A Texas oil drilling company has determined that it costs $25,000 to sink a test well. If oil is hit,
the revenue for the company will be $500,000. If natural gas is found, the revenue will be
$150,000. If the probability of hitting oil is 3% and of hitting gas is 6%, find the expected value of
sinking a test well.
ev=-25000+500000*.03+150000*.06
looks like a losing venture.
However, I wonder what "revenue" means. Getting oil or gas out costs much more than a "test" well. For instance, wellhead piping, distribution piping, etc. So this venture is likely to really be a sour investment.
To find the expected value of sinking a test well, we need to calculate the probability-weighted average of the potential outcomes.
First, let's calculate the expected revenue if oil is hit:
Expected revenue from oil = Probability of hitting oil * Revenue from oil = 0.03 * $500,000 = $15,000
Next, let's calculate the expected revenue if gas is found:
Expected revenue from gas = Probability of hitting gas * Revenue from gas = 0.06 * $150,000 = $9,000
Now, let's calculate the cost of sinking a test well:
Cost of sinking a test well = $25,000
The expected value is calculated by subtracting the cost from the sum of the expected revenues:
Expected value = (Expected revenue from oil + Expected revenue from gas) - Cost of sinking a test well
Expected value = ($15,000 + $9,000) - $25,000
Expected value = $24,000 - $25,000
Expected value = -$1,000
The expected value of sinking a test well is -$1,000.