Chap 010

Chapter 10: Valuation and Rates of Return

Chapter 10 Valuation and Rates Rate s of Return 1.

Bond value (LO3) The Lone Star Company has $1,000 par value bonds outstanding at 9 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is: a.

6 percent.

b.

8 percent.

c.

12 percent. A

B

C

FV

$1000

$1000

$1000

PMT

90

90

90

N

20

20

20

I

6

8

12

PV

$1344.10

$1098.18

$775.92

3.

Bond value (LO3) Barry’s Steroids Company has $1,000 par value bonds outstanding at 12 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is: a

.

b.

4 percent. 14 percent. A

B

FV

$1000

$1000

PMT

120

120

N

50

50

I

4

14

PV

$2718.57

$857.35

10-1

Chapter 10: Valuation and Rates of Return

5.

Bond value (LO3) Essex Biochemical Co. has a $1,000 par value bond outstanding that pays 10 percent annual interest. The current yield to maturity on such bonds in the market is 7 percent. Compute the price of the bonds for these maturity dates: a

.

30 years.

b.

15 years.

c.

1 year. A

B

C

FV

$1000

$1000

$1000

PMT

100

100

100

N

30

15

1

I

7

7

7

PV

$1372.27

$1273.24

$1028.04

10-2

Chapter 10: Valuation and Rates of Return

6.

Bond value (LO3) The Hartford Telephone Company has a $1,000 par value bond outstanding that pays 11 percent annual interest. The current yield to maturity on such bonds in the market is 14 percent. Compute the price of the bonds for these maturity dates: a

.

30 years.

b.

15 years.

c.

1 year.

7. Bond maturity effect (LO3) For problem 6 graph the relationship in a manner similar to the bottom half of Figure 10-2. Also explain why the pattern of price change takes place. A

B

C

FV

$1000

$1000

$1000

PMT

110

110

110

N

30

15

1

I

14

14

14

PV

$789.92

$815.73

$973.68

11% Bond, $1,000 Par Value

Bond Value $1,000 900 800 700 30

25

15

5

Years

As the time to maturity becomes less and less, the importance of  the difference between the rate the bond pays and the yield to maturity becomes less significant. Therefore, the bond trades closer to par value.

10-3

0

Chapter 10: Valuation and Rates of Return

9.

Interest rate effect (LO3) Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) increase from 9 to 12 percent. a

.

What is the bond price at 9 percent?

b.

What is he bond price at 12 percent?

c.

What would be your percentage loss on the investment if you bought when rates were 9 percent and sold when rates were 12 percent? A

B

FV

$1000

$1000

PMT

100

110

N

20

15

I

9

12

PV

$1091.29

$850.61

10-4

($240.68) or 22.05%

Chapter 10: Valuation and Rates of Return

11.

Effect of maturity on bond price (LO3) Using Table 10-2: a

.

Assume the interest rate in the market (yield to maturity) goes down to 8 percent for the 10 percent bonds. Using column 2, indicate what the bond price will be with a 5-year, a 15-year, and a 30-year time period.

b.

Assume the interest rate in the market (yield to maturity) goes up to 12 percent for the 10 percent bonds. Using column 3, indicate what the bond price will be with a 5-year, a 10-year, and a 30-year period.

c.

Based on the information in part a, if you think interest rates in the market are going down, which bond would you choose to own?

d .

Based on information in part b, if you think interest rates in the market are going up, which bond would you choose to own?

A FV

$1000

$1000

$1000

PMT

100

100

100

N

5

15

30

I

8

8

8

PV

$1079.85

$1171.19

$1225.16

FV

$1000

$1000

$1000

PMT

100

100

100

N

5

15

30

I

12

12

12

PV

$927.90

$863.78

$838.90

B

c. Based on information in Part a, you would want to own the longest-term bond possible to maximize your gain. d. Based on information in Part b, you would want to own the shortest-term bond possible to minimize your loss.

10-5

Chapter 10: Valuation and Rates of Return

13.

Effect of yield to maturity on bond price (LO3) Tom Cruise Lines, Inc., issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 12 percent. This return was in line with the required returns by bondholders at that point as described below: Real rate of return ............ Inflation premium ............ Risk premium................... Total return...................

3% 5 4 12%

Assume that five years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 20 years remaining until maturity. Compute the new price of the bond. A FV

$1000

PMT

120

N

25-5=20

I

10

PV

$1170.27

10-6

Chapter 10: Valuation and Rates of Return

15.

Effect of yield to maturity on bond price (LO2 & 3) Media Bias, Inc. issued bonds 10 years ago at $1,000 per bond. These bonds had a 35-year life when issued and the annual interest payment was then 10 percent. This return was in line with the required returns by bondholders at that point in time as described below: Real rate of return ............ Inflation premium ............ Risk premium................... Total return...................

2% 4 4 10%

Assume that 10 years later, due to good publicity, the risk premium is now 2 percent and is appropriately reflected in the required return (or yield to maturity) of  the bonds. The bonds have 25 years remaining until maturity. Compute the new price of the bond. A FV

$1000

PMT

100

N

35-10=25

I

8

PV

$1213.50

10-7

Chapter 10: Valuation and Rates of Return

17.

Deep discount bonds (LO3) Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below part value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 16 years remaining to maturity. The current yield to maturity on similar bonds is 10 percent. a What is the current price of the bonds? b. By what percent will the price of the bonds increase between now and maturity? c. What is the annual compound rate of growth in the value of the bonds? (An approximate answer is acceptable.) .

A

C

FV

$1000

$1000.00

PMT

40

0

N

16

16

I

10

4.04%

PV

$530.58

$530.58

b. Percent increase at maturity Maturity Value Current price Dollar increase

$1,000.00 – 530.58 $ 469.42

Percent Increase = 469.42 / 530.58 = 88.47%

10-8

Chapter 10: Valuation and Rates of Return

19.

Approximate yield to maturity (LO3) Bonds issued by the Tyler Food Corporation have a par value of $1,000, are selling for $1,080, and have 20 years remaining to maturity. The annual interest payment is 12.5 percent ($125). Compute the approximate yield to maturity, using Formula 10-2.

FV

$1000.00

PMT

125

N

20

I

11.46

PV

-$1080.00

21.

Bond value––semiannual analysis (LO3) Heather Smith is considering a bond investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual interest rate of 9 percent and the interest is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 15 years to maturity. Compute the price of the bonds based on semiannual analysis.

FV

$1000.00

PMT

90 / 2 = 45

N

15 *2 =30

I

12 / 2 =6

PV

$793.53

10-9