Sample Problems
- Chapter 7

1. Which of the following
statements is most correct?

a. Bond prices and interest rates move in the same direction, i.e., if interest
rates rise, so will bond prices.

b. The market price of a discount bond will approach the bond's par
value as the maturity date approaches. Barring changes in the probability of
default, there is no way the value of the bond can fail to increase each year
as the time to maturity approaches.

c. The "current yield" on a noncallable discount bond will
normally exceed the bond's yield to maturity.

d. The "current yield" on a noncallable discount bond will
normally exceed the bond's coupon interest rate.

e. All of the
statements above are false.

2. If the yield to
maturity decreased 1 percentage point, which of the following bonds would have
the largest percentage increase in value?

a. A 1-year bond with
an 8 percent coupon.

b. A 1-year
zero-coupon bond.

c. A 10-year
zero-coupon bond.

d. A 10-year bond with
an 8 percent coupon.

e. A 10-year bond with
a 12 percent coupon.

3. Which of the following
statements is most correct?

a. The discount or premium on a bond can be expressed as the difference
between the coupon payment on an old bond, which originally sold at par, and
the coupon payment on a new bond, selling at par, where the difference in
payments is discounted at the new market rate.

b. The price of a coupon
bond is determined primarily by the number of years to maturity.

c. On a coupon paying bond, the final interest payment is made one
period before maturity and then, at maturity, the bond's face value is paid as
the final payment.

d. The actual capital gains yield for a one-year holding period on a
bond can never be greater than the current yield on the bond.

e. All of the
statements above are false.

4. Which of the following
statements is most correct?

a. The market value of a bond will always approach its par value as its
maturity date approaches, provided the issuer of the bond does not go bankrupt.

b. If the Federal Reserve unexpectedly announces that they expect
inflation to increase, then we would probably observe an immediate increase in
bond prices.

c. The total yield on a bond is derived from interest payments and
changes in the price of the bond.

d. Statements a and c
are correct.

e. All of the
statements above are correct.

5. Which of the following
statements is most correct?

a. If a bond is selling for a premium, this implies that the bond's
yield to maturity exceeds its coupon rate.

b. If a coupon bond is
selling at par, its current yield equals its yield to maturity.

c. If rates fall after its issue, a zero coupon bond could trade for an
amount above its par value.

d. Statements b and c
are correct.

e. None of the
statements above is correct.

6. Which of the following
statements is most correct?

a. A *callable* 10-year, 10 percent bond should sell at a higher price
than an otherwise similar noncallable bond.

b. Two bonds have the same maturity and the same coupon rate. However,
one is callable and the other is not. The difference in prices between the
bonds will be greater if the current market interest rate is *below* the
coupon rate than if it is above the coupon rate.

c. Two bonds have the same maturity and the same coupon rate. However,
one is callable and the other is not. The difference in prices between the
bonds will be greater if the current market interest rate is *above* the
coupon rate than if it is below the coupon rate.

d. The actual life of a callable bond will be equal to or less than the
actual life of a noncallable bond with the same maturity date. Therefore, if
the yield curve is upward sloping, the required rate of return will be lower on
the callable bond.

e. Corporate treasurers *dislike* issuing callable bonds because
these bonds may require the company to raise additional funds earlier than
would be true if noncallable bonds with the same maturity were used.

7. Which of the following
types of debt protect a bondholder against an increase in interest rates?

a. Floating rate debt.

b. Bonds that are
redeemable ("putable") at par at the bondholders' option.

c. Bonds with call
provisions.

d. All of the answers
above.

e. Only answers a and
b above.

8. A company is planning
to raise $1,000,000 to finance a new plant. Which of the following statements
is most correct?

a. If debt is used to raise the million dollars, the cost of the debt
would be lower if the debt is in the form of a fixed rate bond rather than a
floating rate bond.

b. If debt is used to raise the million dollars, the cost of the debt
would be lower if the debt is in the form of a bond rather than a term loan.

c. If debt is used to raise the million dollars, but $500,000 is raised
as a first mortgage bond on the new plant and $500,000 as debentures, the
interest rate on the first mortgage bond would be lower than it would be if the
entire $1 million were raised by selling first mortgage bonds.

d. The company would be especially anxious to have a call provision
included in the indenture if its management thinks that interest rates are
almost certain to rise in the foreseeable future.

e. All of the
statements above are false.

