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Homework answers / question archive / A 40-year maturity bond has a 8% coupon rate, paid annually
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A 40-year maturity bond has a 8% coupon rate, paid annually. It sells today for $957.42. A 30-year maturity bond has a 7.5% coupon rate, also paid annually. It sells today for $969.50. A bond market analyst forecasts that in five years, 35-year maturity bonds will sell at yields to maturity of 9% and that 25-year maturity bonds will sell at yields of 8.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 7%. |
| a-1. |
Calculate the annual rate of return for the 40-year maturity bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
| Annual rate of return | % |
| a-2. |
Calculate the annual rate of return for the 30-year maturity bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
| Annual rate of return | % |
| b. | Which bond offers the higher expected rate of return over the five-year period? | ||||
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Answer : (a-1) Calculation of Annual Rate of Return of 40-year maturity Bond :
Maturity of the 40-year bond to be taken as 35 years, Therefore Yield will be 9%.
Now we need to calculate Price after 5 years of 40-year Bond
using PV function of Excel
=PV(rate,nper,pmt,fv)
where
rate is the yield to maturity i.e 9%
nper is the years to maturity i.e 35
pmt is the periodic coupon payment i.e 80(1000 * 8%)
Fv is the face value i.e 1000
Price after 5 years will be 894.33
Given Coupons will be reinvested at the rate of 7% ,
Using FV function of Excel :
=FV(rate,nper,pmt,pv)
where
rate is the yield to maturity i.e 7%
nper is the years to maturity i.e 5
pmt is the periodic coupon payment i.e 80(1000 * 8%)
pv is the face value i.e 0
Future Value of Coupon is 460.06
Total proceeds = 460.06 + 894.33
= 1354.39
Return for 5 year = (1354.39 / 957.42) - 1 = 1.4146257 - 1
= 0.4146257 or 41.46257%
Annual rate of return is= (1 + rate)^(1/5) – 1
= (1.4146257)^(1/5) - 1
= 0.0718359 or 7.18%
(a-2) Calculation of Annual Rate of Return of 30-year maturity Bond :
Maturity of the 30-year bond to be taken as 25 years, Therefore Yield will be 8.5%.
Now we need to calculate Price after 5 years of 25-year Bond
using PV function of Excel
=PV(rate,nper,pmt,fv)
where
rate is the yield to maturity i.e 8.5%
nper is the years to maturity i.e 25
pmt is the periodic coupon payment i.e 75(1000 * 7.5%)
Fv is the face value i.e 1000
Price after 5 years will be 897.66
Given Coupons will be reinvested at the rate of 7% ,
Using FV function of Excel :
=FV(rate,nper,pmt,pv)
where
rate is the yield to maturity i.e 7%
nper is the years to maturity i.e 5
pmt is the periodic coupon payment i.e 75(1000 * 7.5%)
pv is the face value i.e 0
Future Value of Coupon is 431.31
Total proceeds = 431.31 + 897.66
= 1328.96
Return for 5 year = (1328.96 / 969.5) - 1 = 1.370772066 - 1
= 0.370772066 or 37.0772066%
Annual rate of return is= (1 + rate)^(1/5) – 1
= (1.370772066)^(1/5) - 1
= 0.065106535 or 6.51%
(b.) 40-year maturity bond will have higher expected return over 5 year
