Calculate gaining ratio, new profit-sharing ratio, and goodwill payable when a partner retires and remaining partners split the share.

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Gaining (Gain) Ratio Formula

The following formulas are used in partnership accounting to determine the gaining ratio (often called the โ€œgain ratioโ€) when a partner retires. 

Gainแตข = New Shareแตข - Old Shareแตข\ Gaining Ratio = GainA:GainB
  • Where Gaini is the increase in profit share of continuing partner i (dimensionless fraction/ratio)
  • New Sharei is partner iโ€™s new profit-sharing fraction after retirement
  • Old Sharei is partner iโ€™s old profit-sharing fraction before retirement

In words: each continuing partnerโ€™s gain is their new profit-sharing share minus their old share. The gaining ratio is the ratio of these gains among the continuing partners. If an acquisition split is given, the retiring partnerโ€™s share is distributed to the continuing partners in that split, and the gaining ratio follows the same split.

How to Calculate Gain Ratio?

The following example problem outlines how to calculate the gaining (gain) ratio.

Example Problem #1:

  1. First, determine the old profit-sharing ratio (parts).
    • The old ratio is given as: A : B : C = 3 : 2 : 1.
  2. Next, identify the retiring partner and the acquisition ratio among the continuing partners.
    • Partner C retires, and Cโ€™s share is acquired by A and B in the ratio 3 : 2.
  3. Finally, calculate each continuing partnerโ€™s gain and express it as a ratio:

Old shares: A = 3/6, B = 2/6, C = 1/6, so the retiring partnerโ€™s share is 1/6.

Gain of A = (1/6) ร— (3/(3+2)) = (1/6) ร— (3/5) = 1/10

Gain of B = (1/6) ร— (2/(3+2)) = (1/6) ร— (2/5) = 1/15

Gaining (Gain) Ratio = Gain of A : Gain of B = (1/10) : (1/15) = 3 : 2

FAQ

What is the significance of the Gain (Gaining) Ratio in business partnerships?

In partnership accounting, the gaining ratio shows the proportion in which the continuing partners increase their profit-sharing shares when a partner retires. It is commonly used to distribute adjustments (such as goodwill, reserves, or revaluation profit/loss) among the continuing partners in a fair and agreed manner.

Can the Gain Ratio be negative?

In a retirement scenario, each continuing partnerโ€™s gain should be zero or positive (because the retiring partnerโ€™s share is redistributed to the continuing partners). If a computed value is negative, that partner is actually sacrificing share under the stated โ€œnew ratio,โ€ and the situation is better described using a sacrifice ratio rather than a gaining ratio for that partner.

How does the acquisition ratio affect the Gain (Gaining) Ratio?

The acquisition ratio states how the retiring partnerโ€™s share is taken over by the continuing partners. That split determines each continuing partnerโ€™s gain, so the gaining ratio typically matches the acquisition ratio (for example, if A and B acquire the retiring partnerโ€™s share in the ratio 3:2, their gaining ratio is 3:2).