9. Which of the following
statements is most correct?

a. If a bond sells for less than par, then its yield to maturity is
less than its coupon rate.

b. If a bond sells at
par, then its current yield will be less than its yield to maturity.

c. Assuming that both bonds are held to maturity and are of equal risk,
a bond selling for more than par with ten years to maturity will have a lower
current yield and higher capital gain relative to a bond that sells at par.

d. Answers a and c are
correct.

e. None of the answers
above is correct.

10. You just purchased a
10-year corporate bond that has an annual coupon of 10 percent. The bond sells
at a premium above par. Which of the following statements is most correct?

a. The bond's yield to
maturity is less than 10 percent.

b. The bond's current
yield is greater than 10 percent.

c. If the bond's yield to maturity stays constant, the bond's price
will be the same one year from now.

d. Statements a and c
are correct.

e. None of the answers
above is correct.

11. Which of the following
statements is most correct?

a. The expected return
on corporate bonds will generally exceed the yield to maturity.

b. Firms that are in
financial distress are forced to declare bankruptcy.

c. All else equal, senior debt will generally have a lower yield to
maturity than subordinated debt.

d. Answers a and c are
correct.

e. None of the answers
above is correct.

12. Marie Snell recently
inherited some bonds (face value $100,000) from her father, and soon thereafter
she became engaged to Sam Spade, a University of Florida marketing graduate.
Sam wants Marie to cash in the bonds so the two of them can use the money to
"live like royalty" for two years in Monte Carlo. The 2 percent
annual coupon bonds mature on January 1, 2018, and it is now January 1, 1998.
Interest on these bonds is paid annually on December 31 of each year, and new
annual coupon bonds with similar risk and maturity are currently yielding 12
percent. If Marie sells her bonds now and puts the proceeds into an account
which pays 10 percent compounded annually, what would be the largest equal
annual amounts she could withdraw for two years, beginning today (i.e., two
payments, the first payment today and the second payment one year from today)?

a. $13,255

b. $29,708

c. $12,654

d. $25,305

e. $14,580

13. JRJ Corporation
recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in
interest each six months. Their price has remained stable since they were
issued, i.e., they still sell for $1,000. Due to additional financing needs,
the firm wishes to issue new bonds that would have a maturity of 10 years, a
par value of $1,000, and pay $40 in interest every six months. If both bonds
have the same yield, how many new bonds must JRJ issue to raise $2,000,000 cash?

a. 2,400

b. 2,596

c. 3,000

d. 5,000

e. 4,275

14. Assume that you own a
hundred $1,000 par value bonds, with a total face value of $100,000. These
bonds have a 4 percent coupon, pay interest semiannually, and have 5 years
remaining until they mature. New bonds with the same risk and maturity provide
yields to maturity of 14 percent. You are considering selling your bonds and
depositing the proceeds in a savings account which pays interest at a rate of 6
percent, annual compounding. If you do make the transaction, you will liquidate
the savings account by making 5 equal withdrawals, the first coming 1 year from
now. What will be the amount of each annual withdrawal?

a. $12,940

b. $15,403

c. $24,860

d. $29,425

e. $64,880

15. An 8 percent annual
coupon, noncallable bond has ten years until it matures and a yield to maturity
of 9.1 percent. What should be the price of a 10-year noncallable bond of equal
risk which pays an 8 percent semiannual coupon? Assume both bonds have a par
value of $1,000.

a. $ 898.64

b. $ 736.86

c. $ 854.27

d. $ 941.15

e. $ 964.23

16. A bond that matures in
11 years has an annual coupon rate of 8 percent with interest paid annually.
The bond's face value is $1,000 and its yield to maturity is 7.5 percent. The
bond can be called 3 years from now at a price of $1,060. What is the bond's
nominal yield to call?

a. 9.82%

b. 8.41%

c. 8.54%

d. 8.38%

e. 7.86%

17. A company is issuing
$1,000 bonds at par value. The coupon rate (and yield to maturity) on the bonds
is 8 percent (with annual payments) and the bonds will mature in 10 years. The
bonds can be called at a call premium of 5 percent above face value after 3
years. What is the *after-tax yield to call* for an investor with a 31
percent tax rate?

