1. Micson is a multinational company that provides a range of products and

services. Micson has recently developed a new product. Micson is

considering whether it should manufacture and sell the product in South

America. Micson expects that demand for the new product in South America

could be low (S1), medium (S2) or high (S3). It predicts that the profit (or loss)

is -£12m (millions) if the demand is low, £32m if the demand is medium, and

£76m if the demand is high. South America can also choose to transfer the

right of manufacturing and selling the product to a local company in South

America for £40m.

i. Suppose Micson is pessimistic and does not like to take risk. Use an

appropriate decision rule to help Micson decide which option to choose.

ii. Micson predicts that the probabilities of the different demand levels are

p(S1)=0.3, p(S2)=0.4 and p(S3)=0.3. Draw a decision tree for the

problem. What should Micson do to maximise its expected profit? State

the optimal strategy and maximum expected profit.

Since Micson is not very familiar with the market in South America, it

considers requiring a local consulting company to conduct a market survey

for £1.2m. There are two local consulting companies: SA and SB. The view

of SA or SB may result in a favourable (I1) or an unfavourable (I2) evaluation.

Both SA and SB have conducted similar market surveys before.

The performances of SA can be evaluated by the following prior

conditional probabilities:

p(I1/S1)=0.2, p(I2/S1)=0.8, p(I1/S2)=0.4, p(I2/S2)=0.6

p(I1/S3)=0.8, p(I2/S3)=0.2

iii. Calculate the posterior probabilities for SA, i.e. p(I1), p(I2), p(S1/I1),

p(S2/I1), p(S3/I1), p(S1/I2), p(S2/I2), p(S3/I2). Provide your comments on

the performances of the consulting company SA.

After analysing the past performances of the other consulting company SB,

Micson finds that if SB is commissioned to conduct the market survey, the

posterior probabilities can be generated as follows:

p(I1) = 0.7, p(I2) = 0.3,

p(S1/I1) = 0.1, p(S2/I1) = 0.2, p(S3/I1) = 0.7,

p(S1/I2) = 0.5, p(S2/I2) = 0.3, p(S3/I2) = 0.2

iv. Suppose Micson decides to consider commissioning SB to conduct the

market survey rather than SA. Draw a decision tree for this new problem.

Given that Micson is neutral to risk, find the new optimal strategy and

maximum expected profit for Micson. Explain the optimal strategy to

Micson. Is it worth paying a higher fee of £1.2m to SB for conducting the

market survey?

Aptitudini: Financial Modeling, Data Analysis, Managementul riscului

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