Question

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 2-year 8% annual coupon bond: FV (par value) = 1,000; PMT (annual coupon) = coupon rate*par value = 8%*1,000 = 80; N (number of coupons) = 2; rate (annual YTM) = 5.95%, solve for PV.

Price = 1,037.61

If the 1-year zero coupon bond YTM is r and the 2-year zero coupon bond YTM is 6% then

1,037.61 = sum of present values of annual cash flows discounted at the respective zero coupon rates

1,037.61 = 80/(1+r) + (1,000+80)/(1+6%)^2

Solving, we get r = 4.692% (1-year zero coupon bond yield)

1-year zero coupon bond price = par value/(1+yield) = 1,000/(1+4.692%) = 955.18