a. 5.52%

b. 5.90%

c. 6.60%

d. 7.07%

e. 9.52%

18. A 15-year bond with a
10 percent semiannual coupon has a par value of $1,000. The bond may be called
after 10 years at a call price of $1,050. The bond has a nominal yield to call
of 6.5 percent. What is the bond's yield to maturity, stated on a nominal, or
annual basis?

a. 5.97%

b. 6.30%

c. 6.75%

d. 6.95%

e. 7.10%

19. Trickle Corporation's
12 percent coupon rate, semiannual payment, $1,000 par value bonds which mature
in 25 years, are callable at a price of $1,080 five years from now. The bonds
currently sell for $1,230.51 in the market, and the yield curve is flat.
Assuming that the yield curve is expected to remain flat, what is Trickle's
most likely *before-tax cost* of debt if it issues new bonds today?

a. 4.78%

b. 6.46%

c. 7.70%

d. 9.56%

e. 12.92%

20. Meade Corporation
bonds mature in 6 years and have a yield to maturity of 8.5 percent. The par
value of the bonds is $1,000. The bonds have a 10 percent coupon rate and pay
interest on a semiannual basis. What are the current yield and capital gains
yield on the bonds for this year? (Assume that interest rates do not change
over the course of the year).

a. Current yield
= 8.50%, capital gains yield =
1.50%

b. Current yield
= 9.35%, capital gains yield =
0.65%

c. Current yield
= 9.35%, capital gains yield =
-0.85%

d. Current yield =
10.00%, capital gains yield = 0.00%

e. None of the answers
above is correct.

ANSWER KEY

1. d. The "current
yield" on a noncallable discount bond will normally exceed the bond's
coupon interest rate.

Discount bonds

2. c. A 10-year
zero-coupon bond.

Price risk

The correct answer is
c; the other statements are false. All other things equal, a zero coupon bond
will experience a larger percentage change in value for a given change in
interest rates than will a coupon-bearing bond. Further, bonds with long
remaining lives experience greater percentage changes in value than do bonds
with short remaining lives. Thus, the 10-year zero coupon bond has the largest
percentage increase in value.

3. a. The discount or
premium on a bond can be expressed as the difference between the coupon payment
on an old bond, which originally sold at par, and the coupon payment on a new
bond, selling at par, where the difference in payments is discounted at the new
market rate.

Bond concepts

4. d. Statements a and c
are correct.

Bond concepts

Statements a and c are
correct; therefore, statement d is the correct choice. If inflation were to
increase, interest rates would rise, thus bond prices would fall.

5. b. If a coupon bond is
selling at par, its current yield equals its yield to maturity.

Bond concepts

Statement b is
correct; the other statements are false. If a bond is selling at a premium, the
YTM would be less than the coupon rate. In addition, as long as interest rates
are greater than zero, zeros should never trade above par.

6. b. Two bonds have the
same maturity and the same coupon rate. However, one is callable and the other
is not. The difference in prices between the bonds will be greater if the
current market interest rate is *below* the coupon rate than if it is
above the coupon rate.

Callable bond

Statement b is
correct; the other statements are false. The bonds' prices would differ
substantially only if investors think a call is likely, in which case investors
would have to give up a high coupon bond. Calls are most likely if the current
market rate is well below the coupon rate. Note that if the current rate is
above the coupon rate, the bond won't be called.

7. e. Only answers a and
b above.

Types of debt

8. c. If debt is used to raise
the million dollars, but $500,000 is raised as a first mortgage bond on the new
plant and $500,000 as debentures, the interest rate on the first mortgage bond
would be lower than it would be if the entire $1 million were raised by selling
first mortgage bonds.

Types of debt

9. e. None of the answers
above is correct.

Current yield and
yield to maturity

Statement e is the
correct choice. If a bond sells for less than par, then its yield to maturity
will exceed its coupon rate. If a bond sells at par, then its current yield,
yield to maturity, and coupon rate are all the same. The bond selling for more
than par will have a lower current yield than a bond selling at par. However,
the bond selling for more than par will have a negative capital gain (i.e., a
capital loss) while the bond selling at par will have no capital gain.

10. a. The bond's yield to
maturity is less than 10 percent.

