When the profit sharing ratio among partners changes, some partners might gain a share of profits while others might sacrifice a share. To determine the sacrifice or gain, we compare each partner's old profit share with their new profit share.

Calculating Partner's Sacrifice or Gain on Ratio Change

The formula to calculate the sacrifice or gain for a partner is:

Sacrifice/Gain = Old Profit Share - New Profit Share

If the result is positive, it indicates a sacrifice (the partner's share has decreased). If the result is negative, it indicates a gain (the partner's share has increased).

Determine Old Profit Shares

The old profit sharing ratio of A, B, and C is 3 : 3 : 4.

Total parts in the old ratio = \(3 + 3 + 4 = 10\).

• A's old share = \(\frac{3}{10}\)
• B's old share = \(\frac{3}{10}\)
• C's old share = \(\frac{4}{10}\)

Determine New Profit Shares

The partners decide to share future profits equally. This means the new profit sharing ratio is 1 : 1 : 1.

Total parts in the new ratio = \(1 + 1 + 1 = 3\).

• A's new share = \(\frac{1}{3}\)
• B's new share = \(\frac{1}{3}\)
• C's new share = \(\frac{1}{3}\)

Calculate Sacrifice or Gain for Each Partner

We now apply the formula (Old Share - New Share) for each partner.

Partner A:

A's change = Old Share - New Share

\( = \frac{3}{10} - \frac{1}{3} \)

To subtract fractions, we find a common denominator, which is 30 (LCM of 10 and 3).

\( \frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30} \)

\( \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30} \)

A's change = \( \frac{9}{30} - \frac{10}{30} = \frac{9 - 10}{30} = \frac{-1}{30} \)

Since the result is negative \((-1/30)\), Partner A gains \(\frac{1}{30}\) share.

Partner B:

B's change = Old Share - New Share

\( = \frac{3}{10} - \frac{1}{3} \)

Using the common denominator 30:

\( = \frac{9}{30} - \frac{10}{30} = \frac{9 - 10}{30} = \frac{-1}{30} \)

Since the result is negative \((-1/30)\), Partner B gains \(\frac{1}{30}\) share.

Partner C:

C's change = Old Share - New Share

\( = \frac{4}{10} - \frac{1}{3} \)

Using the common denominator 30:

\( \frac{4}{10} = \frac{4 \times 3}{10 \times 3} = \frac{12}{30} \)

\( \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30} \)

C's change = \( \frac{12}{30} - \frac{10}{30} = \frac{12 - 10}{30} = \frac{2}{30} \)

Since the result is positive \((2/30)\), Partner C sacrifices \(\frac{2}{30}\) share.

Summary of Sacrifice and Gain

Here is a summary of the calculation results:

The total gain (\(\frac{1}{30} + \frac{1}{30} = \frac{2}{30}\)) equals the total sacrifice (\(\frac{2}{30}\)), which confirms the calculation is correct.

Revision Table: Accounting Adjustments on Ratio Change

When the profit sharing ratio changes, certain accounting adjustments are often made in partnership accounts. These may include:

• Goodwill Adjustment: Goodwill may be valued, and the gaining partners compensate the sacrificing partners by adjusting their capital accounts.
• Revaluation of Assets and Liabilities: Assets and liabilities may be revalued to reflect their current market values. The profit or loss on revaluation is distributed among partners in the old profit sharing ratio.
• Adjustment for Accumulated Reserves and Undistributed Profits/Losses: These are typically distributed among partners in the old profit sharing ratio before the change takes effect, or adjusted through capital accounts.

Additional Information: Why Profit Sharing Ratio Changes

A change in the profit sharing ratio can occur due to various reasons in a partnership, such as:

• Admission of a new partner.
• Retirement or death of an existing partner.
• Change in the role or contribution of partners.
• Agreement among existing partners to change the ratio.

This change is a form of reconstitution of the partnership. The adjustment for sacrifice or gain in profit shares is crucial for correctly accounting for the value of the firm's goodwill and other reserves/profits at the time of the change.