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 = 0.03 (debt/equity) + 0.65 (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.

Question

Quizplus · Accepted Answer

To find the firm's net income, we first need to calculate the profit margin using the given linear probability model. The model is: PD = 0.03(debt/equity) + 0.65(profit margin). Given PD = 0.07 and debt/equity = 1.05 (105%), we solve for the profit margin: 0.07 = 0.03(1.05) + 0.65(profit margin). Solving gives a profit margin of 0.07. The profit margin is net income divided by sales, so net income = 0.07 * $3,000,000 = $210,000.

A Linear Probability Model You Have Developed Finds There Are