Question

A 10-year, 6% semiannual coupon bond, with a par value of $1,000 is 1 year old, and may be called in another 3 years at a call price of $1,045. Assume you purchase this bond today for $1,050. What is the nominal yield to call?

5.57 percent

5.39 percent

5.05 percent

5.22 percent

Answer 1

Current Price = Purchase Price = $ 1050, Call Price = $ 1045, Coupon Rate = 6 % payable semi-annually, Time to Call = 3years or (3 x 2) = 6 half-years, Let the nominal yield to call be 2r , Par Value = $ 1000

Semi-Annual Coupon = 0.06 x 0.5 x 1000 = $ 30

Therefore, 1050 = 30 x (1/r) x [1-{1/(1+r)^(6)}] + 1045 / (1+r)^(6)

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

r = 0.02783 or 2.783 %

Nominal Yield to Call = 2 x r = 2 x 2.783 = 5.566 % ~ 5.57 %

Hence, the correct option is (a)