Machine Works is a firm supplying quality metal gears

Subject: Mathematics / Statistics
Machine Works is a firm supplying quality metal gears to manufacturers of high-end clocks.
Machine Works is faced with the problem of extending credit to a new customer,
Qualclocks, in connection with a contract for next year’s season. Machine Works has
three risk categories for credit – "poor”, "average" and "good" according to repayment behavior. Its experience is that 30% of companies similar to Qualclocks are "poor”, 50%
"average", and 20% ”good". If credit is extended, the expected net contribution from the work is a loss of 400,000 for "poor" credit behavior, a profit of 200,000 for "average", and a profit of 300,000 for "good". If Machine Works does not extend credit, Qualclocks will go elsewhere. Address the following questions using decision trees and the expected
value criterion:

(a) Based only on the information presented so far, advise Machine Works as to whether
or not to offer credit to Qualclocks.

(b) What is the most that would be worth paying a rating agency to provide information regarding the credit risk category of the fashion clock manufacturer?

(c) Machine Works is able to consult a credit rating agency, who, for a fee of £20,000 will rate the manufacturer as A, B or C. The reliability of this credit rating agency is reported in the table below. Each row gives the probability of each credit rating given the actual risk state for the company. For example, if the company truly has a "poor" credit risk, the probability of the credit rating agency giving an A rating is 10%. Advise Machine Works as to what it should do.

(d) How does the optimal course of action in part (c) change with respect to the fee
charged by the credit rating agency?

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