Expected value (EV) is a crucial concept that can transform your decision-making process and significantly increase your chances of success. In simple terms, EV is the sum of all possible values for a random variable, each value multiplied by its probability of occurrence. By understanding and applying EV, you can make more informed, profitable decisions.
Consider this simple example from poker. If a player bets $15 to win a $30 pot, they only need their opponent to fold more than one-third of the time to break even. If the opponent folds 40% of the time, the expected value is positive (+EV), making the bet profitable in the long run. This principle applies to business decisions as well.
Applying EV to Business Acquisitions
When evaluating business opportunities, especially in acquiring software companies, the same EV principles apply. Let’s say you’re considering purchasing a software business for $50,000. This business generates $5,000 per month in revenue, with expenses of $3,000, leaving a net profit of $2,000 per month.
First, calculate the potential gains and losses. If the business continues to perform as expected, you’d recover your initial investment in 25 months ($50,000 / $2,000). However, consider the probabilities of different outcomes:
70% probability the business continues performing well: EV = 0.7 * $2,000 = $1,400 per month.
20% probability of a performance decline reducing profits to $1,000 per month: EV = 0.2 * $1,000 = $200 per month.
10% probability of business failure leading to no profits: EV = 0.1 * $0 = $0 per month.
Summing these gives an expected monthly profit of $1,600. Over 25 months, this totals $40,000, indicating a +EV decision.
Example of Neutral EV
A straightforward example of Expected Value (EV) is flipping a coin. Suppose you and a friend each bet $1, with you picking heads and your friend picking tails. The winner takes the $2 pot. Since both of you have a 50% chance of winning, the EV for each of you is $1. Because you're risking $1 to potentially win $1, this bet has a neutral EV, meaning there is no advantage or disadvantage.
How to Calculate EV
In poker, finding +EV (positive expected value) spots is key. Let's say there's $30 in the pot, and I bet $15 with nothing in hand. If my opponent folds more than 1/3 of the time, it's +EV to bet.
For example:
If the opponent folds 40% of the time:
60% of the time, I lose $15.
40% of the time, I win $30.
EV calculation:
(60% x -$15) + (40% x $30) = -$9 + $12 = +$3
So, the EV is +$3, meaning that, on average, this bet is profitable.
Acquisition Scenario
You are considering acquiring a software business for $100,000. This business currently generates $10,000 in monthly revenue with $5,000 in monthly expenses, resulting in a net profit of $5,000 per month.
Assumptions:
70% probability that the business continues to perform as expected.
20% probability that the business's performance declines, reducing the net profit to $2,000 per month.
10% probability that the business fails, resulting in no profit.
EV Calculation:
Expected profit if the business continues to perform well:
Probability: 70%
Monthly profit: $5,000
EV = 0.7 * $5,000 = $3,500
Expected profit if the business's performance declines:
Probability: 20%
Monthly profit: $2,000
EV = 0.2 * $2,000 = $400
Expected profit if the business fails:
Probability: 10%
Monthly profit: $0
EV = 0.1 * $0 = $0
Total Expected Monthly Profit:
EV = $3,500 + $400 + $0 = $3,900 per month
Total Expected Annual Profit:
EV (monthly) = $3,900 EV (annual) = $3,900 * 12 = $46,800
Investment Recoup Time:
Initial Investment: $100,000
Expected annual profit: $46,800
Time to recoup investment: $100,000 / $46,800 ≈ 2.14 years
By calculating the EV, you can see that the expected annual profit is $46,800, and you would recoup your investment in just over 2 years. This calculation helps you understand the potential profitability and risks associated with acquiring the software business, enabling you to make a more informed decision.
Conclusion
Adopting an EV mindset helps you recognize and seize profitable opportunities others might overlook. It enables you to make decisions grounded in logic rather than fear of loss. Whether in poker, business acquisitions, or everyday financial choices, understanding and applying expected value can pave the way for a more prosperous future. Embrace risk where the numbers support it, and let EV guide you to success.
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