6-1

SESSİONS 5 & 6

6-2

Key Concepts and Skills

• Know the important bond features and bond types

• Understand: – Bond values and why they fluctuate– Bond ratings and what they mean– The impact of inflation on interest rates– The term structure of interest rates and

the determinants of bond yields

6-3

Bond Definitions

• Bond– Debt contract– Interest-only loan

• Par value (face value) ~ $1,000• Coupon rate• Coupon payment• Maturity date• Yield to maturity

6-4

Key Features of a Bond

• Par value: –Face amount–Re-paid at maturity –Assume $1,000 for corporate bonds

• Coupon interest rate: –Stated interest rate –Usually = YTM at issue–Multiply by par value to get coupon

payment

6-5

Key Features of a Bond• Maturity:

– Years until bond must be repaid

• Yield to maturity (YTM): – The market required rate of return for bonds of

similar risk and maturity– The discount rate used to value a bond– Return if bond held to maturity– Usually = coupon rate at issue– Quoted as an APR

6-6

Bond Value

• Bond Value = PV(coupons) + PV(par)• Bond Value = PV(annuity) + PV(lump sum)• Remember:

– As interest rates increase present values decrease ( r → PV )

– As interest rates increase, bond prices decrease and vice versa

6-7

Spreadsheet Formulas

=FV(Rate,Nper,Pmt,PV,0/1) =PV(Rate,Nper,Pmt,FV,0/1)=RATE(Nper,Pmt,PV,FV,0/1)=NPER(Rate,Pmt,PV,FV,0/1)=PMT(Rate,Nper,PV,FV,0/1)

• Inside parens: (RATE,NPER,PMT,PV,FV,0/1)• “0/1” Ordinary annuity = 0 (default)

Annuity Due = 1 (must be entered)

6-8

Graphical Relationship Between Price and Yield-to-maturity

600

700

800

900

1000

1100

1200

1300

1400

1500

0% 2% 4% 6% 8% 10% 12% 14%

Bon

d P

rice

Yield-to-maturity

6-9

Bond Prices: Relationship Between Coupon and Yield

• Coupon rate = YTM Price = Par• Coupon rate < YTM Price < Par

–“Discount bond” … Why?• Coupon rate > YTM Price > Par

–“Premium bond” … Why?

6-10

M

Premium

1,000

Discount

30 25 20 15 10 5 0

CR>YTM

CR<YTM

YTM = CR

Bond Value ($) vs Years remaining to Maturity

6-11

Interest Rate Risk

• Price Risk–Change in price due to changes in

interest rates–Long-term bonds have more price risk

than short-term bonds–Low coupon rate bonds have more price

risk than high coupon rate bonds

6-12

Interest Rate Risk

• Reinvestment Rate Risk– Uncertainty concerning rates at which

cash flows can be reinvested– Short-term bonds have more reinvestment

rate risk than long-term bonds– High coupon rate bonds have more

reinvestment rate risk than low coupon rate bonds

6-13

Figure 6.2

6-14

Computing Yield-to-Maturity YTM

• Yield-to-maturity (YTM) = the market required rate of return implied by the current bond price

• With a financial calculator, – Enter ,, ., /, and 0 – Remember the sign convention

• / and 0 need to have the same sign (+)• . the opposite sign (-)• %-

6-15

YTM with Annual CouponsConsider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09.– Will the yield be more or less than 10%?

15 n928.09 pv (- for fin calc)1000 fv100 pmt

I 11% Result = YTM

Using Excel: =RATE(15, 100, -928.09, 1000, 0)

6-16

Table 6.1

6-17

Debt versus Equity• Debt

– Not an ownership interest– No voting rights– Interest is tax-deductible– Creditors have legal

recourse if interest or principal payments are missed

– Excess debt can lead to financial distress and bankruptcy

• Equity– Ownership interest– Common stockholders

vote to elect the board of directors and on other issues

– Dividends are not tax deductible

– Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared

– An all-equity firm cannot go bankrupt

6-18

The Bond Indenture“Deed of Trust”

Contract between issuing company and bondholders includes:

– Basic terms of the bonds– Total amount of bonds issued– Secured versus Unsecured– Sinking fund provisions– Call provisions

• Deferred call• Call premium

– Details of protective covenantsReturn to Quiz

6-19

Bond Ratings – Investment Quality

• High Grade– Moody’s Aaa and S&P AAA – capacity to pay is

extremely strong– Moody’s Aa and S&P AA – capacity to pay is very

strong

• Medium Grade– Moody’s A and S&P A – capacity to pay is strong,

but more susceptible to changes in circumstances

– Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay Return

to Quiz

6-20

Bond Ratings - Speculative• Low Grade

– Moody’s Ba, B, Caa and Ca– S&P BB, B, CCC, CC– Considered speculative with respect to capacity

to pay. The “B” ratings are the lowest degree of speculation.

