Chapter 1, Section 4

[Pages:16]Chapter 6 Section 2

1. (F11HW) Yancy purchases a 10 year zero coupon bond for 500 and will be paid 1000 at end of 10 years. Calculate the annual effective return received by Yancy.

Solution:

Remember

the

formula,

P Fra n

Cvnj .

Since this is a zero coupon bond, our formula simplifies to P Cvnj .We are given

that P=500, n=10, C=1000 and we need to find j.

500 1000v10

0.5 1 j 10 j 0.5 1/10 1 0.071773

We could also find this value using our calculator.

PV 500 N 10 FV 1000 CPT I / Y 7.1773

2. (F11HW) A 20 year bond with a par value of 10,000 will mature in 20 years for 10,500. The coupon rate is 8% convertible semi-annually. Calculate the price that Andrew would pay if he bought the bond to yield 6% convertible twice a year.

Solution:

Once again, start with

the

formula

P Fra n

Cvnj .

We are given that F 10,000 ; C 10,500 ; n 20*2 40 ; i 0.08 0.04 ; and 2

j 0.06 0.03 . We can find the coupon Fr 10,000*0.04 400 . 2

Now we can plug these values in to find P.

P

Fra n

Cv

n j

P

400

1

1.0340

10500

1.0340

0.03

P 12, 464.76

You may also use your calculator:

N 40 I / Y 3 PMT 400 FV 10500 CPT PV 12464.76

March 11, 2013

3. (F11HW) A 20 year bond with a 20,000 par value pays semi-annual coupons of 500 and is redeemable at par. Audrey purchases the bond for 21,000. Calculate Audrey's semi-annual yield to maturity on the bond.

Solution:

P

Fra n

Cvnj

We know Fr 500; C 20,000; P 21,000 .

This gives us We cannot solve this algebraically so we will solve it using our calculator.

N 40 PV 21000 PMT 500 FV 20000 CPT I / Y 2.3072

This give us i(2) 0.023072 . Our answer is 0.023072*2 4.614% convertible 2

semi-annually.

4. (F11HW) Marissa purchases 20 year bond. The bond matures for 100,000. The

bond has annual coupons. The first coupon is 1000. The second coupon is 2000. The third coupon is 3000. The coupons continue to increase until the 20th coupon

is 20,000. Marissa purchase the bond to yield an annual effective rate of 8%.

Calculate the price that Marissa pays for the bond.

Solution:

P

Fra n

Cvnj

is equivalent to

P

PV

(Coupons)

Cv

n j

.

We know n 20; C 100,000; j 0.08 .

First, let's find the present value of the coupons.

Coupons: 1000, 2000, 3000,.....,20,000. We can use the shortcut to the P,Q

formula with P=Q=1.

PV (Coupons) 1000 Ia20

a 20v20

1000

20

0.08

1000

1.08

1

1.0820

0.08

0.08

20

1.0820

78,

907.93815

Now we can find the price of the bond.

P 78,907.93815 100, 0001.0820 100,362.76 .

5. (S12HW) Siqi bought a 10 year bond four years ago. The bond matures for 100,000 which is the par value. The bond has a coupon rate of 9.2% convertible semi-annually. Siqi paid 102,000 for the bond.

March 11, 2013

Today the bond has exactly six years until maturity. Calculate the price at which Siqi could sell the bond if:

a. The bond is sold to yield the same yield that was used to when Siqi bought the bond.

b. The bond is sold to yield 8% convertible semi-annually.

Solution:

P

Fra n

Cvnj

N 10*2 20; C 100,000 ; r 0.092 0.046 ; Fr 100000(0.046) 4600 ; 2

P 102000

Using our calculator we should first solve for i.

N 20 PV 102000 PMT 4600 FV 100000 CPT I / Y 4.44693627

Keep in mind that 4.44693627 j i(2) 2

a) We now have 12 semiannual periods left until maturity.

P

Fra n

Cvnj

4600a 12

100, 000v12

101399.81 .

This

value

can

easily

be

obtained using your calculator.

2ND AMORT P1 8 P2 8 BAL 101,399.81

or

N 12 I / Y 4.446953627 PMT 4600 FV 100000 CPT PV 101399.81

b) Now we will use j 0.08 0.04 . As above we can either use 2

P

Fra n

Cvnj

4600a 12

100, 000v12

105631.04 and

just

plug

in

the

new

interest rate or use our calculator.

N 12 I / Y 4 PMT 4600 FV 100000 CPT PV 105631.04

6. (S12HW) Katherine buys a bond to yield 8% convertible semi-annually for a price of 19,001.44. The bond has a coupon rate of 7% convertible semi-annually. The bond matures for 20,000 which is its face value.

Determine how many years until the bond matures.

Solution:

P

Fra n

Cvnj where

n

denotes

the

number

of

semiannual

payments.

j 0.08 0.04; P 19,001.44 ; r 0.07 0.035 ; Fr 20000(.035) 700 ;

2

2

We need to use our calculator to find n.

PV 19001.44 I / Y 4 PMT 700 FV 20000 CPT N 13

13 semiannual periods is equal to 6.5 years.

March 11, 2013

7. (S09T2) Charles buys a 50 year bond with semi-annual coupons. The bond matures for 1000. Each semi-annual coupon is 5 during the first year. Each semi-annual coupon is 10 during the second year. The semi-annual coupon continues to increase each year until each semi-annual coupon is 250 in the 50th year.

