168 Brooks ◼ Financial Management: Core Concepts, 4e
11. Bond prices and maturity dates. Moore Company is about to issue a bond with
semiannual 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
Chapter 6 ◼ Bonds and Bond Valuation 169
© 2018 Pearson Education, Inc.
ANSWER (B)
The longer the maturity of a bond selling at a discount, all else held constant, the lower
the price of the bond!
12. Bond prices and maturity dates. Les Company is about to issue a bond with
semiannual coupon payments, a coupon rate of 10%, and par value of $1,000. The
yield to maturity for this bond is 8%.
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
At ten years to maturity
170 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT 40 8.0 ? 50.00 1000.00
KEYS N I/Y PV PMT FV
CPT –1,197.93
ANSWER (B)
13. 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 bond’s price using a semiannual convention if the bond matures
a. in 20 years?
b. in 30 years?
c. in 50 years?
d. in 100 years?
ANSWER (A)
172 Brooks ◼ Financial Management: Core Concepts, 4e
6
$747.26
$747.26 × 0.06 = $44.83
$792.09
7
$792.09
$792.09 × 0.06 = $47.53
$839.62
8
$839.62
$839.62 × 0.06 = $50.38
$890.00
9
$890.00
$890.00 × 0.06 = $53.40
$943.40
10
$943.40
$943.40 × 0.06 = $56.60
$1,000.00
The first year’s interest is: $33.51 + $35.51 or ($627.41 – $558.39) = $69.02
The second year’s interest is: $37.65 + $39.90 or ($704.96 – $627.41) = $77.55
The third year’s interest is: $42.30 + $44.83 or ($792.09 – $704.96) = $87.13
The fourth year’s interest is: $47.53 + $50.38 or ($890.00 – $792.09) = $97.91
The fifth year’s interest is: $53.40 + $56.60 or ($1,000 – $890.00) = $110.00
Total interest is $1,000 – $558.39 = $441.61
16. Callable bond. Corso Books has just sold a callable bond. The bond is a thirty-year
semiannual bond with a coupon rate of 6%. Investors, however, can call the bond
starting at the end of ten years. If the yield to call on this bond is 8% and the call
requires Corso Books to pay one year of additional interest at the call (two coupon
payments), what is the bond price if priced with the assumption that it will be called
on the first available call date?
ANSWER
Determine the cash flows until the call date.
The coupons are 0.06 × $1,000 / 2 = $30.00
Chapter 6 ◼ Bonds and Bond Valuation 173
17. Callable bond. McCarty Manufacturing Company makes baseball equipment. The
company decides to issue a callable bond that it expects to sell for $840 per bond. If
the bond is a twenty-year semiannual bond with a 6% coupon rate and a current yield
to maturity of 7%, what is the cost of the option attached to the bond? (Assume
$1,000 par value). Hint: find the price of an equivalent bond without the call option.
ANSWER
First determine the price of the bond without the option attached.
18. Missing information on a bond. Your broker faxed you the following information on
two semiannual coupon bonds that you are considering as a potential investment.
Unfortunately, your fax machine is blurring some of the items and all you can read
from the fax on the two different bonds is the following information:
IBM Coupon Bond
AOL Coupon Bond
Face Value (Par)
$1,000
$1,000
Coupon Rate
9.5%
Yield to Maturity
7.5%
9.5%
Years to Maturity
10
20
Price
$689.15
Fill in the missing data from the information sent by the broker.
ANSWER
174 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
AOL’s Coupon Rate? This will be a little more difficult, but we can solve first for the
coupon and then backtrack to the coupon rate.
AOL’s Variables:
n = 20 × 2 = 40
r = 0.095 / 2 = 0.0475
Par Value = $1000
Price = $689.15
$689.15 =
( )
( )
40
40
1
11 0.0475
1
$1,000 Coupon 0.0475
1 0.0475
−
+
+
+
Now we need to isolate the coupon amount on the left-hand side of the equation and we
have:
Coupon
( )
40
1
11 0.0475
0.0475
−
+
= $689.15 –
( )
40
1
$1,000 1 0.0475
+
Coupon × (17.7630) = $689.15 – $1000 × 0.15626 = $532.89
Coupon = $532.89 / 17.7630 = $30.00
So if the coupon is $30.00 every six months, the annual interest is $60.00 (2 × $30), and
the coupon rate is the annual interest divided by the par value:
Coupon rate = $60.00 / $1000 = 0.06 or 6%
Treasury notes and bonds. For Problems 19 through 23 use the information in the
following table.
