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Stock & Bond Valuation
Professor XXXXXCourse Name / Number
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Valuation FundamentalsPresent Value of Future Cash Flows
Link Risk & Return
Expected Return on Assets
Valuation
3
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.
4
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 01/30/05– Assume annual interest payments
• Investors in company’s bond 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
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P0 < par value
P0 > par value
BondsPremiums & DiscountsWhat happens to bond values if required return is not equal to
the coupon rate?
The bond's value will differ from its par value
R > Coupon Interest Rate
R < Coupon Interest Rate
DISCOUNT =
PREMIUM =
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BondsTime to Maturity
What does this tell you about the relationship between bond prices & yields for bonds with the equal coupon rates, but different maturities?
7
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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The Fisher Effect And Expected Inflation• The relationship between nominal and real (inflation-
adjusted) interest rates and expected inflation called the Fisher Effect (or Fisher Equation).
• Nominal rate (r) is approximately equal to real rate of interest (a) plus a premium for expected inflation (i).– If real rate equals 3% (a = 0.03) and expected
inflation equals 2% (i = 0.02):r a + i 0.03 + 0.02 0.05 5%
• True Fisher Effect multiplicative, rather than additive:(1+r) = (1+a)(1+i) = (1.03)(1.02) = 1.0506; so r = 5.06%
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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
What to you think a Yield Curve would look like graphically?
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Yield CurvesU.S. Treasury Securities
2
4
6
8
10
12
14
16
5 10 15 20 30
Years to Maturity
Inte
rest
Rat
e %
August 1996October 1993
May 1981
January 1995
1 3
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Valuation FundamentalsPreferred Stock
Preferred stock is an equity security that is expected to pay a fixed annual dividend for its life
rD = P 1t
0 • P0 = Preferred stock’s market
price• Dt+1 = next period’s dividend
payment• r = discount rate
An example: A share of preferred stock pays $2.3 per share annual dividend and with a required return
of 11% share= =r
D = P t0 /90.20$
11.03.2$1
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Valuation FundamentalsCommon Stock
• P0 = Present value of the expected stock price at the end of period 1
• D1 = Dividends received • r = discount rate
Value of a
Share of
Common Stock
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• But how is P1 determined? – This is the PV of expected stock price P2, plus
dividends– P2 is the PV of P3 plus dividends, 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
Valuation FundamentalsCommon Stock
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Zero Growth Valuation 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:
rDP 0
16
Constant Growth Valuation 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:
This is commonly called the Gordon Growth Model.
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Variable Growth ModelExample• Estimate the current value of Morris
Industries' common stock, P0 = P2005 • 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%
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Variable Growth ModelValuation Steps #1 & #2• Compute the value of dividends in 2006, 2007, and
2008 as (1+g1)=1.08 times the previous year’s dividendDiv2006= Div2005 x (1+g1) = $4 x 1.08 = $4.32Div2007= Div2006 x (1+g1) = $4.32 x 1.08 = $4.67
Div2008= Div2007 x (1+g1) = $4.67 x 1.08 = $5.04
• Find the PV of these three dividend payments:PV of Div2006= Div2006 (1+r) = $ 4.32 (1.12) = $3.86
PV of Div2007= Div2007 (1+r)2 = $ 4.67 (1.12)2 = $3.72
PV of Div2008= Div2008 (1+r)3 = $ 5.04 (1.12)3 = $3.59
Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17
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• 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 D2008 by 1+g2, the lower constant growth rate: D2009 = D2008 x (1+ g2) = $ 5.04 x (1.05) = $5.292
• Then use D2009=$5.292, g =0.05, r =0.12 in Gordon model:
60.7507292.5
2292.5 $ =
0.$ =
0.05 -0.1$ =
g -rD = P
2
92008200
Variable Growth ModelValuation Step #3
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• Find the present value of this stock price by discounting P2008 by (1+r)3
81.53405.1
60.75$)12.1(
60.75$)1( 33
$ = = = r
P =PV 0820
Variable Growth ModelValuation Step #3
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• Add the PV of the initial dividend stream (Step #2) to the PV of stock price at the end of the initial growth period (P2008):
P2005 = $11.17 + $53.81 = $64.98
Variable Growth ModelValuation Step #4
Current (year 2005) stock price
Remember: because future growth rates might change, the variable growth model
allows for changes in the dividend growth rate.
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Common Stock ValuationOther Options• Book value
– Net assets per share available to common stockholders after liabilities are paid in full
• Liquidation value– Actual 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
• Price / Earnings (P / E) multiples– Reflects the amount investors will pay for each dollar of
earnings per share– P / E multiples differ between & within industries– Especially helpful for privately-held firms
Questions?