65

1.—14

13. The cost of the benefits contained in the various schemes submitted has been computed as follows :— (a.) Mortality : The mortality assumed is that relating to healthy districts of England, computed by the late Dr. Farr. This experience is very suitable for the purpose, and has an advantage over a table founded on the population of New Zealand, as it contains the experience of a greater number of people living and dying at advanced ages. The probabilities of leaving a widow at death are also derived, from English statistics. (6.) Rate of Withdrawal: In the case of males this has not been taken into account in the calculations, as the inducement to remain in the service caused by the adoption of a pension scheme must considerably diminish the number of those retiring voluntarily, and therefore render any rate based on past experience of the members quite unreliable for practical purposes. This would have little effect on the liability, however, if surrender values be granted on early retirement as proposed. Female teachers are in a different position, for they rarely enter the service for life, and, with few exceptions, retire from it on getting married. Probably, therefore, the scheme would not have much effect on the rate of withdrawal hitherto experienced, and allowance has consequently been made, in computing the cost of the benefits, for withdrawals according to the actual rate recently experienced among female teachers. (c.) Retiring medically unfit: There are no available data on which to base a calculation of the cost of these benefits. Any additional liability on this head must, therefore, be left to be provided for among miscellaneous contingencies. (d.) Age at Retirement for Pension : Males will retire between ages 60 and 65, and from the experience of other funds it is considered a reasonable assumption that they will remain in the service for three years after becoming entitled to retire on pension, and that they will all retire at 63. Females will retire between 53 and 60, and the age has been taken as 57. In both cases the retiring-age can only be fixed with greater accuracy after the fund has been established some years, when more exact calculations can be made, based on the actual numbers retiring at different ages (c.) Rate of Interest: I have assumed a net rate of 3| per cent, compound interest in the calculations. In the draft Bill it is provided that the Public Trustee shall allow at least 4 per cent, on the funds, but seeing that there must be deducted from the gross interest earnings (1) the expenses of administering the fund (no loading having been included for this purpose) ; (2) any losses arising from investments (which are almost inevitable with any large fund in course of time) ; and (3) any losses arising from adverse fluctuations in other respects than interest earnings. I do not think a higher rate than 3J per cent, could properly be taken for the purpose of estimating the real liability involved in such a scheme. Certainly, no higher rate should be taken by a private institution at the present time for such a purpose, and most of the annuity business transacted in this colony (including annuityassurances issued under " The Civil Service Insurance Act, 1893 ") is on a 3-per-cent. basis. Although, however, no complete valuation has been made at 4 per cent., I have ascertained that a scheme of pensions at the rate of hundredths of average salaries, including the accompanying subsidiary benefits, but not providing pensions on account of back service to existing members, would be practically self-supporting on a 4-per-cent. interest basis. General Remarks. 14. I have reported that £17,323 per annum in the scheme proposed by the teachers, and £9,459 per annum in the scheme contained in the Bill, would be necessary to provide interest on the outstanding liability considered as a permanent debt, a present debt which would continue to increase if such interest were not provided as it accrued. I have also explained the assumptions upon which these estimates are based, and if the latter are admitted to be sound it may be thought that nothing further remains to be said. There is, however, a prevalent feeling in the minds of many who are interested in these matters that, even admitting the estimates to be correct from an actuarial point of view, the orthodox actuarial methods are unnecessarily conservative. It is maintained by such objectors that the existence of a considerable balance in hand during the first few years of a scheme, after paying the claims and other expenses, proves it to be in a sound and prosperous condition, and that so long as there is a constant stream of new members the fund cannot become insolvent. Apart from the weight of the evidence of past sad experience against these unduly optimistic opinions, I will endeavour to explain the fallacy contained in them, so that it may be evident to those who are without the advantage of actuarial knowledge. If we take a body of 10,000 men now aged 30, and charge them £6 per annum each in consideration of receiving pensions of. £45 per annum if they arrive at age 60, the simple scheme so formed will be solvent, on the assumptions that the resulting funds will be invested at not less than 4 per cent., and that the members will experience a mortality similar to that of the general male population of New ZeaSuch a scheme is simplicity itself, providing for no expenses or benefits or withdrawal, and there will be no outgo at all for thirty years. In thirty years there will be 6,973 members still alive who will be entitled to pensions amounting to £307,132 per annum in the aggregate. The funds will then have accumulated to the large sum of £3,182,254, and thenceforth there will be no income except from interest earnings. This fund will decreasejiyear by year till the death of all the members, when ittwill be used up. "T If, instead of £45, pensions of £60 had been granted, the fund would nevertheless accumulate as before to £3,182,254 before being drawn upon, but being insufficient for the pensions of £60 would be used up by the time the members were about 75, leaving over 3,000 of the original contributors without pensions in their remaining years of life. 9—l. 14.