1. Security Valuation FIN 461: Financial Cases & Modeling
George W. Gallinger
Associate Professor of Finance
W. P. Carey School of Business
Arizona State University

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.
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3. Model expresses the price of any asset at t = 0 mathematically.
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)
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
Patents, trademarks: PV of future royalties
Valuation is the process linking risk & return
Output of process is asset’s expected market price
A key input is the required [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 found using CAPM or other asset pricing model
Beta determines risk premium: higher beta, higher reqd return
Model expresses the price of any asset at t = 0 mathematically.
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4. Start with Bonds Calculate price Calculate yields Current
Holding period
Yield to maturity.
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5. 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.
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6. 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:
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7. Pure Discount Bonds Present value of a pure discount bond at time 0:
Information needed for valuing pure discount bonds:
Time to maturity (T) = Maturity date - today’s date
Face value (F)
Discount rate (r)
Present value of a pure discount bond at time 0:
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8. 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%.
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9. Level-Coupon Bonds Value of a level-coupon bond
Information 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
Value of a level-coupon bond
= PV of coupon payment annuity + PV of face value
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10. 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:
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11. Current Yield
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12. Holding Period Rate of Return
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13. 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
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14. Price & Yield Relationships
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15. 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.
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16. Semi-Annual Bond Interest Payments …
An example....
Value a T-Bond
Par value = $1,000
Maturity = 2 years
Coupon pay = 4%
r = 4.4% per year
= $992.43
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17. Characteristics of Bonds
Important factors can be stated using 5 bond theorems.
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18. 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.
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19. Bond Theorem 2 The longer the maturity, the greater the price change.
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20. Bond Theorem 3
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21. 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.
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22. Bond Theorem 5
Maturity has no affect if coupon rate equals market rate.
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23. Bond Risk Premiums February 97-November 98
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24. 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
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25. Some Historical Perspective16 14
May 1981 12 10
Interest Rate %
January 1995 8
August 1996 6
October 1993 4 2 1 3 5 10 15 20 30
Years to Maturity
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26. Shapes & Levels of Treasury Yield Curve October 1998
5.1
October 9
4.9
October 8
4.7
October 2
4.5
Yield %
4.3
4.1
3.9
3.7 1 5 10 30
Maturity in Years
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27. YTM & Forward Rates
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28. Bond Duration Coupon rate = 8%; market rate = 8%
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29. Factors Influencing Duration
Duration increases with maturity
Decreases with higher yield, higher coupon rates, and higher payment frequency.
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30. Discuss Common Stocks
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31. Valuation of Stocks Value a function of expected future cash flows
Capital gains
Dividends
Growth prospects
Zero
Constant
Differential.
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32. 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.
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33. Types of Dividends Types of cash dividends Types of dividend policies
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).
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34. U.S. Firms Paying Dividends, by Exchange
100
NYSE 80 60
AMEX
Percent 40 20
NASDAQ
Year
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35. Aggregate Dividend Payout %, U.S. Corporate Sector (1970-2000)
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36. Mkt. Value Share Repurchase Announcements, (1980-1999)
$US
Bns
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37. Market Reaction to Share Repurchase Announcements
25%
20%
15%
10%
CUMULATIVE MEAN RATE OF RETURN 5% 0%
-5%
-10%
TRADING DAY
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38. 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.
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39. 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.
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40. 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.
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41. Key Dividend Dates
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42. Calculating Intrinsic Price of a Non-constant Dividend Stream
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43. Valuation of Perpetual Dividend Streams
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44. Valuation of Two-Stage Dividend Streams
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45. 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?
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46. Where Does r Come From? Best to use the CAPM Discussed last lesson.
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47. Formula for Stock’s Growth Rate
g = (1 – EPS / DPS) × ROE / [1 – RR × ROE]
This is sustainable growth!
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48. 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).
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49. 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.
No, it’s not exactly in the book, but it’s a great big world out there and you don’t want your students to learn this voodoo on the streets do you? Just delete the slide if you want to ignore it (I will).
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50. The End
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