BUSINESS FINANCE (FIN 312) - Faculty Pages

BUSINESS FINANCE (FIN 312)

Spring 2009

Assignment 2

Instructions: please read carefully

? You can either do the assignment by yourself or work in a group of no more than two.

? You should show your work how to get the answer for each calculation question to get full credit.

? You should make two copies. One copy to turn in for grading purposes, the other to study for the exam.

? The due date is Thursday April 02, 2009. Late assignments will not be graded.

Name(s):

Student ID

Chapter 7

1. A semi-annual corporate bond has a face value of $1,000, a yield to maturity of 6.9 percent, and a coupon rate of 6.5 percent. The bond matures 8 years from today. This bond:

1. c

a. pays interest payments of $34.50 every six months.

b. sells at a premium.

c. has a current yield that is greater than 6.5 percent.

d. is currently quoted at a price of 97:18.

1

-

1

/1

+

.069

8?2

P

=

.065

?

$1,000

?

2

2 .069

2

+

$1,000 1 + .069 8?2 2

;

P

=

$394.54

+

$581.18

=

$975.72

Enter

8?2 6.9/2

65/2 1,000

N

I/Y PV PMT FV

Solve for

-975.72

Current yield = (.065 ? $1,000) ? $975.72 = .0666 = 6.66 percent

2. The price you receive when you sell a Treasury bond is the _____ price.

a. bid

b. yield

c. call

d. asked

2. a You receive the bid price when you sell a Treasury bond.

3. Which one of the following bonds has the most interest rate risk? a. 5-year; 6 percent coupon b. 5-year; zero coupon c. 10-year; zero coupon d. 10-year; 6 percent coupon

3. c The longest term, lowest coupon bond is the most sensitive to interest rate changes.

4. Jenny earned 6.7 percent on her investments last year. What was her real rate of return if the inflation rate was 1.6 percent? (using the Fisher exact version) a. 5.02 percent b. 5.10 percent c. 8.30 percent d. 10.74 percent

4. a r = [(1 + .067) ? (1 + .016)] - 1 = .0502 = 5.02 percent

5. Kiddy and Kat, Inc. has 9 percent semi-annual bonds outstanding with 13 years to maturity. The latest quote on these bonds is 110.23. What is the yield to maturity? a. 5.81 percent b. 6.87 percent c. 6.92 percent d. 7.74 percent

5. d

Enter Solve for

13?2 N

/2 -1102.30 I/Y PV 7.74

90/2 PMT

1,000 FV

6. Black and White, Inc. offers a 7.5 percent bond with a yield to maturity of 6.65 percent. The bond pays interest annually and matures in 17 years. What is the market price of one of these bonds if the face value is $1,000? a. $1,046.02 b. $1,046.88 c. $1,085.04 d. $1,085.78

6. c

[ ] P

=

(.075

?

$1,000)?

1

-

1/

(1

+

.0665)17

.0665

+

$1,000

(1+ .0665)17

; P = $750.33 + $334.71

= $1,085.04

Enter

17 6.65

75 1,000

N

I/Y PV PMT FV

Solve for

-1,085.04

7. A zero coupon bond is currently priced to yield 5.87 percent if held to maturity 6.9 years

from now. What is the current price of this bond if the face value is $1,000?

a. $674.63

b. $675.13 c. $675.29 d. $676.01

7. a

P=

$1,000

(1+ .0587)6.9

; P = $674.63

Enter

6.9

N

Solve for

5.87 I/Y PV

-674.63

1,000 PMT FV

8. The bonds of B&O, Inc. are currently quoted at 98.72 and have a 6.75 percent coupon. The bonds pay interest semi-annually and mature in 9 years. What is the current yield on these bonds? a. 6.82 percent b. 6.84 percent c. 6.87 percent d. 6.91 percent

8. b CY = $67.50 ? $987.20 = .06837 = 6.84 percent

9. A semi-annual, five-year bond is currently selling for $1,034.60 and has a yield to maturity of 5.94 percent. What is the coupon rate of this bond if the face value is $1,000? a. 6.50 percent b. 6.60 percent c. 6.75 percent d. 7.0 percent

9. c

1

-

1

/1

+

.0594

5?2

$1,034.60

=

C

? $1,000 2

?

2 .0594

2

+

$1,000 1 + .0594 5?2 2

;

C

=

.0675

=

6.75%

Enter Solve for

5?2 5.94/2 -1,034.60

1,000

N

I/Y PV PMT FV

33.75

Coupon rate = ($33.75 ? 2) ? $1,000 = .0675 = 6.75%

Current yield 10. 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%

Answer: b

Numerical solution: VB = $70((1- 1/1.109)/0.10) + $1,000(1/1.109)

= $70(5.7590) + $1,000(0.4241) = $403.13 + $424.10 = $827.23.

Financial calculator solution: N = 9, I = 10, PMT = 70, FV = 1,000, and solve for PV = ? = $827.23.

Current yield = $70/$827.23 = 8.46%.

YIELD TO MATURITY

11.

The bonds issued by Jensen & Son bear a 6 percent coupon, payable semiannually. The

bond matures in 8 years and has a $1,000 face value. Currently, the bond sells at par.

What is the yield to maturity?

a. 5.87 percent

b. 5.97 percent

c. 6.00 percent

d. 6.09 percent

e. 6.17 percent

11. c

$1,000

=

.06 ?

$1,000 2

?

1 -

1/(1 + r

r 2

)8?2

+

$1,000 (1 + r )8?2

;

This

can

not

be

solved

2

2

directly, so it's easiest to just use the calculator method to get an answer. You can then

use the calculator answer as the rate in the formula just to verify that your answer is

correct.

Enter

8?2

N

Solve for

/2 -1,000 I/Y PV 6

60/2 1,000 PMT FV

Answer is 6.00 percent

Bond value - semiannual payment 12. 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

Bond value - semiannual payment

Time Line:

0 5% 1

2

|

|

|

40 40

PV = ?

Answer: d

3

4

|

|

..

40 40

40

| 40 FV = 1,000

6-month Periods

Numerical solution: VB = $40((1- 1/1.0540)/0.05) + $1,000(1/1.0540)

= $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; VB $828.

Bond coupon rate 13. The current price of a 10-year, $1,000 par value bond is $1,158.91. Interest on

this bond is paid every six months, and the nominal annual yield is 14 percent. Given these facts, what is the annual coupon rate on this bond?

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