adoption. It is far easier and simpler to keep the profits in one account until the end of the year, and then apportion them by one of the rules. above given.

As to results obtained by these intricate systems, they do not vary so greatly from those obtained by the shorter and simpler methods as to make compensation for the increased labor. The same charge of overapportionment to the younger series that we have preferred against the Wrigley and other rules holds against the Hewel and Meyberg plans. (See subsequent tables giving comparisons of results.)

THE FORTUNA RULE.

1. Multiply the total amount of interest collected by the average rate paid premiums during the year, and deduct the amount from the premiums collected and add the interest collected.

2. Divide the result by value of shares at the last report plus the average investment for the year, for the per cent of profit gained from interest and premiums on interest.

3. Multiply each share's investment by per cent, for the gain on one share from interest and premiums on interest.

4. Diride balance of premiums collected during the year by number of dollars collected for dues during the year, for rate per cent of profit gained on premiums.

5. Multiply each share's investment by per cent of profit, for gain on one share from premiums.

6. Divide gross losses by value of shares at last report plus the average investment for the year, for the per cent of loss.

7. Multiply each share's investment by per cent of loss, for loss on one share, and deduct from the sum of profits gained on one share from premium and interest, the result showing the gain on one share.

FORT BRAGG RULE.

First-Find the rate of interest as follows: Add the entire value of the shares of the first series at last report to half of the amount of dues this year. Divide the interest received during the year by this amount. This gives the rate of interest.

Second-Find the rate of premium as follows: Multiply the number of shares by the amount paid in on each share. Divide the entire amount of premium received by the answer thus found and get the rate.

1,000 shares @ $12.
Entire premiums received.

Example.

$5,000 $12,000 = 41 per cent, about.

$12,000 00 5,000 00

Thus the value of a share of the first series at the end of the first year, $20, added to the average dues for this year, $6, gives $26. Multiply this $26 by the rate of interest found in the first paragraph, 10 per cent, and find the interest earnings of each share for the year, $2 60.

Then find the amount of premiums earned by the interest on each share of the first series.

$2 60 interest earnings × 41 per cent = $1 06.

Multiply the number of shares of the first series by this amount, $3 66.

Follow the same plan as above for the second series and add to the result of the first ($3,660), and deduct the amount thus found from the net profits of the association for the year. Divide the difference equally among all shares of both series.

The two rules just given appear to be the most involved of any that deserve classification as rules. They are in use by the Fortuna Building and Loan Association of Fortuna, and by the People's Building and Loan Association of Fort Bragg. They seem to present a long detour for arriving at results to be attained much more directly, and we have therefore not attempted an exemplification of them. Only the shortest and simplest processes are to be commended.

COMPARISON OF RESULTS.

For the purpose of making an accurate comparison of results obtained by the several rules and plans here given, we have calculated the following tables, based on the actual transactions of a Building and Loan Association of this State. We apprehend that a better idea of the merits of the several methods may be obtained from a careful inspection of these tables than in any other way. Here the same transactions are carried through by various systems, and various results are shown side by side.

COMPARATIVE RESULTS: ANNUAL DISTRIBUTION OF PROFITS BY VARIOUS RULES. Given: The number of series; respective ages in months; last book value, and net profit of year. Net profit, $42,730 19.

Required: To apportion net profit and find what is due one share in each series. The following rules are employed to show comparative results: 1, Dexter Rule; 2, Third Dividend Rule; 3, Second Dividend Rule; 4, Meyberg Rule; 5, Wrigley Rule.

PERCENTAGE OF PROFIT.

The percentage of profit secured by each share on its average investment for the year appears in the following table:

The degree of equability in the distribution of profits must be attested by the comparative percentages which the association pays on the invested capital of the various series.

It is apparent from the foregoing table that, by the Dexter Rule, an investment in one series earns the same percentage on its capital as an investment in any other series. All are treated alike in this respect. Each series realizes a gain of 12.32 per cent on its capital. While this holds true there can be no charge of favoritism or discrimination as between the different series. The holder of a share in the last series is treated just as well as the holder of a share in the first series, and no better.

By the Third Dividend Rule there is a slight discrimination in favor of the older shares, and a proportionate discrimination against the later shares. A holder in the first series earns 12.35 per cent on his money, while an eighth series member receives only 11.31 per cent.

DISCRIMINATION IN FAVOR OF YOUNGER SERIES.

By the Second Dividend Rule the discrimination is reversed, and stands in favor of the younger shares. The first series holder is given 11.17 per cent, and the eighth series holder 31.54 per cent.

