(a) A company faces a decision as to whether to continue or not, with a particular product it has developed. It can cease development of the product, in which case all expenditure to date will be written off in the company accounts. Alternatively it can decide to test market the product in a small geographic area. Over the next financial year test marketing is estimated to cost 5 (£’million). If the market for the product when test marketed is favourable then the company will receive 7 (£’million) in revenue. However if the market is unfavourable it will only receive 2.5 (£’million). Alternatively the company could introduce the product to a wider market. Over the next financial year this is estimated to cost 15 (£’million). 

If the market for the product is favourable then the company will receive 23 (£’million) in revenue. However if the market is unfavourable it will only receive 11 (£’million). Assuming that the probability of the market being favourable is 0.40 represent this problem using a decision tree. What course of action for the company would you recommend based upon this decision tree?

b）Copy the table shown below into your answer and fill it in with respect to perfect information for the probability of the market being favourable. Value (£’million) Expected value with perfect information Expected value of perfect information

(c) What would the probability of the market being favourable have to be if the expected value of perfect information was one half of the expected value with perfect information? Note that if no probability exists which can achieve this you should clearly indicate why no such probability exists.