Question

You are considering buying an oil field. If you buy the field, you can extract the oil in one year. There are 100 barrels of oil that can be extracted from the field; the cost of doing so is $4,000. You expect the price of oil in one year to be $50/barrel. However, there are four equally likely prices of oil in one year: $20/barrel, $35/barrel, $40/barrel, and $105/barrel.

If your discount rate is 15%, how much are you willing to pay for the field? Assume the price of oil never changes after one year, and that you have the option to not drill if the price of oil is too low.

		$0
		$869.57
		$1102.38
		$1413.04

Answer 1

Here, we will calculate the expected selling price with probability theory.
The present value of expected profit will be the price that we should be willing to pay for the oil field.
Estimated price	Probability	Estimated price * Probability
$                                 20.00	25%	$                                         5.00
$                                 35.00	25%	$                                         8.75
$                                 40.00	25%	$                                      10.00
$                               105.00	25%	$                                      26.25
	Total	$                                      50.00
Estimated oil in barrels		$                                    100.00
Expected sale revenue		$                                 5,000.00
Estimated drilling cost		$                                 4,000.00
Estimated gain		$                                 1,000.00
PV @ 15%		1000/(1+15%)
PV @ 15%		$                                    869.57
Hence option 2 is correct