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 sales-to-total assets ratio.Based on past bankruptcy experience,the linear probability model is estimated as:
PD_i = 0.45 (debt/equity) + 0.01 (sales/total assets)
A firm you are thinking of lending to has a sales-to-assets ratio of 1.9 and its expected probability of default,or bankruptcy,is estimated to be 7 percent.Calculate the firm's debt ratio.

Question

Quizplus · Accepted Answer

Let D/E = debt-to-equity ratio
S/A = sales-to-total assets ratio

Given, P(default) = 0.07
S/A = 1.9

We know that,
P(default) = 0.45 (D/E) + 0.01 (S/A)

Substituting the values, we get
0.07 = 0.45 (D/E) + 0.01 (1.9)
0.07 = 0.45 (D/E) + 0.019

0.045 = 0.45 (D/E)
D/E = 0.1 or 10%

Therefore, the firm's debt ratio is 10.18%. The closest option to this is option B.

Calculating the Probability of Bankruptcy a Linear Probability Model You