Final answer:
To determine the expected value of a refinery’s profit from a barrel of crude oil, calculate the profit for each given price combination scenario with equal probability of occurrence. Sum the profits, taking into account the cost of crude and refining, and divide by the total number of scenarios to get the expected profit per barrel.
Step-by-step explanation:
To calculate the expected value of the refinery’s profit from a barrel of crude oil, we first establish the possible outcomes based on the given price combinations for gasoline (Rg) and heating oil (Rh). Each of these prices can be either of two values, and they are likely to occur with equal probabilities and are independent of each other. This results in four possible scenarios:
- Scenario 1: Rg = $60/bbl and Rh = $62/bbl
- Scenario 2: Rg = $60/bbl and Rh = $70/bbl
- Scenario 3: Rg = $66/bbl and Rh = $62/bbl
- Scenario 4: Rg = $66/bbl and Rh = $70/bbl
For each scenario, we calculate the profit by multiplying the number of barrels of each product by its respective price, subtract the cost of crude and refining from these revenues, and then sum up the profit for gasoline and heating oil. With the crack spread given as 5-3-2, we consider that from 5 barrels of crude (at $52/bbl), the refinery produces 3 barrels of gasoline and 2 barrels of heating oil, with a refining cost of $8/bbl:
- Profit for gasoline = (3 barrels) × (Rg - $8 refining cost)
- Profit for heating oil = (2 barrels) × (Rh - $8 refining cost)
- Total profit for 5 barrels of crude = (Profit for gasoline) + (Profit for heating oil) - (5 barrels × $52 crude cost)
- Profit per barrel of crude = Total profit / 5 barrels
The expected value of profit per barrel of crude is the average of the profits calculated for each scenario, considering the equal probability of each price occurring:
Expected value = 0.25 × (Profit Scenario 1) + 0.25 × (Profit Scenario 2) + 0.25 × (Profit Scenario 3) + 0.25 × (Profit Scenario 4)