Questions: Answer these questions clearly explaining all the steps.

A pension scheme only allows retirement at exact age 65. An investigation of the mortality of the retired members of the scheme was carried out over the period 1 January 2001 to 31 December 2006. The following data were obtained: Date of death Member Date of retirement (if occurred during the investigation period) 1 April 1998 30 April 2005 1 August 2000 1 February 2001 QUAWN 1 June 2002 31 August 2004 1 August 2002 31 December 2006 1 March 2004 1 May 2004 30 November 2006 1 January 2005 All months should be assumed to be of equal length. (i) Explain the form or forms of censoring that are present in these data and in this observational plan. [2] (ii) Calculate the Kaplan-Meier (product-limit) estimate of the survival function Sos () from these data, stating clearly any additional assumptions that you make. [10] (iii) Estimate the force of transition from alive to dead for a two-state Markov model for age 67 last birthday, using the data given. The exposed to risk should be calculated exactly. State all assumptions required, and state the age to which the estimate would be assumed to apply. [7] [Total 19]17 Explain why shareholders might be worried because a quoted company's diluted earnings per share is significantly lower than its basic earnings per share. [5] 18 (a) Explain what is meant by the term "subsidiary company". (b) Explain why a holding company is required to prepare a set of consolidated financial statements for its shareholders. [5] 19 A major quoted company has had a policy of reinvesting earnings and paying very little in the way of dividends for many years. The company now finds itself with a significant cash balance and very few attractive projects in which to invest. The directors are debating the merits of paying a substantial dividend. (i) Explain why the potential tax implications of receiving a dividend might make this proposal unpopular with this company's shareholders. [8] (ii) Explain why it might not be viable for the company to simply retain the funds and to wait until some attractive investment opportunities arose. [8] (iii) Explain why a quoted company might choose to release commercially sensitive information about investments and performance to the financial markets. [4] [Total 20]