Jorge Fullen is evaluating a 7%, 10-year bond that is callable at par in 5 years. Coupon payments can be reinvested at an annual rate of 7%, and the current price of the bond is $106.50 per $1,000 of face value. The bond pays interest semiannually. Should Fullen consider the yield to first call (YTC) or the yield to maturity (YTM) in making his purchase decision?

A) YTM, since YTM is greater than YTC.

B) YTC, since YTC is less than YTM.

C) YTC, since YTC is greater than YTM.Answer:

The bond is trading at a premium, and if the bond is called at par that premium would be amortized over a shorter period, resulting in a lower return. The lower return is the more conservative number, so the YTC should be used. You could use your financial calculator to solve for YTC assuming 10 semiannual coupon payments of $35 (FV = 1,000; PMT = 35; PV = –1,065; N = 10; solve for i = 2.75; × 2 to get annual YTC = 5.5%). Calculation of YTM would use the same inputs except N = 20, to get YTM = 6.12%

So the answer here is whichever is lower. The yield we’re guaranteed to realize is the YTC.

However, there is something in this question that goes against my intuititions and understanding of FI. Why is YTC lower than YTM, aren’t investors supposed to require a higher yield when there is a call option embedded? Or maybe this bond is priced in a way that goes against that logic (premium)?