Today is February 15, 2008
Type
Issue Date
Price
Coupon
Rate
Maturity
Date
YTM
Current
Yield
Rating
Note
Feb 2000
—
6.50%
2-15-2010
3.952%
6.199%
AAA
Bond
Aug 2005
100.00
4.25%
8-15-2018
—
4.250%
AAA
Bond
Aug 2003
—
7.25%
8-15-2023
4.830%
5.745%
AAA
Bond
Feb 1995
126.19
8.50%
2-15-2015
—
6.736%
AAA
178 Brooks ◼ Financial Management: Core Concepts, 4e
To calculate the Effective Annual Rate we first compute the HPR:
( )
$10,000 $9,841.625
HPR 0.0016092363
$9,841.625
−
==
Then we find the annual compounded rate of return:
EAR = (1 + 0.0016092363)365/181 – 1 = 0.032716911 or ≈ 3.27%.
Thus, the bank discount yield is 3.15%, BEY is 3.245% and EAR is 3.27%
28. What are the bond equivalent yields of the March 30, April 30, and June 30 Treasury
bills?
ANSWER
Bond Equivalent Yield for the March 30 T-Bill is:
012178.0
0120.028360
0120.0365
BEY =
−
=
Chapter 6 ◼ Bonds and Bond Valuation 179
Solutions to Advanced Problems for Spreadsheet Applications
1. Bond ladder.
Bond Data
Years to Maturity Coupon Rate Yield to Maturity Par Value Current Price Cost of Ten Bonds
15.5000% 3.2500% 1,000.00$ $1,021.96 $10,219.63
26.2500% 3.5000% 1,000.00$ $1,052.68 $10,526.75
34.7500% 3.5700% 1,000.00$ $1,033.29 $10,332.90
47.0000% 4.0000% 1,000.00$ $1,109.88 $11,098.82
56.5000% 4.1250% 1,000.00$ $1,106.32 $11,063.20
68.2500% 4.2500% 1,000.00$ $1,209.89 $12,098.92
78.0000% 4.3750% 1,000.00$ $1,216.56 $12,165.58
87.2500% 4.5000% 1,000.00$ $1,183.05 $11,830.49
96.5000% 4.6250% 1,000.00$ $1,136.76 $11,367.64
10 5.5000% 4.7500% 1,000.00$ $1,059.16 $10,591.56
11 5.2500% 4.8750% 1,000.00$ $1,031.64 $10,316.38
12 4.7500% 5.0000% 1,000.00$ $977.64 $9,776.44
13 4.0000% 5.0625% 1,000.00$ $899.70 $8,996.96
14 4.5000% 5.1250% 1,000.00$ $938.10 $9,380.98
15 5.2500% 5.1875% 1,000.00$ $1,006.46 $10,064.60
16 6.0000% 5.2500% 1,000.00$ $1,080.51 $10,805.12
17 6.5000% 5.3125% 1,000.00$ $1,131.86 $11,318.59
18 6.7500% 5.3750% 1,000.00$ $1,157.35 $11,573.47
19 7.5000% 5.4325% 1,000.00$ $1,243.13 $12,431.26
20 8.0000% 5.0000% 1,000.00$ $1,376.54 $13,765.42
$219,724.69 Cost of Portfolio
180 Brooks ◼ Financial Management: Core Concepts, 4e
Payoff Table
Year Coupon Payments Principal Payments Total Payments Month
0.5 6,200.00$ –$ 6,200.00$ June
1 6,200.00$ 10,000.00$ 16,200.00$ December
1.5 5,925.00$ –$ 5,925.00$ June
2 5,925.00$ 10,000.00$ 15,925.00$ December
2.5 5,612.50$ –$ 5,612.50$ June
3 5,612.50$ 10,000.00$ 15,612.50$ December
3.5 5,375.00$ –$ 5,375.00$ June
4 5,375.00$ 10,000.00$ 15,375.00$ December
4.5 5,025.00$ –$ 5,025.00$ June
5 5,025.00$ 10,000.00$ 15,025.00$ December
5.5 4,700.00$ –$ 4,700.00$ June
11.5 2,662.50$ –$ 2,662.50$ June
12 2,662.50$ 10,000.00$ 12,662.50$ December
12.5 2,425.00$ –$ 2,425.00$ June
13 2,425.00$ 10,000.00$ 12,425.00$ December
13.5 2,225.00$ –$ 2,225.00$ June
14 2,225.00$ 10,000.00$ 12,225.00$ December
18 1,112.50$ 10,000.00$ 11,112.50$ December
18.5 775.00$ –$ 775.00$ June
19 775.00$ 10,000.00$ 10,775.00$ December
19.5 400.00$ –$ 400.00$ June
20 400.00$ 10,000.00$ 10,400.00$ December
Chapter 6 ◼ Bonds and Bond Valuation 181
Solutions to Mini-Case
Bay Path Cranberry Products
This case reviews basic calculations for bond prices and yields and examines various
bond features and ratings from the point of view of decisions that must be made by the
issuing company.
For all questions, assume par value is $1,000 and semiannual bond interest
payment.
1. A company in a line of business similar to Bay Path’s recently issued at par
noncallable bonds with a coupon rate of 5.8% and a maturity of twenty years.
The bonds were rated Aa1 by Moody’s and AA by Standard & Poor’s. What
rate of return (yield to maturity) did investors require on these bonds if the
bonds sold at par value?
