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whole period of ten years. If the mortality of the assured should be exactly equal to that of the persons selected for the formation of the tables, it would, probably, be less in the first five, and greater in the second five years. The company would appear to make profits, then, in the first pe. riod, and to lose in the second. If therefore, they should divide all the apparent profits in the first five years, they would be unable to meet all their losses in the second. The experience of two of the companies recently established, the Nautilus and the New York, Mutual Life, has furnished confirmation of this position. In both, no losses were had in the first year. If then, the whole apparent profits had been divided at the end of this time, there would not have been reserved a sufficient fund to meet the losses that would probably happen in subsequent years. To divide all, would be unjust to the new members who are admitted af. ter the first division. If they, for example, should happen to be of the same age as the first set of assured now are, both would be contributing equally to the funds of the company in the second period. The first, by their annual premiums, and by the reserved fund thrown into the common stock, would be paying as much as the larger annual premiums of the second set; yet, as the losses are less likely to happen among the recent members, they suffer by the connection. If the company had any means of examining the assured, at the time of the division, they might learn how many had their constitutions too much impaired to justify the second company in insuring them at the usual 'rates for healthy persons. But this would be troublesome, and lead to no satisfactory result. Even if they should learn that the health of some had suffered, no rules could be laid down for determining their expectation of life, and for thus fixing on a suitable sum to be laid aside out of the accumulated fund, to meet the extra losses anticipated from this source. The proper way to meet the difficulty, would be to make a deduction from the expectation of life of all the assured, by reckoning them all a little older than they really are, when the profits are determined. What this deduction should be, it would be extremely difficult to say. After a long experience, the companies might construct a table from the deaths of the assured, in the first five and second five years after each one's insurance. No such table has yet been made up, and, in the mean time, it is necessary to determine it as near as possible from other sources. If we should examine a list of persons between the ages of twenty and thirty, taken at random in society, there would not be found many whom a company would be unwilling to insure—not, probably, over 3 or 4 per cent of the whole number. Of these, some would be afflicted with hereditary diseases; some would have had their constitutions impaired in early life, so that they could never have obtained insurance in any company. It is not, therefore, probable that over 2 per cent of those insured by the first company would be objectionable to the second. . The expectation of life to some of these, might yet be considerable ; to all of them it would be something. If, out of one thousand, ten had had their constitutions so injured that their expectation of life was reduced one-half, and the other ten of the 2 per cent could only expect to live a single year, the average duration of the life of the whole thousand would be reduced from 37.86 years to 37.30, which is nearly the expectation at twenty-six, instead of twenty-five years of age. This reasoning is not very satisfactory; but the following will lead to a similar result. Of all who are alive between the
of the set he recent
ages of twenty and thirty, less than 2 per cent die annually. Of these, the great majority die without anticipating their end but a short time. Cer. tainly not over one-fourth have looked forward to death for more than a month. Of these, some may have been invalids for two or three years, some for five, and some for a longer period. Out of ten thousand persons at this age, one hundred and sixty may be expected to die in a single year. Of these, one hundred and twenty die at a short warning, so that, at a particular time, of not over ten of these could it be said, these will probably die this year. Of the remaining forty, the greater part may be expected to die within the year.
Of the deaths of the following year, a smaller portion may be anticipated, say three-fourths of those who do not die sud. denly; and the same proportion for subsequent years. This will give the following table :Expectation of life of 10,000 healthy persons,
378,600 years. Deduct for the expectation of fifty,........ 50 mul. by 37.36 1,868
thirty .... 30 36.36 1,091
34.36 550 twelve,.... 12
33.36 400 nine,....... 9
32.36 291 seven,....
31.36 219 five,........ 5
30.36 152 four,..
29.36 117 three,....
28.36 85 two, ........
27.36 55 one,........
27.36 27 Leaving balance, .......
372,968 which gives an expectation of 37.29 years, differing but little from 37.14, the expectation at the age of twenty-six, instead of twenty-five years. If the
persons selected for examination had been older, the reduction would have been greater. But if all the assured should be esteemed, in the cal. culation of the profits, a year older than they are, the result would not, probably, vary much from what would be right and proper. It cannot, in. deed, be pretended that this result is accurate. But it is so important to keep the company perfectly safe, that it is better to estimate the profits too little than too much. Some allowance of this kind ought most certainly to be made, and there can be no doubt that it is more just and fair to all the members, both the new and old, to make this reduction, In the example given above, the amount laid by for re-insurance would be $16.883 X 4.61, or $77.83, instead of $16.074 X 4.50, or $72.33.
