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8/2/2019 (4) Bond and Sock Valuation
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Bonds and Their Valuation
Key features of bonds
Bond valuation
Measuring yield
Assessing risk
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Key Features of a Bond
1. Par value: Face amount; paid
at maturity. Assume $1,000.
2. Coupon interest rate: Statedinterest rate. Multiply by par value to get dollars of interest.Generally fixed.
(More…)
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3. Maturity: Years until bondmust be repaid. Declines.
4. Issue date: Date when bondwas issued.
5. Default risk: Risk that issuer
will not make interest or principal payments.
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How does adding a call provision
affect a bond?
Issuer can refund if rates decline.
That helps the issuer but hurts theinvestor.Therefore, borrowers are willing to
pay more, and lenders require more,on callable bonds.
Most bonds have a deferred call anda declining call premium.
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Financial Asset Valuation
( ) ( ) ( )PV =
CF
1+ r ... +
CF
1+r
1 n
1
2
21
CF
r n .
0 1 2 nr
CF1 CFnCF2Value
...
+ ++
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The discount rate (r i) is theopportunity cost of capital, i.e.,the rate that could be earned onalternative investments of equalrisk.
r i = r * + IP + LP + MRP + DRP
for debt securities.
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What’s the value of a 10-year, 10%
coupon bond if r d = 10%?
( ) ( )
V
r
B
d
=$100 $1,000
1
1 10 10. . . +$100
1+ r d
100 100
0 1 2 10
10%
100 + 1,000V = ?
...
= $90.91 + . . . + $38.55 + $385.54= $1,000.
++
+1 r + )d
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Suppose the bond was issued 20years ago and now has 10 years tomaturity. What would happen to its
value over time if the required rateof return remained at 10%, or at13%, or at 7%?
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M
Bond Value ($)
Years remaining to Maturity
1,372
1,211
1,000
837
775
30 25 20 15 10 5 0
r d
= 7%.
r d = 13%.
r d = 10%.
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At maturity, the value of any bondmust equal its par value.
The value of a premium bond would
decrease to $1,000.The value of a discount bond would
increase to $1,000.
A par bond stays at $1,000 if r d remains constant.
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What’s “yield to maturity”?
YTM is the rate of return earned on
a bond held to maturity. Alsocalled “promised yield.”
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What’s the YTM on a 10-year, 9%
annual coupon, $1,000 par value bondthat sells for $887?
90 9090
0 1 9 10r d=?
1,000PV1
.
.
.PV10
PVM
887 Find r d that “works”!
...
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10 -887 90 1000N I/YR PV PMT FV
10.91
( ) ( ) ( )V
INT
r
M
r B
d
N
d
N1 1
1... +
INT
1+ r d
( ) ( ) ( )887 90
11000
11 10 10
r r d d
+ 901+ r d
,
Find r d
++++
++++
INPUTS
OUTPUT
...
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If coupon rate < r d, bond sells at adiscount.
If coupon rate = r d, bond sells at its par
value.
If coupon rate > r d, bond sells at a
premium.
If r d rises, price falls.Price = par at maturity.
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Find YTM if price were $1,134.20.
10 -1134.2 90 1000
N I/YR PV PMT FV7.08
Sells at a premium. Becausecoupon = 9% > r d = 7.08%,
bond’s value > par.
INPUTS
OUTPUT
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Definitions
Current yield =
Capital gains yield =
= YTM = +
Annual coupon pmtCurrent price
Change in priceBeginning price
Exp totalreturn
ExpCurr yld
Exp capgains yld
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Find current yield and capital gains
yield for a 9%, 10-year bond when thebond sells for $887 and YTM = 10.91%.
Current yield =
= 0.1015 = 10.15%.
$90$887
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YTM= Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% - 10.15%= 0.76%.
Could also find values in Years 1 and 2,get difference, and divide by value in
Year 1. Same answer.
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What’s interest rate (or price) risk?
Does a 1-year or 10-year 10% bondhave more risk?
r d 1-year Change 10-year Change
5% $1,048 $1,38610% 1,000 4.8% 1,000 38.6%
15% 956 4.4% 749 25.1%
Interest rate risk: Rising r d
causes
bond’s price to fall.
