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Chapter

6Interest Rates and Bond Valuation

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Issues in Chapter 6• Financial Markets• Bond market• Bond valuation

• Finding a price (annual vs. semiannual)• Finding a yield (annual vs. semiannual)• Premium, discount, and par bonds• A relationship between price and yield

• Reading Wall Street Journal corporate bond quotation• Assessing risk

• Default risk, interest rate risk, and reinvestment risk

• Types of bonds• The Fisher Effect• Term structures

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Financial MarketsFinancial markets exist in order to allocate the

supply of savings in the economy to the demanders of those savings.

Financial markets are institutions and procedures that facilitate transactions in all types of financial claims. A securities market is simply a place where you can buy and sell securities (example, New York Stock Exchange)

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Public Offerings Versus Private Placements

Public Offering – Both individuals and institutional investors have the opportunity to purchase securities. The securities are initially sold by the managing investment bank firm. The issuing firm never actually meets the ultimate purchaser of securities

Private Placement (direct placement) – The securities are offered and sold to a limited number of investors

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Primary Versus Secondary MarketPrimary Market (initial issue)

Market in which new issues of a security are sold to initial buyers. This is the only time the issuing firm ever gets any money for the securities.

Example: Google raised $1.76 billion through sale of shares to public in August 2004.

Secondary Market (subsequent trading)

Market in which previously issued securities are traded. The issuing corporation does not get any money for stocks traded on the secondary market.

Example: Trading among investors today of Google stocks.

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Money versus Capital MarketMoney Market

Market for short-term debt instruments (maturity periods of one year or less). Money market is typically a telephone and computer market (rather than a physical building)

Examples: Treasury bills (issued by federal government), commercial paper, negotiable CDs, bankers’ acceptances.

Capital Market

Market for long-term securities (maturity greater than one year).

Examples: Corporate Bonds, Common stocks, Treasury Bonds, term loans and financial leases

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Classifying Securities

Basic Types Major Subtypes

Interest-bearing, orDebts

Money market instruments Fixed-income securities

Equities Common stock Preferred stock

Derivatives Futures Options

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• Pay interest, as the name suggests.

• The value of these assets depends, at least for the most part, on interest rates.

• They all begin life as a loan of some sort, so they are all debt obligations of some issuers.

• Relatively low risk and often large denominations

Interest-Bearing Assets

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Interest-Bearing AssetsMoney market instruments are short-term debt

obligations of large corporations and governments. These securities promise to make one future payment. When they are issued, their lives are less than one year. Relatively more liquid than longer-term fixed-income securities.

Fixed-income securities are longer-term debt obligations of corporations or governments. These securities promise to make fixed payments according to a

pre-set schedule. When they are issued, their lives exceed one year. Less liquid.

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Examples:Treasury bills: Short-term debt of U.S.

governmentCertificates of Deposits (CDs): Time deposit

with a bankCommercial Paper: Short-term, unsecured debt

of a companyFed Funds: Very short-term loans between

banks

Money Market Securities

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Fixed-Income SecuritiesExamples: U.S. Treasury notes, corporate bonds (callable and/or convertible, car loans, student loans. Notes and bonds are generic terms for fixed-income securities.

Potential gains/losses: Fixed coupon payments and final payment at maturity, except

when the borrower defaults. Possibility of gain (loss) from fall (rise) in interest rates. (Yes,

there is an inverse relationship between price and market interest rates.)

Depending on the debt issue, illiquidity can be a problem. (Illiquidity means it is possible that you cannot sell these securities quickly.)

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Interest rates : Market data from WSJ

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Bond MarketsPrimarily over-the-counter transactions with

dealers connected electronically

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

Makes getting up-to-date prices difficult, particularly on small company or municipal issues

Treasury securities are an exception

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Bonds Quotation

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Corporate bondsBonds are debt securities.

When a corporation issues bonds, it is in essence issuing an IOU to bondholders.

