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1. Change in Profit Sharing Ratio (PSR)

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Definition

Change in PSR refers to the modification of the ratio in which existing partners share their profits and losses without any change in the number of partners. It is a structural change in the partnership contract that requires an adjustment of existing reserves and goodwill.

Explanation

When the ratio changes, some partners will inevitably get a larger share (Gaining) and others will get a smaller share (Sacrificing). We must ensure that the partner who loses share is compensated by the partner who gains share.

  • The old partnership deed is dissolved.
  • A new partnership deed is created.
  • Goodwill must be adjusted among partners.
  • Accumulated profits and reserves must be distributed according to the old ratio.

Sacrificing and Gaining Ratio

  • Sacrificing Ratio: The ratio in which old partners surrender their share in favor of others.
    Formula: Old Ratio - New Ratio
  • Gaining Ratio: The ratio in which remaining/new partners acquire the share of the sacrificing partner.
    Formula: New Ratio - Old Ratio

Examples

  • Case 1: If A and B share profits 3:2 and they decide to share equally (1:1), A's share goes from 3/5 to 1/2. A has sacrificed.
  • Case 2: If C joins an existing firm and takes a share from A and B, A and B are the sacrificing partners, and C is the gaining partner.
❌ Common Misconception: Gaining ratio and Sacrificing ratio are the same.
✅ Correction: They are opposites. One represents a loss of share, the other a gain. You cannot have both in the same person for the same change.
💡 Takeaway: Always calculate the Sacrifice or Gain first before doing any other adjustment.

2. Admission of a Partner

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Meaning

Admission is the process where a new person becomes a partner in an existing firm, thereby changing the existing agreement and the profit-sharing arrangement. The new partner typically brings in Capital and Premium for Goodwill.

Key Adjustments

  1. Goodwill: The new partner pays for the reputation the firm has built. This is shared by old partners in their Sacrificing Ratio.
  2. Revaluation: Assets and liabilities must be revalued to check for changes in value (e.g., building, machinery, or creditors).
  3. Adjustment of Capital: Partners may decide that their capital in the new firm should be in proportion to their new profit-sharing ratio.

Comparison: Admission vs. Change in PSR

Feature Change in PSR Admission of Partner
Number of Partners Remains the same Increases
New Agreement Required Required
New Partner's Capital Not applicable Introduced
Sacrificing Ratio Calculated among old partners Calculated between old and new

Modern Tools: Accountants use QuickBooks / TallyPrime for journal entries and Microsoft Excel for complex ratio calculations.

3. Retirement and Death of a Partner

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Meaning

Retirement is the withdrawal of a partner from the firm. Death refers to the cessation of a partner's interest due to their demise. Both lead to the reconstitution of the firm.

Key Points

  • Revaluation: Just like admission, assets and liabilities are revalued.
  • Goodwill: The retiring or deceased partner is entitled to their share of the firm's goodwill.
  • Amount Due: Total amount (Capital + Share of Goodwill + Share of Reserves + Revaluation profit/loss) must be calculated.
  • Executor's Account: In case of death, the amount is paid to the partner's legal heir, known as the Executor.
❌ Common Misconception: When a partner retires, the firm ends.
✅ Correction: The firm continues with the remaining partners. Only the partnership agreement changes.

4. Numerical Problems & Formulas

📘 Formulas & Practice

Formula Summary

  • Sacrificing Ratio = Old Ratio - New Ratio
  • Gaining Ratio = New Ratio - Old Ratio
  • New Ratio = Old Ratio - Sacrificing Ratio
  • Amount due to Retiring Partner = Capital + Share of Goodwill + Share of Reserves + Share of Revaluation Profit - Share of Revaluation Loss - Drawings

Problem 1: Sacrificing Ratio

A and B are partners sharing profits in 3:2. They admit C for 1/5th share. Calculate the new ratio and sacrificing ratio.

