Question

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?
	40-year maturity bond 30-year maturity bond

Answer 1

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