The IOU or bond contract sets out the terms, including the principal that will be owed, the interest that will be paid, and the time at which these payments will occur.

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Largest U.S. Corporate Bond Financings

IssuerGM

Ford Motor Co.

AT&T

RJR Holdings

WorldCom

Sprint

DateJune 2003

July 1999

Mar 1999

May 1989

Aug 1998

Nov 1998

Amount$16.5 billion

$8.6 billion

$8.0 billion

$6.1 billion

$6.1 billion

$5.0 billion

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Who issues a bond?• Domestically,

• Treasury bill, note, or bond: Issued by federal government, Called “risk-free” securities, about $4 trillion market

• Municipal bond: Issued by a local government (e.g., state or city), Often called “munis”

• Corporate bond: our focus, about $5 trillion market

• Internationally,• Euro bond: Dollar-denominated bonds sold in Germany

by GM• Foreign bond: “Yankee” bond (dollar-denominated bond

sold in U.S. by non-U.S. issuer), “Samurai” bond (Yen bonds sold in Japan by a non-Japanese borrower), etc

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http://www.usdebtclock.org/

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U.S. National Debt

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Bond Features Bond - evidence of debt issued by a corporation or a

governmental body. A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legal claim on future cash flows from the borrower. The issuer promises to: Make regular coupon (interest) payments every year or

six months until the bond matures, and Pay the face/par/maturity value of the bond when it

matures. That is, principal payment.

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Bond Pricing: Cash flows

AMD(Issuer, Seller, or

Borrower)

Investor(Buyer, Lender)

Price?

Coupons at t=1,2, …. T

Face Value at T

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Elements of Bond Pricing1. Par value (par): Face amount. paid at maturity.

Usually $1,000. Entered into FV.

2. Coupon interest rate (PMT): Stated interest rate on the bond certificate. Multiply by par value to get dollars of interest to be paid. Generally fixed. Entered into to PMT.

3. Maturity (N): Years until bond must be repaid. Declines over time. Entered into N.

4. Yield-to-Maturity (YTM): The required return by investors that is used to discount the future coupon payments and face amount. Entered into I.

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AMD promises to pay investors $60 (=6% coupon rate of $1,000) per year at year-end for next 7 years and one-time only $1,000 upon maturity.

$60 $60

0 1 2 7

$60 + $1,000V = ?

...

AMD Bond

6% Coupon

$1,000 Par

7-year Maturity

10% YTM

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Financial Asset Valuation

PV =

CF

1+ r ... +

CF

1 +r1 n

12

21

CF

rn .

0 1 2 nr

CF1 CFnCF2Value

...

+ ++

The value of any financial asset (e.g., a bond, a stock, a loan, etc) is simply the present value of the cash flows the asset is expected to produce.

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AMD Bond Again: What’s the value of a 7-year, 6% coupon bond if YTM (required return) = 10%?

60 60

0 1 2 7YTM=10%

60 + 1,000V = ?

...

( ) ( ) ( )V

YTM YTM B =

$60 $1,

1

000

11 7 7 . . . +

$60

1+YTM

= $54.55 + . . . + $30.79 + $513.16= $805.26

++++

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Bond ValuationPrice of a bond

= Present value of coupons and face amount (or par value)

= PV of the coupons (annuity) + PV of par value (usually $1,000)

Remember all CFs are discounted at a required return!!!

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7 10 60 1000N I/YR PV PMT FV

-805.26

The bond consists of a 7-year, % annuity of $60/year plus a $1,000 lump sum at t = 7:

$ 292.11 513.16

$805.26

PV annuity PV maturity value Value of bond

===

INPUTS

OUTPUT

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Let’s practice! More Examples

GM Bond 10%, 5-yr, YTM=10% Price =?

Ford Bond 7%, 5-yr, YTM=10% Price =?

Chrysler Bond

15%, 5-yr, YTM=10% Price =?

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If coupon rate > YTM, bond sells at a premium. (Price > Par) The premium price is to compensate the borrower for

above-market coupon rate.

