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8/10/2019 FIN4414 Security Valuation 001
http://slidepdf.com/reader/full/fin4414-security-valuation-001 1/22
Security ValuationBasic Approach: PV (expected future cash flows)
Outline of Topics:
Valuing bonds
Valuing preferred stock
Valuing common stockDiscounted cash flow method
Dividend valuation method assuming:
Zero growth
Constant growth Non-constant growth
Estimating g, the growth rate
Term structure of interest rates
8/10/2019 FIN4414 Security Valuation 001
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Security Valuation
Determine the “intrinsic” value of:
(1) Bonds; (2) Preferred Stock; (3) Common Stock.
Bond Valuation
Assume a $1,000 par value bond, 10 years to maturity, with an 8%
coupon rate.If the investor wants to earn a 10% return on the bond, how much
would he be willing to pay for it?
0 1 2 3 4 5 6 7 8 9 10| | | | | | | | | | |
($877.11) 80 80 80 80 80 80 80 80 80 80
PV, @10%) 1,000
PMT = 80; FV = 1,000; N = 10; %r = 10; PV = ?
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Bond Prices and Interest Rates
(1) Bond prices move inversely to interest rates (as do all security prices).
(2) All else held constant, the longer the maturity of the bond, the more sensitive is
its price to a change in interest rates.
Bond A: 20-year; 12% coupon; initial yield: 10%; Bond’s value: $1,170.27
Bond B: 10-year; 12% coupon; initial yield: 10%; Bond’s value: $1,122.89
Now assume that bond yields drop from 10% to 8%.
Bond A: New Value: $1,392.73; % : +19%Bond B: New Value: $1,268.40; % : +13%
Bond A: sameBond C: 20-year; 4% coupon; initial yield: 10%; Bond’s value: $489.19
(3) All else held constant, the lower a bond’s coupon rate, the more sensitive is
its price to changes in interest rates.
Again, assume r% drops to 8%:
Bond A: same % : +19%
Bond C: New Value: $607.27; % : +24%
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Yield to Maturity
(1) If a bond’s coupon rate = YTM; then its PV = Par value.
(2) If a bond’s coupon rate > YTM; then its PV > Par value.
(3) If a bond’s coupon rate < YTM; then its PV < Par value.
an estimate of the % yield earned on the bondfrom the purchase date to the maturity date.
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Valuing bonds with semi-annual interest payments:
Suppose Bond A has a maturity of $1,000 and a
10% coupon, with interest paid semi-annually.
(a) If there are 5 years to maturity, and the bond is priced to yield
8%, what is the bond’s value today?
n = 10 r = 4 PMT = $50 FV = $1,000
(PV = $1,081.10) Selling at a premium
(b) Same bond, but now the yield is 10%. Price?
(r = 5) Selling at par
(c) Now the yield is 12%. Price?(r = 6) Selling at a discount (PV = $926.40)
What is the effective yield in this case?
Eff. Yield = 12.36%
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Yield-to-Call (YTC): Use the previous bond example (10 yr. bond, 8% coupon, YTM =10%; PV =$877.11), except assume the bond will be called after 5 years with a call
premium of 10%:
Zero-Coupon Bonds
If the bond pays the coupon semi-annually, what is the YTC?PMT = 40; N = 10; FV = 1,100; PV = 877.11; %r = ?
[6.4482% x 2 = 12.896% compounded semi-annually].
Eff. Yield? = 13.31%.
PV = -10,000; FV = 300,000
N = 30; %r = ?
[12%]
0 30
($10,000) $300,000
0 1 3 42 5
($877.11)
1,100
80 80 80 80 80
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Time Path of Bonds
How does the value of a bond change as it approaches itsmaturity date?
_
_
_
| | | | | |
5 4 3 2 1 0
1000
1250
750
Years to maturity
Value
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Example: Bond A has a face value of $40,000 and matures in 20 years. It makes
no payments for the first 6 years, pays $2,000 semiannually for the next 8 years, and
$2,500 the last 6 years. Assume r = 12%, compounded semiannually. What is the
price?
