Question

3. Consider a 10% semi-annual coupon bond with a face value of $1,000 that has three years to maturity. Suppose the 6-month market interest rate is 4%.

a) What is the price of the bond today?

b) Suppose six months has passed and the market interest rate is still 4%. What is the bond’s price in six months.

c) Based on your answers to parts a and b, what is the total six-month return to holding the bond?

Answer 1

a

K = Nx2

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

k=1

K =3x2

Bond Price =∑ [(10*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^3x2

k=1

Bond Price = 1168.04

b

K = Nx2

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

k=1

K =2.5x2

Bond Price =∑ [(10*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^2.5x2

k=1

Bond Price = 1141.4

c

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

=((1141.4+50)/1168.04-1)*100

=2%