# Certainty Equivalent

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 Rs 60,000 next year, he will apply an intuitive correction factor and may work with Rs 40,000 to be on safe side. There is a certainty-equivalent cash flow. In formal way, the certainty equivalent approach may be expressed as:

n tNC Ft

NPV =

t=0 (1+kf)t

Where, NCFt= the forecasts of net cash flow without risk-adjustment

t = the risk-adjustment factor or the certainty equivalent coefficient

kf = risk-free rate assumed to be constant for all periods.

The certainty- equivalent coefficient, t assumes a value between 0 and 1, and varies inversely with risk. A lower t will be used if greater risk is perceived and a higher t will be used if lower risk is anticipated. The coefficients are subjectively or objectively established by the decision maker. These coefficients reflect the decision-maker’s confidence in obtaining a particular cash flow in period t. For example, a cash flow of Rs 20,000 may be estimated in the next year, but if the investor feels that only 80 per cent of it is a certain amount, then the certainty-equivalent coefficient will be 0.80. That is, he considers only Rs 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.

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 inflows with the present value of certainty-equivalent cash outflows. The ratio 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.

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