Finance 3155 - Business
Finance

November 11, 1999 - Exam 3

Dr. Dowling Name____________________

Instructions: You
are to circle the letter representing the correct answer. If calculations are required to arrive
at the answer, you must provide sufficient documentation for your answer to
have any credit awarded.

1. Which of the following events would make
it more likely that a company would choose to call its outstanding callable
bonds?

a. A
reduction in market interest rates.

b. The
company's bonds are downgraded.

c. An
increase in the call premium.

d. Answers
a and b are correct.

e. Answers
a, b, and c are correct.

2. Which of the following statements is most
correct?

a. All
else equal, if a bond's yield to maturity increases, its price will fall.

b.
b.
All else equal,
if a bond's yield to maturity increases, its current yield will fall.

c.
c. If
a bond's yield to maturity exceeds the coupon rate, the bond will sell at a
premium over par.

d. All
of the answers above are correct.

e. None
of the answers above is correct.

3. Assume that you wish to purchase a 20-year
bond that has a maturity value of $1,000 and makes semiannual interest payments
of $40. If you require a 10 percent nominal yield to maturity on this
investment, what is the maximum price you should be willing to pay for the bond?

a. $619

b. $674

c. $761

d. $828

e. $902

4. Consider a $1,000 par value bond with a 7
percent annual coupon. The bond pays interest annually. There are 9 years
remaining until maturity. What is the current yield on the bond assuming that
the required return on the bond is 10 percent?

a. 10.00%

b. 8.46%

c. 7.00%

d. 8.52%

e. 8.37%

5. A corporate bond with a $1,000 face value
pays a $50 coupon every six months. The bond will mature in ten years, and has
a nominal yield to maturity of 9 percent. What is the price of the bond?

a. $634.86

b. $1,064.18

c. $1,065.04

d. $1,078.23

e. $1,094.56

6. The current market price of Smith
Corporation's 10 percent, 10 year bonds is $1,297.58. A 10 percent coupon
interest rate is paid semiannually, and the par value is equal to $1,000. What
is the YTM (stated on a nominal, or annual, basis) if the bonds mature 10 years
from today?

a. 8%

b. 6%

c. 4%

d. 2%

e. 1%

7.
Which of the following has the greatest price risk?

a. A
10-year, $1,000 face value, 10percent coupon bond with semiannual interest
payments.

b. A
10-year, $1,000 face value, 10percent coupon bond with annual interest
payments.

c. A
10-year, $1,000 face value, zero coupon bond.

d. A
10-year $100 annuity.

e. All
of the above have the same price risk since they all mature in 10 years.

8. 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.

9. 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 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

10.Assume
that a 15-year, $1,000 face value bond pays interest of$37.50 every 3 months.
If you require a nominal annual rate of return of 12 percent, with quarterly
compounding, how much should you be willing to pay for this bond? (Hint: The
PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)

a.$821.92

b.$1,207.57

c.$986.43

d.$1,120.71

e.$1,358.24

11. Your client has been offered a 5-year,
$1,000par value bond with a 10 percent coupon. Interest on this bond is paid
quarterly. If your client is to earn a nominal rate of return of 12 percent,
compounded quarterly, how much should she pay for the bond?

a.$800

b.$926

c.$1,025

d.$1,216

e.$981

12. A $1,000 par value bond sells for $1,216.
It matures in 20 years, has a 14 percent coupon, pays interest semiannually,
and can be called in 5 years at a price of $1,100.What is the bond's YTM and
YTC?

__YTMYTC__

a.6.05%9.00%

b.10.00%10.26%

c.10.06%10.00%

d.11.26%14.00%

e.11.26%10.00%

ANSWER KEY FOR TEST - 7

Callable bond

Statement a is correct; the other statements are false. A bond
downgrade generally raises the cost of issuing new debt. Therefore, the
callable bonds would not be called. If the call premium (the cost paid in
excess of par) increases, the cost of calling debt increases; therefore,
callable bonds would not be called.

2. a. All else equal, if a bond's yield to
maturity increases, its price will fall.

Bond concepts

Statement a is correct; the other statements are false. A bond's price
and YTM are negatively related. If a bond's YTM is greater than its coupon
rate, it will sell at a discount.

3. d. $828

Bond value - semiannual payment

Tabular solution:

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

= $40(17.1591) +$1,000(0.1420) = $828.36 ÷ $828.

Financial calculator solution:

Inputs: N = 40; I = 5; PMT = 40; FV = 1,000.

Output: PV = -$828.41; V_{B}÷ $828.

4. b.8.46%

Current yield

Find the price of the bond as N = 9, I = 10, PMT = 70, FV = 1,000, and
solve for PV = ? = -$827.23. The current yield is $70/$827.23 =8.46%.

5. c. $1,065.04

Bond value - semiannual payment

N= 10 x 2 = 20

I= 9/2 = 4.5

PMT= 50

FV= 1,000

Solve for PV = -$1,065.04.

6. b. 6%

Yield to maturity

Financial calculator solution:

Inputs: N = 20; PV = -1,297.58; PMT = 50; FV = 1,000.

Output: I = 3.0% per period. k_{d}= YTM = 3.0% x 2 periods = 6%.

7. c. A 10-year, $1,000 face value, zero
coupon bond.

Price risk

The correct answer is c; the other statements are false. Zero coupon
bonds have greater price risk than either of the coupon bonds or the annuity.

8. a. The bond's yield to maturity is less
than10 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.

9. b. 2,596

Bond value - semiannual payment

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•_{%,}?™) + $1,000(PVIF•_{%,}?™)

= $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.

10. b. $1,207.57

Bond value - quarterly payment

Tabular solution: *(PVIFA and PVIF are given in the problem.)*

V_{B} = $37.50(PVIFA_{%,}•™) + $1,000(PVIF_{%,}•™)

= $37.50(27.6748) +
$1,000(0.1697) = $1,207.51

Financial calculator solution:

Inputs: N = 60; I = 3; PMT = 37.50; FV = 1,000.

Output: PV = -$1,207.57; V_{B} = $1,207.57.

**Note:**
Tabular solution differs from calculator solution due to interest factor
rounding.

11. b. $ 926

Bond value - quarterly payment

Tabular solution:

V_{B} = $25(PVIFA_{%,}Ž™) + $1,000(PVIF_{%,}Ž™)

= $25(14.8775) +
$1,000(0.5537) = $925.64 ÷ $926.

Financial calculator solution:

Inputs: N = 20; I = 3; PMT = 25; FV = 1,000.

Output: PV = -$925.61; V_{B} ÷ $926.

12. e. 11.26%; 10.00%

Yield to call

Financial calculator
solution:

*YTM* Inputs: N = 40;
PV = -1,216; PMT = 70; FV = 1,000.

Output:
I = 5.6307% ÷ 5.63% = k_{d/2}. YTM = 5.63% x 2 = 11.26%.

*YTC* Inputs: N = 10;
PV = -1,216; PMT = 70; FV = 1,100.

Output:
I = 4.9981% ÷ 5.0% = k_{d/2}. YTC = 5.0% x 2 = 10.0%.