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Chapter 4 Stock & Bond Valuation. Professor XXXXX Course Name / Number. Valuation Fundamentals. The greater the uncertainty about an asset’s future benefits, the higher the discount rate investors will apply when discounting those benefits to the present . - PowerPoint PPT Presentation
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© 2007 Thomson South-Western
Chapter 4Stock & Bond Valuation
Professor XXXXXCourse Name / Number
2 2
Valuation Fundamentals
The greater the uncertainty about an asset’s future benefits, the higher the discount rate investors will apply when discounting those benefits to the present.
The valuation process links an asset’s risk and return to determine its price.
3 3
Valuation Fundamentals
Future Cash Flows Risk
Valuation
4 4
Bond Valuation Fundamentals
Bonds are debt instruments used by business and government to raise large sums of money
Most bonds share certain basic characteristics First, a bond promises to pay investors a fixed
amount of interest, called the bond’s coupon. Second, bonds typically have a limited life, or
maturity. Third, a bond’s coupon rate equals the bond’s annual
coupon payment divided by its par value. Fourth, a bond’s coupon yield equals the coupon
payment divided by the bond’s current market price
5 5
Valuation FundamentalsPresent Value of Future Cash Flows
Link Risk & Return
Expected Return on Assets
Valuation
6 6
The 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)
This model can express the price of any asset at t = 0 mathematically.
7 7
Valuation FundamentalsBond Example
Using the P0 equation, the bond would sell at a par value of $1,000.
Company issues a 5% coupon interest rate, 10‑year bond with a $1,000 par value on 01/30/04Assume annual interest payments
Investors who buy company bonds receive the contractual rights$50 coupon interest paid at the end of
each year $1,000 par value at the end of the 10th
year
8 8
P0 < par value
P0 > par value
Bonds: Premiums & Discounts
The bond's value will differ from its par value
R > Coupon Interest Rate DISCOUNT =
PREMIUM =
What Happens to Bond Values if the Required Return Is Not Equal to the Coupon
Rate?
R < Coupon Interest Rate
9 9
The Basic Equation (Assuming Annual Interest)Cash flows include two components:
(1) the annual coupon, C, which equals the stated coupon rate, i, multiplied by M, the par value (that is, C i M), received for each of the n years
(2) the par value, M, received at maturity in n years
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Time Line for Bond: Valuation 91⁄8% Coupon,$1,000 Par Bond, Maturing at End of 2017, Required Return Assumed to be 8%
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BondsSemi-Annual 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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Yield to Maturity (YTM)
Rate of return investors earn if they buy the bond at P0 and hold it until maturity.
The YTM on a bond selling at par will always equal the coupon interest rate.
YTM is the discount rate that equates the PV of a bond’s cash flows with its price.
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Risk-Free Bonds
A risk-free bond is a bond that has no chance of default by its issuerZero-coupon treasuriesCoupon-paying treasuries
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Risky Bonds Treasury bonds provide a known contractual stream of cash
flows if you can observe the market price of a bond, you can infer
what the market’s required return must be. Valuing an ordinary corporate bond involves the same steps:
write down the cash flows determine an appropriate discount rate calculate the present value.
Discount rate on corporate bond should be higher than on Treasury bond with the same maturity because corporate bonds carry default risk the risk that the corporation may not make all scheduled
payments. Yield spread between Treasury bonds and corporate bonds
The difference in yield to maturity between two bonds or two classes of bonds with similar maturities
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Bond Issuers
Bond issuersCorporate bondsMunicipal bondsTreasury billsTreasury notesAgency bonds
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Bond Ratings
Bond ratingsMoody’sStandard & Poor’sFitch
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Bond Ratings
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Bond Ratings and Spreads at DifferentMaturities at a Given Point in Time
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Bond Price Behavior
Bond price quotationsBond spreads reflect a direct
relationship with default riskBond price behavior
Prices change constantlyPassage of timeForces in the economy
2020
Bond Prices and Yields for Bonds with Differing Times to Maturity, Same 6% Coupon Rate
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Bonds: Time to Maturity
What does this tell you about the relationship between bond prices & yields for bonds with the
equal coupon rates, but different maturities?
2222
Bonds: Yield to Maturity (YTM)Rate of return investors earn if they buy the bond at P0 and hold it until maturity.
The YTM on a bond selling at par will always equal the coupon interest rate.
YTM is the discount rate that equates the PV of a bond’s cash flows with its price.
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Evaluating the Yield Curve Yields vary with maturity. Yields offered by bonds must be sufficient to
offer investors a positive real return. The real return on an investment
approximately equals the difference between its stated or nominal return and the inflation rate.
The shape of the yield curve can change over time.
Research shows the yield curve works well as a predictor of economic activity, in the United States and other large industrialized economies.
