Question

A bond with a $1,000 par, 6 years to maturity, a coupon rate of 4%, and annual payments has a yield to maturity of 3.6%. What will be the actual percentage change in the bond price if the yield changes instantaneously to 4.3%? Round to the nearest 0.001%, drop the % symbol (e.g., if your answer is, e.g., 1.1234%, enter it as 1.123.)

Answer 1

Price of the bond at a yield to maturity of 3.6%.

Information provided:

Face value= future value= $1,000

Time= 6 years

Coupon rate= 4%

Coupon payment= 0.04*1,000= $40

Yield to maturity= 3.6%

The price of the bond at YTM of 3.6% is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 40

I/Y= 3.6

N= 6

Press the CPT key and PV to compute the present value.

The value obtained is 1,021.24.

Therefore, the price of the bond at YTM of 3.6% is $1,021.24.

Price of the bond at a yield to maturity of 4.3%.

Information provided:

Face value= future value= $1,000

Time= 6 years

Coupon rate= 4%

Coupon payment= 0.04*1,000= $40

Yield to maturity= 4.3%

The price of the bond at YTM of 4.3% is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 40

I/Y= 4.3

N= 6

Press the CPT key and PV to compute the present value.

The value obtained is 984.43.   

Therefore, the price of the bond at YTM of 4.3% is $984.43.

Hence, the percentage change in the bond price is:

= $984.43 - $1,021.24 / $1,021.24

= $36.81 / $1,021.24

= 0.0360*100

= 3.6044%.

Therefore, there was a 3.6044% decrease in the price of the bond if the yield changes to 4.3%.

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