Question

Bond J has a coupon rate of 7 percent and Bond K has a coupon rate of 13 percent. Both bonds have 20 years to maturity, make semiannual payments, and have a YTM of 10 percent.

If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Percentage change in price of Bond J	%
Percentage change in price of Bond K	%

What if rates suddenly fall by 2 percent instead? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Percentage change in price of Bond J	%
Percentage change in price of Bond K	%

Answer 1

1)

Percentage change in price of Bond J

-15.99%

Percentage change in price of Bond K

-14.49%

2)

Percentage change in price of Bond J

21.33%

Percentage change in price of Bond K

18.88%

Working:

Price of bond is the present value of cash flow from bond.

If Interest rate rises by 2%

Present Price of Bond J:

Present Price of Bond K:

Present Value of Coupon Interest

$                   600.57

Present Value of Coupon Interest

$                1,115.34

Present value of face value

$                   142.05

Present value of face value

$                   142.05

Price of bond

$                   742.61

Price of bond

$                1,257.39

Working:

Working:

Semi annual interest

=

$                    1,000

x

7%

x

6/2

=

$35

Semi annual interest

=

$                    1,000

x

13%

x

6/2

=

$65

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.05)^-40)/0.05

i

=

10%/2

=

0.05

=

(1-(1+0.05)^-40)/0.05

i

=

10%/2

=

0.05

=

17.159

n

=

20*2

=

40

=

17.159

n

=

20*2

=

40

Present value of coupon interest

=

$                         35

x

17.159

=

$600.57

Present value of coupon interest

=

$                         65

x

17.159

=

$1,115.34

Present Value of face value

=

F*(1+i)^-n

Where,

Present Value of face value

=

F*(1+i)^-n

Where,

=

1000*(1+0.05)^-40

F

$1,000

=

1000*(1+0.05)^-40

F

$1,000

=

$                   142.05

i

0.05

=

$                   142.05

i

0.05

n

40

n

40

Changed Price of Bond J:

Changed Price of Bond K:

Present Value of Coupon Interest

$                   526.62

Present Value of Coupon Interest

$                   978.01

Present value of face value

$                     97.22

Present value of face value

$                     97.22

Price of bond

$                   623.84

Price of bond

$                1,075.23

Working:

Working:

Semi annual interest

=

$                    1,000

x

7%

x

6/2

=

$35

Semi annual interest

=

$                    1,000

x

13%

x

6/2

=

$65

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.06)^-40)/0.06

i

=

12%/2

=

0.06

=

(1-(1+0.06)^-40)/0.06

i

=

12%/2

=

0.06

=

15.046

n

=

20*2

=

40

=

15.046

n

=

20*2

=

40

Present value of coupon interest

=

$                         35

x

15.046

=

$526.62

Present value of coupon interest

=

$                         65

x

15.046

=

$   978.01

Present Value of face value

=

F*(1+i)^-n

Where,

Present Value of face value

=

F*(1+i)^-n

Where,

=

1000*(1+0.06)^-40

F

$1,000

=

1000*(1+0.06)^-40

F

$1,000

=

97.222

i

0.06

=

97.222

i

0.06

n

40

n

40

Change in price

=

New Price-Old Price

=

$ 623.84

-

$742.61

Change in price

=

New Price-Old Price

=

$1,075.23

-

$1,257.39

=

$-118.77

=

$ -182.15

% change in price

=

$                 -118.77

/

$742.61

% change in price

=

$                 -182.15

/

$1,257.39

=

-15.99%

=

-14.49%

If Interest rate falls by 2%

Changed Price of Bond J:

Changed Price of Bond K:

Present Value of Coupon Interest

$                   692.75

Present Value of Coupon Interest

$                1,286.53

Present value of face value

$                   208.29

Present value of face value

$                   208.29

Price of bond

$                   901.04

Price of bond

$                1,494.82

Working:

Working:

Semi annual interest

=

$                    1,000

x

7%

x

6/2

=

$35

Semi annual interest

=

$                    1,000

x

13%

x

6/2

=

$65

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.04)^-40)/0.04

i

=

8%/2

=

0.04

=

(1-(1+0.04)^-40)/0.04

i

=

8%/2

=

0.04

=

19.793

n

=

20*2

=

40

=

19.793

n

=

20*2

=

40

Present value of coupon interest

=

$                         35

x

19.793

=

$692.75

Present value of coupon interest

=

$                         65

x

19.793

=

$1,286.53

Present Value of face value

=

F*(1+i)^-n

Where,

Present Value of face value

=

F*(1+i)^-n

Where,

=

1000*(1+0.04)^-40

F

$1,000

=

1000*(1+0.04)^-40

F

$1,000

=

$                   208.29

i

0.04

=

208.289

i

0.04

n

40

n

40

Change in price

=

New Price-Old Price

=

$ 901.04

-

$742.61

Change in price

=

New Price-Old Price

=

$1,494.82

-

$1,257.39

=

$ 158.42

=

$   237.43

% change in price

=

$                  158.42

/

$742.61

% change in price

=

$                  237.43

/

$1,257.39

=

21.33%

=

18.88%