Chapter 07 – Valuing Bonds
LG4 7-22 Compute Bond Price Compute the price of a 5.6 percent coupon bond with 10 years left to
maturity and a market interest rate of 7.0 percent. (Assume interest payments are semiannual.) Is
this a discount or premium bond?
Bond Price = $28 . 00×
[
1−1
(
1+0 . 035
)
20
0.035
]
+$1, 000
(
1+0 . 035
)
20 =$397 . 95+$502 .56=$900 .51
or TVM calculator: N = 20, I = 3.5, PMT = 28, FV = 1000; CPT PV = -900.51
Since the bond’s price is less than $1,000, it is a discount bond.
LG4 7-23 Compute Bond Price Calculate the price of a 5.2 percent coupon bond with 18 years left to
maturity and a market interest rate of 4.6 percent. (Assume interest payments are semiannual.) Is
this a discount or premium bond?
Bond Price = $26 . 00×
[
1−1
(
1+0. 023
)
36
0 .023
]
+1, 000
(
1+0 . 023
)
36 =$631. 87+$441. 04=$1,072 . 91
or TVM calculator: N = 36, I = 2.3, PMT = 26, FV = 1000; CPT PV = -1,072.91
Since the bond’s price is greater than $1,000, it is a premium bond.
LG4 7-24 Compute Bond Price Calculate the price of a 5.7 percent coupon bond with 22 years left to
maturity and a market interest rate of 6.5 percent. (Assume interest payments are semiannual.) Is
this a discount or premium bond?
Bond Price = $28 . 50×
[
1−1
(
1+0 . 0325
)
44
0 .0325
]
+$1, 000
(
1+0 . 0325
)
44 =$662 . 24+$244 . 81=$907 . 05
or TVM calculator: N = 44, I = 3.25, PMT = 28.50, FV = 1000; CPT PV = -907.05
Since the bond’s price is less than $1,000, it is a discount bond.
LG5 7-25 Bond Prices and Interest Rate Changes A 5.75 percent coupon bond with 10 years left to
maturity is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield
to maturity will be 6.0 percent. What is the change in price the bond will experience in dollars?
Compute the current bond price:
Bond Price = $28 . 75×
[
1−1
(
1+0 . 0325
)
20
0. 0325
]
+$1, 000
(
1+0 .0325
)
20 =$418. 01+$527 . 47=$945. 48
7-1
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Education.
Chapter 07 – Valuing Bonds
LG5 7-26 Bond Prices and Interest Rate Changes A 6.5 percent coupon bond with 14 years left to
maturity is priced to offer a 7.2 percent yield to maturity. You believe that in one year, the yield
to maturity will be 6.8 percent. What is the change in price the bond will experience in dollars?
Compute the current bond price:
Bond Price = $32 . 50×
[
1−1
(
1+0 . 036
)
28
0 . 036
]
+$1, 000
(
1+0 .036
)
28 =$567 . 42+$371. 47=$938 . 89
or TVM calculator: N = 28, I = 3.6, PMT = 32.50, FV = 1000; CPT PV = -938.89
Now compute the price in one year:
Bond Price = $32 . 50×
[
1−1
(
1+0 . 034
)
26
0 . 034
]
+$1,000
(
1+0 . 034
)
26 =$555 .14 +$419 .24=$974 . 38
or TVM calculator: N = 26, I = 3.4, PMT = 32.50, FV = 1000; CPT PV = -974.38
So, the dollar change in price is:
$974.38 − $938.89 = $35.49
LG6 7-27 Yield to Maturity A 5.65 percent coupon bond with 18 years left to maturity is offered for
sale at $1,035.25. What yield to maturity is the bond offering? (Assume interest payments are
semiannual.)
7-2
Chapter 07 – Valuing Bonds
LG6 7-28 Yield to Maturity A 4.30 percent coupon bond with 14 years left to maturity is offered for
sale at $943.22. What yield to maturity is the bond offering? (Assume interest payments are
semiannual.)
LG6 7-29 Yield to Call A 6.75 percent coupon bond with 26 years left to maturity can be called in six
years. The call premium is one year of coupon payments. It is offered for sale at $1,135.25.
What is the yield to call of the bond? (Assume interest payments are semiannual.)
LG6 7-30 Yield to Call A 5.25 percent coupon bond with 14 years left to maturity can be called in
four years. The call premium is one year of coupon payments. It is offered for sale at $1,075.50.
What is the yield to call of the bond? (Assume interest payments are semiannual.)
LG6 7-31 Comparing Bond Yields A client in the 39 percent marginal tax bracket is comparing a
municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that
offers a 6.45 percent yield. Which bond will give the client more profit after taxes?
