A 40-year maturity bond has a 7% coupon rate, paid annually. It sells today for

Question

A 40-year maturity bond has a 7% coupon rate, paid annually. It sells today for $907.42. A 30-year maturity bond has a 6.5% coupon rate, also paid annually. It sells today for $919.5. A bond market analyst forecasts that in five years, 35-year maturity bonds will sell at yields to maturity of 8% and that 25-year maturity bonds will sell at yields of 7.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 6%. Calculate the annual return for the 40-year maturity bond over the next five years. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Calculate the annual return for the 30-year maturity bond over the next five years. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Which bond offers the higher expected rate of return over the five-year period? 30-year maturity bond 40-year maturity bond

Explanation / Answer

We must find out the price of both the bonds after 5 years:

Bond Value = C {[1-(1+(YTM))-t/(YTM)] + [F / (1+ (YTM))t]

40-Years Maturity Bond:
B0 =?
C = $1,000 x 7% = $70
F = $1,000
YTM = 8% (Required Return)
t = 35

Bond Value = $70 {[1-(1+(YTM))-35/(YTM)] + [$1,000 / (1+ (YTM))35] = $883

30-Years Maturity Bond:
B0 =?
C = $1,000 x 6.5% = $65
F = $1,000
YTM = 7.5% (Required Return)
t = 25

Bond Value = $65 {[1-(1+(YTM))-25/(YTM)] + [$1,000 / (1+ (YTM))25] = $889

Now, we need to calculate the value of the annual payments deposited in short-term securities at 6%.

FV = PMT (1+i) {[(1+i)n – 1] / i}

40-Years:
      = $70 (1+0.06) {[(1+0.06)5 – 1] / 0.06} = $418.27

35-Years:
       = $65 (1+0.06) {[(1+0.06)5 – 1] / 0.06} = $388.40

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