Leigh Fibers expects its operating income over the coming year to equal $2.5 million with a standard deviation of $800,000. Leigh must pay interest charges of $1.2 million next year and preferred dividends of $300,000. Leigh's marginal tax rate is 35%. What is the probability that Leigh will have negative EPS next year if its operating income is expected to be normally distributed? (Problem requires a normal distribution table.)
A) 14.7%
B) 5.2%
C) 10.6%
D) 15.7%

Question

Quizplus · Accepted Answer

To find the probability of negative EPS, calculate the net income threshold for EPS to be zero: Operating Income - Interest - Preferred Dividends = 0. $2.5M - $1.2M - $0.3M = $1M. Calculate the z-score: (1M - 2.5M) / 0.8M = -1.875. Using a normal distribution table, the probability of a z-score less than -1.875 is approximately 0.147 or 14.7%.

Leigh Fibers Expects Its Operating Income Over the Coming Year