Visually, from the graph, if the expected payoff is $45,000, the promised payoff is around $55,000. The correct value can be obtained by setting Formula 6.1 on page 163 equal to $45,000 and solving for “Loan.”

E(Payoff(Loan Promise = x)) = $20,000 + 80% . ($40,000 − $20,000)

+ 60% . (x − $40,000) = $45,000 which simplifies to 0.6 . (x − $40,000) = $9,000. The solution is indeed $55,000.