• Very Low Grade– Moody’s C and S&P C – income bonds with no

interest being paid– Moody’s D and S&P D – in default with

principal and interest in arrears

6-21

Government Bonds

• Treasury Securities = Federal government debt– Treasury Bills (T-bills)

• Pure discount bonds • Original maturity of one year or less

– Treasury notes • Coupon debt • Original maturity between one and ten years

– Treasury bonds • Coupon debt • Original maturity greater than ten years

6-22

Zero Coupon Bonds• Make no periodic interest payments

(coupon rate = 0%)• Entire yield-to-maturity comes from the

difference between the purchase price and the par value (capital gains)

• Cannot sell for more than par value• Sometimes called zeroes, or deep

discount bonds• Treasury Bills and U.S. Savings bonds are

good examples of zeroes

6-23

Floating Rate Bonds• Coupon rate floats depending on some index

value• Examples – adjustable rate mortgages and

inflation-linked Treasuries• Less price risk with floating rate bonds

– Coupon floats, so is less likely to differ substantially from the yield-to-maturity

• Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”

6-24

Bond Markets

• Primarily over-the-counter transactions with dealers connected electronically

• Extremely large number of bond issues, but generally low daily volume in single issues

• Getting up-to-date prices difficult, particularly on small company or municipal issues

• Treasury securities are an exception

6-25

Inflation and Interest Rates

• Real rate of interest =Change in purchasing power

• Nominal rate of interest = Quoted rate of interest,

= Change in purchasing power and inflation• The ex ante nominal rate of interest

includes our desired real rate of return plus an adjustment for expected inflation

6-26

The Fisher Effect

The Fisher Effect defines the relationship

between real rates, nominal rates and

inflation

(1 + R) = (1 + r)(1 + h)R = nominal rate (Quoted rate)

r = real rate

h = expected inflation rate

Approximation: R = r + h

Return to Quiz

6-27

Example 6.6

If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?– R = (1.1)(1.08) – 1 = .188 = 18.8%– Approximation: R = 10% + 8% = 18%– Because the real return and expected

inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

6-28

Term Structure of Interest Rates

• Term structure: The relationship between time to maturity and yields, all else equal– The effect of default risk, different coupons,

etc. has been removed.• Yield curve: Graphical representation of

the term structure– Normal = upward-sloping L/T > S/T– Inverted = downward-sloping L/T < S/T

Return to Quiz

6-29

Figure 6.5 A – Upward-Sloping Yield Curve

REPLACE with FIGURE 6.5 A

6-30

Figure 6.5 B – Downward-Sloping Yield Curve

6-31

Figure 6.6 – Treasury Yield Curve

6-32

Factors Affecting Required Return

• Default risk premium – bond ratings• Taxability premium – municipal versus taxable• Liquidity premium – bonds that have more

frequent trading will generally have lower required returns

• Maturity premium – longer term bonds will tend to have higher required returns.

Anything else that affects the risk of the cash flows to the bondholders will affect the required returns

Return to Quiz

7-33

Key Concepts and Skills

• Understand how stock prices depend on future dividends and dividend growth

• Be able to compute stock prices using the dividend growth model

• Understand how corporate directors are elected

• Understand how stock markets work• Understand how stock prices are quoted

7-34

Cash Flows for Stockholders

• If you own a share of stock, you can receive cash in two ways– The company pays dividends– You sell your shares, either to another

investor in the market or back to the company• As with bonds, the price of the stock is the

present value of these expected cash flows– Dividends → cash income– Selling → capital gains

7-35

One Period Example

• Suppose you are thinking of purchasing the stock of Moore Oil, Inc. – You expect it to pay a $2 dividend in one year – You believe you can sell the stock for $14 at

that time. – You require a return of 20% on investments of

this risk – What is the maximum you would be willing to

pay?

7-36

One Period Example

• D1 = $2 dividend expected in one year

• R = 20%• P1 = $14

• CF1 = $2 + $14 = $16

• Compute the PV of the expected cash flows

33.13$20.1

)142(P0

7-37

Two Period Example

• What if you decide to hold the stock for two years? – D1 = $2.00 CF1 = $2.00

– D2 = $2.10

– P2 = $14.70

– Now how much would you be willing to pay?

33.13$)20.1(

)70.1410.2(

20.1

2P

20

CF2 = $2.10 + $14.70 = $16.80

7-38

Three Period Example

• What if you decide to hold the stock for three years? – D1 = $2.00 CF1 = $2.00

– D2 = $2.10 CF2 = $2.10

– D3 = $2.205

– P3 = $15.435

– Now how much would you be willing to pay?

