Problem
Consider 3 Treasury bonds which pay semi-annual coupons. Each bond has a face value of $1,000. Bond A has 5 years remaining to maturity and a coupon rate of 10%. Bond B has 20 years remaining to maturity and a coupon rate of 10%, and Bond C has 20 years remaining to maturity and a coupon rate of 4%.
A. If all bonds provided a 10% return (APR, compounded semiannually) if they were purchased today and held to maturity, what is the price today of each of the bonds?
B. What is the price of each bond if the YTM was 4%? What if it was 16%?
C. Using Excel, create a single graph showing the price of Bonds A & B for varying YTMs. Let YTM range from 0.5% to 18% per year (compounded semi-annually) in increments of 50 basis points. Is the graph linear? If not, what shape is it? Does a change in YTM affect the price of each of the two bonds the same way? Why or why not?
D. Create a similar graph for Bonds B & C. Is the graph linear? If not, what shape is it? Does a change in YTM affect the price of each of the two bonds the same way? Why or why not?