Question

 ​(Bond valuation) A bond that matures in 20 years has a ​$1,000 par value. The annual coupon interest rate is 7 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 13 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually?

Answer 1

1.Value of the bond if interest is paid annually:

Future value= $1,000

Time= 20 years

Yield to maturity= 13%

Coupon interest= 7%

Coupon payment= 0.07*1,000= $70

The value of the bond is calculated using a financial calculator.

The below has to be entered in the financial calculator:

FV= 1,000; N= 20; I/Y= 13; PMT= 70

Press CPT and PV to calculate the value of the bond.

The value of the bond is $578.51.

2. Value of the bond if interest is paid annually:

Future value= $1,000

Time= 20 years*2= 40 semi-annual periods

Yield to maturity= 13%/2= 6.50%

Coupon interest= 7%/2= 3.50%

Coupon payment= 0.035*1,000= $35

The value of the bond is calculated using a financial calculator.

The below has to be entered in the financial calculator:

FV= 1,000; N= 40; I/Y= 6.50; PMT= 35

Press CPT and PV to calculate the value of the bond.

The value of the bond is $575.63.