Question

Suppose the yields to maturity of 6-month, 12-month, 18-month and 24-month zero-coupon bonds are, respectively, 10%, 8%, 7%, and 6% per annum convertible semiannually.

a.) What is the 2-year par yield?

b.) Find the price of a 2-year semiannual coupon bond with coupon rate of interest of 3.0407% per annum and face value 100.

c.) Comment of the result in b.

PLEASE SHOW ALL WORK BY HAND, WITHOUT USING A FINANCE CALCULATOR OR EXCEL. THANK YOU.

Answer 1

(a): m = 2, d = e^(-0.06*2) = 0.88692

A = e^(-0.10*0.5) + e^(-0.08*1) + e^(-0.07*1.5) + e^(-0.06*2) = 3.6616

Par yield = (100-100*0.88692)*2/3.6616 = 6.1765

Thus 2 year par yield = 6.1765

(b): 3.0407% will translate into 3.0407%/2 = 1.52035% on a semi-annual basis. Thus semi-annual coupons are 1.52035 and on maturity payment will be 101.52035

Thus price = 1.52035e^(-0.10*0.5) + 1.52035e^(-0.08*1) + 1.52035e^(-0.07*1.5) + 101.52035e^(-0.06*2)

= $94.2589

(c ): The result in ‘b’ shows that price of a -year semiannual coupon bond with coupon rate of interest of 3.0407% per annum and face value 100 will be $94.2589. This is less than the par value of $100 because of the fact that coupon rate of interest of the bond is less than the par yield.