Saturday, July 24, 2010


Certainty Equivalent Method for Risk Analysis

Yet another common procedure for dealing with risk in capital budgeting is to reduce the forecasts of cash flows to some conservative levels. For example, if an investor, according to his “best estimate” expects a cash flow of 60000$ next year, he will apply an intuitive correction factor and may work with 40000$ to be on safe side. There is a certainty-equivalent cash flow. In formal way, the certainty equivalent approach may be expressed as:

Net present value = (the risk adjusted factor X the forecasts of net cash flow) / (1 + Risk free rate)

The certainty equivalent coefficient, the risk adjustment factor assumes a value between zero and one, and varies inversely with risk. A lower risk adjustment rate will be used if lower risk is anticipated. The decision maker subjectively or objectively establishes the coefficients. These coefficients reflect the decision makers’ confidence in obtaining a particular cash flow in period. For example, a cash flow of 20000$ may be estimated in the next year, but if the investor feels that only 80% of it is a certain amount, then the certainty-equivalent coefficient will be 0.8. That is, he consider only 16000$ as the certain cash flow. Thus, to obtain certain cash flows, we will multiply estimated cash flows by the certainty-equivalent coefficients.

The certainty-equivalent coefficient can be determined as a relationship between the certain cash flows and the risky cash flows. That is:

Risk adjustment factor = certain net cash flow / Risky net cash flow

For example, if one expected a risky cash flow of 80000$ in period and certain cash flow of 60000$ equally desirable, then risk adjustment factor will be 0.75 = 60000/80000.
If the internal rate of return method is used, we will calculate that rate of discount, which equates the present value of certainty equivalent cash outflows. The rate so found will be compared with the minimum required risk free rate. Project will be accepted if the internal rate is higher than the minimum rate; otherwise it will be unacceptable.

Evaluation of certainty equivalent

The certainty equivalent approach explicitly recognizes risk, but the procedure for reducing the forecasts of cash flows is implicit and is likely to be inconsistent from one investment to another. Further, this method suffers from many dangers in a large enterprise. First, the forecaster, expecting the reduction that will be made in his forecasts, may inflate them in anticipation. This will no longer give forecasts according to “best estimate”. Second, if forecasts have to pass through several layers of management, the effect may be to greatly exaggerate the original forecast or to make it ultra conservative. Third, by focusing explicit attention only on the gloomy outcomes, chances are increased for passing by some good investments.

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