Question

A 10 year bond with a price of $1040 and face value of $1000 has a 4% coupon rate. If the coupon pays semiannually, what is the YTM of the bond?

Answer 1

Price of the share = Present value of semi annual coupons and face value discounted at semi annual ytm

Face Value = 1000

Price = 1040

Number of payments = 10 *2 = 20

Semi annual coupon = 4%*1000/2 = 20

1040 = 20/(1+semi annual ytm)^1 + 20/(1+semi annual ytm)^2 +20/(1+semi annual ytm)^3 +20/(1+semi annual ytm)^4 +20/(1+semi annual ytm)^5 +20/(1+semi annual ytm)^6 +20/(1+semi annual ytm)^7 +20/(1+semi annual ytm)^8 +20/(1+semi annual ytm)^9 + ...................... 20/(1+semi annual ytm)^20 + 1000/(1+semi annual ytm)^20

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

Semi Annual Ytm = 1.76%

YTM = 3.52% Answer