LG6 7-32 Comparing Bond Yields A client in the 28 percent marginal tax bracket is comparing a
municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that
offers a 6.45 percent yield. Which bond will give the client more profit after taxes?
advanced problems
7-3
Chapter 07 – Valuing Bonds
LG2 7-33 TIPS Total Return Reconsider the 3.5 percent TIPS discussed in problem 7-19. It was
issued with CPI reference of 185.6. The bond is purchased at the beginning of the year (after the
interest payment), when the CPI was 193.5. For the interest payment in the middle of the year,
the CPI was 195.1. Now, at the end of the year, the CPI is 199.6 and the interest payment has
been made. What is the total return of the TIPS in dollars and in percentage terms for the year?
LG2 7-34 TIPS Total Return Reconsider the 2.25 percent TIPS discussed in problem 7-20. It was
issued with CPI reference of 187.2. The bond is purchased at the beginning of the year (after the
interest payment), when the CPI was 197.1. For the interest payment in the middle of the year,
the CPI was 200.1. Now, at the end of the year, the CPI is 203.8 and the interest payment has
been made. What is the total return of the TIPS in dollars and in percentage terms for the year?
LG5 7-35 Bond Prices and Interest Rate Changes A 6.25 percent coupon bond with 22 years left to
maturity is priced to offer a 5.5 percent yield to maturity. You believe that in one year, the yield
to maturity will be 6.0 percent. If this occurs, what would be the total return of the bond in
dollars and percent? (Assume interest payments are semiannual.)
Compute the current bond price:
Bond Price = $31 . 25×
[
1−1
(
1+0 . 0275
)
44
0. 0275
]
+$1,000
(
1+0 . 0275
)
44 =$791 .92+$303 .11=$1, 095. 03
or TVM calculator: N = 44, I = 2.75, PMT = 31.25, FV = 1,000; CPT PV = -1,095.03
Now compute the price in one year:
Bond Price = $31 . 25×
[
1−1
(
1+0 . 03
)
42
0 . 03
]
+$1, 000
(
1+0 . 03
)
42 =$740 . 67+$288 .96=$1, 029. 63
7-4
Chapter 07 – Valuing Bonds
Chapter 07 – Valuing Bonds
LG5 7-36 Bond Prices and Interest Rate Changes A 7.5 percent coupon bond with 13 years left to
maturity is priced to offer a 6.25 percent yield to maturity. You believe that in one year, the yield
to maturity will be 7.0 percent. If this occurs, what would be the total return of the bond in
dollars and percentage terms? (Assume interest payments are semiannual.)
LG6 7-37 Yields of a Bond A 2.50 percent coupon municipal bond has 12 years left to maturity and
has a price quote of 98.45. The bond can be called in four years. The call premium is one year of
coupon payments. Compute and discuss the bond’s current yield, yield to maturity, taxable
equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call.
Chapter 07 – Valuing Bonds
Muni yield 2.65%
Equivalent taxable yield 4.08%
1-Tax rate 1 0.35
= = =
–
TVM calculator: N = 8, PV = -4,922.50, PMT = 62.50, FV = 5125; CPT I = 1.753%
YTC = 1.753% × 2 = 3.51%
The current yield is higher than the coupon rate because this is currently a discount bond. This is
also shown by the YTM, which is greater than the coupon rate. The YTC is comparatively high,
but it is currently unlikely that the bond will be called early since interest rates have risen.
LG6 7-38 Yields of a Bond A 3.85 percent coupon municipal bond has 18 years left to maturity and
has a price quote of 103.20. The bond can be called in eight years. The call premium is one year
of coupon payments. Compute and discuss the bond’s current yield, yield to maturity, taxable
equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call.
(Assume interest payments are semiannual and a par value of $5,000.)
LG7 7-39 Bond Ratings and Prices A corporate bond with a 6.5 percent coupon has 15 years left to
maturity. It has had a credit rating of BBB and a yield to maturity of 7.2 percent. The firm has
recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The
new appropriate discount rate will be 8.5 percent. What will be the change in the bond’s price in
dollars and percentage terms? (Assume interest payments are semiannual.)
7-7
Chapter 07 – Valuing Bonds
7-8
Chapter 07 – Valuing Bonds
Bond price = $32. 50×
[
1−1
(
1+0 . 0425
)
30
0 . 0425
]
+$1, 000
(
1+0 .0425
)
30 =$545 .32+$286 . 89=$832 .21
or TVM calculator: N = 30, I = 4.25, PMT = 32.50, FV = 1000; CPT PV = -832.21
So, the dollar change in price is:
$832.21 − $936.43 = -$104.22
The percentage return is: -$104.22 / $936.43 = -11.13%
LG7 7-40 Bond Ratings and Prices A corporate bond with a 6.75 percent coupon has 10 years left to
maturity. It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm has
recently become more financially stable and the rating agency is upgrading the bonds to BBB.
