Question

1. A 3-year annual coupon bond has a yield to maturity of 8%, coupon rate of 5%. The face value of the bond is $1,000.

a. What is the price of the bond? Is it premium bond or discount bond?

b. Suppose one year later immediately after you receive the first coupon payment, the yield to maturity drops to 7%. What would be your holding period return if you decide to sell the bond at the market price then?

c. Repeat part a and b for a 10-year bond. Everything else remains the same, except the change in the term of the bond from 3 year to 10 year.

Answer 1

Price=Coupon rate*Par value/yield*(1-1/(1+yield)^t)+Par value/(1+yield)^t

a)
=5%*1000/8%*(1-1/1.08^3)+1000/1.08^3=922.687090382564

This is a discount bond as price is less than par

b)
=(5%*1000+5%*1000/7%*(1-1/1.08^2)+1000/1.08^2)/(5%*1000/8%*(1-1/1.08^3)+1000/1.08^3)-1=9.38049025102505%

c)
a)
=5%*1000/8%*(1-1/1.08^10)+1000/1.08^10=798.697558031757

This is a discount bond as price is less than par

b)
=(5%*1000+5%*1000/7%*(1-1/1.08^9)+1000/1.08^9)/(5%*1000/8%*(1-1/1.08^10)+1000/1.08^10)-1=13.5866738900079%