Question

A bond currently has a stated price of 140. It has 11 years left to maturity and a stated coupon rate of 8%. Coupon payments are made semiannually. If you purchase the bond today, what YTM will you earn?

Answer 1

Number of payments = 11*2 =22

Price = 140

Face Value = 100

Semi-annual coupon amount = 0.08*100/2 = 4

we know that,

Price = Present value of all semi-annual coupons and face value discounted at semi-annual ytm

140 = 4/(1+semi-annual ytm)^1 + 4/(1+semi-annual ytm)^2 + 4/(1+semi-annual ytm)^3 + 4/(1+semi-annual ytm)^4 + 4/(1+semi-annual ytm)^5 + 4/(1+semi-annual ytm)^6 + 4/(1+semi-annual ytm)^7 + .......... 4/(1+semi-annual ytm)^22 + 100/(1+semi-annual ytm)^22

We will use heat and trial method to get that value for which above equation satisfies.

Semi-annual ytm = 1.79%

YTM = 1.79*2 = 3.57% Answer