Admission of C: Sacrificing Ratio, Hidden Items and Proportionate Capital
A and B have been partners sharing profits 3:2 with capitals of ₹4,50,000 and ₹3,00,000. On 1 April 2024 they admitted C for a 1/5 share. C brought ₹2,00,000 as capital and ₹90,000 as goodwill, both in cash. The firm's goodwill was valued at ₹4,50,000. On the date of admission the books showed old furniture that had been fully depreciated and carried at nil; its current value is ₹40,000. An electricity bill of ₹15,000 for March 2024 had not been recorded. The partners agreed that C's capital should be proportionate to his share of the total capital of the new firm, and that any excess or shortfall in the old partners' capitals, after all adjustments including goodwill, should be settled in cash in the old profit-sharing ratio. The new profit-sharing ratio is 3:1:1.
1. Compute the sacrificing ratio and show how the ₹90,000 goodwill brought by C should be distributed. Explain why the old profit-sharing ratio is not used.
Read the worked answer
Sacrificing ratio = old share minus new share.
- A: 3/5 − 3/5 = 0
- B: 2/5 − 1/5 = 1/5
- C's share of 1/5 is obtained entirely from B.
Therefore the whole ₹90,000 is credited to B's capital account:
- Bank A/c Dr 90,000; To C's Capital A/c 90,000 (goodwill brought in cash)
- C's Capital A/c Dr 90,000; To B's Capital A/c 90,000 (goodwill transferred to the sacrificing partner)
Using 3:2 would give A ₹54,000 and B ₹36,000, which is wrong because A's share of profits is unchanged at 3/5. A gives up nothing and cannot be compensated for a sacrifice he has not made. The check is that goodwill of ₹4,50,000 × 1/5 = ₹90,000, which equals C's contribution. If goodwill is not brought in cash, the same credit to B is still required, with C's capital debited.
2. Pass the entries for the unrecorded furniture and the unrecorded electricity bill, and compute the revised capitals of A and B after revaluation and goodwill.
Read the worked answer
Entries:
- Furniture A/c Dr 40,000; To Revaluation A/c 40,000
- Revaluation A/c Dr 15,000; To Outstanding Electricity Bill A/c 15,000
The Revaluation Account shows a profit of ₹25,000 (₹40,000 − ₹15,000), shared in the old ratio 3:2:
- A: ₹15,000; B: ₹10,000
Revised capitals:
- A: 4,50,000 + 15,000 = ₹4,65,000
- B: 3,00,000 + 10,000 = ₹3,10,000
After crediting the goodwill of ₹90,000 to B:
- A: ₹4,65,000
- B: ₹4,00,000
- Combined: ₹8,65,000
The key point is that the revaluation profit belongs to the old partners only, because C was not a partner when the asset and liability existed. Sharing it with C would give him a windfall from pre-admission events.
3. Using C's capital as the basis, determine the total capital of the new firm and compute the cash each old partner must bring in or withdraw. State the final capitals.
Read the worked answer
C's capital of ₹2,00,000 represents 1/5 of the new firm, so total capital = ₹2,00,000 × 5 = ₹10,00,000. The old partners together must have 4/5, i.e. ₹8,00,000.
Their adjusted combined capital is ₹8,65,000, an excess of ₹65,000. This is settled in the old ratio 3:2:
- A withdraws 65,000 × 3/5 = ₹39,000
- B withdraws 65,000 × 2/5 = ₹26,000
Final capitals:
- A: 4,65,000 − 39,000 = ₹4,26,000
- B: 4,00,000 − 26,000 = ₹3,74,000
- C: ₹2,00,000
- Total: ₹10,00,000
Entries for withdrawal: A's Capital A/c Dr 39,000 and B's Capital A/c Dr 26,000; To Bank A/c 65,000. If the adjusted capitals had been below ₹8,00,000, the shortfall would have been brought in cash in the same 3:2 ratio. The agreement to use the old ratio for this settlement must be applied consistently.