What is 'Certainty Equivalent'
The certainty equivalent is a guaranteed return that someone would accept rather than taking a chance on a higher, but uncertain, return. To put it another way, the certainty equivalent is the guaranteed amount of cash that would yield the same exact expected utility as a given risky asset with absolute certainty, and represents the opportunity cost of risk.
BREAKING DOWN 'Certainty Equivalent'
Investments must pay a risk premium to compensate investors for the possibility that they may not get their money back. If an investor has a choice between a U.S. government bond paying 3% interest and a corporate bond paying 8% interest, and he chooses the government bond, the payoff is the certainty equivalent. The company would need to offer this particular investor a potential return of more than 8% on its bonds to convince him to buy. A company seeking investors can use the certainty equivalent as a basis for determining how much more it needs to pay to convince investors to consider the riskier option. The certainty equivalent varies because each investor has a unique risk tolerance.
Certainty Equivalent and Cash Flow
The idea of certainty equivalent can also be applied to cash flow. The certainty equivalent cash flow is the riskfree cash flow that an investor or manager considers equal to a different expected cash flow which is higher, but also riskier. The formula for calculating the certainty equivalent cash flow is as follows:
Certainty equivalent cash flow = expected cash flow / (1 + risk premium)
The risk premium is calculated as the riskadjusted rate of return minus the riskfree rate. The expected cash flow is calculated by taking the probabilityweighted dollar value of each expected cash flow and adding them up.
For example, imagine that an investor has the choice to accept a guaranteed $10 million cash inflow or an option with the following expectations:
1. A 30% chance of receiving $7.5 million
2. A 50% chance of receiving $15.5 million
3. A 20% chance of receiving $4 million
Based on these probabilities, the expected cash flow of this scenario is:
Expected cash flow = (30% x $7.5 million) + (50% x $15.5 million) + (20% x $4 million) = $10.8 million
Assume the riskadjusted rate of return used to discount this option is 12% and the riskfree rate is 3%. Thus, the risk premium is (12%  3%), or 9%. Using the above equation, the certainty equivalent cash flow is:
Certainty equivalent cash flow = $10.8 million / (1 + 9%) = $9.908 million.
Based on this, if the investor prefers to avoid risk, he should accept any guaranteed option worth more than $9.908 million.

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