Current yield and
yield to maturity

Statement a is
correct; the other statements are false. If the bond sells for a premium, this
implies that the YTM must be less than the coupon rate. As a bond approaches
maturity, its price will move toward the par value.

11. c. All else equal,
senior debt will generally have a lower yield to maturity than subordinated debt.

Corporate bonds and
default risk

Statement c is the
correct choice; the other statements are false. The expected return may be
greater than, less than, or equal to the yield to maturity. Firms in financial
distress may or may not eventually declare bankruptcy, i.e., they may recover.

12. a. $13,255

Bond value - annual payment

Time line:

1/1/98
1/1/2018

0 12% 1 2
20 Years

TL¨ ³ÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄśśśÄÄÄÄÄÄÄ³

2,000 2,000
2,000

V_{B} = ?
FV = 100,000

0 10% 1 2

TLŽ ³ÄÄÄÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄÄÄÄ³

PMT = ? PMT FV = 0

V_{B} = 25,305.56

Tabular solution:

Step 1 *Calculate PV of the bonds*

V_{B} = $2,000(PVIFA¨Ž_{%,}Ž™)
+ $100,000(PVIF¨Ž_{%,}Ž™)

= $2,000(7.4694) +
$100,000(0.1037) = $25,308.80.

Step 2 *Calculate the equal payments of the annuity due*

$25,308.80 $25,308.80

PMT = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ =
ÄÄÄÄÄÄÄÄÄÄÄÄÄ = $13,257.27.

(PVIFA¨™_{%,}Ž)(1.10) (1.7355)(1.10)

Financial calculator solution:

*Calculate the PV of the bonds*

Inputs: N = 20; I = 12; PMT = 2,000; FV
= 100,000.

Outpue: PV = -$25,305.56.

*Calculate equal annuity due payments*

BEGIN mode Inputs: N = 2; I = 10; PV = -25,305.56; FV = 0.

Output: PMT = $13,255.29 ÷ $13,255.

13. b. 2,596

Bond value -
semiannual payment

Time line:

0 6% 1 2
20 6-month

³ÄÄÄÄÄÄ³ÄÄÄÄÄÄ³ÄÄÄÄÄÄśśśÄÄÄÄÄÄ³ Periods

PMT =
60 60
60

V_{B-Old} =
1,000
FV = 1,000

PMT =
40 40
40

V_{B-New} =
?
FV = 1,000

Tabular solution:

Since the old bond
issue sold at its maturity (or par) value, and still sells at par, its yield
(and the yield on the new issue) must be 6 percent semiannually. The new bonds will be offered at a
discount:

V_{B} =
$40(PVIFA•_{%,}Ž™) + $1,000(PVIF•_{%,}Ž™)

= $40(11.4699) + $1,000(0.3118) =
$770.60.

Number of bonds =
$2,000,000/$770.60 = 2,595.38 ÷ 2,596.

Financial calculator
solution:

Inputs: N = 20; I = 6;
PMT = 40; FV = 1,000.

Output: PV = -$770.60;
V_{B} = $770.60.

Number of bonds:
$2,000,000/$770.60 ÷ 2.596 bonds.^{*}

^{*}Rounded up to next whole bond.

14. b. $15,403

Annuity payments

Time lines:

0 k_{d}/2 = 7% 1 2
10 6-month

TL¨
³ÄÄÄÄÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄÄśśśÄÄÄÄÄÄÄÄ³ Periods

2,000 2,000
2,000

V_{bonds} = ? = 64,877.20
FV = 100,000

0 i = 6 1 2 3 4 5 Years

TLŽ
³ÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄ³ÄÄÄÄÄÄÄ³

PMT = ? PMT PMT PMT PMT

PV = 64,877.20
FV = 0

Tabular solution:

V_{bonds} = $2,000(PVIFA–_{%,}¨™)
+ $100,000(PVIF–_{%,}¨™)

= $2,000(7.0236) + $100,000(0.5083) = $64,877.20.

$64,877.20 $64,877.20

PMT = ÄÄÄÄÄÄÄÄÄÄ = ÄÄÄÄÄÄÄÄÄÄ =
$15,401.48 ÷ $15,403.

PVIFA•_{%,}”
4.2124

Financial calculator solution:

*Calculate PV of bonds*

Inputs: N = 10; I = 7; PMT = 2,000; FV
= 100,000.

