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DON`T ADD FUDGE FACTORS TO DISCOUNT RATES

Risk to an investor arises because an investment adds to the spread of possible portfolio returns. To a diversified investor, risk is predominantly market risk. But in everyday usage risk simply means ¬bad outcome. ­ People think of the ¬risks ­ of a project as the things that can go wrong. For example,

A geologist looking for oil worries about the risk of a dry hole.

A pharmaceutical manufacturer worries about the risk that a new drug which reverses balding may not be approved by the Food and Drug Administration.

The owner of a hotel in a politically unstable part of the world worries about the political risk of expropriation.

Managers sometimes add fudge factors to discount rates to account for worries such as these.

This sort of adjustment makes us nervous. First, the bad outcomes we cited appear to reflect diversifiable risks which would not affect the expected rate of return demanded by investors. Second, the need for an adjustment in the discount rate usually arises because managers fail to give bad outcomes their due weight in cash-flow forecasts.

They then try to offset that mistake by adding a fudge factor to the discount rate. For example, if a manager is worried about the possibility of a bad outcome such as a dry hole in oil exploration, he or she may reduce the value of the project by using a higher discount rate. This approach is unsound, however. Instead, the possibility of the dry hole should be included in the calculation of the expected cash flows to be derived from the well. Suppose that there is a 50 percent chance of a dry hole and a 50 percent chance that the well will produce oil worth $20 million. Then the expected cash flow is not $20 million but (.5 ГЧ 0) + (.5 ГЧ 20) = $10 million. You should discount the $10 million expected cash flow at the opportunity cost of capital: it does not make sense to discount the $20 million using a fudged discount rate.

Expected cash-flow forecasts should already reflect the probabilities of all possible outcomes, good and bad. If the cash-flow forecasts are prepared properly, the discount rate should reflect only the market risk of the project. It should not have to be fudged to offset errors or biases in the cash-flow forecast.

Summary

How can you measure and interpret the market risk, or beta, of a security?

The contribution of a security to the risk of a diversified portfolio depends on its market risk. But not all securities are equally affected by fluctuations in the market. The sensitivity of a stock to market movement is known as beta. Stocks with a beta greater than 1.0 are particularly sensitive to market fluctuations. Those with a beta of less than 1.0 are not so sensitive to such movements. The average beta of all stocks is 1.0.

What is the relationship between the market risk of a security and the rate of return that investors demand of that security?

The extra return that investors require for taking risk is known as the risk premium. The market risk premium ¤that is, the risk premium on the market portfolio ¤averaged almost 9.4 percent between 1926 and 1998. The capital asset pricing model states that the expected risk premium of an investment should be proportional to both its beta and the market risk premium. The expected rate of return from any investment is equal to the riskfree interest rate plus the risk premium, so the CAPM boils down to

The security market line is the graphical representation of the CAPM equation. The security market line relates the expected return investors demand of a security to the beta.

How can a manager calculate the opportunity cost of capital for a project?

The opportunity cost of capital is the return that investors give up by investing in the project rather than in securities of equivalent risk. Financial managers use the capital asset pricing model to estimate the opportunity cost of capital. The company cost of capital is the expected rate of return demanded by investors in a company, determined by the average risk of the company`s assets and operations.

The opportunity cost of capital depends on the use to which the capital is put. Therefore, required rates of return are determined by the risk of the project, not by the risk of the firm`s existing business. The project cost of capital is the minimum acceptable expected rate of return on a project given its risk.

Your cash-flow forecasts should already factor in the chances of pleasant and unpleasant surprises. Potential bad outcomes should be reflected in the discount rate only to the extent that they affect beta.