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Chapter 6
Bonds and Bond Valuation
LEARNING OBJECTIVES (Slide 6-2)
1. Understand basic bond terminology and apply the time value of money equation in
pricing bonds.
2. Understand the difference between annual and semiannual bonds and note the key
features of zero-coupon bonds.
3. Explain the relationship between the coupon rate and the yield to maturity.
4. Delineate bond ratings and why ratings affect bond prices.
5. Appreciate bond history and understand the rights and obligations of buyers and
sellers of bonds.
6. Price government bonds, notes, and bills.
IN A NUTSHELL…
Bonds are debt instruments issued by corporations, as well as state, local, and foreign
governments to raise funds for growth and financing of public projects. In the six sections
within this chapter, the author defines and explains the terminology and methodology
used in the analysis and pricing of bonds; differentiates between annual, semiannual, and
zero-coupon bonds; explains how a bond’s coupon rate and yield to maturity are related;
clarifies how bond ratings affect their prices; provides some perspective on bond history
and the rights and obligations of buyers and sellers of bonds; and shows how Treasury
bonds, notes, and bills are quoted and priced. The quantitative material in this chapter
represents the first practical application of time value techniques (covered in Chapters 3
and 4) in a corporate finance setting and must be well understood by students so as to
grasp the important forthcoming topics of cost of capital and capital budgeting.
LECTURE OUTLINE
6.1 Application of the Time Value
of Money Tool: Bond Pricing (Slides 6-3 and 6-4)
Since bonds are typically long-term debt instruments which provide periodic interest
income along with a return of the principal amount at maturity, their prices can be
calculated by using present value techniques i.e. discounting of future cash flows.
Chapter 6 ◼ Bonds and Bond Valuation 151
Key Components of a Bond
(See Fig. 6.1: Merrill Lynch corporate bond) (Slides 6-5 to 6-6)
Par value: The principal or face value of a bond on which interest is paid,
typically $1000;
Coupon rate: Annual rate of interest paid by issuer.
Coupon: The regular interest payment received by buyer. It is calculated as the
product of the coupon rate and the par value (and divided by 2, if
semiannual)
Maturity date: The expiration date of the bond on which the final coupon and the
principal value is paid by the issuer.
Yield to maturity: The discount rate or expected rate of return on a bond which is used to
determine its price.
Example 1: Key components of a corporate bond
Let’s say you see the following price quote for a corporate bond
Issue Price Coupon (%) Maturity YTM% Current Yld. Rating
Hertz Corp. 91.50 6.35 15-Jun-2010 15.438 6.94 B
This B-rated bond issued by Hertz Corporation is selling at 91.5% of par value, i.e., $915
Pricing a Bond in Steps (Slides 6-7 to 6-10)
Because bonds involve a combination of an annuity (coupons) and a lump sum (par
value), its price is best calculated by using the following steps:
Step 1. Lay out the cash flows on a time line;
152 Brooks ◼ Financial Management: Core Concepts, 4e
Example 2: Calculating the price of a corporate bond
Calculate the price of an AA-rated, twenty-year, 8% coupon (paid annually) corporate
bond (Par value = $1,000) which is expected to earn a yield to maturity of 10%.
Method 1: Using TVM equation
Annual coupon = Coupon rate * Par value = 0.08 * $1,000 = $80 = PMT
Year 0
1
$80
2
$80
3
$80
20
$80
$1,000
18
$80
$80
…
19
Chapter 6 ◼ Bonds and Bond Valuation 153
Method 2: Using a financial calculator
6.2 Semiannual Bonds and Zero-Coupon Bonds(Slides 6-11 to 6-15)
Most corporate and government bonds pay coupons on a semiannual basis. Additionally,
some companies issue zero-coupon bonds by selling them at a deep discount. To
calculate the price of these bonds, the values of the inputs have to be adjusted according
to the frequency of the coupons (or absence thereof). For example, for semiannual bonds,
the annual coupon is divided by 2, the number of years is multiplied by 2, and the YTM
is divided by 2. The price of the bond can then be calculated by using the TVM equation,
a financial calculator, or a spreadsheet.
Pricing Bonds after Original Issue (Slides 6-16 to 6-19)
The price of a bond is a function of the remaining cash flows (i.e., coupons and par value)
that would be paid on it until expiration.
