American Table, to wit, first insurance year 50%, second year 65%, third year 75%, fourth year 85%, fifth year 95%. The superintendent may vary the standards of interest and mortality in the case of corporations from foreign countries as to contracts issued in other countries than the United States; and in particular cases of invalid lives and other extra hazards. The legal minimum standard for the valuation of annuities issued after January 1, 1907, shall be McClintock's "Tables of Mortality Among Annuitants", with interest at 32%, but annuities deferred ten years or more and written in connection with life or term insurance* shall be valued on the same mortality table from which the consideration of premiums were computed with interest not higher than 32%. Any life insurance company may voluntarily value its Policies or any class thereof, according to the American Experience Table **** at a lower rate of interest than that prescribed, but not lower than 3%, and with or without reference to the select and ultimate method of valuation, and in every such case shall report any excess of its valuations over those computed by the legal minimum standard and also the standards used by it in making the same, and if such other standards are adopted they shall not be abandoned without the written consent of the Superintendent of Insurance.† Particular attention is called to the matter in italics, because the New-York Life varies its standard in the case of sub-standard lives, lives insured in tropical and sub-tropical countries, and uses the American Table of Mortality with 3% interest in calculating the reserves on the Policies now under consideration, but does not avail itself of the abatement in the reserves allowed by the select and ultimate method at the end of the first, second, third and fourth years. A condensed statement of Section 87, relating to contingency reserve, or unappropriated surplus, is as follows: A domestic life company may accumulate and maintain, in addition to the net value of its policies computed according to the standard adopted by it under Section 84, a contingency reserve not exceeding the following percentages: The largest percentage is 20% or $10,000, whichever is greater-when net values of its Policies are $100,000 or under. The percentage decreases as net values increase until the minimum of five per cent. is reached when net values exceed seventy-five million dollars. Accumulations held on account of deferred dividend policies are not considered as a part of the contingency reserve. THE SELECT AND ULTIMATE METHOD OF VALUATION. The select and ultimate method of valuation is an attempt to fix the maximum amount that may safely be expended by a life company for new risks in excess of the first year's loading-in view of the lower mortality of such risks during the first five years of insurance. It allows a company to expend during the first year the present value of these assumed mortality gains, and to hold a smaller reserve per $1,000 at the end of the first, second, third and fourth years of insurance. The method, according to its author, Mr. Miles Menander *Such as we have already considered in the payment of life and endowment policies. For the full text of Section 84, see Appendix, page 120. Dawson, "charges the company with its actual liability, as nearly as possible, allowing for selection. The effect of it, as compared with the full net premium reserves by the usual formula, is to allow the gains from mortality during the first five years as an offset to the initial expense incurred in securing those fresh lives *** After the fifth year the reserves are the full net premium reserves by the usual formula. * As the net premium is calculated upon the assumption that the full table rate of mortality will be experienced and the full reserves held at all times, we must now consider: (1) how much less than the amount provided will be necessary for death-losses; (2) how much more will be received in net premiums from the larger number of living; and (3) how much more will be needed as a reserve for the larger number of living at the end of five years. The following table shows the number living and dying, and the present values of the deathlosses in each year at the table rate of mortality: The following table shows the same items by the select and ultimate method: = The new figures of living and dying are obtained as follows: The first year we have the number of living as in the table; the mortality being 50% of the normal the number dying will be half the number of dying by the table. The new number of living at age 36 is 81,822 less 366 81,456. The table rate of mortality for age 36 is (the number of dying divided by the number of living) the decimal .009089, and the select and ultimate rate is 65% of this, or .00591, and at this rate the number of deaths among 81,456 will be 481. Deducting this number from 81,456, we get the next number of the living and proceed as before. The amounts are discounted for one, two, three, four and five years respectively by using the decimals from the table of values of one dollar due in one, two, three, etc., years. The following table shows the excess number of living at each age over the numbers of the Mortality Table-who will pay net annual premiums of $21.08 on the Ordinary Life Policy: There are now 939 more living than the table shows and the reserve for each $1,000 insurance at the end of the fifth year is $68.16; hence the additional reserve required will be $64,002.24, the present value of which is $55,208.84. To sum up-we have Present values provided in net premiums at $3,402,017.54 Excess of present values provided over those needed for death-losses and reserves, $879,480.90. As there was $81,822,000 insurance taken at age 35 this gives an "assumed mortality gain" of $10.75 for each $1,000. The assumed mortality gains under a Twenty-Payment Life Policy taken at age 35 are found in a similar manner to be $10.52, and those under a TwentyYear Endowment Policy, $10.21. The reserve at the end of each of the first four years by the select and ultimate method may be obtained in the same manner as shown in the table on page 108. We begin, as in the table-with 81,822 persons insured. But as $10.75 is assumed mortality gains and is set aside for first year's expenses out of the first net premium, the amount received for death-losses and reserves the first year is $21.08 less $10.75 $10.33. We then proceed as in the first table. The amount received the first year for our present purpose will be = Dividing this by the number living (81,822-366) 81,456 gives $6.19 the reserve per $1,000 by the select and ultimate method at the end of the first year. After the first year the full net premium is used with the number living and dying as shown by the select and ultimate method above. The reserves per $1,000 insured for the Policies under consideration by the American Table and by the select and ultimate method are shown as follows: 5 41.05 44.72 92.05 .. 