University : Edinburgh Napier University UniLearnO is not sponsored or endorsed by this college or university.
Subject Code : BSV11105
Country : United Kingdom
Assignment Task:

Question 1 

(a) Discuss (making reference to the Allais Paradox) why expected utility may be a true reflection of the way people decide on gambles; rather than expected monetary value. 

(b) A building contractor is providing an estimate to a potential client for carrying out a construction project. The contractor views that if they offer to undertake the work for £150k there is a 0.2 probability that the potential client will agree to the price; a 0.5 probability that a price of £100k would be agreed; and a 0.3 probability that the potential client will reject the offer. 

If the contractor offers to undertake the work for £100k they anticipate, there is 0.3 probability that the potential client will accept the price; a 0.6 probability that the potential client will negotiate so that a price of £80k will be agreed; and a 0.1 probability that the potential client will reject the offer. 

(i) Determine the price that the contractor should quote in order to maximise the expected payment that they receive from the client. (7 marks) 

(ii) Suppose that after questioning the company is able to make the following three statements: 

“I am indifferent between receiving £120k for certain; or entering a lottery that will give me a 0.9 probability of winning £150k and a 0.1 probability of winning £0.” 

“I am indifferent between receiving £80k for certain; or entering a lottery that will give me a 0.75 probability of winning £150k and a 0.25 probability of winning £0.” 

“I am indifferent between receiving £100k for certain; or entering a lottery that will give me a 0.85 probability of winning £150k and a 0.15 probability of winning £0.” 

Given the above information: determine the price that the contractor should quote to the client - and - give reasons for your answer. (12 marks) 

[You may assume that U (£150k) = 1 and that U (£0) = 0] 

Question 2

Major Ventures Ltd is considering the production of a new consumer item with a five year product lifetime. In order to manufacture this item it would be necessary to build a new manufacturing facility. You have been appointed as a consultant to advise the senior management of the firm. After considering all possible alternatives, it becomes clear that management only have the following three possible strategies. (Please note that all costs are in present value terms and should not be discounted) 

Strategy A:

Build a large facility (at an estimated cost of £6m). This strategy faces two types of market conditions (a) high demand with a probability of 0.7 or (b) low demand with a probability of 0.3. If the demand is high, the company can expect to receive an annual cash flow of £2.5m for each of the next five years. If the demand is low the cash flow would consist of a loss of £0.5m each year. (This is because of large fixed costs and inefficiencies). 

Strategy B;

Build a small facility (at an estimated cost of £3.5m) This strategy faces the same market conditions types as Strategy A (i.e. (a) and (b)). The cash flow over the five year period for the small facility is £0.25m if the demand is low; and £1.5m if the demand is high. 

Strategy C:

Delay building the manufacturing facility This strategy consists of leaving the decision for 12 months (while more information is collected). The resulting information can be positive or negative (with estimated probabilities of 0.8 and 0.2 respectively). At the end of the 12 months, management may decide to build either a large facility or a small facility at the same cost as at present providing the information is positive. If the resulting information is negative management would decide not to build any facility at all. 

Given positive information the probabilities of high and low demand change to 0.9 and 0.1 respectively (regardless of which facility is built). The annual cash flows for the remaining four-year period (for either facility type) are the same as those given for strategies A and B. 

(a) Draw a Decision Tree to represent the alternative courses of action open to Major Ventures Ltd. (8 marks) 

(b) Determine the expected return for each possible course of action; and hence decide the best course of action for the management of Major Ventures Ltd. 

(c) A building firm offers a discount to Major Ventures Ltd if they agree to have a large facility constructed immediately. Determine the percentage discount necessary to change the best course of action.

 

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