Question

Niendorf Corporation's 25-year maturity bonds have an 8.75% coupon rate with interest paid semiannually, and a par value of $1,000. The bonds are currently selling at a premium price of $1,100 in the bond market. What is their yield to maturity (YTM)?

Answer 1

Tenure of Bonds = 25 years or (25 x 2) = 50 half-years, Coupon Rate = 8.75 % per annum payable semi-annually, Par Value = $ 1000 and Current Price = $ 1100

Let the YTM be 2R %

Semi-Annual Coupon = 0.0875 x 0.5 x 1000 = $ 43.75

Therefore, 1100 = 43.75 x (1/R) x [1-{1/(1+R)^(50)}] + 1000 / (1+R)^(50)

Using EXCEL's Goal Seek Function/ a financial calculator/ hit and trial method to solve the above equation, we get:

R = 0.03916 or 3.916 %

YTM = 2 x R = 2 x 3.916 = 7.832 % ~ 7.83 %