A company issues a callable (at par) 20-year, 5% coupon bond with annual coupon payments. The bond can be called at par in one year after release or any time after that on a coupon payment date. On release, it has a price of $102 per $100 of face value. What is the yield to worst of this bond when it is released?

Question

Quizplus · Accepted Answer

To calculate the yield to worst, we need to calculate the yield to call and the yield to maturity and then choose the lower of the two.
At release, the bond can be called at par in one year, so the yield to call can be calculated using the following formula:
PV = C / (1 + YTC) + C / (1 + YTC)² + ... + C / (1 + YTC)^20 + 100 / (1 + YTC)^20
Where PV = 102, C = 5, and YTC is the yield to call.
By trial and error, we get YTC = 2.94%
To calculate the yield to maturity, we can use a financial calculator or Excel's RATE function:
RATE(20, 5, -102, 100, 1) = 4.84%
Since the bond can be called at par in one year, the yield to worst is the yield to call, which is 2.94%. Therefore, the best choice is B.

A Company Issues a Callable (At Par) 20-Year, 5% Coupon