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148
Chapter 6
Bonds and Bond Valuation
LEARNING OBJECTIVES (Slide 6-‐2)
- Understand basic bond terminology and apply the time value of money equation in
pricing bonds.
- Understand the difference between annual and semiannual bonds and note the key
features of zero-coupon bonds.
- Explain the relationship between the coupon rate and the yield to maturity.
- Delineate bond ratings and why ratings affect bond prices.
- Appreciate bond history and understand the rights and obligations of buyers and
sellers of bonds.
- 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, semi-annual, 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.
6.1 (A) 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
Chapter 6 n Bonds and Bond Valuation 149
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 semi-
annual)
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. $
based on a face value of $1,000. Based on its coupon rate of 6.35%, it will pay $ 6 3. 50 in
coupon interest each year until it matures on June 15, 2010. Based on its price, i.e. $915,
an investor is earning a current yield of 6.94% ($63.5/$915) per year and if held to
maturity will have earned a yield of 15.438%.
6.1 (B) Pricing a Bond in Steps (Slides 6-‐7 to 6-‐10)
Since 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;
Step 2. Determine an appropriate discount rate;
Step 3. Calculate the present value of the coupons and the par value;
Step 4. Add up the two present values to calculate the bond price.
(See Figure 6.2: How to price a bond)
Example 2: Calculating the price of a corporate bond
Calculate the price of an AA-rated, 20-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 = .08 * $1,000 = $80 = PMT
Year 0 1
Chapter 6 n Bonds and Bond Valuation 151
6.2 (A) Pricing Bonds after Original Issue (Slides 6-‐15 to 6-‐18)
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 semi-‐annual coupon bond after original issue
Four years ago, the XYZ Corporation issued an 8 % coupon (paid semi-annually), 20 -
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 semi-annual coupons = (20-4)*2 = 32 coupons = n
Semi-annual coupon = (.08*1000)/2 = $
Par value = $
Annual YTM = 10% èYTM/2è5% = r
Method 1: Using TVM equations
Bond Price =
( )
( )
Par Value Coupon
1
n
n
r
r^ r
× + ×
+ ⎜^ ⎟
Bond Price =
( )
( )
32
32
× + ×
+ ⎜^ ⎟
Bond Price = $1000 × 0.209866 + $40 × 15.
Bond Price = $209.866 + $632.
Bond Price = $841.
Method 2: Using a financial calculator
Mode: P/Y= 2 ; C/Y = 2
Input: N I/Y PV PMT FV
Key: 32 10? 40 1000
Output - 841.
6.2 (B) Zero-‐Coupon Bonds (Slide 6-‐19)
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 $1000. The price of a zero- coupon bond is calculated by
merely discounting its par value at the prevailing discount rate or yield to maturity.
152 Brooks n Financial Management: Core Concepts, 2e
6.2 (C) Amortization of a Zero-‐Coupon Bond. (Slides 6-‐20 to 6-‐24)
Table 6.2 (page 152) 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 semi-annual 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 20-year, AAA-rated, $1000 par value, zero-coupon bond being sold
by Diversified Industries Inc. The yield to maturity on similar bonds is estimated to be
A) How much would he have to pay for it?
Method 1: Using TVM equation
Bond Price =
( )
Par Value
1
n r
×
Bond Price =
( )
40
×
Bond Price = $1000 * .1719287 = $171.
Method 2: Using a financial calculator
Mode: P/Y=2; C/Y = 2
Input: N I/Y PV PMT FV
Key: 40 9? 0 1000
Output - 171.
B) How much will he be taxed on the investment after 1 year, if his marginal tax rate is
Calculate the price of the bond at the end of 1 year.
Mode: P/Y=2; C/Y = 2
Input: N I/Y PV PMT FV
Key: 38 9? 0 1000
Output - 187.
Taxable income = $187.75 – $171.93 = $15.
Taxes due = Tax rate * Taxable income = 0.30*$15.82 = $4.
Alternately, we can calculate the semi-annual interest earned, for each of the two semi-
annual periods during the year.
è $171.93 * .045 = $7.736 => Price after 6 months = $171.93+7.736 = $179.
