Chapter 6
Interest Rates
And Bond
Valuation
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All rights reserved.
Bonds and Their Valuation
 Key features of bonds
 Bond valuation
 Measuring yield
 Assessing risk
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6-2
Cost of Money
• Money can be obtained from debts or equity
both of which has a cost
– Cost of debt = interest
– Cost of equity = dividends
• What is cost for the borrowers of funds is
the return for lenders or investors.
– Return for bond or debt investors = interest,
capital gains
– Return for equity investors = dividends, capital
gains.
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:
•
Par value – face value of the bond, which
is initially borrowed when the bond is sold and then paid at maturity.
•
Coupon interest rate – quoted/stated interest rate (generally fixed) paid
by the issuer. We multiply coupon int. rate by par value to get dollar
payment of interest called coupon payment.
•
Maturity date – years until the bond must be repaid.
•
Issue date – when the bond was issued.
•
Yield to maturity - rate of return earned on a bond held until maturity
(also called the “promised yield”).
Types of Bonds
• Treasury Bonds: Bonds issued by the federal
government. No default risk.
• Corporate Bonds: Bonds issued by corporations.
Different levels of default risk/credit risk.
• Municipal Bonds: Bonds issued by local government.
• Foreign Bonds: Bonds issued by foreign government
or foreign corporations. Exchange rate risk.
Types of Corporate bonds
• Mortgage bonds: A mortgage bond is a bond secured by a mortgage on one or more
assets. These bonds are typically backed by real estate holdings and/or real property such as equipment.
In a default situation, mortgage bondholders have a claim to the underlying property and could sell it off
to compensate for the default.
• Debentures: A debenture is a type of debt instrument that is not secured by physical
assets or collateral. Debentures are backed only by the general creditworthiness and reputation of the
issuer. Both corporations and governments frequently issue this type of bond in order to secure capital.
Ex- T-Bill, T-bond issued by government.
• Subordinated debentures:
A subordinated debenture is a bond classified
lower than more senior debt in the event of a default. This means that the holders of more senior
securities are paid first, before any residual funds are made available to the holder of the subordinated
debenture. Given the higher risk of nonpayment, this security pays out a relatively high interest rate.
• Investment-grade bonds: An investment grade is a rating that indicates
that a municipal or corporate bond has a relatively low risk of default.
• Junk bonds: A junk bond is a informal term for a high-yield or non-investment grade bond.
Junk bonds are fixed-income instruments that carry a rating of 'BB' or lower by Standard & Poor's, or 'Ba'
or below by Moody's. Junk bonds are so called because of their higher default risk in relation to
investment-grade bonds.
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6-6
Types of Bonds
• Fixed-rate bonds: A bond whose coupon rate is
fixed for its entire life.
• Floating-rate bonds: A bond whose coupon rates
fluctuates with shifts in the general level of interest
rates.
• Zero Coupon bond: A bond that pays no periodic
coupon.
• Discount bond: Any bond whose price is lower
than the par value.
• Premium Bond: A bond that sells above it’s par
value.
Types of Bonds
• Convertible bond: A bond that is exchangeable
at the option of the holder for the issuing firm’s
common stock.
• Putable bond: A bond that has the provision to
allow investors to sell the bond back to the
issuer prior to maturity at a prearranged price.
• Callable bond: A bond with a call provision that
gives the issuer right to redeem the bonds prior
to maturity date under specified terms. Most
bonds have a deferred call and a call premium.
Effect of a call provision
•
A call provision is a provision on a bond or other fixed-income
instrument that allows the original issuer to repurchase and retire the
bonds. If there is a call provision in place, it will typically come with a
time window under which the bond can be called, and a specific price to
be paid to bondholders and any accrued interest are defined.
•
Callable bonds will pay a higher yield than comparable non-callable
bonds.
•
Allows issuer to refund the bond issue if rates decline (helps the issuer,
but hurts the investor).
•
A bond call will almost always favor the issuer over the investor; if it
doesn't, the issuer will simply continue to make the current interest
payments and keep the debt active. Typically, call options on bonds will
be exercised by the issuer when interest rates have fallen. The reason
for this is that the issuer can simply issue new debt at a lower rate of
interest, effectively reducing the overall cost of their borrowing, instead
of continuing to pay the higher effective rate on the borrowings.
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6-9
Sinking Fund Provision
•
Provision to pay off a loan over its life rather than all at maturity
(Rather than the issuer repaying the entire principal of a bond on
the maturity date, issuer pays it off over bonds maturity period).
Generally corporations make semiannual or annual payments
that are used to retire the bonds.
•
Similar to amortization on a term loan.
•
Reduces default risk to investor.
•
But not good for investors if rates decline after issuance.
Therefore, if interest rates fall and bond prices rise, a firm will
benefit from the sinking fund provision that enables it to
repurchase its bonds at below-market prices. In this case, the
firm's (issuer’s) gain is the bondholder's (investor's) loss – thus
callable bonds will typically be issued at a higher coupon rate,
reflecting the value of the option.
Corporate Bonds: General Features
of a Bond Issue
• Bonds also are occasionally issued with stock purchase
warrants, which are instruments that give their holders
the right to purchase a certain number of shares of the
issuer’s common stock at a specified price over a certain
period of time. Occasionally attached to bonds as
“sweeteners.”
• Including warrants typically allows the firm to raise debt
capital at a lower cost than would be possible in their
absence.
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6-11
Table 6.4a Characteristics and Priority of
Lender’s Claim of Traditional Types of Bonds
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Table 6.4b Characteristics and Priority of
Lender’s Claim of Traditional Types of Bonds
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Table 6.5 Characteristics of
Contemporary Types of Bonds
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6-14
Corporate Bonds:
International Bond Issues
• Companies and governments borrow internationally by issuing
bonds in two principal financial markets:
– A Eurobond is a bond issued by an international borrower and sold to
investors in countries with currencies other than the currency in which the
bond is denominated.
– In contrast, a foreign bond is a bond issued in a host country’s financial
market, in the host country’s currency, by a foreign borrower.
• Both markets give borrowers the opportunity to obtain large
amounts of long-term debt financing quickly, in the currency of
their choice and with flexible repayment terms.
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6-15
Financial Asset Valuation
Fundamentals
• Valuation is the process that links risk and return to
determine the worth of an asset.
• There are three key inputs to the valuation process:
1. Cash flows (returns)
2. Timing
3. A measure of risk, which determines the required return
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6-16
Basic Valuation Model
• The value of any asset is the present value of all future cash flows it
is expected to provide over the relevant time period.
r
1
2
n
...
PVCF
CF1
CF2
CFn
0
• The value of any asset at time zero, V0, can be expressed as
v0 = Value of the asset at time zero
CFT = cash flow expected at the end of
year t
r = appropriate required return
(discount rate)
where
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6-17
Bond Valuation: Bond
Fundamentals
• As noted earlier, bonds are long-term debt instruments
used by businesses and government to raise large sums of
money, typically from a diverse group of lenders.
• Most bonds pay interest semiannually at a stated coupon
interest rate, have an initial maturity of 10 to 30 years,
and have a par value of $1,000 that must be repaid at
maturity.
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6-18
Bond Valuation: Basic Bond
Valuation
The basic model for the value, B0, of a bond is given by the
following equation:
OR,
Where,
B0= I*(PVIFAk ,n)+M*(PVIFkd,n)
d
B0
I
n
M
rd
=
=
=
=
=
value of the bond at time zero
annual interest paid in dollars
number of years to maturity
par value in dollars
required return on a bond
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6-19
Value of a Bond
• Two cash flows of a bond are periodic
coupon payments and the principal
amount (par value) at the end.
• Thus the value of a bond is
ki = k* + IP + MRP + DRP + LP
(b-p-242-timeline)
Value of a Bond
Bond Valuation: Basic Bond
Valuation (cont.)
• Mills Company, a large defense contractor, on January 1, 2007,
issued a 10% coupon interest rate, 10-year bond with a $1,000 par
value that pays interest annually.
• Investors who buy this bond receive the contractual right to two
cash flows: (1) $100 annual interest (10% coupon interest rate 
$1,000 par value) at the end of each year and (2) the $1,000 par
value at the end of the tenth year.
• Assuming that interest on the Mills Company bond issue is paid
annually and that the required return is equal to the bond’s coupon
interest rate, I = $100, rd = 10%, M = $1,000, and n = 10 years.
• So, Here, bond’s price is equal to the face value 1000.
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6-22
Bond Valuation: Bond Value
Behavior
In practice, the value of a bond in the marketplace is rarely equal to its
par value.
– Whenever the required return on a bond differs from the bond’s
coupon interest rate, the bond’s value will differ from its par
value.
– The required return is likely to differ from the coupon interest
rate because either (1) economic conditions have changed,
causing a shift in the basic cost of long-term funds, or (2) the
firm’s risk has changed.
– Increases in the basic cost of long-term funds or in risk will raise
the required return; decreases in the cost of funds or in risk will
lower the required return.
– Example-1:
http://www.investopedia.com/university/advancedbond/advancedbond2.asp
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6-23
Table 6.6 Bond Values for Various Required Returns (Mills
Company’s 10% Coupon Interest Rate, 10-Year Maturity,
$1,000 Par, January 1, 2010, Issue Paying Annual Interest)
If, rd >c, bond sells at Discount
If, rd =c, bond sells at Par
If, rd <c, bond sells at Premium
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6-24
Figure 6.4 Bond Values and
Required Returns
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6-25
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 reaches par
value.
– The value of a discount bond would
increase over time, until it reaches par
value.
– A value of a par bond stays constant.
Figure 6.5 Time to Maturity and
Bond Values
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6-27
Bonds with Semiannual
Coupons
• Divide annual coupon payment by 2 (INT/2).
• Multiply years to maturity by 2 (N X 2).
• Divide nominal (quoted) interest rate by 2
(rd/2)
Bonds with Semiannual Coupons
(cont.)
• The procedure used to value bonds paying interest semiannually is similar
to that shown in Chapter 5 for compounding interest more frequently than
annually, except that here we need to find present value instead of future
value. It involves
1.
Converting annual interest, I, to semiannual interest by dividing I by 2.
2.
Converting the number of years to maturity, n, to the number of 6-month periods
to maturity by multiplying n by 2.
3.
Converting the required stated (rather than effective) annual return for similar-risk
bonds that also pay semiannual interest from an annual rate, rd, to a semiannual
rate by dividing rd by 2.
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6-29
Bonds with Semiannual Coupons
(cont.)
• Assuming that the Mills Company bond pays interest
semiannually and that the required stated annual return, rd
is 12% for similar risk bonds that also pay semiannual
interest, substituting these values into the previous
equation yields
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6-30
Would you prefer to buy a 10-year, 10% annual
coupon bond or a 10-year, 10% semiannual
coupon bond, all else equal?
The semiannual bond’s effective rate is:
m
2
 iNom 
 0.10 
EFF%  1 
  1  1 
  1  10.25%
m 
2 


10.25% > 10% (the annual bond’s
effective rate), so you would prefer the
semiannual bond.
Bond Yields
• Yields are the returns on bonds based on
market conditions.
• Yield To Maturity is the rate of return earned
on a bond if it is held till maturity.
• At the time of issue YTM is equal to coupon
rate.
• Yield To Call is the rate of return earned when
bonds are held till the call period before
maturity.
Yield to Maturity (YTM)
• The yield to maturity (YTM) is the rate of return that
investors earn if they buy a bond at a specific price and
hold it until maturity. (Assumes that the issuer makes all
scheduled interest and principal payments as promised.)
• The yield to maturity on a bond with a current price equal
to its par value will always equal the coupon interest rate.
• When the bond value differs from par, the yield to
maturity will differ from the coupon interest rate.
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6-33
YTM
YTM
Current Yield
I
Bo
Capital Gain Yield
Premium or discount amount
Bo
YTM should be greater than 10% because Investor bought the bond by 950
(discount bond) which is less than par value 1000. So there is a capital
gain along with the current yield.
*Discount bond is good for investor.
Estimated Yield To Maturity
• Without a financial calculator it is not possible to find
the exact YTM of any bond.
• However YTM can be estimated using the following
formula:
What is the YTM on a 10-year, 9% annual
coupon, $1,000 par value bond, selling for
$887?
YTM of this bond is 10.91%. This bond sells at a
discount, because YTM > coupon rate.
Find YTM, if the bond price was $1,134.20.
YTM of this bond is 7.08%. This bond sells at a
premium, because YTM < coupon rate.
If, YTM>c, bond sells at Discount
If, YTM =c, bond sells at Par
If, YTM <c, bond sells at Premium
Bond’s Riskiness
• Interest rate risk is the chance that interest rates will
change and thereby change the required return and bond
value.
• The risk of a decline in a bond’s price due to an
increase in interest rate.
• Rising rates, which result in decreasing bond values, are
of greatest concern.
