(4) Bond and Sock Valuation

8/2/2019 (4) Bond and Sock Valuation

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6 - 1

Bonds and Their Valuation

Key features of bonds

Bond valuation

Measuring yield

Assessing risk



6 - 2

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…)



6 - 3

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.



6 - 4

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.



6 - 5

Financial Asset Valuation

( ) ( ) ( )PV =

CF

1+ r ... +

CF

1+r

1 n

1

2

21

CF

r n .

0 1 2 nr

CF1 CFnCF2Value

...

+ ++



6 - 6

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.



6 - 7

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



6 - 8

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%?



6 - 9

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%.



6 - 10

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.



6 - 11

What’s “yield to maturity”?

YTM is the rate of return earned on

a bond held to maturity. Alsocalled “promised yield.”



6 - 12

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”!

...



6 - 13

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

...



6 - 14

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.



6 - 15

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



6 - 16

Definitions

Current yield =

Capital gains yield =

= YTM = +

Annual coupon pmtCurrent price

Change in priceBeginning price

Exp totalreturn

ExpCurr yld

Exp capgains yld



6 - 17

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



6 - 18

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.



6 - 19

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.



6 - 20

0

500

1,000

1,500

0% 5% 10% 15%

1-year

10-year

r d

Value



6 - 21

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



6 - 22

Stocks and Their Valuation

Features of common stock

Determining commonstock values



6 - 23

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



6 - 24

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?



6 - 25

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.



6 - 26

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.



6 - 27

Dividend growth model

Using the multiples of comparablefirms

Free cash flow method

Different Approaches for Valuing

Common Stock



6 - 28

( ) ( ) ( ) ( )∞∞

+++++++= 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?



6 - 29

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:



6 - 30

( )D D gtt

= +0 1

( ) t t

t r

D PVD

+=

1

!Pr,>g 0 ∞ If P PVDt0 = ∑

$

0.25

Years (t)0



6 - 31

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

>−

=



6 - 32

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:



6 - 33

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



6 - 34

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



6 - 35

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



6 - 36

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%.



6 - 37

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.

6 38



6 - 38

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%.

^

6 39



6 - 39

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^

6 40



6 - 40

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.

^

6 41



6 - 41

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=

−=

6 42



6 - 42

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…)

6 43



6 - 43

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%.

6 44



6 - 44

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

6 45



6 - 45

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=

^

...

6 46



6 - 46

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%.

6 47



6 - 47

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

6 48



6 - 48

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

6 49



6 - 49

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)

6 50



6 - 50

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

6 51



6 - 51

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.

^

6 52



6 - 52

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

6 - 53



6 - 53

In equilibrium, expected returns mustequal required returns:

r s = D1 /P0 + g = r s = r RF + (r M - r RF)b.^

6 - 54



6 - 54

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.

^

(4) Bond and Sock Valuation

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