154 Brooks n Financial Management: Core Concepts, 2e
Mode: P/Y=2; C/Y = 2
Input: N I/Y PV PMT FV
Key: 38? - 1200 40 1000
Output 6.
Note: This is a premium bond, so it’s YTM < Coupon rate
PV = $
Mode: P/Y=2; C/Y = 2
Input: N I/Y PV PMT FV
Key: 38? - 980 40 1000
Output 8.21%
Note: This would be a discount bond, so it’s YTM>Coupon rate
6.4 Bond Ratings (Slides 6-‐34 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.
6.5 Some Bond History and More Bond
Features (Slides 6-‐36 to 6-‐39)
Over the years, corporate bond features have gone through some major changes. The
addition of newer features such as call provisions, convertibility, and put options has
significantly broadened the array of bond types available.
Bearer bonds: original nature of bonds, whereby the bond holder did not have to be
registered with the issuing company, and whoever held the bond was entitled to the
interest payments and the principal repayment. Currently, firms issue only registered
bonds to avoid the problems associated with stolen bonds and for ease of communicating
with their creditors.
Indenture or deed of trust : a written contract between the bond issuer and the bondholder
which spells out the terms of the bond, the number of bonds to be issued, a description of
any collateral supporting the bond, any special repayment provisions or call options, and
details of protective covenants.
Collateral , or security of a bond : refers to the physical and/or financial assets which
support the bond in case of issuer default.
Mortgaged security: is a security which is backed by real estate.
Chapter 6 n Bonds and Bond Valuation 155
Debentures : are bonds which are not supported by any assets of the issuing firm.
Senior debt : is unsecured debt which was issued earlier than junior debt and has
refunding priority in case of liquidation.
Sinking fund: is a reserve fund set up by some bond issuing companies in which regular
payments are made so as to retire the bonds at maturity.
Protective covenants: specify actions which bond issuers are required and/or prohibited
from doing, in the interest of bondholder protection.
Callable bond: is a bond which is issued with a call option whereby the issuer can retire
the bond prior to its maturity after paying a call premium, which is usually an additional
coupon payment in addition to its par value.
Yield to call : is the relevant yield that an investor can expect to earn on a callable bond,
based on the number of periods until the bond can be first called and its call price, i.e. par
value plus the call premium.
Example 6: Calculating Yield to Call
Two years ago, The Mid-Atlantic Corporation issued a 10% coupon (paid semi-
annually), 20-year maturity, bond with a 5-year deferred call feature and a call penalty of
one coupon payment in addition to the par value ($1000) if exercised. If the current
price on these bonds is $ 10 80, what is its yield to call?
Remaining number of coupons until first call date = 6 = n
Semi-annual coupon = $50 = PMT
Call price = $1050 = FV
Bond price = $ 1080 = PV
Mode: P/Y=2; C/Y = 2
Input: N I/Y PV PMT FV
Key: 6? - 1080 50 1050
Output 8.
YTC
Putable bond: is one which gives the holder the right to sell the bond back to the issuing
firm at a pre-determined 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 which can be exchanged by the holder for other securities,
usually common stock, of the issuer at a pre-determined conversion ratio.
Floating-rate bond: is one that has a variable coupon rate which 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.
Chapter 6 n Bonds and Bond Valuation 157
the market’s assessment of the required return for investments similar to the bond in
terms of risk (default), inflation, maturity, and the current real interest rate.
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 semi-
annual bond splits the annual interest into two equal payments paid six-months apart.
When using the bond pricing equation you need to change the discount rate from the
annual yield to the semi-annual or six-month rate by dividing the annual yield by 2.
You need to increase the number of periods for n from the number of years to the
number of semi-annual periods by multiplying the number of years by 2.
3. When we talk about the yield of a bond, we usually mean the yield to maturity of
the bond. Why?
In order to price a bond we need to know how long we will hold the bond and thus the
number of coupon payments we will receive. Because each bondholder has potentially
a different time horizon we could get many different prices for the same bond.
