Question

Calculate the price change for a 1-percent decrease in market yield for the following bond: par = $1,000; coupon rate = 7 percent, paid semi-annually; market yield = 7 percent; term to maturity = 9 years. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and the final answer to 4 decimal places, e.g. 1,564.2556.)

Change in price

$

Answer 1

Before the price change

Information provided:

Par value= future value= $1,000

Time= 9 years*2= 18 semi-annual periods

Coupon rate= 7%/2= 3.50%

Coupon payment= 0.035*1,000= $35 per semi-annual period

Yield to maturity= 7%/2= 3.50%

The price of the bond is calculated by computing the present value.

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

FV= 1,000

N= 18

PMT= 35

I/Y= 3.5

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

The value obtained is 1,000.

Therefore, the price of the bond is $1,000.

After the price change

Information provided:

Par value= future value= $1,000

Time= 9 years*2= 18 semi-annual periods

Coupon rate= 7%/2= 3.50%

Coupon payment= 0.035*1,000= $35 per semi-annual period

Yield to maturity= 7% - 1%= 6%/2= 3% per semi-annual period

The price of the bond is calculated by computing the present value.

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

FV= 1,000

N= 18

PMT= 35

I/Y= 3

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

The value obtained is 1,068.77.

Therefore, the price of the bond is $1,068.77.

Change in price= $1,068.77 - $1,000

                              = $68.77.

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