How to Calculate the Expected Payoff for an Investment

Expected payoff is one of the most versatile concepts in finance.

Expected payoff is one of the most versatile concepts in finance.

When dealing with 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.

Determine 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 failure 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.

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. Say, you estimate conservatively that you'd make $1 million if that were to happen.

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. Thereafter it is slightly more likely that you will sell the patent, than having to develop and sell the drug yourself. You therefore assign a 50 percent to selling the patent and a 40 percent chance to having to develop it yourself. Remember that the sum of probabilities should add up to 100 percent.

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

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