Comparison of Risk-Adjusted NPV and Utility Theory


Consider two risk averse decision makers facing a 50-50 chance at zero or $100.
Able uses a risk-adjusted discount rate of 10% for ventures this risky,
Baker uses a power utility function with power = .5, so the urility of a dollar amount $X in the 0-100 range is sqrt(X/100).
They both agree that the risk free discount rate for a future sure thing in 5%.

The question posed to each of them is "Would you rather receive an ironclad guarantee of $30 st a specific future date, or a 50-50 chance at zero or $100 on that same date."

Baker says "I'll take the sure thing.  I'd only take the risk if the sure thing were under $25."
Abel say "If the date is in the next 11 years I'll take the risk; if it's later than 11 years from now I'll take the sure thing."

Note that if the payoff date is 12 years from now, Abel will regret his decision two years from now!

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