River Rafts has determined that its expected EBIT for the coming year is $8.3 million. The EBIT is approximately normally distributed with a standard deviation of $5.1 million. If River Rafts has $1.9 million in annual interest payments, what is the probability that the firm will have negative earnings?
A) 4.65%
B) 10.47%
C) 5.16%
D) 35.20%

Question

Quizplus · Accepted Answer

To find the probability that River Rafts will have negative earnings, we first calculate the earnings before taxes (EBT) by subtracting the interest payments from the EBIT. The expected EBT is $8.3 million - $1.9 million = $6.4 million. The standard deviation remains the same, $5.1 million. We are looking for the probability that EBT is less than $0, which means we need to find the Z-score for $0. The Z-score is calculated as (X - mean) / standard deviation = ($0 - $6.4 million) / $5.1 million = -1.2549. Looking up this Z-score in a standard normal distribution table or using a calculator, we find the probability corresponding to a Z-score of -1.2549, which is approximately 10.47%. This means there's a 10.47% chance that River Rafts will have negative earnings.

River Rafts Has Determined That Its Expected EBIT for the Coming