Question

Skolits Corp. issued 20-year bonds 2 years ago at a coupon rate of 7.4 percent. The bonds make semiannual payments. If these bonds currently sell for 104 percent of par value, what is the YTM?

Answer 1

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

Assume that the face value or par value of the bond M = $100

P0 = the current market price of bond = 104% of par value = 104% * $100 = $104

C = coupon payment = 7.4% of $100 = $7.4 but semiannual coupon, therefore C = $7.4/2 = $3.7

Time remaining to maturity = 20 – 2 = 18 years; therefore n = number of payments = 18 *2 = 36

YTM = interest rate, or yield to maturity =?

Now we have,

$104 = $3.7 * [1 – 1 / (1+YTM) ^36] /YTM + $100 / (1+YTM) ^36

By trial and error method we can calculate the value of YTM, which is 3.50% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.50% = 7.0% per year