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0
500
1,000
1,500
0% 5% 10% 15%
1-year
10-year
r d
Value
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Bond Ratings Provide One Measure
of Default Risk
Investment Grade Junk Bonds
Moody’s Aaa Aa A Baa Ba B Caa C
S&P AAA AA A BBB BB B CCC D
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Stocks and Their Valuation
Features of common stock
Determining commonstock values
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Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Since managers are “agents” of shareholders, their goal should be:Maximize stock price.
Common Stock: Owners, Directors,
and Managers
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Classified stock has special provisions.
Could classify existing stock asfounders’ shares, with voting rights butdividend restrictions.
New shares might be called “Class A”shares, with voting restrictions but fulldividend rights.
What’s classified stock? How might
classified stock be used?
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When is a stock sale an initial public
offering (IPO)?
A firm “goes public” through an IPO
when the stock is first offered to thepublic.
Prior to an IPO, shares are typically
owned by the firm’s managers, keyemployees, and, in many situations,
venture capital providers.
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What is a seasoned equity offering
(SEO)?
A seasoned equity offering occurs when
a company with public stock issuesadditional shares.
After an IPO or SEO, the stock trades in
the secondary market, such as theNYSE or Nasdaq.
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Dividend growth model
Using the multiples of comparablefirms
Free cash flow method
Different Approaches for Valuing
Common Stock
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( ) ( ) ( ) ( )∞∞
+++++++= s s s sr
D
r
D
r
D
r
D P
1...
111
ˆ3
3
2
2
1
1
0
One whose dividends are expected togrow forever at a constant rate, g.
Stock Value = PV of Dividends
What is a constant growth stock?
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For a constant growth stock,
( )
( )
( )
D D g
D D g
D D gt t
t
1 0
1
2 0
2
1
1
1
= +
= +
= +
( )
g r
D
g r
g D P
ss −=
−
+= 10
0
1ˆ
If g is constant, then:
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( )D D gtt
= +0 1
( ) t t
t r
D PVD
+=
1
!Pr,>g 0 ∞ If P PVDt0 = ∑
$
0.25
Years (t)0
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What happens if g > r s?
If r s< g, get negative stock price,which is nonsense.
We can’t use model unless (1) g < r s
and (2) g is expected to be constantforever. Because g must be a long-term growth rate, it cannot be > r s.
.rrequiresˆs
10 g
g r
D P
s
>−
=
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Assume beta = 1.2, r RF = 7%, and RPM =
5%. What is the required rate of returnon the firm’s stock?
r s = r RF + (RPM)bFirm
= 7% + (5%) (1.2)= 13%.
Use the SML to calculate r s:
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D0 was $2.00 and g is a constant 6%.
Find the expected dividends for thenext 3 years, and their PVs. r s = 13%.
0 1
2.2472
2
2.3820
3g=6% 4
1.8761
1.7599
1.6508
D0=2.0013%
2.12
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What’s the stock’s market value?
D0 = 2.00, r s = 13%, g = 6%.
Constant growth model:
( )
g r
D
g r
g D P
ss −=
−
+= 10
0
1ˆ
= = $30.29.0.13 - 0.06
$2.12 $2.12
0.07
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What is the stock’s market value one
year from now, P1?
D1 will have been paid, so expected
dividends are D2, D3, D4 and so on.
Thus,
^
D2
P1 = r s - g
= $2.2427 = $32.100.07
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Find the expected dividend yield and
capital gains yield during the first year.
Dividend yield = = = 7.0%.$2.12$30.29D1
P0
CG Yield = =P1 - P0
^
P0
$32.10 - $30.29$30.29
= 6.0%.
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Find the total return during the
first year.
Total return = Dividend yield +
Capital gains yield.Total return = 7% + 6% = 13%.
Total return = 13% = r s.
For constant growth stock:
Capital gains yield = 6% = g.
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Rearrange model to rate of return form:
.rtoˆ
0
1s
1
0g
P
D
g r
D P
s
+
−
=
∧
Then, r s = $2.12/$30.29 + 0.06= 0.07 + 0.06 = 13%.
^
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What would P0 be if g = 0?
The dividend stream would be aperpetuity.
