A quoted company's share price has remained constant for almost a year and theshareholders are becoming impatient because they wish to see the price rise. Oneof the company's directors has suggested that the company should consider makinga one for ten scrip issue, citing evidence that the capital markets often infer that thedividend per share will remain the same after such an arrangement and so the totaldividend to be paid will increase, thereby increasing the share price.

Explain the logic of the director's suggestion. [5marks]

An employer provides the following benefits for his employees: immediately on death in service, a lump sum of $20,000 immediately on withdrawal from service (other than on death or in ill health), a lump sum equal to $1,000 for each completed year of service immediately on leaving due to ill health, a benefit of $5,000 pa payable monthly in advance for 5 years certain and then ceasing, and on survival in service to age 65, a pension of 12,000 pa for each complete year of service, payable monthly in advance from age 65 for 5 years certain and life thereafter. The independent rates of decrement for the employees are as follows: Age x 62 0.018 0.10 0.020 63 0.020 0.15 0.015 64 0.023 0.20 0.010 where d represents death, i ill-health retirement and w withdrawal. Each decrement occurs uniformly over each year of age in its single decrement table. (i) Construct a multiple decrement table with radix (al)62 = 100,000 to show the numbers of deaths, ill-health retirements and withdrawals at ages 62, 63 and 64, and the number remaining in employment until age 65. [6] (ii) Calculate the expected present value of each of the above benefits for a new entrant aged exactly 62. Assume that interest is 6% pa before retirement and 4% pa thereafter, and that mortality after retirement follows the PMA92C20 table. [10] [Total 16]The index of expected earnings during the year of age x to x + 1 used in the valuation of a pension scheme is defined by the formula S = (100 + x )1/2 for x = 16,17,...,64 The corresponding index of average earnings is denoted by z, . If the definition of final average salary is "total earnings during the 12 months immediately prior to retirement" and pay levels are reviewed on members' birthdays, find an approximate value for 260. [2]