# How to Calculate the Expected Payoff for an Investment

When dealing with a business proposition that can have several outcomes, you can calculate the expected value of the payoff. This figure is equally useful whether you are starting a business, buying a stock or investing in a college education. The expected value captures in a single figure the probabilities of outcomes and their potential payoffs.

#### TL;DR (Too Long; Didn't Read)

Calculating the expected payoff of an investment involves first considering all the likely incomes, assigning a dollar amount to each potential outcome and estimating the probability of each outcome. Then you can multiply each outcome amount by its probability and lastly add all the results together to obtain the expected payoff.

## Consider All Likely Outcomes

To get started, jot down a limited number of likely outcomes. When you start a business or buy a publicly-traded stock, the possibilities are practically infinite. To find an expected payoff, however, you must narrow the potential outcomes to a finite number.

Assume you are an experienced biochemist and start a company to patent a novel drug. The three most likely outcomes could be failing to obtain a patent, obtaining a patent and selling the rights to a large pharmaceutical company, or obtaining a patent and getting funds from investors to develop and sell the drug yourself. Mark items off your list until you have it narrowed down to three or four.

## Choose a Dollar Amount

Assign payoffs to each potential outcome. The inability to obtain any patent at all would be a disaster, and you'd lose all \$500,000 of your investment. If you patent it and a large corporation actually purchases the patent from you, you'd perhaps get around \$5 million. Such estimates, of course, must be grounded in reality and based on past experiences of similar corporations.

Finally, developing the drug yourself is a risky proposition. You could end up with a hit, or a large rival firm could crush you with a similar drug introduced before you could get a foothold in the market. You could estimate conservatively that you'd make \$1 million if that were to happen.

## Imagine Each Outcome's Likelihood

Assign probabilities to each outcome. Imagine you did your homework and are convinced that you will very likely get a patent, so the probability of not obtaining a patent is a meager 10 percent. From there, it is slightly more likely that you will sell the patent than having to develop and sell the drug yourself. So you would assign a 50 percent value to selling the patent and a 40 percent value to having to develop it yourself. Remember that the sum of probabilities should add up to 100 percent.

## Calculate the Expected Payoff

Multiply each outcome by its assigned probability. Multiply -\$500,000 by 10 percent – or 0.1 – which makes -\$50,000. Remember that this is a loss, hence a minus sign in front. Then multiply \$5 million by 50 percent – or 0.5 – resulting in \$2.5 million. Finally, multiply \$1 million by 40 percent – or 0.4 – resulting in \$400,000.

Add up the results of your multiplications to arrive at the expected payoff: -\$50,000 + \$2,500,000 + \$400,000 = \$2,850,000.