Question

You are considering an investment in two different bonds. One bond matures in nine years and has a face value of $1,000. The bond pays an annual coupon of 3% and has a 4.5% yield to maturity. The other bond is an 8-year zero coupon bond with a face value of $1,000 and has a yield to maturity of 4.5%. Assume that you plan on holding the coupon bond for nine years and reinvesting all the coupons when they are received at the going interest rate (which is the yield to maturity). Assume that after the zero matures you invest in a 1-year security that earns the going interest rate.

(10 points) Set up a table where you show what happens to the value of each investment (zero and coupon bond) over time if the yield to maturity remains at 4.5%. Specifically, show what the cumulative value of each investment (including the value of the reinvested coupons for the coupon bond) would be at the end of each of the next nine years. For example, at the end of Year 1, you would calculate the value of the coupon bond (with one year less remaining until maturity) and you would receive the interest coupon payment. However, no interest would be earned on that interest coupon payment in Year 1.

Answer 1

Coupon bond

Value of bond at end of each year is calculated using PV function in Excel :

rate = 4.5% (YTM of bond)

nper = Years remaining until maturity

pmt = -1000 * 3% (Annual coupon payment = face value * coupon rate. This is entered with a negative sign because it is a payment from the bond)

fv = 1000 (Face value receivable on maturity. This is entered with a negative sign because it is a payment from the bond)

Value of investment at end of each year = value of bond at end of each year + accumulated value of coupon payments

accumulated value of coupon payments at end of each year is calculated using FV function in Excel :

rate = 4.5% (YTM of bond. The coupons are reinvested at this rate)

nper = number of coupon payments received

pmt = 1000 * 3% (Annual coupon payment = face value * coupon rate. This is entered with a negative sign because we are calculating the FV)

Zero Coupon bond

value of zero coupon bond = face value / (1 + YTM)^{years to maturity}

The value of the zero coupon bond is calculated in this way at the end of years 1 to 9.

Value of the zero coupon bond investment at end of year 9 = face value * (1 + YTM)¹

А Value of Value of zero coupon coupon 1 Year investment investment $931.06 $734.83 $972.96 $767.90 3 $1,016.74 $802.45 $1,062.50 $838.56 5 $1,110.31 $876.30 6 $1,160.27 $915.73 7 $1,212.48 $956.94 8 $1,267.05 $1,000.00 9 $1,324.06 $1,045.00

ДА 1 Year Value of coupon investment 21 =PV(4.5%,9-A2,-1000*3%,-1000) +FV (4.5%,A2,-1000*3%) 32 =PV(4.5%,9-A3,-1000*3%,-1000)+FV (4.5%,A3,-1000*3%) 43 =PV(4.5%,9-A4,-1000*3%,-1000) +FV (4.5%,A4,-1000*3%) 5 4 =PV(4.5%,9-A5,-1000*3%,-1000)+FV (4.5%,A5,-1000*3%) =PV(4.5%,9-A6,-1000*3%,-1000) +FV(4.5%,A6,-1000*3%) 76 =PV (4.5%,9-A7,-1000*3%,-1000) +FV(4.5%, A7,-1000*3%) 87 =PV (4.5%,9-A8,-1000*3%,-1000) +FV(4.5%, A8,-1000*3%) 9 8 =PV(4.5%,9-A9,-1000*3%,-1000)+FV (4.5%,A9,-1000*3%) 10 9 =PV(4.5%,9-A10,-1000*3%,-1000) +FV(4.5%,A10,-1000*3%) Value of zero coupon investment =1000/(1+4.5%)^(8-A2) =1000/(1+4.5%)^(8-A3) =1000/(1+4.5%)^(8-A4) =1000/(1+4.5%)^(8-45) =1000/(1+4.5%)^(8-46) =1000/(1+4.5%)^(8-A7) =1000/(1+4.5%)^(8-48) =1000/(1+4.5%)^(8-49) =C9*(1+4.5%)