Question

1. If 2-year zero coupon bonds are trading at 6%, and 2-year 8% coupon annual pay bonds are trading at 5.95% ytm, what yield and price are 1-year zero coupon bonds trading at?

Answer 1

Price of the bond using ytm=Present value of Cash flows discounted at ytm=8%*100/1.0595+(100+8%*100)/1.0595^2=103.7610901

Also, Price of the bond=Sum(Cash flows at time t /(1+rate for zero coupon bond for time t)^t)

Let yield of 1 year bond be r

Hence,

Price of the bond=8%*100/(1+r)+(100+8%*100)/(1+6%)^2

=>8%*100/(1+r)+(100+8%*100)/(1+6%)^2=103.7610901

=>r=8%*100/(103.7610901-(100+8%*100)/(1+6%)^2)-1=4.6918%

Price of 1 year zero coupon bond=100/(1+4.6918%)=95.51846467% of par