33.13$)20.1(

)435.15205.2(

)20.1(

10.2

20.1

2P

320

CF3 = $2.205 + $15.435 = $17.640

7-39

Developing The Model

• You could continue to push back when you would sell the stock

• You would find that the price of the stock is really just the present value of all expected future dividends

7-40

Stock Value = PV of Dividends

P0 =^

(1+R)1 (1+R)2 (1+R)3 (1+R)∞

D1 D2 D3 D∞+ + +…+

1tt

t0 )R1(

DP̂

How can we estimate all future dividend payments?

7-41

Estimating Dividends Special Cases

• Constant dividend/Zero Growth– Firm will pay a constant dividend forever– Like preferred stock– Price is computed using the perpetuity formula

• Constant dividend growth– Firm will increase the dividend by a constant

percent every period

• Supernormal growth– Dividend growth is not consistent initially, but settles

down to constant growth eventually

7-42

Zero Growth

• Dividends expected at regular intervals forever = perpetuity

P0 = D / R

• Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

20$

410.

50.0P0

7-43

Constant Growth Stock

D1 = D0(1+g)1

D2 = D0(1+g)2

Dt = Dt(1+g)t

One whose dividends are expected togrow forever at a constant rate, g.

D0 = Dividend JUST PAID

D1 – Dt = Expected dividends

7-44

Projected Dividends

• D0 = $2.00 and constant g = 6%

• D1 = D0(1+g) = 2(1.06) = $2.12

• D2 = D1(1+g) = 2.12(1.06) = $2.2472

• D3 = D2(1+g) = 2.2472(1.06) = $2.3820

7-45

P0 = ^ D0(1+g)

R - g=

D1

R - g

1t

t

t

00 )R1(

)g1(DP̂

Dividend Growth Model

“Gordon Growth Model”

7-46

DGM – Example 1

• Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

• D0= $0.50

• g = 2%• R = 15%

92.3$02.15.

)02.1(50.0P

gR

)g1(DP

0

00

7-47

Constant Growth Model Conditions

1. Dividend expected to grow at g forever2. Stock price expected to grow at g forever3. Expected dividend yield is constant4. Expected capital gains yield is constant

and equal to g5. Expected total return, R, must be > g6. Expected total return (R):

= expected dividend yield (DY) + expected growth rate (g) = dividend yield + g

7-48

Nonconstant Growth

• Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

• Remember that we have to find the PV of all expected future dividends.

7-49

Nonconstant Growth – Solution

• Compute the dividends until growth levels off– D1 = 1(1.2) = $1.20

– D2 = 1.20(1.15) = $1.38

– D3 = 1.38(1.05) = $1.449

• Find the expected future price at the beginning of the constant growth period:– P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66

• Find the present value of the expected future cash flows– P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67

7-50

R1

D. . .

R1

D

R1

D

R1

DP̂

33

22

11

0

Nonconstant + Constant growth

gR

DP̂ 1t

t

Basic PV of all Future Dividends Formula

Dividend Growth Model

7-51

22

22

11

0 )R1(

P

R1

D

R1

DP̂

gR

DP

then 2,t after constant g If

)R1(

DP Because

32

3tt

t2

Nonconstant + Constant growth

7-52

Using the DGM to Find R

Start with the DGM:

gP

D g

P

g)1(D R

g-R

D

g - R

g)1(DP

0

1

0

0

100

Rearrange and solve for R:

7-53

Finding the Required Return Example

• A firm’s stock is selling for $10.50.

They just paid a $1 dividend and

dividends are expected to grow at

5% per year.

• What is the required return?

7-54

Finding the Required Return Example

• P0 = $10.50.

• D0 = $1

• g = 5% per year. • What is the required return?

%1505.10.50

1.00(1.05) R

gP

D g

P

g)1(D R

0

1

0

0

7-55

Finding the Required Return Example

• P0 = $10.50

• D0 = $1

• g = 5% per year• What is the dividend

yield?1(1.05) / 10.50 = 10%

• What is the capital gains yield?

g =5% Dividend Capital Gains Yield Yield

%1505. 10.50

1.00(1.05) R

g P

D R

g P

g)1(D R

0

1

0

0

7-56

Table 7.1

7-57

Features of Common Stock

• Voting Rights–Stockholders elect directors–Cumulative voting vs. Straight voting–Proxy voting

• Classes of stock–Founders’ shares–Class A and Class B shares

Return to Quick Quiz

7-58

Features of Common Stock• Other Rights

–Share proportionally in declared dividends

–Share proportionally in remaining assets during liquidation

–Preemptive right • Right of first refusal to buy new stock issue

to maintain proportional ownership if desired

Return to Quick Quiz

7-59

Dividend Characteristics• Dividends are not a liability of the firm until

declared by the Board of Directors– A firm cannot go bankrupt for not declaring

dividends• Dividends and Taxes

– Dividends are not tax deductible for firm– Taxed as ordinary income for individuals – Dividends received by corporations have a

minimum 70% exclusion from taxable income