Step-by-Step Solution:
1. Let the total profit be 1.
2. C's share = 1/5.
3. Remaining share for A and B = 1 - 1/5 = 4/5.
4. A's new share = 3/5 of 4/5 = 12/25.
5. B's new share = 2/5 of 4/5 = 8/25.
6. C's share in 25th part = 1/5 = 5/25.
7. New Ratio = 12:8:5.
8. Since no specific sacrifice is mentioned, the Sacrificing Ratio is the same as the Old Ratio (3:2).
        

5. Case Study: Zenith Tech Solutions

Zenith Tech Solutions was a small software consultancy started by Rohan and Meera in 2020 with a 1:1 ratio. In 2023, they admitted Arjun (an AI specialist) to bring in expertise.

The Reconstitution: Arjun brought 1,000,000 Rupees as capital and 300,000 Rupees as premium for goodwill. The partners revalued assets, noting a 200,000 Rupee increase in equipment value and 50,000 Rupee increase in liabilities.

The Shift: Later, Meera retired. This triggered another reconstitution. The firm's goodwill was valued at 600,000 Rupees, which Rohan and Arjun (the gaining partners) had to compensate Meera for. Her total dues were settled via an Executor's Account.

Multiple Choice Questions

📝 Practice MCQs
  1. At the time of admission of a partner, the old partners sacrifice their share in:
    A) Gaining Ratio | B) New Ratio | C) Sacrificing Ratio | D) Capital Ratio
    Answer: C. Explanation: Old partners give up a part of their profit to provide a share to the new partner.
  2. Revaluation Account is a:
    A) Real Account | B) Personal Account | C) Nominal Account | D) Asset Account
    Answer: C. Explanation: It is prepared to record gains and losses from changes in asset and liability values.
  3. Gaining Ratio is calculated at the time of:
    A) Admission | B) Retirement | C) Death | D) Both B and C
    Answer: D. Explanation: In both retirement and death, existing partners gain the share of the outgoing partner.
  4. If the new partner brings his share of goodwill in cash, it is credited to:
    A) New Partner's Capital Account | B) Old Partners' Capital Accounts | C) Revaluation Account | D) Goodwill Account
    Answer: B. Explanation: The premium is a compensation for the old partners for the sacrifice they made.
  5. The formula for Sacrificing Ratio is:
    A) New Ratio - Old Ratio | B) Old Ratio - New Ratio | C) Old Ratio + New Ratio | D) None of these
    Answer: B. Explanation: Sacrifice is the reduction in the old share.

Exam-Oriented Questions with Answers

📊 Important Questions
  1. Distinguish between Sacrificing Ratio and Gaining Ratio.
    Answer: Sacrificing ratio is (Old - New) and is used during admission to distribute goodwill. Gaining ratio is (New - Old) and is used during retirement/death to compensate the outgoing partner.
  2. What is the purpose of preparing a Revaluation Account?
    Answer: To ensure that the assets and liabilities are recorded at their current market values so that neither the old partners nor the new partner is unfairly treated regarding past value changes.
  3. How is Goodwill treated at the time of admission of a partner?
    Answer: The new partner brings premium for goodwill. This is credited to the old partners' capital accounts in their sacrificing ratio.
  4. Explain the concept of an Executor's Account.
    Answer: When a partner dies, the amount due to them is transferred to an Executor's Account, representing the firm's liability towards the deceased partner's legal heirs.
  5. Write the journal entry for an increase in the value of Machinery during revaluation.
    Answer: Machinery Account (Debit) to Revaluation Account (Credit).

Revision Notes & Memory Tricks

⚡ Quick Revision
  • Reconstitution: Changing the old agreement while the firm continues.
  • Admission: Increases number of partners; uses Sacrificing Ratio.
  • Retirement/Death: Decreases number of partners; uses Gaining Ratio.
  • Revaluation: Done to update asset/liability values.

Mnemonic (The "S-O-N" Rule):
Sacrifice = Old - New.

⚠️ Final Confusion Alert:
Don't confuse Retirement (firm continues) with Dissolution (firm shuts down)!