Output: PV = -$64,882.09.

*Calculate annuity payment*

Inputs: N = 5; I = 6; PV = -64,882.09;
FV = 0.

Output: PMT = $15,402.77 ÷ $15,403.

Note: Difference between financial
calculator and tabular solutions

due to rounding of tabular interest
factors.

15. d. $ 941.15

Bond value -
semiannual payment

The 8% annual coupon
bond's YTM is 9.1%. The effective annual rate (EAR) is 9.1% because the bond is
an annual bond. Now, we need to find the nominal rate for the semiannual bond
which has the same EAR, so we can calculate its price.

EFF% = 9.1

P/YR = 2

Solve for NOM% =
8.9019%.

An equally risky 8% semiannual
coupon bond has the same EAR.

Now solve for the
semiannual bond's price. N = 2 x 10 = 20, I/YR = 8.9010/2 = 4.4505, PMT = 80/2
= 40, FV = 1,000, and solve for PV = $941.15.

16. b. 8.41%

Yield to call

The price of the bond
today is found as N = 11, I = 7.5, PMT = 80, FV = 1,000 and PV = ? =
-$1,036.58. Solve for the yield to call as follows: N = 3, PV = -1,036.58, PMT
= 80, FV = 1,060, and solve for I = ? = 8.41%.

17. c. 6.60%

After-tax yield to
call

First, find the call price
on the bonds, Call price = 1.05 x $1,000 = $1,050. Now, we know the bonds will
pay 0.08 x $1,000 = $80 per year and, if called, will last for 3 years. Then,
solve for yield to call: N = 3, PV = -1,000, PMT = 80, FV = 1,050, and solve
for I/YR = 9.5176%. Finally, find the after-tax YTC = YTC x (1 - Tax rate) =
9.5176% x (1 - 0.31) = 6.5672% ÷ 6.60%.

18. d. 6.95%

Yield to maturity

a. First find what the bond is selling for today based on the
information given about its call feature:

N = 10(2) = 20; I = 6.5/2 = 3.25;
PMT = 100/2 = 50; FV = 1,050.

Solve for PV = -$1,280.81 =
Current price.

b. Use this current
price solution to solve for the YTM:

N = 15(2) = 30; PV = -1,280.81;
PMT = 100/2 = 50; FV = 1,000.

Solve for I = 3.4775%.

c. Since this is a
semiannual rate, multiply it by 2 to solve for the nominal, annual YTM:

YTM = 3.4775%(2) = 6.955% ÷ 6.95%.

19. c. 7.70%

Cost of debt

Time line:

0 i = ? 1 2 3 4 5 10 50 6-month

³ÄÄÄÄÄÄÄÄÄÄÄÄ³ÄÄÄÄÄÄ³ÄÄÄÄÄ³ÄÄÄÄÄÄ³ÄÄÄÄÄÄ³ÄÄśśśÄÄ³ÄÄśśśÄÄÄ³ Periods

V_{B} =
1,230.51 60 60 60 60 60 60 60

Call price = 5 = 1,080 FV = 1,000

*Calculate the
nominal yield to call:* The bonds are selling
at a premium because the coupon rate is above the market rate. Under the
expectation of a flat yield curve, the bonds will most likely be called so that
the firm can issue new, cheaper bonds. The FV is the call price and the period
is 5 years or 10 semiannual periods.

Financial calculator
solution:

Inputs: N = 10; PV =
-1,230.51; PMT = 60; FV = 1,080.

Output: I = 3.85
periodic rate (semiannual).

The nominal annual
rate equals 2 x 3.85% = 7.70%. Thus, the before-tax cost of debt is 7.70%.

20. c. Current yield
= 9.35%, capital gains yield =
-0.85%

Current yield and
capital gains yield

First, calculate the
price of the bond as follows: N = 6 x 2 = 12, I = 8.5/2 = 4.25, PMT = 10%/2 x
1,000 = 50, FV = 1,000, and PV = ? = -$1,069.3780. The current yield (CY) is
then $100/$1,069.3780 = 9.35%. Recognizing that the CY and capital gains yield
(CG) constitute the total return (YTM) on the bond or CY + CG = YTM, solve
9.35% + CG = 8.5% for CG = -0.85%.