Bonds and Bond Valuation_chapter 5

Cal State East Bay 5 - 1

Chapter 5Bonds and Bond Pricing

• Key features of bonds• Bond valuation• Measuring yield• Assessing risk• Bond types


What is a bond?• A long-term debt instrument in which a

borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.


Key Features of a Bond (Terminology)

• Par value – face amount of the bond, which is paid at maturity (assume $1,000 unless otherwise stated).

• Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. – Percentage of the par value– Multiply by par to get dollar payment of interest.

• Maturity date – years until the bond must be repaid.


Key Features of a Bond (Terminology)

• Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”).– The required rate of return (rd) that makes the

PV of the future payments to be received from the bond equal to the price paid for it.

– The rd used in the formula that would make both sides equal to each other.


Financial Asset Valuation

PV =

CF1+ r

... +CF

1+r1 n

12

21CF

r n .

0 1 2 nr

CF1 CFnCF2Value

...

+ ++

Price of any financial asset = PV of its future cash flows

Present Value of Cash Flows as Rates Change

• Bond Value = PV of coupons + PV of par• Bond = PV annuity + PV of lump sum• As interest rates increase the PV’s

decrease• As interest rates increase, bond prices

decrease and vice versa



What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?

$1,000 P$385.54 $38.55 ... $90.91 P

(1.10)$1,000

(1.10)$100 ...

(1.10)$100 P

B

B

10101B

0 1 2 10r

100 100 + 1,000100PB = ?

...

Relationship Between Price andYield-to-maturity

600

700

800

900

1000

1100

1200

1300

1400

1500

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

Cal State East Bay 8

Valuing a Bond Example 1• Suppose you are looking at a bond that has a

10% coupon rate, annual coupons, and a face value of $1000. There are 5 years to maturity and the YTM is 11%. What is the price of this bond? Value = PV of annuity + PV of lump sumValue = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5

Value = 369.59 + 593.45 = 963.04

100 PMT,1000 FV, 5 N, 11 I/Y, CPT PV => -963.04


Valuing a Bond Example 2• Suppose you are looking at a bond that has a

9% coupon rate, semi-annual coupons, and a face value of $1000. There are 20 years to maturity and the YTM is 9%. What is the price of this bond? Value = PV of annuity + PV of lump sumValue = 45[1 – 1/(1.045)40] / .045 + 1000 / (1.045)40

Value = 828.07 + 171.93 = 1000.00

45 PMT,1000 FV, 40 N, 4.5 I/Y, CPT PV => -1000.00


Bond Prices: Relationship Between Coupon Rate and Yield to Maturity

1. If YTM = coupon rate, par value = bond price

2. If YTM > coupon rate, par value > bond price– Why?– Selling at a discount, called a discount bond

3. If YTM < coupon rate, par value < bond price– Why?– Selling at a premium, called a premium bond


Interest Rate Risk• Price Risk

Change in price due to changes in interest ratesLong-term bonds have more price risk than

short-term bonds• 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


Figure 7.2


YTM with Semiannual CouponsSuppose a bond with a 9% coupon rate andsemiannual coupons, has a face value of$1000, 20 years to maturity and is selling for$1197.93. What is the YTM? Is the YTMmore or less than 9%?

45 PMT; 1000 FV; -1197.93 PV; 40 N; CPT I/Y => 3.5639%

YTM = 3.5639%*2 = 7.13%Cal State East Bay 5 - 14


What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?

PB=

0 1 2 10r

100 100 + 1,000100PB = ?

...

1000

10.11000

10.)10.1(

11100

10

10


Relationships between price and face value and between coupon rate and YTM

c > YTM Price > Face ValuePremium Bond

c = YTM Price = Face ValueBond trades at par

c < YTM Price < Face ValueDiscount Bond


Bond values over time

• At maturity, the value of any bond must equal its par value.

• If rd remains constant:– The value of a premium bond would

decrease over time, until it reached $1,000.

– The value of a discount bond would increase over time, until it reached $1,000.

– A value of a par bond stays at $1,000.


Callable bond

• In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is likely.

• So, expect to earn:– YTC on premium bonds.– YTM on par & discount bonds.


What is interest rate (or price) risk?

• Interest rate risk is the concern that rising cost of debt (rd) will cause the value of a bond to fall

% change 1 yr rd 10yr % change+4.8% $1,048 5% $1,386 +38.6%$1,000 10% $1,000-4.4% $95615% $749 -25.1%

The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.