Therefore, it is generally agreed that the price of the bond reflects all remaining
coupon payments and the repayment of the principal at maturity. Thus we state the
yield on the bond based on holding the bond to maturity and that yield is the yield-to-
maturity.
4. Does a zero-coupon bond pay interest?
Yes, it just does not pay annual coupon payments. The price appreciation of the bond
is the interest earned on the bond.
5. If a zero-coupon bond does not pay coupons each year, why buy it?
The value of owning a zero-coupon bond is the appreciation in price from period to
period. The bond sells for a discount but at maturity pays the par value and therefore a
gain is realized on the bond.
6. How does the potential for default of a bond affect the yield of the bond?
The greater is the potential for default, the higher the yield. Investors want to be
compensated for taking on more risk and default is one type of risk. So for bonds with
higher potential for default the yield goes up and the price goes down.
7. Why are some bonds sold with a premium, some at par value, and some at a
discount?
Bonds promise a coupon payment based on the coupon rate of the bond. When this
coupon rate is above the yield that the market requires for this type of investment, the
potential buyers bid the price above par value. For example, if a company is
promising a coupon rate of 10% on a new bond, but similar bonds are paying 7% in
the market, the 10% coupon rate provides interest well above the required level.
Buyers will compete for the right to purchase the limited supply of these bonds,
bidding the price above par value. That is, they will pay a premium to own this 10%
coupon bond. The market will bid the price up until the actual yield on the investment
falls to the current market rate of 7%. The opposite is true for bonds with coupon rates
below the current market yield. Bond buyers will discount the price until the yield on
the bond rises to the current market yield for similar investments. Finally, if the
158 Brooks n Financial Management: Core Concepts, 2e
coupon rate is equal to the current yield on similar investments the bond buyer gets
the required yield by paying the par value of the bond.
8. How does collateral impact the price of a bond?
Collateral reduces the potential loss for a bondholder if the company defaults on the
promised bond payment. Because the collateral can be seized as partial or full
repayment of the bond if a default should take place, bondholders will pay more for a
bond with collateral versus a bond without collateral (a debenture bond).
9. What role do Moody’s, Standard & Poor’s, or Fitch’s bond ratings play in the
pricing of a bond?
Moody’s and Standard & Poor’s provide reliable information to potential bond buyers
about the riskiness of the bond. That is, these rating agencies analyze the firm’s ability
to make the future promised payments (potential for default) and therefore provide the
appropriate default premium for pricing the bond. The higher the bond rating the
lower the required yield (higher the selling price).
10. What must happen for a bond to be called a “fallen angel”?
A bond must have been an investment grade bond prior to a downgrade to a
speculative bond in order to it to be called a “fallen angel.”
Prepping for Exams
- b.
- d.
- a.
- a.
- c.
- a.
- a.
- b.
Problems
Bond Prices: Use the following table for problems 1 through 4.
Par Value
Coupon
Rate
Years to
Maturity
Yield to
Maturity Price
160 Brooks n Financial Management: Core Concepts, 2e
Price = $5,000.00 × 0.2584 + $75.00 × 10.
Price = $1,292.10 + $3,178.20 = $4,
Price = $5,000.00 × 1/(1.0125)
120
120 )/ 0.
Price = $5,000.00 × 0.2314 + $150.00 × 15.
Price = $1,156.89 + $9,223.47 = $10,423.5 0
- Price the bonds from the above table with monthly coupon payments.
ANSWER
Price = $1,000.00 × 1/(1.005)
120
120 )/ 0.
Price = $1,000.00 × 0.5584 + $6.67 × 7.
Price = $558.39 + $588.81 = $1,150.
Price = $1,000.00 × 1/(1.0067)
120
120 )/ 0.
Price = $1,000.00 × 0.4632 + $5.00 × 6.
Price = $463.19 + $402.60 = $860.
Price = $5,000.00 × 1/(1.0058)
240
240 )/ 0.
Price = $5,000.00 × 0.2476 + $37.50 × 128.
Price = $1,238.01 + $4,836.84 = $6,074.
Price = $5,000.00 × 1/(1.0042)
360
360 )/ 0.
Price = $5,000.00 × 0.2314 + $50.00 × 15.
