Y5

3. A diamond mining company is considering exploring a mine (project A). If the company is successful and finds diamonds the net present value of the project will be 90 million. If unsuccessful the net present value will be zero. The probability of finding diamonds is 0.5. The firm's owners wish to maximise expected utility according to a utility function U=\\iW where W is the money value of the outcome. a) What is the expected money value of the exploration mine E(W) and what is the expected utility E(U) of the project? (4 marks) b) Show the E(U) on a diagram and also show the Utility function U=v'W as a function of the utility of wealth, U(W). Are the firm's owners risk averse or risk neutral? (4 marks) c) Calculate the 'certainty equivalent' value of the exploration mine and show this position on your diagram. Deduce the 'cost of risk' associated with exploring the diamond mine (project A). (6 marks) An alternative to the Project A is another mine that has already been discovered (project B) that will yield the firm a certain outcome of 15 million. d) How much better off, in their own estimation will the firm's owners be, if they undertake project A compared to project B? (6 marks)