7.6 The YTC, YTM, CY Relationships for Premium Bonds with Call Penalty Assumed
For simplicity’s sake, we have, thus far, ignored a call penalty. In the cases of discount and Par bonds, it would not matter. What if there were a call penalty in the case of a premium bond?
| Premium Bond | |||
| Coupon | 12% | 12% | 12% |
| YTM | 10% | 10% | 10% |
| Price | 102% | 102% | 102% |
| Call Penalty | 100% | 102% | 105% |
| Current Yield | $12 ÷ $102 = 11.8% | $12 ÷ $102 = 11.8% | $12 ÷ $102 = 11.8% |
| Therefore | YTM < CY | YTM < CY | YTM < CY |
| Summary | YTC < YTM < CY | YTC = YTM < CY | YTC > YTM < CY |
When a bond sells at a premium, it is suggested that interest rates have gone down since issuance. This assumes that the bond had been issued at Par. In such an interest rate environment, the call risk to the investor is great. It is increasingly probable, as rates continue to go down, that the issuer will call the bond away – if the bond is in the later period when it becomes callable. (Most callable bonds will not be callable for the first five to ten years after the date of issuance.) In such a circumstance it is also suggested that the YTM will – possibly – exceed the YTC.
