Question 1 (11 marks) Riley owns a super yacht, La Vagabonde, currently valued at $10mn. Riley is evaluating whether to upgrade La Vagabonde before he sells her. He did some research and came up with the following estimates for three different outcomes good, normal, and bad. All cash flow amounts are in millions of dollars. Ignore the time value of money. Bad Outcome Probability of outcome Net cash flow of project (alone) Cash cost of project manager Cash savings due to project manager 30% -8.5 3 5.5 Normal 45% 3.5 3 Good 25% 5 3 3 1 The choices Riley faces now are: Choice A: Do not undertake the upgrade project Choice B: Undertake the upgrade project alone Choice C: Undertake the project together with a project manager a) What is the expected net cash flow of each of the choices listed above, choices A, B, and C? Which choice maximizes Riley's expected net cash flow? (4 marks) b) Riley does not have any other assets and has a utility over total wealth that can be represented by the utility function U(W) = W0.3, where W is his total wealth in millions of dollars. Calculate Riley's expected utility for each of the choices. Assuming Riley wishes to maximize his expected utility, which choice should he make? (4 marks) c) Briefly explain in words why answers in parts a) and b) are different. (3 marks) Question 1 (11 marks) Riley owns a super yacht, La Vagabonde, currently valued at $10mn. Riley is evaluating whether to upgrade La Vagabonde before he sells her. He did some research and came up with the following estimates for three different outcomes good, normal, and bad. All cash flow amounts are in millions of dollars. Ignore the time value of money. Bad Outcome Probability of outcome Net cash flow of project (alone) Cash cost of project manager Cash savings due to project manager 30% -8.5 3 5.5 Normal 45% 3.5 3 Good 25% 5 3 3 1 The choices Riley faces now are: Choice A: Do not undertake the upgrade project Choice B: Undertake the upgrade project alone Choice C: Undertake the project together with a project manager a) What is the expected net cash flow of each of the choices listed above, choices A, B, and C? Which choice maximizes Riley's expected net cash flow? (4 marks) b) Riley does not have any other assets and has a utility over total wealth that can be represented by the utility function U(W) = W0.3, where W is his total wealth in millions of dollars. Calculate Riley's expected utility for each of the choices. Assuming Riley wishes to maximize his expected utility, which choice should he make? (4 marks) c) Briefly explain in words why answers in parts a) and b) are different
