A 40-year maturity bond has a 7% coupon rate, paid annually. It sells today for
ID: 2768562 • Letter: A
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%. a-1. 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.) a-2. 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.) b. Which bond offers the higher expected rate of return over the five-year period? 40-year maturity bond 30-year maturity bondExplanation / Answer
Now let us first calculate the value of the bond with 35 years to maturity
Coupon =7% =70
N=25
=PV(8%,35,-70,-1000,0) =883.5
For the bond wth 25 year bond
the =PV(7.5%,25,-65,-1000,0)=888.5
Price after 5 years
Return can be calculated as follows
First for the bond with 40 years maturity
Initial price = 907.5
Final price =883.5
Coupons reinvested will become = 70*(1.06)^4 +70*(1.06)^3 + ....70 =394.60
So In final price we can add the future value of coupns =394.60
Final pricew =883.5+394.60 =1278.1
returns = 907.42*(1+r)^5=1278.1
r=7.08
For the 30 year bond
Initial Price = 919.5
Final Price = 883.5
Future value of coupons =366.5
Add the above figure to final price =366.5+ 883.5
=1250
1250 = 919.5*(1+r)^5
r =6.33%
Hence bond woth forty years to maturity offers higher returns
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