Valuing an Uncertain Payoff

5.0. Introduction: What Is the Issue?

Business managers need to anticipate the future. The problem is that the future is uncertain. Very few performance measures and also many costs are inherently unpredictable. Next month's sales, the return on an investment, and the price I will receive on an asset—none of these can be predicted exactly in advance. Yet we will have some idea of the most likely value and the level of uncertainty. There are also unpredictable costs such as the price I will need to bid to secure an asset, the fine or penalty the business might incur, the cost of a new housing project, and the interest rate in 6 months time.

Quantities that cannot be predicted exactly are called random variables. The payout an insurance company faces on a policy is one example. The actuarial section of the company spends a great deal of effort assessing the likelihood that an insuree will make claims of various sizes. Many will probably make no claim in a given year. Some will make modest claims. A small proportion might make a large claim. The probabilities of these outcomes are critical for the insurance company in setting the premium. What they care about is that the total premium of all insurees will more than cover the total claims. So they really care about the average claim per insuree. With thousands of contracts, the company “plays the game” thousands of times each year.

Many other decisions faced by managers are “once off.” You will ...

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