The case would be different if Y came into the business with a one-half interest on the payment of $10,000. Under these circumstances, the opening balance sheet of the firm of X and Y would appear as follows: If the good-will is written off, the balance sheet would reveal the following condition: 7. Illustration of purchase of an interest in the profits.—Let us assume that the agreement in the first case provided that X would admit Y and give him one-half of the profits, upon the payment of $10,000. When Y had made his payment the open ing balance sheet would reveal the following condition : It should be noted that in this case the agreement stipulated that the profits and losses are to be shared equally, altho the capital ratios are unequal. This is not an uncommon situation in actual business relations.
8. Other illustrations.—Another variation may be illustrated if it is assumed that Y is admitted to a two-thirds interest in the business on the payment of $6,000. Here it is evident that Y is bringing into the business, good-will and business connections in ad dition to the cash which he contributes, which will make his capital account twice that of X. Under these conditions the balance sheet of the new firm may be represented as follows : In all such cases, it is necessary to determine the exact nature of the agreement between the parties; the division of interest between the partners, and what each actually contributes to the new firm.
9. Division of profits.—The basis upon which profits and losses are to be distributed to the mem bers of the firm .should invariably be stated. If the copartnership agreement does not definitely provide the method of division, the law assumes that the part ners intended to divide the profits and losses equally.
There are a number of different ways in which the profits and losses may be shared. Profits may be di vided (1) in proportion to the amount of capital contributed by each partner and according to the time such capital has remained in the business; (2) in pro portion to the amount of capital originally contrib uted by each; (3) on the basis of a ratio agreed be tween the partners, which may be different from the capital ratio.
10. Illustration of division of profits in proportion to the capital invested and the time such capital has been and Y are partners under arti cles of copartnership which provide that the profits at the end of the year shall be divided on the basis of the capital invested and the time it has remained em ployed. The profits for the period amount to $4,
120. How much should each partner receive? The capital accounts in the ledger appear as follows: 11. Solution of problem.—To solve this problem, we must find first, the average investment of each partner, and, second, what portion of the total profits, $4,120, is to be paid to each. The average invest ment of a firm may be defined as a fund which, if placed at interest for a given unit of time, will pro duce the same amount of interest as the various amounts invested by the partners for different lengths of time. Inasmuch as the investments and with drawals in this instance were all made on the first day of the month, we may compute the average investment using the month as the unit of time. If, however, the investments were not made on the same date, it would be necessary for us to use the day as the unit of time. If we inspect the account of X, we will note that he had the sum of $3,000 invested for a period of two months, after which he withdrew $2,000, leaving his net investment $1,000, which remained unchanged for three months. On June 1st, he in vested $4,000 additional which brought his invest ment up to $5,000, and which amount remained MI changed for four months, or until October 1st, on which date he contributed an additional $5,000, bringing his capital up to $10,000, which remained invested for one month. On November 1st, he with drew $3,000, leaving his net investment $7,000, which remained unchanged until the end of the year.
The rule for finding the average investment is as follows: Multiply each amount on the credit side of the account by the number of months or days inter vening between the date of investment and the end of the unit period. Make a similar calculation of each of the individual amounts withdrawn, from the date of withdrawal to the end of the period. Subtract the sum of the products of the withdrawn amounts from the sum of the products of the contributed amounts. The difference will be the average investment for the unit period whether this be one month or one day. To find the average investment for one year, divide by 12 or 365. It will not be necessary to do this, how ever, for the purposes of our problem inasmuch as the division by 12 or 365 would not alter the ratio.