Question

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 8.5%, has a YTM of 7%, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7%, has a YTM of 8.5%, and has 13 years to maturity. What is the price of each bond today? If interest rates are unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years? Illustrate your answers by graphing bond prices versus time to maturity

Answer 1

To calculate the price of the bond, we use PV function in Excel with these inputs :

rate = YTM per period (for semiannual bond, divide the annual YTM by 2)

nper = number of periods (for semiannual bond, multiply the number of years left to maturity with 2)

pmt = coupon payment per period (for semiannual bond, coupon payment per period = face value * coupon rate / 2)

fv = face value (the face value of the bond receivable on maturity)

In this question, the face value is not given. We will assume its $100

Price of Bond X today =PV(7%/2,13*2,100*8.5%/2,100) ==> $112.67

Price of Bond Y today =PV(8.5%/2,13*2,100*7%/2,100) ==> $88.33

To calculate the price 1 year from now, the formula remains the same except for nper which is changed to 12*2

Price of Bond X 1 year from now =PV(7%/2,12*2,100*8.5%/2,100) ==> $112.04

Price of Bond Y 1 year from now =PV(8.5%/2,12*2,100*7%/2,100) ==> $88.85

To calculate the price 3 years from now, the formula remains the same except for nper which is changed to 10*2

Price of Bond X 3 years from now =PV(7%/2,10*2,100*8.5%/2,100) ==> $110.66

Price of Bond Y 3 years from now =PV(8.5%/2,10*2,100*7%/2,100) ==> $90.03

To calculate the price 8 years from now, the formula remains the same except for nper which is changed to 5*2

Price of Bond X 8 years from now =PV(7%/2,5*2,100*8.5%/2,100) ==> $106.24

Price of Bond Y 8 years from now =PV(8.5%/2,5*2,100*7%/2,100) ==> $93.99

To calculate the price 12 years from now, the formula remains the same except for nper which is changed to 1*2

Price of Bond X 12 years from now =PV(7%/2,1*2,100*8.5%/2,100) ==> $101.42

Price of Bond Y 12 years from now =PV(8.5%/2,1*2,100*7%/2,100) ==> $98.59

To calculate the price 13 years from now, the formula remains the same except for nper which is changed to 0*2

Price of Bond X 13 years from now =PV(7%/2,0*2,100*8.5%/2,100) ==> $100.00

Price of Bond Y 13 years from now =PV(8.5%/2,0*2,100*7%/2,100) ==> $100.00