FIN4414 Security Valuation 001

8/10/2019 FIN4414 Security Valuation 001

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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



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 = ?



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%



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.



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%



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



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



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



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



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



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%



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%



Yield Curve

www.bloomberg.com/markets

3Y 5Y 10Y 30Y

1%

5%



Yield Curve

www.bloomberg.com/markets

6%

3Y 5Y 10Y 30Y

8%



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.





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



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



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%



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



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



PROPERTIES

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FIN4414 Security Valuation 001