Question

You own a 6.5 percent, semiannual coupon bond that matures in 12 years. The par value is $1,000 and the current yield to maturity is 6.4 percent. What will the percentage change in the price of your bond be if the yield to maturity suddenly increases by 25 basis points?

		-2.04 percent
		-2.11 percent
		-2.31 percent
		-2.44 percent
		-2.26 percent

Answer 1

Information provided:

Par value= future value= $1,000

Time= 12 years*2= 24 semi-annual periods

Coupon rate= 6.5%/2= 3.25%

Coupon payment= 0.0325*1,000= $32.50

Yield to maturity= 6.4%/2= 3.2%

First, the price of the bond before the increase in the yield to maturity needs to be calculated.

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= 24

PMT= 32.50

I/Y= 3.2

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

The value obtained is 1,008.29.

Therefore, the price of the bond is $1,008.29.

Next, the price of the bond after the increase in the yield to maturity needs to be calculated.

Yield to maturity= 6.4% + 0.25%= 6.65%/2= 3.3250%

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

FV= 1,000

N= 24

PMT= 32.50

I/Y= 3.3250

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

The value obtained is 987.73.

Therefore, the price of the bond after the yield to maturity increases by 25 basis points is $987.73.

Change in the price of the bond= $987.73 - 1,008.29/ 1,008.29*100

                                                            = -$20.5582/$1,008.29*100

                                                            = -0.0204*100

                                                            = -2.04%.

Hence, the answer is option a.

In case of any query, kindly comment on the solution.