Chapter 7
Interest Rates and Bond
Valuation
Prof. Glass

Key Concepts and Skills
• Know the important bond features and bond types
• Understand bond values and why they fluctuate
• Understand bond ratings and what they mean
• Understand the impact of inflation on interest rates
• Understand the term structure of interest rates and
the determinants of bond yields
7-2
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Chapter Outline
• Bonds and Bond Valuation
• More about Bond Features
• Bond Ratings
• Some Different Types of Bonds
• Bond Markets
• Inflation and Interest Rates
• Determinants of Bond Yields
7-3
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Takeaways
• Bond prices are affected by maturity
• A general interest rate increase will decrease the price of long-term
bonds most
• Yield to maturity is based on face value of the bond and coupon rate
• Key factors affecting interest rates
• Productivity
• Inflation
• Maturity
• Liquidity
• Risk

Bond Definitions
• Bond
• Par value (face value)
• Coupon rate
• Coupon payment
• Maturity date
• Yield or Yield to maturity
7-5
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The Way they Used to Look

Present Value of Cash Flows
as Rates Change
• Bond Value = PV of coupons + PV of par
• Bond Value = PV of annuity + PV of lump sum (par)
• As interest rates increase, present values decrease
• So, as interest rates increase, bond prices decrease
and vice versa
7-7
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Methods of calculating a bond price
• Common Piece – the discounted face (par) value
• Example: 1000 par value matures in 10 years, annual market rate (Yield to
Maturity) is 8%
• Solution – 1000/(1+.08)^10 = $463.19
• Annuity – coupon value
• Example: coupon rate is 8% paid annually
• Set up spreadsheet with $80 in each period for 10 periods
• Use the annuity formula = 536.81 (C/r)*(1-1/(1+r)^t)
• Sum Common Piece and Annuity Piece = 463.19+536.81 = 1000
• Alternatively, use PV formula =-PV(rate,nper,paymnt,FV)
• =-PV(.08,10,80,1000) = 1000

Alternative 1: Coupon Value
Alternative 1 Discounted Discounted
time Payment 1/(1+r)^n Payment
1 80 0.93 74.07
2 80 0.86 68.59
3 80 0.79 63.51
4 80 0.74 58.80
5 80 0.68 54.45
6 80 0.63 50.41
7 80 0.58 46.68
8 80 0.54 43.22
9 80 0.50 40.02
10 80 0.46 37.06
536.81

Alternative 2: Coupon Value
Add PV Par= $463.10
PV(Coupon+Par) = 1000

Valuing a Discount Bond with Annual
Coupons
• Consider a bond with a coupon rate of 10% and
annual coupons. The par value is $1,000, and
the bond has 5 years to maturity. The yield to
maturity is 11%. What is the value of the bond?
 Using the formula:
• B = PV of annuity + PV of lump sum
• B = 100[1 – 1/(1.11)5] / .11 + 1,000 / (1.11)5
• B = 369.59 + 593.45 = 963.04
• Or –PV(.11, 5,, 100,1000)= 963.04
7-11
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Valuing a Premium Bond with Annual
Coupons
• Suppose you are reviewing a bond that has a
10% annual coupon and a face value of $1000.
There are 20 years to maturity, and the yield to
maturity is 8%. What is the price of this bond?
 Using the formula:
• B = PV of annuity + PV of lump sum
• B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20
• B = 981.81 + 214.55 = 1196.36
7-12
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If the coupon rate was 8%, B=1000 because the coupon rate equals
the amount you could earn in the next best investment

Graphical Relationship Between Price and Yield-
to-maturity (YTM)
Bond
Price
7-13
Bond characteristics: 10-year maturity, 8% coupon rate, $1,000 par value
Yield-to-Maturity (YTM)
Bond
Price,
in
dollars
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Notice,
when
coupon
rate=
yield to
maturity,
bond sells
at par
($1,000)

Bond Prices: Relationship Between Coupon
and Yield
• If YTM = coupon rate, then par value = bond price
• If YTM > coupon rate, then par value > bond price
 Why? The discount provides yield above coupon rate
 Price below par value, called a discount bond
• If YTM < coupon rate, then par value < bond price
 Why? Higher coupon rate causes value above par
 Price above par value, called a premium bond
7-14
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The Bond Pricing Equation
t
t
r)
(1
FV
r
r)
(1
1
-
1
C
Value
Bond
















7-15
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Bond Value = -PV(r,t,c,Par) where r=YTM,
t=nper,c=pmts,Par=FV)

Example 7.1
• If an ordinary bond has a coupon rate of
14 percent, then the owner will get a total
of $140 per year, but this $140 will come in
two payments of $70 each. The yield to
maturity is quoted at 16 percent. The bond
matures in seven years.
• Note: Bond yields are quoted like APRs;
the quoted rate is equal to the actual rate
per period multiplied by the number of
periods.
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Example 7.1
 How many coupon payments are there?
 What is the semiannual coupon payment?
 What is the semiannual yield?
 What is the bond price?
 B = 70[1 – 1/(1.08)14] / .08 + 1,000 / (1.08)14 =
917.56
 Or using the PV function: PMT = 70; N = 14; YTM/2
= 8; FV = 1,000; -PV = 917.56
7-17
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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
• 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
7-18
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Figure 7.2
7-19
One-year IOU much
less sensitive to
yield-to-maturity
changes. Only one
period affected by
market rate change.

