Question

and 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

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of Bond X is calculated using PV function in Excel :

rate = 7%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 13 * 2 (18 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8.5% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,126.68

A1 x Foc =PV(7%/2,13*2,1000*8.5%/2, 1000) B C D E F G A ($1,126.68)! 1

Price of Bond Y is calculated using PV function in Excel :

rate = 8.5%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 13 * 2 (18 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 7% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $883.33

Al X f =PV(8.5%/2,13*2,1000*7%/2, 1000) ($883.33)!

The prices of both bonds at each time is calculated in the same way above. Only the input for "nper" is changed as per the time left to maturity

с А в Years to 1 Maturity Bond X $1,126.68 12 $1,120.44 11 $1,113.75 10 $1,106.59 9 $1,098.92 $1,090.71 т $1,081.90 $1,072.48 5 $1,062.37 4 $1,051.55 3 $1,039.96 2 $1,027.55 1 $1,014.25 о $1,000.00 8 Bond Y $883.33 $888.52 $894.16 $900.29 $906.96 $914.20 $922.07 $930.62 $939.92 $950.02 $961.00 $972.94 $985.90 $1,000.00

A Years to 1 2 13 4 11 5 10 69 7 8 8 7 Bond X =PV(7%/2, A2*2,1000*8.5%/2,1000)*-1 =PV(7%/2,A3*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A4*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A5*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A6*2,1000*8.5%/2,1000)*-1 =PV(7%/2,A7*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A8*2,1000*8.5%/2,1000)*-1 =PV(7%/2,19*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A10*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A11*2,1000*8.5%/2,1000)*-1 =PV(7%/2,A12*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A13*2,1000*8.5%/2,1000)*-1 =PV(7%/2,A14*2,1000*8.5%/2,1000)*-1 =PV(7%/2, A15*2,1000*8.5%/2,1000)*-1 Bond Y =PV(8.5%/2, A2*2,1000*7%/2,1000)*-1 =PV(8.5%/2,A3*2,1000*7%/2, 1000)*-1 =PV(8.5%/2, A4*2,1000*7%/2, 1000)*-1 =PV(8.5%/2, A5*2,1000*7%/2, 1000)*-1 =PV(8.5%/2, A6*2,1000*7%/2,1000)*-1 =PV(8.5%/2,A7*2,1000*7%/2, 1000)*-1 =PV(8.5%/2,A8*2,1000*7%/2, 1000)*-1 =PV(8.5%/2,99*2,1000*7%/2, 1000)*-1 =PV(8.5%/2, A10*2,1000*7%/2,1000)*-1 =PV(8.5%/2, A11*2,1000*7%/2, 1000)*-1 =PV(8.5%/2,A12*2,1000*7%/2,1000)*-1 =PV(8.5%/2,A13*2,1000*7%/2,1000)*-1 =PV(8.5%/2,A14*2,1000*7%/2,1000)*-1 =PV(8.5%/2, A15*2,1000*7%/2,1000)*-1 O 10 5 114 12 3 13 2 14 1 N 15 0 O

Years to maturity Vs. Bond Price $1,200.00 $1,000.00 $800.00 Bond Price $600.00 $400.00 $200.00 $0.00 1 2 3 4 5 10 11 12 13 14 6 7 8 9 Years to maturity - Bond X — Bond Y