The yield to maturity on 1-year zero-coupon bonds is currently 7%; the YTM on a 2-year zero is 8%. The Treasury plans to issue a 2-year maturity coupon bond, paying coupons once per year with a coupon rate of 9%. The face value of the bond is $100. a. At what price will the bond sell?

The bonds will sell at $ 103.62

Explanation:

as the market YTM differs from the coupon rate

the face value will not be discounted at the bond rate to determinate their market value.

Their cash flow will be discounted at the market rate:

cash flow: 100 x 9% = 9 coupon in one year

100 x 9% = 9 coupon + 100 maturity = 109

The first year will be discounted at 7%

and the second year discouted at 8%

9/1.07 + 109 / (1.07^2) = 103.6160363