When the profits are cautiously and correctly determined, they belong to the assured, and may be paid out to them with propriety and safety. They may be retained for the purpose of securing to the company more of the public confidence, or of giving greater benefit to the family of each member, by making the company a kind of savings bank to accumulate his earnings. How, now, ought these profits to be divided
among sured? The gains from expired policies should evidently be divided in proportion to the interest each one has in the company. So, also, if the different members be supposed to have paid too large a premium, or if the interest received by the company from its investments has been larger than was expected, the earnings of this kind should be divided in propor. tion to the payments of each. There will be a little difference, on account of interest, between those who insure at the beginning, and those at the
ce The from the Ite older is deduc
. hem it institu. nd the arer.
end of the five years. Every dollar paid too much by the first, will amount, by compound interest, to $5.63, while the last will only be $1.00, the exact amount paid. To divide in proportion to the payments, or in proportion of 5 to 100, would not give enough to the older members. But this difference would be slight, and it might be regarded as fully made up by the smaller risk there is of loss from the recent member. It would also be very troublesome to take into account the interest on each one's payment, in making out the distribution of profits. It would seem, therefore, both easy and proper to divide the profits according to the payments of each. If the first profits awarded to each member be not paid out to the assured, but retained by the company, interest ought to be allowed on them before the amount of profit is determined the second time. Those who come into the company afterwards, can claim no share in the interest of these profits, any more than they can in the profits themselves. The amount is placed to the credit of the members, and belongs to them, and the company ought not to appropriate its income to others. They would poorly perform the duties of a savings bank, if they divide the income of the early profits with those who join the company afterwards. If excessive exactions have been made of the members, when these are returned, they should belong to those who paid them, both principal and interest.
It is no good objection to this proposition, that the new members are paying the same as the old, and should divide equally all the profits. The new and old members are both, indeed, now paying the same sums, and all the profits from these payments should be equally shared. But if at some former period, the old members had paid too much, and if there had been a careful determination of the exact amount belonging to them, when the new partners joined the company, it cannot possibly be just that each set should come in for a share in the income of this amount.
Some companies do not pay out these profits, but issue stock bearing interest. This is founded on proper principles; and those which retain the money, and issue no evidences of debt, should follow the same rule. If the money was paid to the assured, or if interest-bearing notes were issued, the old members would get the benefit of the interest on the accruing profits, and they should do it also if the amount is retained, and merely placed to their credit. It might be supposed that this would not make much difference; but when it is recollected how long some of the policies will run, and how rapidly money accumulates at compound interest, the difference will no longer be regarded as unimportant. The following example will illustrate the matter more fully:—Suppose a new member should join the company in the 1st, 6th, 11th, 16th, 21st, and 26th year of its existence, and should live but three years, while another joins with the first, and survives till the thirtieth year of the company. Let them all be supposed to be of such ages that the new members shall, in each period, pay the same as the old ones. Let the nett interest of the company be 4 per cent. The course of the profits, and the amounts put to the credit of each, by dividing in proportion to the payments without allowing interest on the preceding profits, and also by first crediting the old member with the interest on his last preceding balance, will appear in the following table. For every dollar overpaid by the assured, the profits made and divided will be as follows:–
Profits from Profits from Amount divided, if Amount divided, if
payments of payments of in ratio of the the interest is old inembers. new niembers. payments. first credited.
In 5 years, 5.63 3.51 5.71 3.43 5.71 3.43 10 * 6.85 3.51 6.48 3.88 6.93 3.43 15 “ 8.34 3.51 7.41 4.44 8.42, 3.43 20 “ 10.18 3.51 8.56 5.13 10.26 3.43 25 “ 12.35 3.51 9.91 5.95 12.43 3.43 30 “ 15.02 3.51 11.58 6.95 15.10 3.43
From this table it appears that the new member admitted in the 26th year, receives more than twice as much profits on a division, as the one admitted in the first year, if no allowance is made for interest on the balances due to the old member; which is manifestly unjust and improper. The increase is derived from the profits of the older member. He who has longest trusted to the company, who has run most risk from their failure or mismanagement, who will receive at last little or no benefit from his insurance, on account of the large amount he has had to pay in premiums, this man is made to divide the interest from his accumulated profits to one whose only connection with the company is one of great advantage. In fact, the old member ought to receive all his profits, and the compound interest on those profits at the full rate received from the company's investments. If the company make more than 4 per cent on his money, he should receive more.
