Decision Trees

Problem $1$

$($a$)$ You have an option to develop an oil field, which has known reserves of $50,000$ barrels. Production costs are $$30$ per barrel. You may drill the oil in the first year or in the second year, but you must recover all $50,000$ barrels at the same time. If you drill in the first period, you may sell the oil at the period one price or store it at a cost of $$2$ per barrel. You pay storage costs at the time you decide to store the oil. If you do not drill in either the first or the second period, you may abandon the project and sell the option for $$200,000.$

The current price of oil is $$40$ per barrel, but the price will increase by $20$ percent or decrease by $10$ percent each year with equal probability. $($So$,$ for example, the price per barrel the first year will be either $$48$ per barrel or $$36$ per barrel.$)$

Construct a decision tree to show all the possible outcomes over the two years and the net income for each outcome. Assume that you must make the decision to drill or not to drill in period one before observing the period one price. If you drill in period one, you must decide to sell or store before observing period two price. If you do not drill in period one, you make the decision whether or not to drill in period two after observing the period one price, but before observing the period two price.

If the discount rate is $10$ percent per year, what is the best action to take in each period? What is the expected NPV of the oil concession at time zero $($i$.$e$.$ before the price change in the first period$)?$

There is a spreadsheet attached that you may use as a guide in solving this problem.

Sensitivity Analysis

$($b$)$

Suppose in the above problem that each year there is a $50$ percent probability that the price will increase by $30$ percent and a $50$ percent probability that the price will not change. How do the above answers change?

$($c$)$

Now suppose in the above problem that each year there is a $50$ percent probability that the price will increase by $10$ percent and a $50$ percent probability that the price will decrease by $30$ percent. How do the above answers change?