By the Meyberg Plan the discrimination seems to be particularly against the holders of the second series shares. The list of awards stands:

While, in the main, there is an ascending scale of profits from the oldest to the youngest series, there are two notable exceptions, due to circumstances which we are not able to point out, as they involve transactions as between the several partnerships, whose affairs have been

handled separately in the account-keeping. But, as a general proposition, the assumed fairness of awarding a profit of only 11.28 per cent to the investment of a first series share, while giving an eighth series share 58.46 per cent, is open to serious challenge. However the accounts may be treated, the fact remains that all are members of the same association, under one management, and that this management discriminates widely between different series shares in the percentage of profits awarded.

By the Wrigley Rule this discrimination is carried to even greater lengths. The table shows:

If there is any ground upon which to defend the award of a dividend of 70.45 per cent on the investment of an eighth series share, while giving to a first series share only 10.27 per cent, we fail to discover it. This exhibit is prima facie proof of an unjust discrimination by this method of apportionment.

It is urged in extenuation, that the large profits shown to accrue to the younger shares are not actually paid them. In case of withdrawal, by an arbitrary system of withdrawal values nearly all of these fanciful profits are withheld, and thus the association is protected from paying more than the shares have actually earned. This, however, is no argument in favor of an inequitable system of apportionment. If, instead of withdrawing, the younger shares remain in the association, then the apportioned profits, excessive as they are, remain to the credit of those shares, and permanently swell their book values.

Under this system, unless the withdrawal values are carefully and systematically guarded by an arbitrary rule, it would pay a member to remain in the organization for the first three or four years, and then withdraw and purchase shares in the latest series. It is not a good plan to establish such a system of premiums for withdrawal, even hypothetically.

IN A MEASURE SELF-EQUALIZING.

It may be said in justice to the Wrigley system, that shares remaining to maturity, while receiving an undue proportion of dividend credits during their earlier years, will be, in turn, discriminated against during their later years; and thus the inequality will be measurably offset in the long run, and the final result will not be far out of the way. But we fail to see the utility of this ascending and descending scale of discrimination. At best it is liable to lead to unfair results as between members of different classes. And, in the case of the original first series, which never has an older series to recoup itself from, the discrimination amounts to a permanent injustice. What this injustice amounts to will be shown in the subjoined table of book values, obtained by several systems of apportionment.

Before passing, we should state that results by the Partnership Rules are not set forth in the foregoing tables, for the reason of fundamental

differences in calculation which render comparisons as to apportionment of profits for a single year impossible. The Partnership Rules apportion all accrued profits from the beginning of the association in a lump sum. A fair comparison of results by the foregoing and by the Partnership Rules can only be made in a table of book values as shown below:

COMPARISON OF BOOK VALUES ASCERTAINED BY VARIOUS SYSTEMS.*

In computing this table, the last preceding book values as arbitrarily taken in the table showing year's profits, was discarded, and a calculation was made going back to the beginning of the association and re-distributing the ascertained profits each year according to each system. Hence, the addition of arbitrary book values previously taken to dues paid in and profits of the year, do not check entirely with this table. The former is only a comparative statement, but this is absolute as to the workings of the several systems and final results produced.

OBSERVATIONS ON THE ABOVE EXHIBIT.

While the object must be the same with each association, i. e., a fair division of the net earnings among the stockholders, the methods adopted for arriving at apportionments, as shown above, are as diverse as could well be imagined.

In summing up our observations as to the operation of these various rules and systems, we cannot do better than quote a paragraph from the Fifteenth Annual Report of the Bureau of Statistics of Labor and Industries of New Jersey (p. 534), which is as follows:

"Great diversity of opinion exists as to the best rule for dividing profits. It is an important question, and the reputation of an association depends in some measure on the solution of the problem. Every association desires to mature its old series at the earliest date compatible with equity, and the method of apportioning profits used has a marked bearing upon the date of maturity. Many associations whose reports the Secretary has examined have, by a faulty system of profitsharing, retarded the maturity of their older series from two to eight months. The most common mistake noticed in the methods consist in allowing too much profit to the younger series and ignoring the compound interest idea."

This fully states our experience and conclusions. Without doubt many of the associations withhold from their older series a portion of the profits justly belonging to them, in order to apportion to the younger series larger profits than they are entitled to. In order to convince Secretaries of this fact, we must appeal to first principles.

Assuming as axiomatic that the object of an apportionment must be a fair division of the profits among the stockholders, the whole question resolves itself into this: "What is the basis of a fair division?" We say that the only true and equitable basis is that of investment, amount and time being both considered as factors.

4BL