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 sales-to-total assets ratio. Based on past bankruptcy experience, the linear probability model is estimated as:
PD_i = 0.65 (debt/equity) + 0.10 (sales/total assets)
A firm you are thinking of lending to has a sales-to-assets ratio of 0.9 and its expected probability of default, or bankruptcy, is estimated to be 11 percent. Calculate the firm's debt ratio.

Question

Quizplus · Accepted Answer

To find the firm's debt-to-equity ratio, we use the linear probability model equation: PD = 0.65(debt/equity) + 0.10(sales/total assets). Given PD = 0.11 and sales/total assets = 0.9, we solve for debt/equity: 0.11 = 0.65(debt/equity) + 0.10(0.9). Solving gives debt/equity = 0.0299 or 2.99 percent.

A Linear Probability Model You Have Developed Finds There Are