It will be well, perhaps, to refer to a charter of one of these companies, and show how these principles are to be applied. The charter of the Mutual Life Insurance Company of New York requires an account to be opened with the assured ; and in this, each is to be charged with a proportionate part of the losses and expenses, and to be credited with his premium, and with an equal share of the profits of the company derived from investments and earnings in proportion to his premium. This account is to be made up every five years, and the balance paid to each member at his decease, but not till then.
The losses and ordinary expenses are known from the books of the company. Under the head of expenses must be included the cost of reinsuring each of the surviving members, and that cost must be determined by imagining each one of the assured to take out policies in a new company, reckoning their ages to be one year greater than they really are. After the first division of profits there must be estimated, also, as part of the expenses, the amount due to those who have a balance to their credit, at the preceding distribution, for interest on this balance; the interest to be compound, and at the rate the company shall actually receive on their investments. These are real expenses, not paid out, indeed, but none the less real ; the first for a fund to meet the future losses, the other for interest on sums belonging to the assured, but retained by the company for the sake of increasing the strength of the company, and for other purposes. The credit side of the account, as far as made up from premiums, will be easily determined from the books of the company. The profits from investments and earnings will be found by taking losses and expenses from the premiums received, understanding by expenses what has just been explained. The account would stand as follows:—
SECOND FIVE YEARS.
By premiums...... To balance
By interest on preceding balance.....
By profits......... It would not do to keep the profits in two separate items of interest and earnings; for, after a while, the interest might exceed the profits. Should it never exceed the profits, as the charge for losses cannot, according to the charter, exceed the premiums, the assured would ultimately receive his assurance, and all the interest ever earned by the company; which, of course, might not happen.
In conclusion, it cannot be impressed too strongly on the companies to use caution and wisdom in determining their profits. Life insurance com. panies, with a paid-up capital, are exposed to failures; and the weaker basis of the mutual system renders this prudence the more necessary. Let no anxiety to declare large profits lead to an over-estimate of the gains they have made. Ignorance, miscalculations, extravagant estimates of the value of stocks belonging to the company, besides the ordinary sources of failure, mismanagement, unfortunate investments, and corruption of offi. cers, may ruin the company, and change what promised to be a blessing to the assured, into a curse. The mutual system is not only honest and fair, but eminently suited for this kind of insurance. The objections that lie against it in fire and sea risks, do not apply in life insurance ; for the laws which govern the duration of life are far more regular than those which govern the preservation of houses and ships. The effect of an epidemic is never so irregular as a great fire or a sea-storm. But, while the system is good, it must be managed, not only with integrity and prudence, but with all that skill and exactness which mathematical science can bring to its aid. The former are necessary for success, but not more so than the latter. Both are indispensable.
Art. II.--ADMINISTRATION OF THE RAILROADS OF MASSACHUSETTS :
WITH REFERENCE TO THE RATES OF FREIGHT AND FARE.
To construct a railroad in Massachusetts, has ceased to be a Herculean enterprise. Experience and science now light the path of the engineer, and indicate the route, materials, and mode of construction. Capi. tal, too, has ceased to be coy and repulsive when the line is feasible and the traffic sufficient. The undertaking, however, is not complete when the rails are down. The first movement of the locomotive opens another field of action ; a field which demands close investigation and rigid analy. sis, which puts in requisition commercial as well as professional skill, and philosophical research. The administration of a great line of iron-way, affecting both public and private interests, with powers still undefined, and latent resources still undeveloped, is a subject alike worthy of the study of the merchant, the man of science, and the philanthropist
.. In discussing the rates of charge appropriate to a modern railroad, its relation to the State must not be forgotten.
One of the first objects of association, and one of the first trusts which devolves on government, is the construction of roads ; without them, property is nearly worthless, and society but little advanced from barbarism.