Admission of a Partner – Sacrificing Ratio (Partnership Accounting)

 Sacrificing Ratio

At the time of admission of a new partner, the existing partners are required to surrender a portion of their profit share in favour of the incoming partner. The ratio in which the old partners agree to sacrifice their share is known as the sacrificing ratio.

Since the incoming partner acquires a part of the profit share from existing partners, he compensates them for this sacrifice. This compensation is generally paid in the form of premium or goodwill. The amount of goodwill brought in by the new partner is distributed among the existing partners in the sacrificing ratio.

1. Formula to Calculate Sacrificing Ratio: Sacrificing Ratio = Old Profit-Sharing Ratio – New Profit-Sharing Ratio
2. The sacrifice made by a partner equals: Old Share of Profit – New Share of Profit

In summary, the sacrificing ratio is the ratio in which existing partners give up their share of future profits in favour of the new partner and receive compensation in proportion to their sacrifice.

Case 1: When the New Partner’s Share Is Given Without Details of Sacrifice by Old Partners

Illustration:  A and B are partners sharing profits in the ratio of 5: 3. They admit Bijoy as a new partner for 1/7 share in the profits. The new profit-sharing ratio becomes 4: 2: 1. Calculate the sacrificing ratio of A and B.

Solution

• A’s old share = 5/8
• A’s new share = 4/7
• A’s sacrifice = 5/8 − 4/7 = 3/56
• B’s old share = 3/8
• B’s new share = 2/7
• B’s sacrifice = 3/8 − 2/7 = 5/56
• Sacrificing Ratio A: B = 3/56: 5/56 = 3: 5

Case 2: When Old Ratio and New Ratio of All Partners Are Given

Illustration A and B share profits in the ratio of 4: 3. They admit C as a new partner. The new profit-sharing ratio is 2: 3: 1. Calculate the gain or sacrifice of A and B.

Solution

• A’s old share = 4/7
• A’s new share = 2/6
• A’s sacrifice = 4/7 − 2/6 = 10/42
• B’s old share = 3/7
• B’s new share = 3/6
• B’s gain = 3/6 − 3/7 = 3/42
• C’s share = 1/6 = 7/42

Verification (Total Sacrifice = Total Gain)

• A’s total sacrifice = B’s gain + C’s gain
• = 3/42 + 7/42 = 10/42

Conclusion: In this case, A alone sacrifices, and B gains.

Why Sacrificing Ratio Matters?

1. Goodwill Adjustment: The goodwill brought by the new partner is divided among old partners in the sacrificing ratio.
2. Fairness: Ensures that partners who give up a higher share are properly compensated.
3. Foundation for Future Profit Sharing: It helps set the new ratio clearly.
4. Basis for Capital Adjustments: Used in revaluing assets and liabilities during admission.

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