145.91 .. 145.50 68.16 68.16 .. 117.52 117.52 .. 185.71 .. 185.71 At the end of the fifth year the full reserve is held on each policy, and although the number of policies is now greater than in the table on page 108 the reserve for each Policy is in hand and the net annual premiums will be hereafter paid by each, so it does not matter whether the number is great or smallthe reserve, together with the net premiums and interest, will pay all deathlosses as they occur. What we have just gone over has its bearing on the question of dividends in this way it shows that if the full amount allowed by law is used in first year's expenses there will be no surplus at the end of the first year from (a) loading, nor from (b) mortality gains actually realized. All that remains of premium and interest at the end of the first year is $6.19 per $1,000, the small reserve allowed by the select and ultimate method. Moreover, there will be no surplus from mortality gains during the next four years, because such gains have already been appropriated to bring the reserve up to the regular table rate at the end of the fifth year. Still further-we have not charged the new Policy in its first year with its proportion of the general expense of the company. As the law allows the whole present value of assumed mortality gains to be used for first year's expenses, and makes no provision for general expenses in the first policy year, it virtually authorizes a company to pay those expenses out of surplus-in other words, to borrow this amount from the other policyholders, assuming that it will be made up in the years following. We shall see the bearing of this assumption and how the loan may be adjusted as we proceed with our study of the policies under consideration. ASCERTAINING THE EXPENSE RATE. In order that we may follow these policies through several years we will assume that they were written in 1908, and will now ascertain the actual expense rate of the Company during that year under three heads (a) acquisition expenses to be borne by new business only; (b) renewal expenses to be borne by old business only; (c) general expenses to be borne alike by new and old business. We give here a résumé of the method by which expenses are apportioned to old and new business and print in the appendix the full text as made up by the Actuaries' Department of the Company. From the total disbursements shown in the annual report to the Insurance Department are deducted the sums paid policy-holders under all forms of contract. To the balance thus obtained are added commissions paid on reinsurance premiums, such commissions and reinsurance premiums not being included in income and disbursements for reasons explained on page 62. From this total are deducted (a) certain bookkeeping items which appear in both the income and disbursement accounts (and so balance each other); (b) certain items which are deducted from the interest account in making up the net effective rate of interest (including investment expenses); and (c) expenses on annuities and on single premiums. The balance shows the amount of insurance expenses to be assessed upon annual premiums for insurance. remaining items are divided into three parts according as they represent (1) direct acquisition expenses, (2) renewal expenses, and (3) general expenses. The following results are shown: I. Direct acquisition expenses. II. $2,722,672 1,076,472 5,180,742 We have already seen in our examination of the loading on Limited-Payment Life Policies and Endowment Policies that it consists approximately of the Ordinary Life loading plus one-half this rate on the excess of the premium over the Ordinary Life premium. This excess is called the higher premium element. In order to bring all premiums to a common basis for the assessment of expenses an adjustment is made of other than Ordinary Life premiums as follows: To an amount equal to the Ordinary Life element is added one-half the balance or higher premium element. The same result is reached by adding together the total premiums and the Ordinary Life element in all and taking half the sum. To illustrate the premiums on the three Policies under consideration are The sum of the three adjusted premiums is 84.33 + 17.01. To the Company's ordinary renewal premiums are added the reinsurance. premiums, and the above adjustment is made with the following result: Dividing the corresponding amounts of expenses by the amounts here shown gives the following ratios of expense: I. Ratio of acquisition expenses II. Ratio of renewal expenses.. 56.63% 1.75% 7.81% III. Ratio of general expenses. Considering the expense rate from its legal side we have the following:* We will now consider the interest rate, following the same method as in the case of expenses. It should be noted at the outset that we are not seeking to obtain the real rate of interest earned upon the Company's investments, but the Net Effective Rate received, for the purpose of the dividend, upon the Policies under consideration. If we were doing the former we should take the ledger assets of the Company as the basis of our divisor; but for our present purpose we take a divisor based upon those liabilities of the Company which from their nature need to earn interest. With this thought in mind the division of the liabilities of the Company into (a) liabilities not required to bear interest, and (b) liabilities normally drawing interest, will be understood.† *See N. Y. Ins. Report, business of 1908, page 216. †See Appendix, page 109. |