A compelling reason for engaging in on-market buy-backs is that it provides a signal about the undervaluation of the company. In this paper an alternative, accounting based, method of determining fundamental value and undervaluation is used, namely the Ohlson residual income valuation framework. It is found that prior to the announcement buy-back companies are significantly undervalued relative to comparable non-buy-back companies. This undervaluation is largely but not totally removed in the period immediately following the on-market buy-back implying on-market buy-backs are predominantly an effective signaling mechanism. Where the firm cites undervaluation as a specific motive for the buy-back then, in fact, a higher degree of undervaluation prior to the buy-back is evident. The results provide evidence that management can, and does, identify undervaluation and reduces this through the signaling mechanism of on-market buy-backs.