Calculating the Probability of Bankruptcy A linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the debt-to-equity ratio and the profit margin. Based on past bankruptcy experience, the linear probability model is estimated as: PD_i = .03 (debt/equity) + .65 (profit margin)
A firm you are thinking of lending to has a debt-to-equity ratio of 105 percent and its expected probability of default, or bankruptcy, is estimated to be 7 percent. If sales are $3 million, calculate the firm's net income.

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The probability of default (PD) is given by the equation: PD = 0.03(debt/equity) + 0.65(profit margin). With a debt-to-equity ratio of 105% (or 1.05) and PD of 0.07, solve for profit margin: 0.07 = 0.03(1.05) + 0.65(profit margin). This gives a profit margin of 0.1. Net income = profit margin * sales = 0.1 * $3,000,000 = $300,000.

Calculating the Probability of Bankruptcy a Linear Probability Model You