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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