Question

Kim Shaw is considering the purchase of a 5 year bond that pays a coupon rate of 7.75% over the life of the bond (annual payments) and a face value of $1000 that is returned at the bond's maturity. Using a yield to maturity of 8.50%, calculate to the nearest penny the value of the bond today.

Answer 1

Time = t = 5 years

Coupon rate = 7.75%

Face value = fv = $1000

Yield to maturity = r = 8.50%

Coupon = c = fv * coupon rate

              = 1000*0.0775

             = $77.50

 

Bond price = (c * (1-(1/(1+r)^t)) / r) + (fv / (1+r)^t)

                    = (77.50 * (1-(1/(1+0.085)^5)) /0.085) + (1000/(1+0.085)^5)

                   = (77.50 * 0.334954577 / 0.085) + (1000 / 1.50365669)

                   = 305.399761 + 665.045423

                   = 970.445184

                   = $970.45

 

Thus, the value of bond today is $970.45.

Thus, the value of bond today is $970.45.