Example 3: Pricing a semiannual coupon bond after original issue
Four years ago, the XYZ Corporation issued an 8% coupon (paid semiannually), twenty-
year, AA-rated bond at its par value of $1000. Currently, the yield to maturity on these
bonds is 10%. Calculate the price of the bond today.
Remaining number of semiannual coupons = (20 – 4)*2 = 32 coupons = n
Semiannual coupon = (0.08*1000)/2 = $40
Par value = $1000
Annual YTM = 10% ➔YTM/2➔5% = r
Method 1: Using TVM equations
( )
1
11
1
n
r
−
+
154 Brooks ◼ Financial Management: Core Concepts, 4e
Method 2: Using a financial calculator
Zero-Coupon Bonds (Slide 6-20)
Also known as “pure” discount bonds, zero-coupon bonds are sold at a discount from
face value and do not pay any interest over the life of the bond. At maturity, the investor
receives the par value, usually $1,000. The price of a zero-coupon bond is calculated by
merely discounting its par value at the prevailing discount rate or yield to maturity.
Amortization of a Zero-Coupon Bond. (Slides 6-21 to 6-25)
Table 6.2 (page 158) demonstrates how the discount on a zero-coupon bond is amortized
over its life. The price appreciation is calculated for each six-month period by
multiplying the zero-coupon bond’s beginning price by its semiannual YTM, and
represents the interest earned on the bond. Zero-coupon bond investors are taxed on the
annual price appreciation, even though no cash is received from the issuing firm.
Example 4: Price of and taxes due on a zero-coupon bond
John wants to buy a twenty-year, AAA-rated, $1,000 par value, zero-coupon bond being
sold by Diversified Industries Inc. The yield to maturity on similar bonds is estimated to
be 9%.
A) How much would he have to pay for it?
Method 1: Using TVM equation
1
Method 2: Using a financial calculator
Chapter 6 ◼ Bonds and Bond Valuation 155
B) How much will he be taxed on the investment after one year if his marginal tax rate is
30%?
Calculate the price of the bond at the end of one year.
6.3 Yields and Coupon Rates (Slide 6-26)
Students must learn how to differentiate between a bond’s coupon rate and its yield to
maturity (YTM). This is often confusing for many students. It is important to explain to
them that the coupon rate is set by the company at the time of issue and is fixed (except
for newer innovations which have variable coupon rates) while its YTM is dependent on
market, economic, and company-specific factors and is therefore variable.
The First Interest Rate: Yield to Maturity (Slide 6-27)
The YTM is the expected rate of return on a bond if held to maturity. The price that
willing buyers and sellers settle at determines a bond’s YTM at any given point. Thus,
changes in economic conditions and risk factors will cause bond prices and their
corresponding YTMs to change. A bond’s YTM can be calculated by entering the bond’s
coupon amount (PMT), price (PV), remaining number of coupons (n), and par value
(FV) into the TVM equation, financial calculator, or spreadsheet.
The “Other” Interest Rate: Coupon Rate (Slide 6-28)
The coupon rate on a bond is set by the issuing company at the time of issue and
represents the annual rate of interest that the firm is committed to pay over the life of the
bond. Thus, if the rate is set at 7%, the firm is committing to pay 0.07*$1000 = $70 per
year on each bond, either in a single check or two checks of $35 paid six months apart.
156 Brooks ◼ Financial Management: Core Concepts, 4e
Relationship of Yield to Maturity and Coupon Rate (Slides 6-29 to 6-34)
Typically, an issuing firm gets the bond rated by a rating agency such as Standard &
Poor’s or Moody’s. Then, based on the rating and planned maturity of the bond, it sets
the coupon rate to equal the expected yield as indicated in the Yield Book available in the
capital markets at that time and sells the bond at par value ($1,000). Once issued, if
investors expect a higher yield on the bond, its price will go down and the bond will sell
below par or as a discount bond and vice versa. Thus, a bond’s YTM can be equal to (par
bond), higher than (discount bond), or lower than (premium bond) its coupon rate.
Example 5: Computing YTM
Last year, The ABC Corporation had issued 8% coupon (semiannual), twenty-year,
AA-rated bonds (Par value = $1,000) to finance its business growth. If investors are
currently offering $1,200 on each of these bonds, what is their expected yield to maturity
on the investment? If you are willing to pay no more than $980 for this bond, what is
your expected YTM?
