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 = 0.60 (debt/equity) + 0.02 (sales/total assets)
A firm you are thinking of lending to has a sales-to-assets ratio of 1.75 and its expected probability of default,or bankruptcy,is estimated to be 8.1 percent.Calculate the firm's debt ratio.

Question

Quizplus · Accepted Answer

From the given linear probability model, we can write:

P(default) = 0.60(debt-to-equity) + 0.02(sales-to-assets)

We know that the sales-to-assets ratio for the firm is 1.75 and the estimated probability of default is 8.1%.

Therefore,

0.081 = 0.60(debt-to-equity) + 0.02(1.75)

Solving for the debt-to-equity ratio, we get:

debt-to-equity = (0.081 - 0.035) / 0.60

debt-to-equity = 0.076

So the debt-to-equity ratio for the firm is 7.6%.

Therefore, the best choice is B) 7.12 percent, which is closest to the calculated debt-to-equity ratio of 7.6%.

Calculating the Probability of Bankruptcy a Linear Probability Model You