A 30-year maturity bond has a 4.9% coupon rate, paid annually. It sells today for $872.42. A 20-year maturity bond has a 4.4% coupon rate, also paid annually. It sells today for $899.5. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 5.9% and 15-year maturity bonds will sell at yields of 5.4%. Because the yield curve is upward sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 6.1%. a. Calculate the (annualized) expected rate of return of the 30-year bond over the 5-year period. (Round your answer to 2 decimal places.)

The annualized rate if return is 5.64%

Explanation:

In calculating the annualized expected return on the bond, I set up a table in excel in order to calculate the sum of cash flows that would been received from the bond in five years coupled with the fact that the inflow from the bond on yearly basis can be reinvested at 6.1% on yearly basis.

Note that the coupon payment received at end of the year can be reinvested for 4 years, the one on year can be reinvested for 3 years and so on.

Then the amount of the inflow in year 5 is the sum of the coupon and the market price of the bond calculated as $870.94  

We can then compute annualized rate of return from the below fv formula:

FV=PV*(1+r)^N

where FV is $ 1,147.71  

PV is the cost of bond at ($872.42)

r is the rate of return that is unknown

N is 5 years period

$ 1,147.71  =872.42*(1+r)^5

$ 1,147.71 /$872.42=(1+r)^5

divide the reciprocal of each side by 5

($1,147.71/$872.42)^(1/5)=1+r

r=  ($1,147.71/$872.42)^(1/5)-1

=5.64%

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