Question

1. A manager's utility function for profit is U(p) 10 In(p), where p is the dollar amount of profit. The manager is considering a risky decision, choosing between three different projects with four possible profit outcomes as shown below. The manager makes the subjective assessments shown below the table about the probability of each profit outcome Project Alpha Bravo Charlie Profit $ 1,000 $ 14,000 S12,000 $ 8,000 $ 14,000 12,000 14,000 12,000 0.35 S 20,000 $14,000 $17,000 12,000 Prob 0.05 0.1 0.5 a. Calculate the expected profit of projects Alpha, Bravo and Charlie b. Calculate the coefficient of variation of projects Alpha, Bravo and Charlie c. Calculate the manager's expected utility of profit for projects Alpha, Bravo and Charlie d. If the manager is maximizing expected profit, which project will be chosen? e. If the manager is minimizing coefficient of variation, which project will be chosen?

Answer 1

a) Expected profit = sigma profit * probability Expected profit for Alpha [E(X_A)] = 1,000 (0.05) + 8,000 (0.1) + 12,000 (0.35) + 20,000 (0.5) = 50 + 800 + 4,200 + 10,000 = $ 15, 050 Expected profit for Bravo [E(x_4)] = 14,000 (0.05) + 14,000 (0.1) + 14,000 (0.35) + 14,000(0.5) = 700 + 1,400 + 4,900 + 7000 = $14,000 Expected profit for charlie [E(x_c)] = 12,000 (0.05) + 12,000 (0.1) + 12,000 (0.35) + 17,000 (0.5) = 600 + 1,200 + 4,200 + 8,500 = $14,500 sigma^2_c = [12,000^2 (0.05) + 12000^2 (0.1) + 12,000^2 (0.35) + 17,000^2 (0.5)] - (14,500)^2 = 216500000 - 210250000 = 6250000 sigma_c = 2500 coefficient of vaiation for Charlie (cV_c) = (2500/14500) * 100 = 17.24% (c) u(p) = 10 ln (p) Expected utility of profit for Alpha [E(u)_*] = sigma u(p) * probability = (10 ln (1000) * 0.05) + (10 ln (8000)*0.1)