Bond J has a coupon rate of 4 percent and Bond K has a coupon rate of 10 percent. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 7 percent

Bond J has a coupon rate of 4 percent and Bond K has a coupon rate of 10 percent. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 7 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	%

 

Explanation:

Initially, at a YTM of 7 percent, the prices of the two bonds are:

PJ	=	$20(PVIFA3.50%,36)	+	$1,000(PVIF3.50%,36)	=	$695.64
PK	=	$50(PVIFA3.50%,36)	+	$1,000(PVIF3.50%,36)	=	$1,304.36

If the YTM rises from 7 percent to 9 percent:

PJ	=	$20(PVIFA4.50%,36)	+	$1,000(PVIF4.50%,36)	=	$558.35
PK	=	$50(PVIFA4.50%,36)	+	$1,000(PVIF4.50%,36)	=	$1,088.33

The percentage change in price is calculated as:

Percentage change in price = (New price – Original price) / Original price

ΔPJ%	=	($558.35 – 695.64) / $695.64	=	– 19.74%
ΔPK%	=	($1,088.33 – 1,304.36) / $1,304.36	=	– 16.56%

If the YTM declines from 7 percent to 5 percent:

PJ	=	$20(PVIFA2.50%,36)	+	$1,000(PVIF2.50%,36)	=	$882.22
PK	=	$50(PVIFA2.50%,36)	+	$1,000(PVIF2.50%,36)	=	$1,588.91

ΔPJ%	=	($882.22 – 695.64) / $695.64	=	+ 26.82%
ΔPK%	=	($1,588.91 – 1,304.36) / $1,304.36	=	+ 21.82%

All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates.

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Initially, at a YTM of 7 percent, the prices of the two bonds are:

PJ

Enter

36

7% / 2

$40 / 2

$1,000

N

I/Y

PV

PMT

FV

Solve for

$695.64

PK

Enter

36

7% / 2

$100 / 2

$1,000

N

I/Y

PV

PMT

FV

Solve for

$1,304.36

If the YTM rises from 7 percent to 9 percent:

PJ

Enter

36

9% / 2

$40 / 2

$1,000

N

I/Y

PV

PMT

FV

Solve for

$558.35

ΔPJ% = ($558.35 – 695.64) / $695.64 = – 19.74%

PK

Enter

36

9% / 2

$100 / 2

$1,000

N

I/Y

PV

PMT

FV

Solve for

$1,088.33

ΔPK% = ($1,088.33 –1,304.36) / $1,304.36 = – 16.56%

If the YTM declines from 7 percent to 5 percent:

PJ

Enter

36

5% / 2

$40 / 2

$1,000

N

I/Y

PV

PMT

FV

Solve for

$882.22

ΔPJ% = ($882.22 – 695.64) / $695.64 = + 26.82%

PK

Enter

36

5% / 2

$100 / 2

$1,000

N

I/Y

PV

PMT

FV

Solve for

$1,588.91

ΔPK% = ($1,588.91 – 1,304.36) / $1,304.36 = + 21.82%

All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates.