In making a valuation of the ordinary whole-life assurance contracts of a company according to the methods in general use at the present day, there are two separate sets of questions to be considered.

In the first place, the basis of valuation has to be chosen; that is to say, we have to select the table of mortality and the rate of interest which are to be employed. The questions that arise in this connection are of great importance, and for their settlement we have the assistance of the powerful instrument devised by Mr. King—the Model Office and its Valuations by various Tables of Mortality and at various Rates of Interest.

The effect of alcohol on the human economy and on the health and prosperity of the community has occupied the close attention of statesmen, physiologists and philanthropists for many generations past, and the question of total abstinence has been probably the most widely discussed social problem for more than half a century. That excess, as compared with moderation in the use of alcohol, is prejudicial in every way is a proposition hardly to be disputed. And many authorities who have given the matter careful consideration contend that even as moderation is superior to excess, so is total abstinence from alcohol superior to moderation. It is the purpose of this paper to examine the truth of this contention in regard to Mortality; with which must be closely associated the questions of health and general well being.

“In this world,” said Benjamin Franklin, “nothing is certain but death and taxes”, a remark with which all taxpayers, and not least those responsible for the management of life offices, will feel at the present time in cordial agreement. The great increase in the last few years in the rate of income tax undoubtedly presses very hardly upon the tax-paying community, and it is probably, in part, owing to this increase that there have recently been several cases before the Courts on the subject of the tax, which are not without interest to those engaged in the business of life assurance. To some of these I propose to direct your attention to-night.

In a Paper entitled “Some Remarks on the Valuation of Endowment Assurances in Groups”, read before the Institute in January 1898 (vide J.I.A., xxxiv, 61 et seq.), the writer described a new method of valuation by which it was claimed the labour of dealing with Endowment Assurances might be reduced to a minimum, and at the same time results might be obtained differing by only an insignificant amount from the exact results. In preparing that Paper it was felt that to encumber it with a mass of technical detail would have been to court the neglect which is the common fate of a lengthy essay, and that the method would be more likely to receive consideration and a fair trial if, in the first instance, no more than an outline of its main principles were given. Since then the author has applied the method, with very satisfactory results, to a volume of Endowment Assurance business much larger than that which was dealt with in the original Paper (vide J.I.A., xxxiv, 510-14), and very gratifying testimony has been received from a number of leading Actuaries who have adopted the plan, and have found it to work smoothly and efficiently in practice. It is thought, therefore, that the time has arrived when it will be useful to consider the subject in greater detail, and with special reference to some of the points that arise in the application of the method.

The subject of lapses or secessions has received comparatively little attention from writers in the Journal of the Institute. The question of secessions in connection with the valuation of Friendly Societies has been incidentally dealt with by Mr. G. F. Hardy (vol. xxvii, p. 312), and Mr. A. W. Watson (vol. xxxv, p. 313). Mr. A. Hunter, in his paper on “The effect of using the Lapse Element in calculating Premiums and Reserves” (vol. xxxvi, p. 51), makes some interesting comparisons of policy reserves, with and without allowance for discontinuances, but limits his investigations to the first 10 years of assurance, with a rate of exit over that period deduced from the tabulated HM data. One of the present writers has also contributed to the Journal (vol. xxxiii, p. 164) an account of the methods followed and results arrived at in the valuation, with and without allowance for lapses, of Clerks' Associations granting benefits to their members during unemployment, but the results arrived at are, of course, only applicable to those particular Societies.

I Have been asked to explain how the benefits of a pension to widows and an allowance to children can be valued when they are included in a pension scheme; and as I have had no experience whatever of a fund providing such benefits, I am, of course, eminently qualified to lecture on the subject. At least, I approach the subject with an unprejudiced mind, and am not affected by anything I may have said or done.

The subject to which I invite your attention is one which has never been directly submitted to the Institute of Actuaries, although reference has on various occasions been incidentally made to it. In the discussion which followed the reading of my essay of 1895, to which was awarded the Messenger Prize, it was suggested that I should give a whole set of forms of books necessary for conducting the business of an office, and a classification book for valuation purposes, showing how the information in each would afford a perfect check in the end, and this paper is, to some extent, the outcome of that suggestion. While this is the position of matters in the Institute, it is otherwise with the Faculty, which has now undertaken the functions hitherto performed by the Actuarial Society of Edinburgh. There the subject has frequently been brought before them, more particularly by Mr. McLauchlan, and, on the last occasion, reference was made to the suggestion I have referred to, and it was added that it was a point to which attention might profitably be given. In these circumstances, I do not offer any apology for bringing the matter before you, but I shall not attempt, on this occasion, to give a whole set of forms of books. I shall confine my remarks chiefly to premiums, as I think that in this way the paper will be more easily followed, while it will be possible, within this compass, to show the application of the various checks by means of the Valuation Books described in my essay.

In considering the various methods of graduation open to us, we were impressed, having regard to the large number of series to be dealt with, by the great facility and rapidity with which formulæ of summation can be applied with the certainty that the results obtained will conform closely to the unadjusted facts. For the Sickness Tables the summation method is especially suitable, since the average number of weeks (or rate) of sickness at any age is necessarily separable for practical purposes into “periods of attack”, e.g., in the case of the Manchester Unity Experience, 1893–97, “First 3 Months”, “Second 3 Months”, “Second 6 Months”, “Second 12 Months,” and “After 2 years”, the successive values of each of which must form a regular series, whilst the sum of any two sections forming a “period of attack” in general use (e.g., First 6 Months = First 3 Months + Second 3 Months) must be equally regular in progression. It is obvious that if a summation method be adopted, and the same formula be used throughout, a combination of any two or more of the graduated series will be itself a graduated series, and will, indeed, be identical with the result of an independent graduation of the combined unadjusted rates.

Readers of the Journal will remember that in February 1901 our then President, Mr. Higham, addressed a letter on behalf of the Council to the Royal Commissioners of the Patriotic Fund, offering the services of the Council of the Institute in respect of any actuarial advice which might be necessary in connection with the various Funds administered by the Commissioners.

When an investor buys a life interest, or an annual charge upon a life interest, the income does not reach him until tax has been deducted from the whole amount, and yet the purchaser has to pay away a material portion of the income in life assurance premiums, on which he is unable to recover the tax.