A note on selling distressed loans with bank bailouts: modelling of bank interest margins with default probabilities

This article extends the framework of Merton (1974 Merton, R. C. 1974. On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance, 29: 449–70. [Crossref], [Web of Science ®] , [Google Scholar]) with Vassalou and Xing (2004 Vassalou, M. and Xing, Y. 2004. Default risk in equity returns. Journal of Finance, 59: 831–68. [Crossref], [Web of Science ®] , [Google Scholar]) to value a troubled but solvent bank's equity by explicitly incorporating distressed assets purchased by the government in an imperfectly competitive loan market. We show that the bank may be willing to take this bailout when the purchased amount is relatively small and the margin is relatively low. However, the bank may be harder to entice even when the unit price of the bailed-out assets subsidized by the government is relatively high. As a consequence, most of the first half of the Troubled Asset Relief Program's money is not used to buy troubled assets (Wilson, 2010 Wilson, L. 2010. The put problem with buying toxic assets. Applied Financial Economics, 20: 31–5. [Taylor & Francis Online] , [Google Scholar]).