# Certainty Equivalent Cash Flow

Certainty equivalent cash flow is the risk-free cash flow which an investor considers equivalent to a higher but risky expected cash flow.

An investor might be indifferent between \$20 million guaranteed annual net cash flow from a project, and an opportunity to earn \$25 million with 60% probability and \$18 million with 40% probability. Though the expected cash flows in second option is \$22.2 million (0.6×\$25 million + 0.4×\$18 million), the investor may actually prefer the first option of guaranteed cash flow of \$20 million because that first option is risk free. \$20 million is the certainty equivalent cash flow.

## Formula

Certainty equivalent cash flow is calculated using the following formula:

 Certainty Equivalent Cash Flow = Expected Cash Flow 1 + Risk Premium

Where risk premium is the excess of risk-adjusted discount rate over the risk free rate.

## Example

You are the senior financial analyst at Schon Real Estate which invested heavily in Dubai real estate in 20X5. Unfortunately, the projects did not turn out as profitable as they were expected. The company's board of director recently appointed Al-Fatih Al-sisi as the new CEO to turn the company around. He has requested Subramanian Ramasamy, the finance director, to brief him on the extent to which the projects fell behind on profitability. You prepared a report for the finance director in which you talked about risk-adjusted discount rate, expected NPV built into the investment appraisals back in 20X5 and how they compare with actual performance. Subramanian sent you memo: “The CEO is from general management background and I fear he might not digest all the complex rate stuff we are talking about. I would like to brief him in simple cash flow. Please find me certainty equivalent cash flow for the IT Tower project.”

A risk-adjusted rate of return of 13% was used to discount the uniform expected annual net cash flows of \$2.3 million. The project had a useful life of 15 years and relevant risk free rate was 5%.

Solution:

Risk Premium
= Risk Adjusted Rate of Return − Risk Free Rate
= 13% − 5%
= 8%

Certainty Equivalent Cash Flow
= \$2.3 million ÷ (1 + 8%)
= \$2.13 million

You can send the following memo back to the finance director:

IT Tower project was expected to generate \$2.13 million certainty equivalent cash flow per year for 15 years.

by Obaidullah Jan, ACA, CFA and last modified on

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