Exesses is a family-owned company that is in the process of recovering from a majorcorporate scandal. Exesses is a substantial business that is not quoted. None of itsshareholders owns more than 5% of the equity shares. None of the shareholders is

able to take an active role in the company's management.

Exesses' directors were all forced to step down because of the discovery that thedirectors had been overstating reported profits, which had the effect of inflating theirprofit-related bonuses. The directors also provided themselves with lavish lifestylesat the company's expense. For example, the company provided chauffeur-drivenlimousines to transport the directors on bothbusiness and personal travel.

The entire board of Exesses has resigned. The shareholders have met and haveappointed a new chairman and a chief executive. Neither of these appointees havehad anything to do with Exesses in the past. They have both agreed that their firstpriority is to appoint a new board and to structure the management arrangements so

that the shareholders' confidence is restored.

The chairman has suggested that the new board should be structured as follows:

? The chairman will work on a part-time basis and will be responsible for the

management of the board, including chairing board meetings. The chairman willbe paid a fixed annual salary that offers an appropriate rate for the time that he isexpected to commit to the company.

? The chief executive will be employed on a full-time basis to manage the companyitself and will receive both a substantial salary and a profit-related bonus.

? Four additional full-time directors will be appointed to take charge of particularareas such as marketing and finance. Each will receive a similar package to thechief executive.

? Two part-time directors will be appointed to participate in board meetings and toreview corporate strategy. They will be paid a fixed salary.

? The chief executive and each of the full-time directors will receive a 5%

shareholding after satisfactorily completing three years on Exesses' board.

? The chairman and the two part-time directors will appoint a new external auditfirm. They will negotiate a contract with a much larger firm than the outgoingauditor and will pay a larger fee for the new auditor's services.

(i) Discuss the suitability of the proposals for the appointment and remunerationof the new board of directors from the perspective of maintaining shareholderconfidence. [12]

(ii) Discuss the implications of appointing a larger and more expensive externalaudit firm to replace the present auditor. [8] [Total 20]

Claims under a certain type of insurance policy occur as a Poisson process so that the number of claims arising from a policy in one calendar year is a Poisson random variable with mean u. In order to estimate / a random sample of n such policies is examined and it is found that no of these policies incurred no claims during the last full calendar year, m of them incurred one claim and the remainder incurred more than one claim. (i) Write down the likelihood of these observations and show that the maximum likelihood estimator / is a solution of the equation: m - (notn )At e-"(naz + nol -m)=0 [ You do not need to verify that a maximum is attained.] [10] (ii) A random sample of 20 such policies yields no =8 and m =7. By using the tables of the cumulative Poisson distribution, or otherwise, to find a good starting approximation for / and then using trial and error (or a more sophisticated method), determine / correct to two decimal places. [7] [Total 17]A random sample of n observations is taken from a normal distribution with variance 02 . The sample variance is an observation of a random variable S. Show that: (i) E($2) =02 [2] (ii) var($2) - 204 [2] 1-1 [Total 4]