0 1 … 12 28 29 …
0 … 0 2000 2500
40,000
40
2000 … 2500…
13…
0
PV of 2 annuities + principal:
PV of $2,000 annuity:
n=16, PMT=2000, r = 6%, PV = ? (20,211.79 as of t = 12)
20,211.79 / (1.06)12 10,044.64 PV of $2,500 annuity:
n=12, PMT=2500, r = 6%, PV = ? (20,959.61 as of t = 28)
20,959.61 / (1.06)28 4,100.33
PV (40,000 in pd. 40) = 3,888.8910,044.64 + 4,100.33 + 3,888.89 = $18,033.86
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Bond Valuation Example (continued)Financial Calculator: Cash Flow Inputs
CF0 = 0
CF1 = 0
n j = 12
CF2 = 2,000
n j = 16CF3 = 2,500
n j = 12
NPV = 14,144.97 r = 6%
+PV(40,000) = 3,888.89
18,033.86
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Preferred Stock Valuation
Ex. What is the value of preferred stock with a$100 par value, paying a 6% dividend;
r = 12%:
PV = $6.00/.12 = $50
returnof rateRequired
Dividend psV
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Preferred Stock Example
A share of PS pays a quarterly dividend of $2.50. Ifthe price is currently $50, what is the annual rate of
return?
Recall: V = Div/r
r = Div/V = $10/$50 = 20%
EAR=?
21.55%
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Term Structure of Interest Rates
the relationship between bond yields and
maturities
Recently: March 1980:
2-3 year: 4.85% 14%5 year: 4.80% 13.5%
10 year: 4.87% 12.8%
30 year: 5.02% 12.5%
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Yield Curve
www.bloomberg.com/markets
3Y 5Y 10Y 30Y
1%
5%
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Yield Curve
www.bloomberg.com/markets
6%
3Y 5Y 10Y 30Y
8%
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What determines the shapeof the yield curve?
(1) Expectations theory
the yield curve depends on expectations
about future inflation.
(2) Liquidity preference theory
there is a positive maturity risk premium.
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Nonconstant Growth Example
Bailey Inc. expects to pay a dividend of $1.25 next year and then have
it grow @ 9% for the next 3 years before growing @ 5% indefinitely
thereafter. (r = 10%)
What is the intrinsic value of the stock?
0 1 3 42 5
1.25 1.36 1.49 1.62 1.70
P4 = D5 / r-gP4 = 1.70/(.10-.05) = $34.00
P0 = 1.25/1.10 + 1.36/(1.10)2 + 1.49/(1.10)3 + 1.62/(1.10)4 + 34/(1.10)4
= $27.71
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Estimating the Capitalization Rate (r)on a Stock
Recall: P0 = D1/(r-g)
r = D1/P0 + g or
r = DY + capital gains yield
How to calculate g?
g = Retention ratio x ROE
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Example
The Taylor Co. had net income of $150,000 this past year.
It paid $45,000 in dividends on the company’s equity of$2,500,000.
There are 100,000 shares outstanding with a current
market value of 12 5/8 per share.What is the required rate of return? (r = D1/P0 + g)
g = retention ratio x ROE = (1-Div. Payout) x NI/Equity
(1 - 45,000/150,000) x 150,000/2,500,000= .7(.06) = 4.2%
r = D1/P0 + g = .45 (1.042) / 12.625 + .042 = 7.91%
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Growth Opportunities
• Growth opportunities refer to opportunities to
invest in positive NPV projects.
• The value of a firm can be expressed as the sum of
the value of a firm that pays out 100% of its
earnings as dividends, plus the NPV of the growth
opportunities.
NPVGO R
EPS P
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NPVGO Model
Example: Consider a firm that has forecasted EPS of
$5 and is currently priced at $75 per share; r = 16%.
• Calculate the value of the firm as a cash cow.
NPVGO must be:
$75 - $31.25 = $43.75
25.31$16.
5$EPS0
R P
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