A company is considering drilling a well. Drilling costs $$350{,}000$, paid before anything is known. If oil is found (probability $p$), the well brings in $$1{,}400{,}000$ of revenue; otherwise it earns nothing. What is the smallest $p$ for which a risk-neutral company should drill?

Break-even chance of striking oil

Question

A company is considering drilling a well. Drilling costs $\text{\char36}350{,}000$ , paid before anything is known. If oil is found (probability $p$ ), the well brings in $\text{\char36}1{,}400{,}000$ of revenue; otherwise it earns nothing. What is the smallest $p$ for which a risk-neutral company should drill?

Short answer

$1/4$ . Drilling is worthwhile when expected revenue covers the cost: $1{,}400{,}000\,p\ge350{,}000$ , i.e. $p\ge\tfrac14$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited
Sample Spaces, Events, and the Probability Axioms

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