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have not yet expired; and by prorating the premium we find that at the end of the year there still remains to be earned $16,666.67 of the premiums collected in 1907 on these policies. As regards the business written in 1908, the company by the end of 1909 has only earned one half of the premiums from three-year policies and three tenths of the premiums from five-year policies, thus leaving $60,000 of premium income not yet earned. From its new business, yielding $450,000 of premiums, the company earns only $135,000 during the year in which the policies were written, and $315,000 must be assigned to the unearned premium fund. In all, therefore, the reserve at the end of the third year amounts to $391,666.67. If our illustration were extended to the fourth year, the reserve computation would be still more elaborate, because the company would then have to consider four classes of policies, viz., the three and five year policies of 1907, the three and five year policies of 1908, the one, three, and five year policies of 1909, and all the policies of 1910.

While the foregoing rule of equating the unearned premium is fairly safe for practical purposes, and meets the demands of the law, it should be remembered that it is only a system of averages, which does not always conform to real business conditions. Where a company's business is rapidly gaining, and more policies are written in the latter part of the year than in the early part, it is apparent that on the average the policies have not run for six months, and the reserve will, therefore, not be sufficiently high. Vice versa, if the company's business is declining, the reserve, if computed on the assumption that all policies written in the year have run six months, will be more than sufficient.

For this reason, if a large company wishes to know at any time exactly what its progress is, and whether its unearned premium liability is increasing or decreasing, it will be desirable to compute the unearned premium fund by months instead of years. In fact, a few companies have adopted this method. Thus, in the case of one-year policies the assumption is made that as much business is done in one part of a given month as in another, and that consequently all policies written during a month may be assumed to have been in existence fifteen days. If the policy is written in January the company considers fifteen days, or one twenty-fourth of the premium earned at the end of the month, the remaining twenty-three twenty-fourths belonging to the reserve, while on the 31st of December twenty-three twentyfourths of the premium is earned, and one twenty-fourth unearned. If the policy was written in February, three twentyfourths of the premium will be unearned on December 31st. Similarly, as regards its three and five year business written in January, the company will consider fifteen days of premium as earned at the end of the month, while on December 31st the reserve on the three-year policies will be forty-nine seventy-secondths of the premium, and on the five-year policies ninety-seven one hundred and twentieths.

CHAPTER XV

COINSURANCE

Under the principle of coinsurance the property owner has his losses paid only in the proportion that the amount of insurance he takes out bears to the amount of insurance that the company requires him to carry. The insured is free to buy as little or as much insurance as he deems necessary, but whatever the amount may be, it is arranged that he shall recover losses from the company only in the proportion that he is willing to insure his property and pay his just share of the community's fire-insurance tax.

The New York standard coinsurance clause, or the "reduced average clause," as it is generally called, reads as follows:

"This company shall not be liable for a greater proportion of any loss or damage to property described herein than the sum

hereby insured bears to per centum (...%) of the actual'

cash value of said property at the time sueh loss shall happen.

"If the insurance under this policy be divided into two or more items this average clause shall apply to each item separately."

In many instances a further provision is inserted to the effect that "in case of claim for loss on the property described herein not exceeding 5 per cent (5%) of the maximum amount named in the policies written thereon and in force at the time such loss shall happen, no special inventory or appraisement of the undamaged property shall be required." This waiving of a special inventory or appraisal does in no way waive the operation of the coinsurance clause; although it is sometimes expressly provided that the "application of the coinsurance clause shall be waived," where the aggregate amount of any loss does not exceed five per cent of the total cash value.

It is apparent from the above clause that the insurance company can designate the amount of insurance, expressed in the form of a percentage of the value of the property, which it desires the property owner to carry. Thus under a "full coinsurance clause," or for 100 per cent, the company agrees to indemnify any losses only in the proportion that the insurance actually taken out bears to the full value (100%) of the property. It is the general practice of companies, however, in well-protected cities, to require the property owner to insure his property to 80 per cent of its value. If the 80 per cent coinsurance clause is used, the company considers itself liable for only that portion of any loss resulting from fire which is represented by the proportion that the actual insurance purchased bears to the required 80 per cent. Thus if we assume the value of a building to be $20,000, then, under the 80 per cent coinsurance clause, the company will require the insured to take a policy for at least $16,000. If this is done the company agrees to pay in full any loss, not exceeding the face value of the policy. Suppose, however, that the insured decides to take only $8,000 of insurance, or one half of the required amount, and that a loss of $4,000 takes place. Under these circumstances, the coinsurance clause prevents the insured from collecting his claim in full, as he otherwise would, by providing that this $4,000 loss is to be paid only in the proportion that the insurance actually carried ($8,000) bears to the 80 per cent insurance required ($16,000), i.e., one half of $4,000, or $2,000. Since the insured elected to take only half insurance, he became, as far as any losses are concerned, coinsurer for the other half. If $10,000 of insurance had been taken, instead of $8,000, the $4,000 loss would have been paid in the proportion that $10,000 bears to $16,000, i.e., five eighths of $4,000, or $2,500. If, on the other hand, a 100 per cent, or full coinsurance clause had been used, and only $8,000 of insurance taken, the property owner would have had his loss paid in the proportion that $8,000 bears to $20,000 (the full value of the property) i.e.: to the extent of two fifths of $4,000, or $1,600.

The adoption of the coinsurance principle is absolutely essential to secure justice between property owners, and to enable the company to collect premiums from all, commensurate with the risk assumed. It is a well-known fact that in cities with good fire protection only about one out of every twenty fire losses is a total one, many of the remaining nineteen losses being only nominal in amount. Thoroughly appreciating this fact, many property owners are willing to run the chance of carrying a small amount of insurance, thus paying a proportionately small premium, with the hope that their policies will be large enough to cover their partial loss, if any should occur. The total fire waste, however, is not in the least diminished, and the insurance companies must collect the same aggregate premium income to meet their claims. The result is that those property owners who do not wish, or because of credit obligations cannot afford, to gamble with chance, and must insure their property to nearly its full value, are obliged to pay a much larger premium when compared with the losses they suffer during a given period of time, since they help to pay the many partial losses of those numerous owners who shirk the payment of their just portion of the fire tax. Let us assume two persons, each owning a house valued at $10,000, and that the premium rate is 1 per cent. Let us also assume that one of these owners insures his property to the extent of $8,000, but that the other owner, knowing that the great majority of losses are partial and relatively small, decides to take chances

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