An analyst has established the following prior probabilities regarding a company's next quarter's earnings per share (EPS) exceeding, equaling, or being below the consensus estimate.
| Prior probabilities | |
| EPS exceed consensus | 25% |
| EPS equal consensus | 55% |
| EPS are less than consensus | 20% |
Several days before releasing its earnings statement, the company announces a cut in its dividend. Given this information, the analyst revises his opinion regarding the likelihood that the company will have EPS below the consensus estimate. He estimates the likelihoods the company will cut the dividend given that EPS exceed/meet/fall below consensus as reported below.
| Probabilities the company cuts dividends conditional on EPS exceeding/equaling/falling below consensus | |
| P(Cut div | EPS exceed) | 5% |
| P(Cut div | EPS equal) | 10% |
| P(Cut div | EPS below) | 85% |
Bayes' formula:
Updated probability of event given the new information
B is correct. First, calculate the unconditional probability for a cut in dividends:
P(Cut div) = P(Cut div∣ EPS exceed) × P(EPS exceed)+ P(Cut div∣ EPS equal) × P(EPS equal)+ P(Cut div∣ EP5 below) × P(EPS below)= 0.05 × 0.25 + 0.10 × 0.55 + 0.85 × 0.20 = 0.2375.
Then update the probability of EPS falling below the consensus as:
P(EPS below∣ Cut div) = [P(Cut div Ⅰ EPS below) + P(Cut div)] × P(EPS below)
= [0.85 + 0.2375] × 0.20 = 0.71579 ≈ 72%.