This paper investigates two elements of agency costs, namely the wealth-transfer and the value destruction problems, associated with the equity-conversion and writedown CoCo bonds. By focusing on the costs as those stemming from the deviation from absolute priority rule (DAPR), we derive the expressions for the CoCo bonds and show that both agency costs are aggravated under these structures. We demonstrate this by studying the case of Monte Di Paschi bail-out in 2010. We argue that the replacement of government bailout by bail-in is akin to replacing moral hazard for agency costs, and that by encouraging bail-in structures the regulator prioritises the reduction of the former while ignoring the aggravation of the latter.