Question 1 [ 20 Marks] New Zealand Gas & Oil Company (NZG) is considering a compression installation project. The inlet compression project will reduce inlet pressure and allow extension of the plateau production rate while maximizing recovery from a natural gas field. Once installed, the project will generate gross cash flows depending on the future natural gas price which in turn will be determined by the state of the world: State probability Project gross cash flow 0.2 0 State of the world Covid-19 Mega Waves Covid-19 Contained Covid-19 Eliminated 0.7 $200,000 $1,000,000 0.1 The project requires an initial outlay of $150,000. a) What is the Sharpe ratio of the project? The current risk-free market interest rate is 5%. [7 Marks] b) NZG decided to securitize the project and auction it off. The winner of the auction will receive the project's gross cash flow tabulated above in return for the bidding amount, which NZG will use to fund the project. Ashley is an expected utility maximizer. His utility over his final wealth is given by U(W) = 0.3W + 7 and his initial wealth is $1,000,000. What is the maximum amount Ashley would be prepared to pay to win the auction? Assume that the auction is the only investment Ashley can make - i.e., if he does not win the auction, his wealth will stay at $1,000,000. [7 Marks] c) Another expected utility maximizer, Anthony, has a utility function over his final wealth given by U(W) = W0.8 with an initial wealth of $1,000,000. If Ashley and Anthony know each other's utility functions (as well as theirs), who will win the auction? Explain. (Hint: No calculation is necessary.) [6 Marks] Question 1 [ 20 Marks] New Zealand Gas & Oil Company (NZG) is considering a compression installation project. The inlet compression project will reduce inlet pressure and allow extension of the plateau production rate while maximizing recovery from a natural gas field. Once installed, the project will generate gross cash flows depending on the future natural gas price which in turn will be determined by the state of the world: State probability Project gross cash flow 0.2 0 State of the world Covid-19 Mega Waves Covid-19 Contained Covid-19 Eliminated 0.7 $200,000 $1,000,000 0.1 The project requires an initial outlay of $150,000. a) What is the Sharpe ratio of the project? The current risk-free market interest rate is 5%. [7 Marks] b) NZG decided to securitize the project and auction it off. The winner of the auction will receive the project's gross cash flow tabulated above in return for the bidding amount, which NZG will use to fund the project. Ashley is an expected utility maximizer. His utility over his final wealth is given by U(W) = 0.3W + 7 and his initial wealth is $1,000,000. What is the maximum amount Ashley would be prepared to pay to win the auction? Assume that the auction is the only investment Ashley can make - i.e., if he does not win the auction, his wealth will stay at $1,000,000. [7 Marks] c) Another expected utility maximizer, Anthony, has a utility function over his final wealth given by U(W) = W0.8 with an initial wealth of $1,000,000. If Ashley and Anthony know each other's utility functions (as well as theirs), who will win the auction? Explain. (Hint: No calculation is necessary.) [6 Marks]
