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why calculate certainty equivalent cashflow, if discounting at wacc is one step lighter in calculating?

Finance
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Good question. If the way you compute certainty equivalents is to use the risk premium you would have used anyway in your cost of capital, why bother? If you do compute certainty equivalents in other ways (using risk aversion coefficients, for instance), it may still make a difference.
The only advantage I can think of is to communicate the the present value into its risky component and its time value component. For example, suppose you expect to receive a risky cash flow of $1,000 one year from today. The risk free rate is 5% and the equity risk premium is 4%. Therefore, the discount rate is 9% and the present value of this risky cash flow is $1,000/(1.09) = $917.43. But, how much of this discount is related to risk and the time value of money. Using certainty equivalent cash flows, we can determine the answer to this question. The certainty equivalent ratio is 1.09/1.05 = 1.0381 and the certainty equivalent cash flow of $1,000 is therefore $1,000/1.0381 = $963.3028; that is, an investor would be indifferent from paying $1,000 for a certain cash flow of $1,000 and $963.3028 for an uncertain cash flow of $1,000. The $36.69725 discount reflects the cost to compensate for risk. The present value of the certainty equivalent cash flow is $963.3028/(1.05) = $917.43. The $45.87156 difference is compensation for the time value of money (i.e. the inflation rate and the real cost of money). Thus, the total dollar discount of $82.56881 is composed of a $36.69726 discount to compensate for risk and a $45.87156 discount to compensate for inflation and the real rate of interest.

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