Computing Yield to Maturity
• Yield to Maturity (YTM) is the rate implied by the
current bond price
• Use Rate formula
7-20
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Calculating yield to maturity
• Given
• Bond price = 1134.20
• Coupon = 100
• Nper = 10 years
• Par = 1000
• Find YTM (r) ?
• =rate(nper, pay, -PV, FV) where FV=par
• =rate(10,100,-1134.20,1000) = .08

YTM with Semiannual Coupons
• Suppose a bond with a 10% coupon rate and
semiannual coupons, has a face value of $1,000, 20
years to maturity and is selling for $1,197.93.
 Is the YTM more or less than 10%?
 What is the semiannual coupon payment?
 How many periods are there?
 N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4%
(Is this the YTM?)
 Use rates formula =rate(40, 50. -1,197.93,1000)
 YTM = 4%* 2 = 8%, that is why investors bid up the price
7-22
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Table 7.1
7-23
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Current Yield vs. Yield to Maturity
• Current Yield = annual coupon / price
• Yield to maturity = current yield + capital gains yield
• Example: 10% coupon bond, with semiannual coupons,
face value of 1,000, 20 years to maturity, $1,197.93 price
 Current yield = 100 / 1,197.93 = .0835 = 8.35%
 Price in one year, assuming no change in YTM = 1,193.68
 Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 = -
.35%
 YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier
7-24
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Bond Pricing Theorems
• Bonds of similar risk (and maturity) will be priced to
yield about the same return, regardless of the coupon
rate
• If you know the price of one bond, you can estimate
its YTM and use that to find the price of the second
bond
• This is a useful concept that can be transferred to
valuing assets other than bonds
7-25
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Bond Prices with a Spreadsheet
• There is a specific formula for finding bond
prices on a spreadsheet
 PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis) see spreadsheet lecture 7 for
an example
 YIELD(Settlement,Maturity,Rate,Pr,Redemption,
Frequency,Basis)
 Settlement and maturity need to be actual dates
 The redemption and Pr need to be input as % of
par value
• Click on the Excel icon for an example
7-26
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Differences Between
Debt and Equity
• Debt
 Not an ownership interest
 Creditors do not have voting
rights
 Interest is considered a cost
of doing business and 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
for the board of directors and
other issues
 Dividends are not considered
a cost of doing business and
are not tax deductible
 Dividends are not a liability of
the firm, and stockholders
have no legal recourse if
dividends are not paid
 An all-equity firm can not go
bankrupt merely due to debt
since it has no debt
7-27
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The Bond Indenture
• Contract between the company and the
bondholders that includes
 The basic terms of the bonds
 The total amount of bonds issued
 A description of property used as security, if
applicable
 Sinking fund provisions
 Call provisions
 Details of protective covenants
7-28
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Bond Classifications
• Registered vs. Bearer Forms
• Security
 Collateral – secured by financial securities
 Mortgage – secured by real property, normally land or
buildings
 Debentures – unsecured
• Seniority
• Type based on maturity
• Notes – unsecured debt with original maturity less than 10
years; bonds are 10 years or greater
7-29
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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
(periodic payments towards paying off the bonds at
maturity)
 A callable bond versus a non-callable bond
7-30
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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
7-31
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Bond Ratings –
Speculative Grade
• Low Grade
 Moody’s Ba and B
 S&P BB and B
 Considered possible that the capacity to pay will
degenerate.
• Very Low Grade
 Moody’s C (and below) and S&P C (and below)
• income bonds with no interest being paid, or
• in default with principal and interest in arrears
7-32
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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. See Whoops bonds
https://www.investopedia.com/ask/answers/09/wp
ps-municipal-bond-default-whoops.asp
 Interest received is tax-exempt at the federal level 7-33
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Example 7.4
• A 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
 At what tax rate would you be indifferent between the two
bonds?
• 8%(1 – T) = 6%
• T = 25%
7-34
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Zero Coupon Bonds
• Make 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, deep discount bonds, or original
issue discount bonds (OIDs)
• Treasury Bills and principal-only Treasury strips are good
examples of zeroes
7-35
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Floating-Rate Bonds
• Coupon rate floats depending on some index value
• Example: Adjustable-rate mortgages (ARMs)
• linked to a major index – for example, one-year T-Bill rate plus a premium
• Usually has a cap on increase per period
• There is less price risk with floating rate bonds
 The coupon floats, so it 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” --
• Example: Treasuries (TIPS – Treasury Inflation Protected – Bonds)
• doesn’t really work well because market bids them up when people
expect inflation
7-36
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Other Bond Types
• Disaster bonds
• Income bonds
• Convertible bonds
• Put bonds
• There are many other types of provisions that
can be added to a bond and many bonds have
several provisions – it is important to recognize
how these provisions affect required returns
7-37
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Sukuk
• Sukuk are bonds have been created to meet a
demand for assets that comply with Shariah, or
Islamic law
• Shariah does not permit the charging or paying of
interest
• Pay profit from an investment. Like a bond, however,
the profit payments are for a fixed time period.
• Sukuk are typically bought and held to maturity, and
are extremely illiquid
7-38
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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
• Makes getting up-to-date prices difficult,
particularly on small company or municipal
issues
• Treasury securities are an exception
7-39
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Work the Web Example
• Bond quotes are available online
• One good site is FINRA’s Market Data Center
• Click on the web surfer to go to the site
 Choose a company, enter it in the Issuer Name bar, choose
Corporate, and see what you can find!
7-40
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Treasury Quotations
• Highlighted quote in Figure 7.4
Maturity Coupon Bid Asked Chg Asked yield
5/15/2030 6.250 136.8359 136.9141 -0.7813 3.289
 What is the coupon rate on the bond? 6.250%
 When does the bond mature? May 15, 2030
 What is the bid price? What does this mean? Broker will buy at 136.8359% of
Par =10,000
 What is the ask price? What does this mean? Broker will sell at 136.9141 of
Par
 How much did the price change from the previous day? The asked price
dropped by .7813% from yesterday or $781.3
 What is the yield based on the ask price? 3.289% YTM based on asked –
lower than coupon since price is at a premium
7-41
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Source of bond information
• FINRA data
• https://finra-
markets.morningstar.com/MarketData/Default.jsp?sdkVersion=2.40.0
• Click on corporate button
• Click on Search
• Click on edit search
• Type in AT&T (corporation) – symbol is T
• Bond Data https://finra-markets.morningstar.com/BondCenter/Default.jsp
• Click on Bonds in Market Data Column
• Click next to Market Activity; click on search; t in issuer name; scroll down and
agree