Price = $1,156.89 + $9,223.47 = 10,377.
Yield-to-Maturity: Use the following table for problems 5 through 8.
Par Value Coupon Rate Years to
Maturity
Yield to
Maturity
Price
- What is the yield of the above bonds if interest (coupon) is paid annually?
ANSWER
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 10? - 1000.00 80.00 1000.
KEYS N I/Y PV PMT FV
CPT 8.
Chapter 6 n Bonds and Bond Valuation 161
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 10? - 850.00 60.00 1000.
KEYS N I/Y PV PMT FV
CPT 8.
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 20? - 5400.00 450.00 5000.
KEYS N I/Y PV PMT FV
CPT 8.
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 30? - 4300.00 600.00 5000.
KEYS N I/Y PV PMT FV
CPT 13.
- What is the yield of the above bonds if interest (coupon) is paid semiannually?
ANSWER
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 20? - 1000.00 40.00 1000.
KEYS N I/Y PV PMT FV
CPT 8.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 20? - 850.00 30.00 1000.
KEYS N I/Y PV PMT FV
CPT 8.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 40? - 5400.00 225.00 5000.
KEYS N I/Y PV PMT FV
CPT 8.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 60? - 4300.00 300.00 5000.
KEYS N I/Y PV PMT FV
CPT 13.
- What is the yield of the above bonds if interest (coupon) is paid quarterly?
ANSWER
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT 40? - 1000.00 20.00 1000.
KEYS N I/Y PV PMT FV
CPT 8.
Chapter 6 n Bonds and Bond Valuation 163
$5,000.00 9%? 8.1838% $5,400.00 Quarterly
$5,000.00 12%? 16.0938% $4,300.00 Monthly
ANSWER:
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT? 8.7713 - 950.00 80.00 1000.
KEYS N I/Y PV PMT FV
CPT 9.
Approximately 10 years to maturity
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT? 7.7038 - 850.00 30.00 1000.
KEYS N I/Y PV PMT FV
CPT 30.
Approximately 30 six-month periods or 30/2 = 15 years to maturity
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT? 8.1838 - 5400.00112.50 5000.
KEYS N I/Y PV PMT FV
CPT 79.
Approximately 80 quarters or 80 / 4 = 20 years to maturity
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT? 16.0938 - 4300.0050.00 5000.
KEYS N I/Y PV PMT FV
CPT 60.
Approximately 60 months or 60 / 12 = 5 years to maturity
- Coupon rates. What are the coupon rates for the bonds listed below?
Par Value
Coupon
Rate
Years to
Maturity
Yield to
Maturity Price
Coupon
Frequency
$1,000.00? 30 6.0% $1,412.94 Annual
$1,000.00? 25 10.0% $1,182.56 Semi-Annual
$1,000.00? 20 9.0% $907.63 Quarterly
$1,000.00? 10 8.0% $862.63 Monthly
ANSWER
(TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT 30 6.0 - 1412.94? 1000.
KEYS N I/Y PV PMT FV
CPT 90.
164 Brooks n Financial Management: Core Concepts, 2e
Coupon payments are $90.00 every year so coupon rate is:
$1,000 × rate = $90.
rate = $90 / $1,000 = 0.09 or 9%
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 50 10.0 - 1,182.56? 1000.
KEYS N I/Y PV PMT FV
CPT 60.
Coupon payments are $60.00 every six months so coupon rate is:
$1,000 × rate / 2 = $60.
$1,000 × rate = $120.
rate = $120 / $1,000 = 0.12 or 12%
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT 80 9.0 - 907.63? 1000.
KEYS N I/Y PV PMT FV
CPT 20.
Coupon payments are $20.00 every four months so coupon rate is:
$1,000 × rate / 4 = $20.
$1,000 × rate = $80.
rate = $80 / $1,000 = 0.08 or 8%
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT 120 8.0 - 862.63? 1000.
KEYS N I/Y PV PMT FV
CPT 5.
Coupon payments are $5.00 every month so coupon rate is:
$1,000 × rate / 12 = $5.