The new appropriate discount rate will be 7.1 percent. What will be the change in the bond’s
price in dollars and percentage terms? (Assume interest payments are semiannual.)
Compute the current bond price:
Bond price = $33. 75×
[
1−1
(
1+0 . 041
)
20
0. 041
]
+$1, 000
(
1+0 .041
)
20 =$454 . 64 +$447 .70=$902. 34
or TVM calculator: N = 20, I = 4.1, PMT = 33.75, FV = 1000; CPT PV = -902.34
Now compute the price after the rating change:
Bond price = $33. 75×
[
1−1
(
1+0 . 0355
)
20
0. 0355
]
+$1, 000
(
1+0 . 0355
)
20 =$477 .51+$497 . 73=$975 . 24
or TVM calculator: N = 20, I = 3.55 PMT = 33.75, FV = 1000; CPT PV = -975.24
So, the dollar change in price is:
$975.24 − $902.34 = $72.90
The percentage return is: $72.90 / $902.34 = 8.08%
7-41 Spreadsheet Problem Say that in June of 2014, a company issued bonds that are
scheduled to mature in June of 2017. The coupon rate is 5.75 percent and is paid semiannually.
The bond issue was rated AAA.
a. Build a spreadsheet that shows how much money the firm pays for each interest rate payment
and when those payments will occur if the bond issue sells 50,000 bonds.
b. If the bond issue rating would have been BBB, then the coupon rate would have been 6.30
percent. Show the interest payments with this rating. Explain why bond ratings are important to
firms issuing capital debt.
Chapter 07 – Valuing Bonds
c. Consider that interest rates in the economy increased in the first half of 2012. If the firm
would have issued the bonds in January of 2012, then the coupon rate would have only been 5.40
percent. How much extra money per year is the firm paying because it issued the bonds in June
instead of January?
The spreadsheet might look like:
Jun-16 1,437,500 1,575,000 1,350,000
Dec 16 1,437,500 1,575,000 1,350,000
June 17 1,437,500 1,575,000 1,350,000
1
research it!
Bond Information Online
Information on the bond market is widely available in papers like The Wall Street Journal and
Barron’s. Bond information can also be found online at financial websites like
finance.yahoo.com and http://www.finra.org. The bond credit rating agencies also
maintainwebsites with their own bond market news.
You can follow the bond market easily at places like Yahoo! Finance . Click on the Bond
link in the menu to go to their Bond Center. Bond yields for various maturity Treasury securities
are shown for today and for previous days. The Bond Composite Rates link shows similar
comparisons for municipal and corporate bonds too.
Bond calculators are also available for free on the Web. Compare a bond price result from
your calculator or the price equation with the online bond calculator result at Investopedia.
(www.investopedia.com/calculator/BondPrice.aspx)
Chapter 07 – Valuing Bonds
SOLUTION: All answers will be different. Here is an example answer:
integrated mini-case: Corporate Bond Credit Risk Changes and Bond Prices
Land’o’Toys is a profitable, medium-sized, retail company. Several years ago, it issued a 6.5
percent coupon bond, which pays interest semiannually. The bond will mature in 10 years and is
currently priced in the market as $1,037.19. The average yields to maturity for 10-year corporate
bonds are reported in the following table by bond rating.
Bond Rating Yield (%) Bond Rating Yield (%)
AAA 5.4 BB 7.3
AA 5.7 B 8.2
A 6.0 CCC 9.2
BBB 6.5 CC 10.5
C 12.0
D 14.5
Periodically, one company will purchase another by buying all of the target firm’s stock. The
bonds of the target firm continue to exist. The debt obligation is assumed by the new firm. The
credit risk of the bonds often changes because of this type of an event.
7-11
Education.
Chapter 07 – Valuing Bonds
Suppose that the firm Treasure Toys makes an announcement that they are purchasing
Land’o’Toys. Due to Treasure Toy’s projected financial structure after the purchase, Standard &
Poor’s states that the bond rating for Land’o’Toys bonds will change to BB.
a. Compute the yield to maturity of Land’o’Toys bonds before the purchase announcement
and use it to determine the likely bond rating.
b. Assume the bond’s price changes to reflect the new credit rating. What is the new price?
Did the price increase or decrease?
c. What is the dollar change and percentage change in the bond price?
d. How do the bond investors feel about the announcement?