AT&T Bonds

At&T’s Bonds – 1 year later
Notice the effect of inflation

Clean vs. Dirty Prices
• Clean price: quoted price
• Dirty price: price actually paid = quoted price plus accrued
interest
• Example: Consider a T-bond with a 4% semiannual yield and a
clean price of $1,282.50:
 Number of days since last coupon = 61
 Number of days in the coupon period = 184
 Accrued interest = (61/184)(.04*1000) = $13.26
 Dirty price = $1,282.50 + $13.26 = $1,295.76
• So, you would actually pay, $ 1,295.76 for the bond
7-45
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Inflation and Interest Rates
• Real rate of interest – change in purchasing
power
• Nominal rate of interest – quoted rate of
interest, change in actual number of dollars
• The ex ante nominal rate of interest includes
our desired real rate of return plus an
adjustment for expected inflation
7-46
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The Fisher Effect
• The Fisher Effect defines the relationship between
real rates, nominal rates, and inflation
• (1 + R) = (1 + r)(1 + h), where
 R = nominal rate
 r = real rate
 h = expected inflation rate
• Approximation
 R = r + h
7-47
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Example 7.5
• 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.
7-48
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Term Structure of
Interest Rates
• Term 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
7-49
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Term structure example
• 1-year T-bill rate is 2%
• 2-year T-note rate is 3%
• Why would anyone invest in a 1-year T-bill?
• Ans: the implicit projection is that a 1-year T-bill, one year from now
will yield about 4%

Figure 7.6 – Upward-Sloping Yield Curve
7-51
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Figure 7.6 – Downward-Sloping Yield
Curve
7-52
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Figure 7.7
7-53
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Source: https://fred.stlouisfed.org/series/T10Y2Y

Supposed meaning
• A normal yield curve is upward sloping
• One would suppose that changes in its shape would predict general
economic behavior
• See next chart

Real GDP growth

inflation

Factors Affecting
Bond Yields
• Real rate of interest
• Expected future inflation premium
• Interest rate risk premium
• Default risk premium
• Taxability premium
• Liquidity premium
7-58
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Quick Quiz
• How do you find the value of a bond, and why do bond
prices change?
• What is a bond indenture, and what are some of the
important features?
• What are bond ratings, and why are they important?
• How does inflation affect interest rates?
• What is the term structure of interest rates?
• What factors determine the required return on bonds?
7-59
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Ethics Issues
• In 1996, allegations were made against Moody’s that it was issuing
ratings on bonds it had not been hired to rate, in order to pressure
issuers to pay for their service.
• The government conducted an inquiry, but charges of antitrust
violations were dropped. Even though no legal action was taken, does
an ethical issue exist?
7-60
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Warning: False Security
• Mortgage-backed securities defaulted in 2007-2008
• Definition: a bond back by a collection of mortgages
• Rating agencies termed them attractive – high yield, low risk
• Turned out that many were backed by subprime mortgages
• Mortgages had adjustable interest rates
• Government raised the federal funds rate
• Housing prices plummeted; many defaults
• Many bankrupcies

Comprehensive Problem
• What is the price of a $1,000 par value bond with a 6% coupon rate
paid semiannually, if the bond is priced to yield 5% and it has 9 years
to maturity?
• What would be the price of the bond if the yield rose to 7%.
• What is the current yield on the bond if the YTM is 7%?
7-62
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