Question

Consider a bond (with par value = $1,000) paying a coupon rate of 9% per year semiannually when the market interest rate is only 7% per half-year. The bond has three years until maturity.

a. Find the bond's price today and six months from now after the next coupon is paid. (Round your answers to 2 decimal places.)

b. What is the total (six-month) rate of return on the bond? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Answer 1

Par Value = $1000

Semi-annual Coupon Payment = $1000*9%*1/2 = $45

Semi-annual YTM = 7%*1/2 = 3.5%

No of years to maturuty = 3

n = 3yrs*2 = 6

- Calculating the Price of the Bond Today:-

Price = $ 239.785 + $ 813.501

Price(P0) = $ 1053.29

So, price of bond today is $ 1053.29

- Now calculating the Price of the Bond 6 months after the next coupon is paid :-

now, after 1 coupon payment(after 6 months),n will be 5

Price = $ 203.18 + $ 841.97

Price(P1) = $ 1045.15

So, price of bond 6 months from now after coupon is paid is $ 1045.15

b). Total return on Bond = [(Price 6 months from now - Current Price) + Coupon Income]/Current Price

= [(1045.15 - 1053.29)+45]/1053.29

= 3.50%

So, Total(6-month) return is 3.50%

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