• The shorter the amount of time until a bond’s maturity,
the less responsive is its market value to a given change in
the required return.
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6-37
Bond’s Riskiness
• Reinvestment Risk: The risk of short-termed bonds due to a
decline in interest rates. (It affects YTM which is calculated
on the premise that all future coupon payments will be
reinvested at the interest rate in effect when the bond was
first purchased.) Zero coupon bonds are the only fixedincome instruments to have no reinvestment risk, since they
have no interim coupon payments.
• Which risk is more relevant to an investor depends on his/her
investment horizon
– Investment horizon is the period of time an investor plans to hold a particular
investment.
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6-38
Bond’s Riskiness
• Default risk: If an issuer defaults,
investors receive less than the
promised return. Therefore, the
expected return on corporate and
municipal bonds is less than the
promised return.
• Influenced by the issuer’s financial
strength and the terms of the bond
contract.
Table 6.1 Debt-Specific Issuer- and
Issue-Related Risk Premium Components
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6-40
Evaluating default risk:
Bond ratings
Investment Grade
Junk Bonds
Moody’s
Aaa Aa A Baa
Ba B Caa C
S&P
AAA AA A BBB
BB B CCC D
• Bond ratings are designed to reflect the
probability of a bond issue going into
default.
Table 6.3 Moody’s and Standard &
Poor’s Bond Ratings
Bond ratings are designed to reflect the probability of a bond
issue going into default.
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6-42
Bond markets
• Primarily traded in the over-the-counter (OTC)
market.
• Most bonds are owned by and traded among large
financial institutions.
• Full information on bond trades in the OTC market is
not published, but a representative group of bonds is
listed and traded on the bond division of the NYSE.
Review of Learning Goals
(cont.)
LG2
Review the legal aspects of bond financing and bond cost.
– Corporate bonds are long-term debt instruments indicating that a
corporation has borrowed an amount that it promises to repay in the
future under clearly defined terms. The bond indenture, enforced by a
trustee, states all conditions of the bond issue. It contains both standard
debt provisions and restrictive covenants, which may include a sinkingfund requirement and/or a security interest. The cost of a bond to an
issuer depends on its maturity, offering size, and issuer risk and on the
basic cost of money.
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6-44
Review of Learning Goals
(cont.)
LG3
Discuss the general features, yields, prices, ratings, popular
types, and international issues of corporate bonds.
– A bond issue may include a conversion feature, a call feature, or stock
purchase warrants. The yield, or rate of return, on a bond can be
measured by its current yield, yield to maturity (YTM), or yield to call
(YTC). Bond prices are typically reported along with their coupon,
maturity date, and yield to maturity (YTM). Bond ratings by
independent agencies indicate the risk of a bond issue. Various types of
traditional and contemporary bonds are available. Eurobonds and
foreign bonds enable established creditworthy companies and
governments to borrow large amounts internationally.
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6-45
Review of Learning Goals
(cont.)
LG4
Understand the key inputs and basic model used in the
valuation process.
– Key inputs to the valuation process include cash flows (returns), timing,
and risk and the required return. The value of any asset is equal to the
present value of all future cash flows it is expected to provide over the
relevant time period.
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6-46
Review of Learning Goals
(cont.)
LG5
Apply the basic valuation model to bonds and describe the
impact of required return and time to maturity on bond values.
– The value of a bond is the present value of its interest payments plus
the present value of its par value. The discount rate used to determine
bond value is the required return, which may differ from the bond’s
coupon interest rate. The amount of time to maturity affects bond
values. The value of a bond will approach its par value as the bond
moves closer to maturity. The chance that interest rates will change and
thereby change the required return and bond value is called interest rate
risk. The shorter the amount of time until a bond’s maturity, the less
responsive is its market value to a given change in the required return.
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6-47
Review of Learning Goals
(cont.)
LG6
Explain yield to maturity (YTM), its calculation, and the
procedure used to value bonds that pay interest semiannually.
– Yield to maturity is the rate of return investors earn if they buy a bond
at a specific price and hold it until maturity. YTM can be calculated by
using a financial calculator or by using an Excel spreadsheet. Bonds
that pay interest semiannually are valued by using the same procedure
used to value bonds paying annual interest, except that the interest
payments are one-half of the annual interest payments, the number of
periods is twice the number of years to maturity, and the required return
is one-half of the stated annual required return on similar-risk bonds.
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6-48