If coupon rate = YTM, bond sells at its par value. (Price = Par)

If coupon rate < YTM, bond sells at a discount. (Price < Par) The discount price is to compensate the lender for

below-market coupon rate.

Premium, Discount, and Par bond

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Price Changes over Time

10%, 20-year, YTM = 8%Price today?Price five years from today?Price ten years from today?

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Coupon rate = A stated interest rate on the bond at the time of issuance

Yield-to-maturity = YTM is the rate of return earned on a bond held to maturity. Usually, same as the current market interest rate

for a similar investment. The discount rate that equates a bond’s price

with the present value of its future cash flows.

We are dealing with two rates!

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YTM = Rate of return on a bond you will earn if you hold the bond until maturitySuppose you bought an AMD bond for $1,009.17. An

AMD bond pays 10% and will mature one year from now. Find the YTM.

PMT =$100 N = 1, FV = 1,000, PV = -1009.17 YTM = ?

Find the rate of return on this investment. Rate of Return = (Future Income – Initial Investment) / Initial Investment = (1,100-1009.17)/1009.17 = ?

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What if a price is given?: What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887?

90 90 90

0 1 9 10YTM=?

1,000PV1 . . .PV10

PVM

887 Find YTM that “works”!

...

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Computing Yield-to-MaturityYield-to-maturity is the rate implied by the current

bond price

Finding the YTM requires trial and errortrial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity

If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

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( ) ( ) ( )887

90

1

1000

11 10 10 +

90

1+

,++

++ ...

YTMYTMYTM

10-year, 9% annual coupon, $1,000 par value bond that sells for $887. YTM = ?

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Annual vs. Semiannual

Find the value of 10-year, 10% coupon, annual bond if YTM = 13%.

Find the value of 10-year, 10% coupon, semiannual bond if YTM = 13%.

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Semiannual Bonds1. Multiply years by 2 to get periods = 2n.2. Divide nominal rate by 2 to get periodic rate = r / 2, or start with 2 Payment Per

Year.3. Divide annual INT by 2 to get PMT = INT/2.

2n r / 2 OK INT/2 OK

N I/YR PV PMT FV

INPUTS

OUTPUT

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2(10) 13 100/220 (2 P) 50 1000N I/YR PV PMT FV

-834.72

Find the value of 10-year, 10% coupon,semiannual bond if YTM = 13%.

INPUTS

OUTPUT

N Multiply by 2

YTM 2 payments per year

INT Divide by 2

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What’s the YTM on a 10-year, 9% semiannual coupon, $1,000 par value bond that sells for $887?

45 45 45

0 1 9 20 6 mth periods

YTM=?

1,000PV1 . . .PV10

PVM

887 Find YTM that “works”!

...

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20 -887 45 1000N I/YR PV PMT FV

10.88(2 P)

887

45

1

1000

11 20 20

YTM +

45

1+

,

Find YTM for Semiannual Bonds

++++

INPUTS

OUTPUT

...YTM YTM

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Example 1: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 10%.

Example 2: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 13%.

Example 3: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 7%.

Premium, Discount, and Par bond(continued)

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Graphical Relationship Between Price and Yield-to-maturity

400

600

800

1000

1200

1400

1600

0% 5% 10% 15% 20% 25%

Yield

Pri

ce

•Price and Yield move in an opposite direction!

•If YTM rises, price falls.

Microsoft Excel Worksheet

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Premium, Discount, and Par bond

Which of the following bonds would you buy, if you must choose one?Bond A: 12%, 1-yr, YTM = 10%, PV = 1,018.18Bond B: 10%, 1-yr, YTM = 10%, PV = 1,000Bond C: 5%, 1-yr, YTM = 10%, PV = 954.55

All of these bonds yield the same 10% return!Bond A: $1,018.18 *(1+YTM) = 1,018.18*1.1 = $1,120 Bond B: $1,000 *(1+YTM) = 1,000*1.1 = $1,100 Bond C: $954.55 *(1+YTM) = 954.55*1.1 = $1,050

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Risks in the bond marketDefault risk

“A seller may not pay me coupons and/or principal.” The failing firm is in a financial difficulty and may not

pay coupons or principal.

Interest rate risk “A volatile interest movement may depress the value of

my bonds. (also called price risk)” Change in price due to changes in interest rates. Long-term bonds have more price risk than short-term

bonds.

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Bond Ratings Provide One Measureof Default Risk

Low Quality, speculative, Investment-Quality Bond Ratings and/or “Junk”

High Grade Medium Grade Low Grade Very Low Grade

Standard & Poor’s AAA AA A BBB BB B CCC CC C DMoody’s Aaa Aa A Baa Ba B Caa Ca C C

Moody’s S&P

Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong.

Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rating, this group

comprises the high-grade bond class.

A A Debt rated A has a strong capacity to pay interest and repay principal, although it is somewhat more susceptible to the

adverse effects of changes in circumstances and economic conditions than

debt in high rated categories.

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Bond Ratings (continued)Baa BBB Debt rated Baa and BBB is regarded as having an

adequate capacity to pay interest and repay principal. Whereas it normally exhibits adequate protection

parameters, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity to pay interest and repay principal for debt in this category than in higher rated categories. These bonds are medium-grade obligations.

Ba, B BB, B Debt rated in these categories is regarded, on balance, as Caa, CCC predominantly speculative with respect to capacity to pay Ca CC interest and repay principal in accordance with the terms of the C C obligation. BB and Ba indicate the lowest degree of speculation, and Ca, CC, and C are the highest degree of speculation. Although such debt will likely have some quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures to adverse conditions. Some issues may be in default.

D D Debt rated D is in default, and payment of interest and/or repayment of principal is in arrears.

Bond ratings are like a GPA of the firm.

Go to www.moodys.com and find a debt rating of your favorite company.

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What’s interest rate (or price) risk? Does a 1-year or 30-year 10% bond have more risk?

YTM 1-year Change 30-year Change

5% $1,048 $1,769

10% 1,000 +4.8% 1,000 +76.9%

15% 956 -4.4% 672 -32.8%

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B o n dv a lu e ( $ )

2 ,0 0 0

1 ,5 0 0

1 ,0 0 0

5 0 0

5 1 0 1 5 2 0

$ 1 ,0 4 7 .6 2

$ 1 ,7 6 8 .6 2

$ 9 1 6 .6 7

$ 5 0 2 .1 1

1 - y e a r b o n d

3 0 - y e a r b o n d

In t e r e s tr a t e ( % )

Interest Rate 1 Year 30 Years 5% 1,047.62$ 1,768.62$

10 1,000.00 1,000.00 15 956.52 671.70 20 916.67 502.11

Time to Maturity

ST vs LT

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Does a low coupon or high coupon bond have more risk?

Bond “Stingy Corp” is a 4% coupon bond and Bond “Generous Corp.” is a 10% coupon bond. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 9%.

If interest rates rise by 2%, what is the percentage price change of these bonds? What if rates suddenly fall by 2% instead?

What does this problem tell you about the interest rate risk of lower-coupon bonds?

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True or False: “All 10-year bonds have the same price risk.”

False! Low coupon bonds have more price risk than high coupon bonds.

If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the value amount to be received at maturity.

Nothing is riskless!

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In general,

Low coupon or long maturity bonds have a greater interest

rate risk.

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Government bond: Federal government debt Callable bond: The seller has an option to buy back

their bonds from bond investors. Convertible bond: The seller grant bondholders the

right to exchange each bond for a designated number of common stock shares of the issuing firm.

Zero-coupon bonds: “zeros” or “deep discount” bonds

Floating-rate bonds: The coupon payments are adjustable.

Inflation-indexed bonds: Protecting against inflation, Fairly new.

Other Types of Bonds

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Government BondsTreasury Securities

Federal government debt issues T-Securities To control over money supply To fund national projects

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 – also called “munis” 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

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Municipal Bond ExampleA taxable bond has a yield of 8% and a municipal

bond has a yield of 6%If you are in a 40% tax bracket, which bond do

you prefer? 8%(1 - .4) = 4.8% The after-tax return on the corporate bond is 4.8%,

compared to a 6% return on the municipal

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Callable BondIssuer can refund (“buy back”) if rates decline. That

helps the issuer but hurts the investor.

Therefore, borrowers are willing to pay more, and lenders pay less, on callable bonds.

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Zero-Coupon BondsMake no periodic interest payments (coupon rate =

0%)

The entire yield-to-maturity comes from the difference between the purchase price and the par value

Cannot sell for more than par value

Sometimes called zeroes, or deep discount bonds

Treasury Bills are good examples of zeroes

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Bond Characteristics, Risk and Return

Secured bond vs. a debenture – Which bond is riskier?

Subordinated (or junior) vs. senior bond – Which bond is riskier?

A callable bond vs. a non-callable bond – Which bond is riskier?

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Two Kinds of Interest RatesReal rate of interest

change in purchasing power the percentage change in the amount of stuff you can

actually buy.Nominal rate of interest

quoted rate of interest, change in purchasing power and inflation

the percentage change in the amount of money you have.The nominal rate of interest includes our desired real

rate of return plus an adjustment for expected inflation

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Two Kinds of Interest Rates (continued)

Example:

Suppose we have $1000, and Diet Coke costs $2.00 per six pack. We can buy 500 six packs. Now suppose the rate of inflation is 5%, so that the price rises to $2.10 in one year. We invest the $1000 and it grows to $1100 in one year. What’s our return in dollars? In six packs?

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Two Kinds of Interest Rates (continued)

A. Dollars. Our return is

($1100 - $1000)/$1000 = $100/$1000 = .10.

The percentage increase in the amount of green stuff is 10%; our return is 10%.

B. Six packs. We can buy $1100/$2.10 = 523.81 six packs, so our return is

(523.81 - 500)/500 = 23.81/500 = 4.76%

The percentage increase in the amount of brown stuff is 4.76%; our return is 4.76%.

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The Fisher EffectThe Fisher Effect defines the relationship

between real rates, nominal rates and inflation

(1 + R) = (1 + r)(1 + h), whereR = nominal rater = real rateh = expected inflation rate

ApproximationR = r + h

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The Fisher Effect (concluded)According to the Fisher Effect:

1 + R = (1 + r) (1 + h)

Example: The nominal return is 10%, and the inflation is 5%. Calculate the real turn.

More example: 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%

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3-M T-Bill, 30-Y T-Bond, Aaa Corp B, Inflation Rate

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Term Structure of Interest RatesTerm structure is the relationship between time to

maturity and yields, all else equal

It is important to recognize that we pull out the effect of default risk, different coupons, etc.

Yield curve – graphical representation of the term structure Normal – upward-sloping, long-term yields are higher

than short-term yields Inverted – downward-sloping, long-term yields are

lower than short-term yields

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Upward-Sloping Yield Curve

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Downward-Sloping Yield Curve

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Factors Affecting Required Return or Yield of Corporate Bonds (rather than T-securities)

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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Quiz 1Suppose you purchase a zero coupon bond,

face value $1,000 maturing in twenty years, for $214.55. If the yield to maturity on the bond remains unchanged, what will the price of the bond be at the end of five years from now? A) $315.24 B) $387.52 C) $410.91 D) $680.58 E) $1,000.00

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Quiz 2 If the following bonds are identical except for coupon and

price, what is the price of bond B?

Bond A Bond BFace value $1,000 $1,000Semiannual coupon$45 $35Years to maturity 20 20 Price $1,098.96 ?

A. $901.03B. $925.31C. $960.44D. $1,037.86E. $1,079.63