Note: This is a premium bond, so its YTM < Coupon rate.
6.4 Bond Ratings (Slides 6-35 to 6-35)
Rating agencies such as Moody’s, Standard and Poor’s, and Fitch produce bond ratings
ranging from AAA (top-rated) to C (lowest-rated) or D (default). These ratings, which
are based on the issuing firm’s riskiness, can help investors assess the likelihood of
default and assist issuing companies establish a yield on their newly issued bonds.
Junk bonds is the label given to bonds that are rated below BBB. These bonds are
considered to be speculative in nature and carry higher yields than those rated BBB or
above (investment grade).
Fallen angels is the label given to bonds that have had their ratings lowered from
investment to speculative grade.
158 Brooks ◼ Financial Management: Core Concepts, 4e
Example 6: Calculating yield to call
Two years ago, the Mid-Atlantic Corporation issued a 10% coupon (paid semiannually),
twenty-year maturity, bond with a five-year deferred call feature and a call penalty of one
coupon payment in addition to the par value ($1,000) if exercised. If the current price on
these bonds is $1,080, what is its yield to call?
Remaining number of coupons until first call date = 6 = n
Putable bond is one that gives the holder the right to sell the bond back to the issuing
firm at a predetermined price at any time prior to maturity. It is especially valuable when
the bond’s price is dropping due to rising interest rates or increased riskiness of the
issuing firm.
Convertible bond is one that can be exchanged by the holder for other securities, usually
common stock, of the issuer at a predetermined conversion ratio.
Floating-rate bond is one that has a variable coupon rate that adjusts to some interest rate
benchmark such as the prime rate.
Prime rate is the rate that money-center banks charge their most credit-worthy customers.
Income bond are bonds where the coupon amount and payment schedule are tied to the
firm’s income.
Exotic bonds are bonds with special features distinct to that particular bond.
6.6 U.S. Government Bonds (Slides 6-41 to 6-46)
U.S. government securities include bills, notes, and bonds sold by the Department of the
Treasury, as well as state bonds, issued by state governments, and municipal bonds issued
by county, city, or local government agencies. Treasury bills, are zero-coupon, pure
discount securities with maturities ranging from one, three, and six months up to one
Chapter 6 ◼ Bonds and Bond Valuation 159
Pricing a Treasury bill is done by discounting the bill’s face value for the number of
days until maturity and at the prevailing bank discount yield. (Slides 44 to 46)
Bank discount yield is a special discount rate used in conjunction with treasury bills
under a 360 day-per-year convention commonly assumed by bankers.
Bond equivalent yield (BEY) is the APR equivalent of the bank discount yield
calculated by adjusting it as follows,
( )
365 Bank discount yield
360 days to maturity discount yield
BEY
=−
.
Example 7: Calculating the price and BEY of a Treasury bill
Calculate the price and BEY of a treasury bill that matures in 105 days, has a face value
of $10,000, and is currently being quoted at a bank discount yield of 2.62%.
Questions
1. What is a bond? What determines the price of this financial asset?
A bond is a promised set of future payments from the issuer to the buyer of the bond
2. What is the primary difference between an annual bond and a semiannual
bond? What changes do you need to make in finding the price of a semiannual
bond versus an annual bond?
The primary difference is the timing and the amount of the cash flow of the interest
payments. An annual bond pays the annual interest in one payment while a
162 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
Price = $5,000.00 × 1/(1.07)20 + $450.00 (1 – 1/(1.07)20)/ 0.07
Price = $5,000.00 × 0.2584 + $450.00 × 10.5940
Price = $1,292.10 + $4,767.30 = $6,059.40
Price = $5,000.00 × 1/(1.05)30 + $600.00 (1 – 1/(1.05)30)/ 0.05
Price = $5,000.00 × 0.2314 + $600.00 × 15.3725
Price = $1,156.89 + $9,223.47 = $10,380.36
2. Price the bonds from the table with semiannual coupon payments.
ANSWER
Price = $1,000.00 × 1/(1.03)20 + $40.00 (1 – 1/(1.03)20)/ 0.03
3. Price the bonds from the table with quarterly coupon payments.
ANSWER
Price = $1,000.00 × 1/(1.015)40 + $20.00 (1 – 1/(1.015)40)/ 0.015