Bond Data
Call Date (YEARS) Call Price Coupon Yield to Maturity Price If Called on Date Price of Noncallable Call Premium
10.0 1,080.00$ 8.00% 6.50% $1,151.24 $1,109.05 $42.20
10.5 1,076.00$ 8.00% 6.50% $1,151.70 $1,112.88 $38.83
11.0 1,072.00$ 8.00% 6.50% $1,152.21 $1,116.59 $35.62
11.5 1,068.00$ 8.00% 6.50% $1,152.77 $1,120.18 $32.59
12.0 1,064.00$ 8.00% 6.50% $1,153.37 $1,123.66 $29.70
12.5 1,060.00$ 8.00% 6.50% $1,154.01 $1,127.03 $26.97
13.0 1,056.00$ 8.00% 6.50% $1,154.68 $1,130.30 $24.38
13.5 1,052.00$ 8.00% 6.50% $1,155.39 $1,133.46 $21.93
14.0 1,048.00$ 8.00% 6.50% $1,156.13 $1,136.52 $19.60
14.5 1,044.00$ 8.00% 6.50% $1,156.89 $1,139.49 $17.40
15.0 1,040.00$ 8.00% 6.50% $1,157.69 $1,142.36 $15.32
15.5 1,036.00$ 8.00% 6.50% $1,158.50 $1,145.15 $13.36
16.0 1,032.00$ 8.00% 6.50% $1,159.34 $1,147.84 $11.50
16.5 1,028.00$ 8.00% 6.50% $1,160.20 $1,150.45 $9.75
17.0 1,024.00$ 8.00% 6.50% $1,161.07 $1,152.98 $8.09
17.5 1,020.00$ 8.00% 6.50% $1,161.96 $1,155.43 $6.53
18.0 1,016.00$ 8.00% 6.50% $1,162.86 $1,157.80 $5.06
18.5 1,012.00$ 8.00% 6.50% $1,163.77 $1,160.10 $3.67
19.0 1,008.00$ 8.00% 6.50% $1,164.69 $1,162.32 $2.37
19.5 1,004.00$ 8.00% 6.50% $1,165.63 $1,164.48 $1.15
20.0 1,000.00$ 8.00% 6.50% $1,166.56 $1,166.56 $0.00
182 Brooks ◼ Financial Management: Core Concepts, 4e
2. Bay Path has one outstanding bond issue with a coupon of 8% which will mature
in five years. The bond now sells for $1,141.69. What is the yield to maturity on
these bonds? You may want to use a calculator or spreadsheet in determining
your answer.
Formula:
3. Based on your answers to Questions 1 and 2, what coupon rate should Bay Path
offer if it wants to realize $50 million from the bond issue and to sell the bonds as
close to par value as possible? (Ignore the cost of selling the bonds.)
4. Suppose Bay Path actually offers a coupon rate of 6% on its twenty-year bonds,
expecting to sell the bonds at par. What will happen to the price of a single bond
with a par value of $1,000 if the required yield on the bonds unexpectedly falls to
5% or rises to 7%?
Chapter 6 ◼ Bonds and Bond Valuation 183
5. How much money will Bay Path realize from its $50 million bond issue if the
actual yield is either 5% or 7%? Hint: Refer to your answers to Question 4 and
ignore selling costs.
If rates fall just before the bonds are issued, the bonds will sell at a premium and the
6. How would the following affect the yield on Bay Path’s newly issued bonds?
a. The bonds are callable.
b. The bonds are subordinated to Bay Path’s existing bond issue.
c. The bond rating is better or worse than the Moody’s Aa1 that Bay Path
anticipates.
Additional Problems with Solutions
1. Pricing a semiannual bond. Last year, The Harvest Time Corporation sold
$40,000,000 worth of 7.5% coupon, fifteen-year maturity, $1,000 par value, AA–
rated; noncallable bonds to finance its business expansion. Currently, investors are
demanding a yield of 8.5% on similar bonds. If you own one of these bonds and want
to sell it, how much money can you expect to receive on it?
ANSWER (Slides 6-47 to 6-48)
Using a financial calculator
184 Brooks ◼ Financial Management: Core Concepts, 4e
2. Yield to maturity. Joe Carter is looking to invest in a four-year bond that pays
semiannual coupons at a coupon rate of 5.6 percent and has a par value of $1,000. If
these bonds have a market price of $1,035, what yield to maturity is being implied in
the pricing?
ANSWER (Slides 6-49 to 6-50)
Using a financial calculator
3. Price of a zero-coupon bond. Krypton Inc. wants to raise $3 million by issuing ten-
year zero coupon bonds with a face value of $1,000. Their investment banker informs
them that investors would use a 9.25% discount rate on such bonds. At what price
would these bonds sell in the market place assuming semiannual compounding? How
many bonds would the firm have to issue to raise $3 million?
ANSWER (Slides 6-51 to 6-52)
Using a financial calculator: Price of zero-coupon bond