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Yield Curves for U.S. Government Bonds
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Term Structure TheoriesExpectations theoryLiquidity preference theoryPreferred habitat theory
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Expectations Theory
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Term Structure of Interest Rates Relationship between yield and maturity is
called the Term Structure of Interest Rates Graphical depiction is called a Yield Curve Usually, yields on long-term securities are
higher than on short-term securities Generally look at risk-free Treasury debt
securities Yield curves normally upwards-sloping
Long yields > short yields Can be flat or even inverted during times of
financial stress
2828
Stock Valuation: Preferred Stock
Preferred stock is an equity security that is expected to pay a fixed annual dividend for its life
PS0 = Preferred stock’s valueDP = preferred dividendrp = required rate of return
An example: A share of preferred stock pays $2.3 per share annual dividend and with a required return of 11%
PS0=
DP
= $2.30 = $20.90 /
sharerp 0.11
2929
Valuation FundamentalsCommon Stock
P0=P1 + D1
(1+r)
Value of a Share of
Common Stock
P0 = Present value of the expected stock price at the end of period 1D1 = Dividends received r = discount rate
3030
Valuation Fundamentals: Common Stock But how is P1 determined?
This is the PV of expected stock price P2, plus dividend at time 2
P2 is the PV of P3 plus dividend at time 3, etc...
Repeating this logic over and over, you find that today’s price equals PV of the entire dividend stream the stock will pay in the future
3131
Zero Growth Model
To value common stock, you must make assumptions about the growth of future dividends
Zero growth model assumes a constant, non-growing dividend stream:
D1 = D2 = ... = D
Plugging constant value D into the common stock valuation formula reduces to simple equation for a perpetuity:
P0 = Dr
3232
Constant Growth Model Assumes dividends will grow at a constant rate
(g) that is less than the required return (r) If dividends grow at a constant rate forever,
you can value stock as a growing perpetuity, denoting next year’s dividend as D1:
P0=D1
r-g
Commonly called the Gordon Growth Model.
3333
Variable Growth
3434
Variable Growth ModelExample Estimate the current value of Morris Industries'
common stock, P0 = P2003
Assume
The most recent annual dividend payment of Morris Industries was $4 per share
The firm's financial manager expects that these dividends will increase at an 8% annual rate over the next 3 years
At the end of the 3 years the firm's mature product line is expected to result in a slowing of the dividend growth rate to 5% per year forever
The firm's required return, r , is 12%
3535
Variable Growth ModelValuation Steps #1 & #2 Compute the value of dividends in 2004, 2005, and
2006 as (1+g1)=1.08 times the previous year’s dividendDiv2004= Div2003 x (1+g1) = $4 x 1.08 = $4.32Div2005= Div2004 x (1+g1) = $4.32 x 1.08 = $4.67
Div2006= Div2005 x (1+g1) = $4.67 x 1.08 = $5.04
Find the PV of these three dividend payments:PV of Div2004= Div2004 (1+r) = $ 4.32 (1.12) = $3.86
PV of Div2005= Div2005 (1+r)2 = $ 4.67 (1.12)2 = $3.72
PV of Div2006= Div2006 (1+r)3 = $ 5.04 (1.12)3 = $3.59
Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17
3636
Find the value of the stock at the end of the initial growth period using the constant growth model
Calculate next period dividend by multiplying D2006 by 1+g2, the lower constant growth rate: D2007 = D2006 x (1+ g2) = $ 5.04 x (1.05) = $5.292
Then use D2007=$5.292, g =0.05, r =0.12 in Gordon model:
60.7507292.5
2292.57
6 $ = 0.
$ = 0.05 -0.1
$ = g -r
D = P2
200200
Variable Growth ModelValuation Step #3
3737
Variable Growth ModelValuation Step #3 Find the present
value of this stock price by discounting P(2006) by (1+r)3
81.53405.1
60.75$)12.1(
60.75$)1( 336 $ = = =
rP =PV 200
3838
Add the PV of the initial dividend stream (Step #2) to the PV of stock price at the end of the initial growth period (P2006):
P2003 = $11.17 + $53.81 = $64.98
Variable Growth ModelValuation Step #4
Current (end of year 2003)
stock price
Remember: Because future growth rates might change, the variable growth model
allows for a changes in the dividend growth rate.
3939
Time Line for Variable Growth Valuation
4040
Free Cash Flow Approach Begin by asking, what is the total operating
cash flow (OCF) generated by a firm? Next subtract from the firm’s operating
cash flow the amount needed to fund new investments in both fixed assets and current assets.
The difference is total free cash flow (FCF). Represents the cash amount a firm could
distribute to investors after meeting all its other obligations
4141
Common Stock Valuation:Other Options
Book valueNet assets per share available to
common stockholders after liabilities are paid in full
Liquidation valueActual net amount per share likely to
be realized upon liquidation & payment of liabilities
More realistic than book value, but doesn’t consider firm’s value as a going concern
4242
Common Stock Valuation:Other Options
Price / Earnings (P / E) multiplesReflects the amount investors will pay
for each dollar of earnings per shareP / E multiples differ between & within
industriesEspecially helpful for privately-held
firms