What is reinvestment rate risk?

• Reinvestment rate risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

EXAMPLE: Suppose you just won$500,000 playing the lottery. You intend to invest the money and live off the interest.


Reinvestment rate risk example

• You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%.

• If you choose the 1-year bond strategy:– After Year 1, you receive $50,000 in income

and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000.

• If you choose the 10-year bond strategy:– You can lock in a 10% interest rate, and

$50,000 annual income.


Conclusions about interest rate and reinvestment rate risk

• CONCLUSION: Nothing is riskless!

Short-term AND/OR High coupon bonds

Long-term AND/OR Low coupon bonds

Interest rate risk

Low High

Reinvestment rate risk High Low


Evaluating default risk:Bond ratings

• Bond ratings are designed to reflect the probability of a bond issue going into default.

Investment Grade Junk Bonds

Moody’s Aaa Aa A Baa Ba B Caa C

S & P AAA AA A BBB BB B CCC D

The Bond Indenture• Contract between the company and the

bondholders and includes:1. The basic terms of the bonds2. The total amount of bonds issued3. A description of property used as security, if

applicable4. Sinking fund provisions5. Call provisions6. Details of protective covenants


Bond Classifications• Registered vs. Bearer Forms• Security

– Collateral – secured by financial securities– Mortgage – secured by real property, normally

land or buildings– Debentures – unsecured– Notes – unsecured debt with original maturity

less than 10 years• Seniority


Bond RatingsInvestment Quality High Grade

Moody’s Aaa and Aa, S&P AAA and AA Medium Grade

Moody’s A and Baa, S&P A and BBBSpeculative Low Grade

Moody’s Ba, B, Caa and Ca, S&P BB, B, CCC, CC Very Low Grade

Moody’s C and S&P C no interest being paidMoody’s D and S&P D in default


Bond Characteristics and Required Returns

• The coupon rate depends on the risk characteristics of the bond when issued

• Which bonds will have the higher coupon, all else equal?– Secured debt versus a debenture– Subordinated debenture versus senior debt– A bond with a sinking fund versus one without– A callable bond versus a non-callable bond


Government Bonds• Treasury Securities: Federal government debt

– T-bills – pure discount bonds with original maturity of one year or less

– T-notes – coupon debt with original maturity between one and ten years

– T-bonds coupon debt with original maturity greater than ten years

• Municipal Securities: Debt of state and local governments– Varying degrees of default risk, rated similar to

corporate debt– Interest received is tax-exempt at the federal level


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 (Thin Market, illiquid)

• Treasury securities are an exception (Deep Market, liquid)


Inflation and Interest Rates• Nominal rate of interest (R): percentage

change in dollars, all periodic rates to now• Real rate of interest (r): percentage

change in purchasing power, consumption• Expected inflation (h): expected

percentage change in prices, CPI• Nominal rate of interest includes our

desired real rate of return plus an adjustment for expected inflation


Inflation and Interest RatesIntuitive Example

You are offered an investment that pays a 25% return per year risk free. Is it a good deal?

What if inflation is 25% per year?

The implication here is that your investment will just offset inflation and you won’t be able to consume more stuff one year from now than you can consume today. So a 25% return in this case does not seem like such a good deal.


The Fisher Effect• Defines the relationship between real rates

(r), nominal rates (R), and inflation (h)

(1 + R) = (1 + r)(1 + h) Or, 1 + R = 1 + h + r + r*h

R = h + r + r*h

Approximation: Only use it outside of class R r + h if r*h is very small »Cal State East Bay 5 - 32

Fisher Effect Example• A 20 oz Diet Coke costs $1 and I drink 10

a day. One year from now they are expected to cost $1.05 each. If I invest today I would like to be able to consume 10% more Diet Cokes in a year. What nominal rate do I need to get on my investment?


Fisher Effect Examplea. Direct Calculation Today: 10 x $1 = $10. In a Year: 11 x $1.05 = $11.55 Target Nominal Rate: 15.5%b. Fisher Equation Real Rate = 10%, Inflation = 5% 1 + R = (1 + .10)(1 + .05) => R = 15.5% Cal State East Bay 5 - 34

Factors Affecting Required Return

• Default risk premium – remember bond ratings

• Taxability premium – remember municipal versus taxable

• Liquidity premium – bonds that have more frequent trading will generally have lower required returns

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


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Bonds and Bond Valuation_chapter 5