Lecture: 3 - Stock and Bond Valuation

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Lecture 3 - Stock and Bond Valuation
How to Get a k to Discount Cash Flows - Two
Methods I. Required Return on a Stock (k) -
CAPM (Capital Asset Pricing Model) or Other
Securities k rf B(rm - rf) where
rf Risk-Free Rate B Beta (Risk
Measure) rm Expected Market
Return Example k .05 2(.12 - .05) .19
II. Risk Premium Approach kb Rb rreal
rrisk E(I) Productivity Growth Risk
Premium Expected Inflation 2 - 4
0 - 10 2 - 6 (Estimates)
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Lecture 3 - Stock and Bond Valuation
III. Bond Valuation Bond Annuity Plus
Single Par Payment (often Semi-Annual
Payments) a. Par Value -face value, maturity
value - usually 1000 b. Coupon
Interest Rate - stated as a of Par -
10 coupon on 1000 par gt coupon
100. c. Maturity - length of time until
Par value is paid off
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Lecture 3 - Stock and Bond Valuation
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Bond Valuation A Bond is an Annuity Plus a
Single Face Value Payment Annual Coupon Lecture
3 - Stock and Bond Valuation
I. Bond Valuation General Formula B0
IPVAk,n MPVk,n B0 Bond Price I
Interest (coupon) Payment M Par
Value II. Example Suppose a bond offers a
10 coupon, on 1000 par, for 3 years, and the
expected inflation rate is 2, the real rate
is 3 and the bonds risk is 1. What is its
price? B0 100PVA.06,3
1000PV.06,3 100(2.673)
1000(.84) 1107
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QUESTION If the company only agrees to pay 1000
at maturity, wont those who buy this bond lose
107 at maturity? QUESTION Would you buy this
bond? Why? - greater coupon than par bonds.
A par bond would cost 1000 but only pays a
60 coupon. The present value of the difference
in coupons (100 - 60)(2.673) 107 which is the
difference in price between this bond and a par
bond. Alternatively, a bond that offered a 2
coupon when rates are 6 will have a price of B0
20PVA.06, 3 1000PV.06, 3 893 or 107
less than the par bond.
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Bond Valuation A Bond is an Annuity Plus a
Single Face Value Payment Semi-Annual
Coupon Lecture 3 - Stock and Bond Valuation
I. Adjustments For Semi-Annual Coupon
Bonds a. n the number of semi-annual
payments (maturity x 2) b. k
one-half the bonds annual yield c. I
one-half the bonds annual coupon II. Example
Suppose a bond pays 10 coupon,
semi-annually, has 10 years until maturity and
has a required return (or Yield to Maturity)
of 8. What is its price? B0
50PVA.04,20 1000PV.04,20
50(13.59) 1000(.456)
1135.5 QUESTION Consider two identical bonds
except that one pays an annual coupon and the
other a semi-annual coupon. Which should have
the higher price? ANSWER The semi-annual bond.
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Yield to Maturity and Realized Yield Lecture 3 -
Stock and Bond Valuation
YIELD TO MATURITY - The return one can expect on
an investment in a bond if the bond pays all its
coupons and par and yields do not change after
you purchase the bond. PROBLEM Suppose you
observe a bond in the market with a price of
803 that pays a coupon of 10 till maturity in
5 years. What is its implied yield to
maturity? Try 16 803 100(PVA?,5)
1000(PV?,5) 100(3.274) 1000(.476)
803 REALIZED YIELD - The actual return one
receives on the initial investment in a
bond. QUESTION If you buy a 20 coupon, par
bond, with 3 years maturity and you hold it for
three years are you sure to earn 20? ANSWER
No because the calculation of YTM assumes that
the coupons are reinvested at 20, if rates
change your realized yield will change because
you'll earn more or less than 20 on their
reinvested coupons.
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Example When you bought the bond, YTM was 20.
But suppose rates fell to 5 the day after
you bought and stay there for three years.
Your realized yield will be use PV
FVPVk,n 1000 (200(1.05)2 200(1.05)
1200)PVk,3 1630.5PVk,3 gt
1000/1630.5 PVk,3 .6133 gt k 17
realized yield falls when reinvestment rate
falls QUESTION Then how can you truly lock-in a
rate? ANSWER Buy a bond with no coupons -
called zero coupon bonds. QUESTION How would
you price a zero coupon bond? ANSWER Use the
second term in the bond pricing
formula. QUESTION Some find this attractive but
is there a problem with being locked-in? ANSWER
Yes. How about if rates rise. You lose out on
earning extra interest on reinvested coupons.
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Stock Valuation Valuation is Based Upon Expected
Dividend Flow and the Future Expected Market
Value of the Stock Lecture 3 - Stock and Bond
Valuation
I. Common Stock Valuation General
Formula P0 E(D1)/(1ke) E(D2)/(1ke)2
... E(Dn)/(1ke)n E(Pn)/(1ke)n where
E means expectation, Dt means dividend at time
t, P means stock price, and ke is the cost of
equity. II. Example Suppose a firm pays
4 in Dividends, which will increase by 1
in each of the next 3 years and we expect the
price to be 30 at the end of the 3rd year.
Assume stock beta 1, the risk free rate is
10, and the expected market return is 15.
What is the stock price? Ke .10 1(.15
- .10) P0 4/(1.15) 5/(1.15)2
6/(1.15)3 30/(1.15)3 4(.87) 5(.756)
6(.658) 30(.658) 30.94
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Stock Valuation - Constant Growth Valuation is
Based Upon Expected Dividends That Grow at a
Constant Rate For Ever Lecture 3 - Stock and
Bond Valuation
Constant Growth Discounted Cash Flow Model, or
DCF. P0 where D0 present dividend
paid at time 0 D1 dividend expected at time
1 g constant future growth in dividends k
required return (discount rate) Note Works
only for kgtg and dividend paying firm
PROBLEM Suppose a company will pay a dividend of
5 in one year, has a required return
of 10 and dividends grow 5 per
year. What is the stock price? P
Mixture of Dividends PROBLEM Suppose a firm
will pay a dividend of 5 per year for 5 years
and then increases the dividend by 10 per year
thereafter. The firm has a required return of
15. What is its price now? P 5(PVA.15,
5) PV.15, 5 5(3.352)
110(.497) 71.43
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Stock Valuation - Implied Required Returns and
Growth Rates Just Manipulate the Constant
Growth Formula Lecture 3 - Stock and Bond
Valuation
PROBLEM Suppose we know the price of the stock
in the market is 80, and it pays a dividend of
3 that will grow by 10 per year. What is the
return the market requires on the stock? k
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PROBLEM If the market price of a stock is 50,
its required return is 15 percent and next
years dividend is expected to be 5, by what
percent must the market expect the companys
dividends to grow. g k - so g
.15 - .05
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PRICE-EARNINGS RATIOS PEs Are Commonly Used to
Compare Stocks Lecture 3 - Stock and Bond
Valuation
PE Ratio - This is the number of dollars
investors are willing to pay for each dollar
of a companys earnings. You can use the growth
model to see why stocks have different
price-earnings ratios P
gt where E earnings per
share d dividend payout ratio Clearly, a
larger growth rate and payout ratio and a smaller
discount rate (k) makes for a larger price
earnings ratio.