$1,000 × rate = $60.
rate = $60 / $1,000 = 0.06 or 6%
- Bond prices and maturity dates. Moore Company is about to issue a bond with semi-
annual coupon payments, a coupon rate of 8%, and par value of $1,000. The yield-to-
maturity for this bond is 10%.
a. What is the price of the bond if the bond matures in five, ten, fifteen, or twenty
years?
b. What do you notice about the price of the bond in relationship to the maturity of
the bond?
ANSWER (A)
At five years to maturity
Price = $1,000.00 × 1/(1.05)
10
10 )/ 0.
Price = $1,000.00 × 0.6139 + $40.00 × 7.
Price = $613.91 + $308.87 = $922.
166 Brooks n Financial Management: Core Concepts, 2e
ANSWER (A)
At five years to maturity
Price = $1,000.00 × 1/(1.04)
10
10 )/ 0.
Price = $1,000.00 × 0.6756 + $50.00 × 8.
Price = $675.56 + $405.55 = $1,081.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 10 8.0? 50.00 1000.
KEYS N I/Y PV PMT FV
CPT - 1,081.
At ten years to maturity
Price = $1,000.00 × 1/(1.04)
20
20 )/ 0.
Price = $1,000.00 × 0.4564 + $50.00 × 1 3.
Price = $456.39 + $679.51 = $1,135.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 20 8.0? 50.0 0 1000.
KEYS N I/Y PV PMT FV
CPT - 1,135.
At fifteen years to maturity
Price = $1,000.00 × 1/(1.04)
30
30 )/ 0.
Price = $1,000.00 × 0.3083 + $50.00 × 17.
Price = $308.32 + $864.60 = $1,172.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 30 8.0? 50.00 1000.
KEYS N I/Y PV PMT FV
CPT - 1,172.
At twenty years to maturity
Price = $1,000.00 × 1/(1.04)
40
40 )/ 0.
Price = $1,000.00 × 0.2083 + $50.00 × 19.
Price = $208.29 + $989.64 = $1,197.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 40 8.0? 50.00 1000.
KEYS N I/Y PV PMT FV
CPT - 1,197.
ANSWER (B)
The longer the maturity of a bond selling for a premium, all else held constant, the higher
the price of the bond!
- Zero-coupon bond****. Addison Company will issue a zero coupon bond this coming
month. The projected yield for the bond is 7%. If the par value of the bond is $1,000,
what is the price of the bond using a semiannual convention if
a. The maturity is 20 years?
Chapter 6 n Bonds and Bond Valuation 167
b. The maturity is 30 years?
c. The maturity is 50 years?
d. The maturity is 100 years?
ANSWER (A)
Price = $1,000 × 1 / (1.035)
40 = $1,000 × 0.2526 = $252.
ANSWER (B)
Price = $1,000 × 1 / (1.035)
60 = $1,000 × 0.1269 = $126.
ANSWER (C)
Price = $1,000 × 1 / (1.035)
100 = $1,000 × 0.0321 = $32.
ANSWER (D)
Price = $1,000 × 1 / (1.035)
200 = $1,000 × 0.0010= $1.
- Zero-coupon bond****. Wesley Company will issue a zero-coupon bond this coming
month. The projected yield for the bond is 5%. If the par value of the bond is $1,000,
what is the price of the bond using a semiannual convention if
a. The maturity is 20 years?
b. The maturity is 30 years?
c. The maturity is 50 years?
d. The maturity is 100 years?
ANSWER (A)
Price = $1,000 × 1 / (1.025)
40 = $1,000 × 0.3724 = $372.
ANSWER (B)
Price = $1,000 × 1 / (1.025)
60 = $1,000 × 0.2273 = $227.
ANSWER (C)
Price = $1,000 × 1 / (1.025)
100 = $1,000 × 0.0846 = $84.
ANSWER (D)
Price = $1,000 × 1 / (1.025)
200 = $1,000 × 0.0072= $7.
- Zero-coupon bond****. What is the annual implied interest of a five-year zero-coupon
bond (using the semiannual pricing convention) with a current yield of 12% and a par
value of $1,000.00?
ANSWER
Step One is to find the price of the zero coupon bond:
