Hamish owns a vintage passenger steam ship. He makes a living from it by taking tourists, all year round, on sight-seeing trips along the Scottish coast. The ship is valued at 400,000 with an estimated life expectancy such that it would become completely destroyed (through sinking or shipwreck) 'approximately once in every 20 years'. The engine on the ship, being rather old, is rather unreliable and breaks down approximately twice a month, and, each time it happens, it costs Hamish around 200 in repairs and 1,500 in lost or refunded passenger fares Hamish is looking at two contracts (Contract X and Contract Y) Contract X is for a steam engine servicing arrangement with a local marine engineer who would perform regular maintenance operations which would reduce the number of engine breakdowns by 50%. Entering into this contract would cost Hamish 20,000 per year. Contract Y is an insurance contract which would cover the cost of total destruction of the steam ship if it ship sank or became wrecked. The cost of entering into Contract Y is also 20,000 per year. REQUIRED (making any necessary assumptions and showing all workings): a) Calculate the f annual expected monetary value (EMV) of breakdowns by the steam engine on Hamish's ship. (8 marks) b) Calculate the f annual EMV of total destruction of the steam ship from sinking or by shipwreck. (8 marks) c) Calculate the annual expected savings from entering into Contract X (8 marks) and Contract Y. (8 marks) d) Offer your views on whether or not Hamish should enter into EACH of the contracts and EXPLAIN WHY. (18 marks)