Calculating the new profit-sharing ratio
On admission, the new partner gets his share from the old partners. Common cases:
- Only the new partner's share given: old partners keep the rest in their old ratio. New share of old partner = old share × (1 − new partner's share).
- Sacrifice by old partners given: New share = Old share − Sacrifice.
- New partner takes his share from one partner only: only that partner's share falls.
Sacrificing ratio = old share − new share for each old partner.
Goodwill on admission (AS 26)
The new partner pays for his share of goodwill because he will share future extra profits.
- Premium brought in cash: Bank A/c Dr, To Premium for Goodwill A/c; then Premium for Goodwill A/c Dr, To Sacrificing Partners' Capital A/cs (sacrificing ratio).
- Premium not brought in cash: New Partner's Current/Capital A/c Dr, To Sacrificing Partners' Capital A/cs.
- Partly brought: combine both.
- Premium withdrawn by old partners: Old Partners' Capital A/cs Dr, To Bank.
AS 26: no goodwill account is raised for self-generated goodwill. If old goodwill exists in books, write it off among old partners in the old ratio.
Hidden goodwill
If the new partner's capital implies a total capital higher than the combined capitals (after adjustments), the difference is hidden goodwill: Goodwill = Implied total capital − (Old capitals after adjustments + New partner's capital).
Revaluation of assets and liabilities
Assets and liabilities are revalued so the new partner neither gains nor loses from changes that happened earlier. The Revaluation Account balance goes to old partners in the old ratio. Alternatively, a Memorandum Revaluation Account keeps book values unchanged and adjusts through capitals.
Reserves and accumulated profits
General Reserve, credit balance of P&L, Workmen Compensation Reserve (excess over claim), Investment Fluctuation Reserve (excess over fall) go to old partners in the old ratio. Accumulated losses are debited to them in the old ratio.
Adjustment of capitals
Case 1: old partners' capitals set on the new partner's capital. Total capital = New partner's capital × reciprocal of his share. Each old partner's new capital = total × his new share. Compare with adjusted capital: surplus is withdrawn (Capital Dr, To Bank/Current A/c); shortage is brought in (Bank Dr, To Capital).
Case 2: new partner's capital set on old partners'. Total = combined adjusted old capitals ÷ their combined new share; new partner's capital = total × his share.
Balance sheet of the new firm
After all entries, prepare the partners' capital accounts (with columns for each partner) and the new balance sheet: revised values of assets and liabilities, new cash/bank balance (including amounts brought in or taken out), and the partners' closing capitals. The totals must agree.
Key formulas and definitions
- Old partner's new share = Old share × (1 − New partner's share)
- Sacrifice = Old share − New share
- Premium share of each sacrificer = Premium × his sacrifice ÷ total sacrifice
- Hidden goodwill = New partner's capital ÷ his share − (Old adjusted capitals + New partner's capital)
- Total capital of new firm = New partner's capital ÷ his share
- Old partner's required capital = Total capital × his new share
Worked examples
1. A, B share 3:2. C admitted for 1/5. Find new ratio and sacrificing ratio.
Left for A, B = 4/5. A = 3/5 × 4/5 = 12/25; B = 2/5 × 4/5 = 8/25; C = 5/25. New 12:8:5. Sacrifice: A 15/25 − 12/25 = 3/25; B 10/25 − 8/25 = 2/25 → 3:2.
2. X, Y 2:1. Z admitted for 1/4, which he takes 1/6 from X and 1/12 from Y. New ratio?
X = 2/3 − 1/6 = 1/2 = 6/12; Y = 1/3 − 1/12 = 3/12; Z = 3/12. New 6:3:3 = 2:1:1.
3. C brings ₹20,000 premium; sacrificing ratio 3:2. Entries.
Bank Dr 20,000, To Premium for Goodwill 20,000. Premium for Goodwill Dr 20,000, To A's Capital 12,000, To B's Capital 8,000.
4. Firm's goodwill ₹90,000. D joins for 1/3 share but brings no cash for goodwill. Old ratio A:B = 1:1, sacrifice equal.
D's share of goodwill = 30,000. D's Current A/c Dr 30,000, To A's Capital 15,000, To B's Capital 15,000.
5. A and B have capitals ₹60,000 and ₹40,000 (after adjustments). C brings ₹50,000 for 1/4 share. Find hidden goodwill.
Implied total = 50,000 × 4 = 2,00,000. Actual = 60,000 + 40,000 + 50,000 = 1,50,000. Goodwill = ₹50,000; C's share = 12,500, credited to A, B in sacrificing ratio.
6. C brings ₹1,00,000 for 1/5; new ratio 12:8:5. A's adjusted capital ₹2,70,000, B's ₹1,50,000. Adjust capitals.
Total = 5,00,000. A needs 2,40,000 → surplus 30,000 withdrawn. B needs 1,60,000 → brings 10,000.
7. Balance before admission: Cash 20,000, Stock 50,000, Building 1,30,000 = 2,00,000; Creditors 40,000, Capitals A 1,00,000, B 60,000. Building +20,000; C brings capital 50,000 and premium 10,000 (to A, B 3:2). New totals?
Revaluation gain 20,000 → A 12,000, B 8,000. Premium → A 6,000, B 4,000. Capitals: A 1,18,000, B 72,000, C 50,000 = 2,40,000. Assets: Cash 80,000, Stock 50,000, Building 1,50,000 = 2,80,000 = Creditors 40,000 + 2,40,000.
Common mistakes
- Giving goodwill premium to old partners in the old ratio when the sacrificing ratio is different.
- Crediting revaluation gain or reserves to the new partner.
- Raising a goodwill account for the new partner's share (not allowed under AS 26).
- Forgetting to include the new partner's capital when computing hidden goodwill.