividends Types of cash dividends

Regular Cash Dividend Special Cash Dividend

Types of dividend policies Constant payout policy (almost never observed) Constant nominal payments (standard

worldwide) Low regular and extra dividend

Stock dividends and stock splits Stock repurchase (3 methods)

Buying shares on the market Tender Offer to Shareholders Private Negotiation (Green Mail).


U.S. Firms Paying Dividends, by Exchange

1926 1936 1946 1956 1966 1976 1986 1996

80

60

40

20

Per

cent

0

100

NYSE

AMEX

NASDAQ

Year


Aggregate Dividend Payout %, U.S. Corporate Sector (1970-2000)

0

10

20

30

40

50

60

70

80

90

70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 2000

%


Mkt. Value Share Repurchase Announcements, (1980-1999)

0

50

100

150

200

250

80 82 84 86 88 90 92 94 96 98

$USBns


Market Reaction to Share Repurchase Announcements

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60

TRADING DAY

CU

MU

LAT

IVE

ME

AN

RA

TE

OF

RE

TU

RN 25%

20%

15%

10%

5%

0%

-5%

-10%


Patterns Observed in Dividend Policies Dividend policies show distinct national patterns

Companies in common law countries tend to have higher payouts than those from civil law countries

Dividend policies have pronounced industry patterns, and these are the same worldwide

Profitable firms in mature industries tend to pay out much larger fractions of their earnings

Within industries, dividend payout tends to be directly related to asset intensity and the presence of regulation

But payout is inversely related to growth rate Almost all firms maintain constant nominal dividend

payments per share for long periods of time Companies tend to "smooth" dividends, and these are far

less variable than are corporate profits.


Real-World Influences on Dividends

Personal taxes on dividends should discourage payments Empirical evidence is ambiguous Dividends paid before 1936 (no taxes) and after Some evidence of positive relation between payout and PS

Security issuance costs should discourage dividends If costly to issue new stocks & bonds, firm should retain cash

Investor trading costs argue in favor of dividends But cost of selling shares for income has fallen steadily

Dividends might be a “residual” after funding investments

But dividends are most stable of all cash flow series May convey information in markets with info asymmetries

But what specific info & isn’t there a cheaper way to signal? Latest empirical evidence: div signal the past, not the future.


How Do Corporations Really Set Dividend Payments?

Dividends determined today as they were for Lintner (1956)

Managers believe investors value steady dividend payments Managers have a target payout ratio, but only over time Will allow payout to vary in the short term to keep $div same Will only raise $div if permanent earnings increase Will only cut $div if firm facing financial disaster

Managerial reluctance to change nominal dividend payment gives rise to partial adjustment model

Assume target payout ratio = 0.50, profits initially $2.00/sh Implies annual dividend of $1.00/sh; quarterly div of $0.25/sh Suppose permanent earnings suddenly rise to $3.00/sh Will not increase dividend to $1.50/year immediately. Instead, May do so in $0.05 quarterly increments, over 2.5 yrs.


Key Dividend Dates


Calculating Intrinsic Price of a Non-constant Dividend Stream


Valuation of Perpetual Dividend Streams


Valuation of Two-Stage Dividend Streams


Estimates of Parameters in the Dividend-Discount Model

The value of stock depends upon its discount rate, r, and growth rate, g. Where does r come from? Where does g come from?


Where Does r Come From?

Best to use the CAPM Discussed last lesson.


Formula for Stock’s Growth Rate

g = (1 – EPS / DPS) × ROE / [1 – RR × ROE]

This is sustainable growth!


Other Approaches to Common Stock Valuation

Book value: Assumes assets can be sold at book value

Liquidation value: More realistic than book value, but doesn’t consider

firm’s value as a going concern Price/Earnings (P/E) multiples:

Reflects the amount investors will pay for each dollar of earnings per share

P/E multiples differ between and within industries May be helpful for privately-held firms A “lazy person’s” approach to valuation

Discounting Free cash flows Economic value added (aka EVA).


Other Price Ratio Analysis

Many analysts frequently relate earnings per share to variables other than price, e.g.: Price/Cash Flow Ratio

Cash flow = Net income + depreciation = cash flow from operations or operating cash flow

Price/Sales Current stock price divided by annual sales per

share Price/Book (aka market-to-book ratio)

Price divided by book value of equity, which is measured as assets – liabilities.


The End

Security Valuation FIN 461: Financial Cases & Modeling George W. Gallinger Associate Professor of...

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Transcript of Security Valuation FIN 461: Financial Cases & Modeling George W. Gallinger Associate Professor of...