A linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the equity multiplier and the total asset turnover ratio. Based on past bankruptcy experience, the linear probability model is estimated as:
PDi = 0.02 (equity multiplier) + 0.06 (total asset turnover)
A firm has an equity multiplier of 1.1 times and a probability of default of 6.2 percent. Calculate the firm's total asset turnover ratio.
A) 0.53 times
B) 0.67 times
C) 1.2 times
D) 0.84 times

Question

Quizplus · Accepted Answer

Given the linear probability model $PDi = 0.02 \times (\text{equity multiplier}) + 0.06 \times (\text{total asset turnover})$ and the information that the firm has an equity multiplier of 1.1 times and a probability of default (PDi) of 6.2 percent (or 0.062 in decimal form), we can substitute the known values into the equation and solve for the total asset turnover ratio.$$0.062 = 0.02 \times 1.1 + 0.06 \times (\text{total asset turnover})$$$$0.062 = 0.022 + 0.06 \times (\text{total asset turnover})$$$$0.062 - 0.022 = 0.06 \times (\text{total asset turnover})$$$$0.04 = 0.06 \times (\text{total asset turnover})$$$$(\text{total asset turnover}) = \frac{0.04}{0.06} = \frac{2}{3} \approx 0.67$$Therefore, the firm's total asset turnover ratio is approximately 0.67 times.

A Linear Probability Model You Have Developed Finds There Are