2.00 2.002.00
0 1 2 3r s=13%
P0 = = = $15.38.PMT
r
$2.00
0.13^
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If we have supernormal growth of
30% for 3 years, then a long-runconstant g = 6%, what is P0? r is
still 13%.
Can no longer use constant growthmodel.
However, growth becomes constant
after 3 years.
^
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Nonconstant growth followed by constant
growth:0
2.3009
2.6470
3.0453
46.1135
1 2 3 4r s=13%
54.1067 = P0
g = 30% g = 30% g = 30% g = 6%
D0 = 2.00 2.603.38 4.394 4.6576
^
5371.66$06.013.0
6576.4$P̂
3=
−=
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What is the expected dividend yield and
capital gains yield at t = 0? At t = 4?
Dividend yield = = = 4.8%.$2.60$54.11
D1
P0
CG Yield = 13.0% - 4.8% = 8.2%.
At t = 0:
(More…)
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During nonconstant growth, dividend
yield and capital gains yield are notconstant.If current growth is greater than g,
current capital gains yield is greater
than g.After t = 3, g = constant = 6%, so the t
t = 4 capital gains gains yield = 6%. Because r s = 13%, the t = 4 dividend
yield = 13% - 6% = 7%.
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The current stock price is $54.11.
The PV of dividends beyond year 3 is$46.11 (P3 discounted back to t = 0).
The percentage of stock price due to“long-term” dividends is:
Is the stock price based on
short-term growth?
^
= 85.2%.$46.11
$54.11
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Suppose g = 0 for t = 1 to 3, and then g
is a constant 6%. What is P0?
0
1.76991.56631.3861
20.9895
1 2 3 4r s=13%
25.7118
g = 0% g = 0% g = 0% g = 6%
2.00 2.00 2.00 2.12
2.12
.P3 0 07
30.2857=
^
...
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What is dividend yield and capital
gains yield at t = 0 and at t = 3?
t = 0:D1
P0
CGY = 13.0% - 7.8% = 5.2%.
= =
2.00$25.72 7.8%.
t = 3: Now have constant growthwith g = capital gains yield = 6% anddividend yield = 7%.
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Analysts often use the P/E multiple (the priceper share divided by the earnings per share)or the P/CF multiple (price per share dividedby cash flow per share, which is the earningsper share plus the dividends per share) tovalue stocks.
Example:Estimate the average P/E ratio of
comparable firms. This is the P/E multiple.Multiply this average P/E ratio by the
expected earnings of the company toestimate its stock price.
Using the Stock Price Multiples toEstimate Stock Price
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The entity value (V) is:the market value of equity (# shares of
stock multiplied by the price per share)
plus the value of debt.Pick a measure, such as EBITDA, Sales,
Customers, Eyeballs, etc.Calculate the average entity ratio for a
sample of comparable firms. For example,V/EBITDAV/Customers
Using Entity Multiples
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Find the entity value of the firm in question.For example,Multiply the firm’s sales by the V/Sales
multiple.Multiply the firm’s # of customers by theV/Customers ratio
The result is the total value of the firm.
Subtract the firm’s debt to get the total valueof equity.Divide by the number of shares to get the
price per share.
Using Entity Multiples (Continued)
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It is often hard to find comparable firms. The average ratio for the sample of
comparable firms often has a wide range.For example, the average P/E ratio might
be 20, but the range could be from 10 to 50.How do you know whether your firm
should be compared to the low, average, or
high performers?
Problems with Market Multiple Methods
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Why are stock prices volatile?
gr
D0
Ps
1−
=
r s = r RF + (RPM)bi could change.
Inflation expectations
Risk aversion Company risk
g could change.
^
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Stock value vs. changes in r s and g
D1 = $2, r s = 10%, and g = 5%:
P0 = D1 / (r s-g) = $2 / (0.10 - 0.05) = $40.
What if r s or g change?g g g
r s
4% 5% 6%
9% 40.00 50.00 66.6710% 33.33 40.00 50.0011% 28.57 33.33 40.00
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In equilibrium, expected returns mustequal required returns:
r s = D1 /P0 + g = r s = r RF + (r M - r RF)b.^
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Why do stock prices change?
1
0 g r
D P
i −
=
r i = r RF + (r M - r RF )bi could change.
Inflation expectations Risk aversion Company risk
g could change.
^
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