Calculate the price that Charles should pay to receive a yield of 10% convertible semi-annually.

Solution:

P PV (Coupons) Cvnj C 1000

j 0.1 0.05 i(2) i 1.052 1 0.1025

2

2

The coupons are a series of payments whose PV is found but using the formula

that doesn't follow the rules.

PV

(Coupons)

5

a 50

0.1025

50v05.01025

1029.4078

0.05

P 1029.4078 1000v01.0005 1037.01

8. (S09T2) An 8 year bond has a par value of X. The redemption value is X+500. The bond pays quarterly coupons at a rate of 6% convertible quarterly. Jacque bought this bond for 1368.64 to yield 8% convertible quarterly. Calculate X.

Solution:

P

Fra n

Cvnj

n 8*4 32; j 0.08 0.02; P 1368.64; r 0.06 0.015; Fr 0.015X ;

4

4

C X 500

P

Fra n

Cv

n j

1368.64 0.15Xa (X 500)v32 32

X

1368.64 0.015a

500v32 v32

1250.00

32

March 11, 2013

Chapter 6, Section 3

9. (S09T2) A five year bond with a par value of 1000 pays annual coupons of 10%. The bond has a maturity value of 1200. Calculate the premium or discount when this bond is purchased to yield 9% annually. (Be sure to state whether it is a premium or a discount.)

Solution:

P

Fra n

Cvnj

Fr 0.1(1000) 100 ; n 5; j 0.09; C 1200

P

Fra n

Cv

n j

100a 5

1200v5

1168.88

This shows that we are buying it for less that maturity value which means we are

buying this at a discount.

The amount of discount= C P 1200 1168.88 31.12 .

10. (S12HW) Justin buys a bond at a discount of 500. The bond is a 15 year bond with a par value of 8,000 and a coupon rate of 6% convertible semi-annually. The bond matures for its par value.

Calculate the yield convertible twice a year on this bond.

Solution:

Using your calculator: PV 7500 N 30 PMT 240 FV 8000 CPT I / Y 3.33276923 2(3.332736923) 6.6655%convertible semiannually.

March 11, 2013

11. (S08T2) Hannah is considering buying two bonds both priced to produce the same yield rate.

The first bond is a 20 year bond with annual coupons of 500. The bond matures for 10,500. The purchase price of this bond is 7,000.

The second bond is a 15 year bond which matures for 8,000 and pays annual coupons of 100t in year t. In other words, the coupon is 100 in the first year, 200 in the second year, etc until it is 1,500 in year 15.

Calculate the amount of premium or discount in the purchase of the second bond. Be sure to state whether it is discount or premium.

Solution:

Use your calculator to find I: PV 7500 N 30 PMT 240 FV 8000 CPT I / Y 3.33276923

Use I to calculate the price of the second bond:

P 100 Ia 8000v15 15

Where

Ia

1.08210176851

1

1.0821027685115

.08210276851

15

1.0821027685115

55.44072251

15

.08210276851

P 10055.4407251 80001.0821027685115 7993.48722

8000-7993.48722=6.51 Discount

March 11, 2013

Chapter 6, Section 5

12. (F11HW) A 20 year bond with a par value of 10,000 will mature in 20 years for 10,500. The coupon rate is 8% convertible semi-annually. The bond is bought to yield 6% convertible twice a year. Determine the book value of the bond immediately after the 10 coupon is paid.

Solution:

Use your calculator to find price:

I / Y 3 N 40 PMT 400 FV 10500 CPT PV 12464.75562

Do not clear your calculator but change to N 10 and then

CPT FV 12166.03751

Now, find P

1 1.0340

P 400a 10500v40 400 40

.03

105001.0340 12464.75562

Now we can solve for the face value after the 10th coupon payment. 12464.75562 400a Cv10

10

C 12166.03752

13. (F11HW) A five year bond with a par value of 1000 will mature in 5 years for 1000. Annual coupons are payable at a rate of 6%. Calculate the Bond Amortization Schedule if the bond is bought to yield 8% annually.

Solution:

I / Y 8 N 5 PMT 60 FV 1000 CPT PV 920.1457993 Use the AMORT function on the calculator. For example, year 1 is P1 1and P2 1.

Year PRN INT

1 -13.61 73.61

2

-14.7 74.7

3 -15.88 75.88

4 -17.15 77.15

5 -18.52 78.52

Book Value 933.76 948.46 964.33 981.48 1000

March 11, 2013

14. (F11HW) Calculate the Bond Amortization Schedule if the bond in Problem 13 is bought to yield 5%.

Solution:

I / Y 5 N 5 PMT 60 FV 1000 CPT PV 1042.294767 Use the AMORT function on the calculator.

Book

Year PRN INT

Value

1

7.84 52.16 1035.46

2

8.23 51.77 1027.23

3

8.64 51.36 1018.59

4

9.07 50.93 1009.52

5

9.52 50.48 1000

15. (F11HW) A 40 year bond with a par value of 5000 is redeemable at par and pays semi-annual coupons at a rate of 7% convertible semi-annually. The bond is purchased to yield 6% convertible semi-annually. Calculate the amortization of the premium in the 61st coupon.

Solution:

I / Y 3 N 80 PMT 175 FV 5000 CPT PV 5755.019086 Use the AMORT function with P1=61 and P2=61 PRN=13.84

March 11, 2013

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