If a project has cash flows of 150 or 300 with equal probability, the expected cash flow per year is 225.

If a project has cash flows of 150 or 300 with equal probability, the expected cash flow per year is 225.

• A. 150
• B. 225
• C. 300
• D. 450

Answer: (B)

The main idea here is how to calculate the expected value when there are two possible cash flows with equal probability. With equal chances, each outcome has probability 1/2. The expected cash flow is 1/2 × 150 plus 1/2 × 300, which equals 75 + 150 = 225. The other numbers are simply one possible outcome (150 or 300) or the sum of the two outcomes (450) and do not represent the average cash flow you’d expect over many years. If the probabilities were different, you would weight each cash flow by its probability. So the per-year expected cash flow is 225.

The main idea here is how to calculate the expected value when there are two possible cash flows with equal probability. With equal chances, each outcome has probability 1/2. The expected cash flow is 1/2 × 150 plus 1/2 × 300, which equals 75 + 150 = 225. The other numbers are simply one possible outcome (150 or 300) or the sum of the two outcomes (450) and do not represent the average cash flow you’d expect over many years. If the probabilities were different, you would weight each cash flow by its probability. So the per-year expected cash flow is 225.