Question

The Sheridan Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 10.325 percent. The current market rate for similar securities is 11.8 percent. Assume that the face value of the bond is $1,000.

Suppose the bond were to mature in 12 years. What will be the bond’s price if rates in the market

(i) decrease to 9.80 percent or

(ii) increase to 12.8 percent?

Answer 1

i.Information provided:

Face value= future value= $1,000

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

Coupon rate= 10.325%/2= 5.1625%

Coupon payment= 0.051625*1,000= $51.6250

Yield to maturity= 9.80%/2= 4.90% per semi-annual period

The price of the bond is computed by calculating the present value.

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

FV= 1,000

N= 24

PMT= 51.625

I/Y= 4.90

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

The value obtained is 1,036.58.

Therefore, the price of the bond when the market rate is 9.80 is $1,036.58.

ii. Information provided:

Face value= future value= $1,000

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

Coupon rate= 10.325%/2= 5.1625%

Coupon payment= 0.051625*1,000= $51.6250

Yield to maturity= 12.80%/2= 6.40% per semi-annual period

The price of the bond is computed by calculating the present value.

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

FV= 1,000

N= 24

PMT= 51.625

I/Y= 6.40

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

The value obtained is 850.27.

Therefore, the price of the bond when the market rate is 12.8 is $850.27.

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