Question

A $1,000 face value has a 7% annual coupon rate. The next coupon is due in one year and the bond matures in 17 years. The current YTM on the bond is 4.6%. What is the dollar value of the price change if the bond's YTM increases to 5.9%? Round to the nearest cent. ​[Hint: 1) If the price drops, the change is a negative number. 2) Do not compute duration. You can calculate the precise impact of a yield change on the bond's price by comparing the prices under the two scenarios.] --> please show how to do this by hand

Answer 1

Compute the change in the price of the bond due to change in yield, using the equation as shown below:

Change in price = Price at 4.6% yield – Price at 5.9% yield

                          = $1,278.87 - $1,116.08

                          = $162.79

Hence, the price of the bond is decreased by $162.79 if the bond yield changed to 5.9%.

Working notes:

a.

Compute the PVIF at 4.6% and 17 years, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.046)¹⁷

         = 1/ 2.1480

         = 0.4655

Hence, the PVIF at 4.6% and 17 years is 0.4655.

b.

Compute the PVIFA at 4.6% and 17 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.046)^-17}/ 4.6%

            = (1 – 0.4655)/ 4.6%

            = 11.6196

Hence, the PVIFA at 4.6% and 17 years is 11.6196.

(c)

Compute the price of the bond at 4.6% yield, using the equation as shown below:

Bond Price = (Interest*PVIFA_{4.6%, 17 years}) + (Face value*PVIF_{4.6%, 17 years})

                   = ($1,000*7%*11.6196) + ($1,000*0.4655)

                   = $1,278.87

Hence, the price of the bond is $1,278.87.

d.

Compute the PVIF at 5.9% and 17 years, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.059)¹⁷

         = 1/ 2.6499

         = 0.3774

Hence, the PVIF at 5.9% and 17 years is 0.3774.

e.

Compute the PVIFA at 5.9% and 17 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.059)^-17}/ 5.9%

            = (1 – 0.3774)/ 5.9%

            = 10.5525

Hence, the PVIFA at 5.9% and 17 years is 10.5525.

f.

Compute the price of the bond at 5.9% yield, using the equation as shown below:

Bond Price = (Interest*PVIFA_{5.9%, 17 years}) + (Face value*PVIF_{5.9%, 17 years})

                   = ($1,000*7%*10.5525) + ($1,000*0.3774)

                   = $1,116.08

Hence, the price of the bond is $1,116.08.