Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.9%, and sells for $1,110. Interest is paid annually. a. If the bond has a yield to maturity of 9.1% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your anser to nearest whole number.) b. What will be the annual rate of return on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.) c. Now assume that interest is paid semiannually. What will be the annual rate of return on the bond? Slightly greater than your part b answer Slightly less than your part b answer d. If the inflation rate during the year is 3%, what is the annual real rate of return on the bond? (Assume annual interest payments.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

Answer 1

a.

Price in 1 year

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =9

Bond Price =∑ [(8.9*1000/100)/(1 + 9.1/100)^k]     +   1000/(1 + 9.1/100)^9

k=1

Bond Price = 988.06

b.

rate of return = ((selling price+coupon)/purchase price-1)*100

=((988.06+89)/1110-1)*100=-2.97%

c.

Price in 1 year

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =9x2

Bond Price =∑ [(8.9*1000/200)/(1 + 9.1/200)^k]     +   1000/(1 + 9.1/200)^9x2

k=1

Bond Price = 987.89

rate of return = ((selling price+coupon)/purchase price-1)*100

=((987.89+89)/1110-1)*100=-2.98%

slightly lesser than part b

d.

Real return = ((1+nominal return)/(1+inflation rate)-1)*100

Real return=((1+-0.0297)/(1+0.03)-1)*100

Real return = -5.8