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Difficulty: HardAdmission of a New Partner

Emeka and Fatima are partners in a commercial enterprise sharing profits and losses in the ratio of 2:12:1. Their capital account balances prior to admission are ₦150,000\text{₦}150,000 and ₦90,000\text{₦}90,000 respectively. They agree to admit Audu into the partnership for a 14\frac{1}{4} share of future profits. Upon admission, a revaluation of assets results in a net loss of ₦15,000\text{₦}15,000, and the goodwill of the firm is valued at ₦60,000\text{₦}60,000. If goodwill is raised in the old ratio and immediately written off in the new profit-sharing ratio, what is Emeka's capital balance after all adjustments?

  1. ₦150,000\text{₦}150,000Answer
  2. B
    ₦140,000\text{₦}140,000
  3. C
    ₦170,000\text{₦}170,000
  4. D
    ₦180,000\text{₦}180,000

Answer

Emeka's capital balance after all adjustments is ₦150,000\text{₦}150,000.
The correct capital balance is ₦150,000\text{₦}150,000. Emeka's starting capital of ₦150,000\text{₦}150,000 is reduced by ₦10,000\text{₦}10,000 (his 23\frac{2}{3} share of the ₦15,000\text{₦}15,000 revaluation loss), increased by ₦40,000\text{₦}40,000 (his 23\frac{2}{3} share of goodwill raised in the old ratio), and reduced by ₦30,000\text{₦}30,000 (his 24\frac{2}{4} share of goodwill written off in the new ratio 2:1:12:1:1). Net adjustments sum to zero, retaining the ₦150,000\text{₦}150,000 balance.

Step-by-Step Solution

1
Allocate the net revaluation loss between the existing partners using the old profit-sharing ratio (2:12:1).
Emeka's share of loss = ₦15,000×23=₦10,000\text{₦}15,000 \times \frac{2}{3} = \text{₦}10,000 (debit to Emeka's Capital Account).
Revaluation profits or losses prior to admission belong strictly to the existing partners in their old sharing ratio.
2
Credit the existing partners with the valuation of firm goodwill using the old ratio (2:12:1).
Emeka's credit for goodwill = ₦60,000×23=₦40,000\text{₦}60,000 \times \frac{2}{3} = \text{₦}40,000.
Goodwill created prior to the new partner's entry is distributed to the old partners in their old profit-sharing ratio.
3
Calculate the new profit-sharing ratio for Emeka, Fatima, and Audu.
Audu's share = 14\frac{1}{4}. Remaining share = 1−14=341 - \frac{1}{4} = \frac{3}{4}. Emeka's new share = 23×34=612=12\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}. Fatima's new share = 13×34=312=14\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}. The new ratio is 2:1:12:1:1.
The new ratio determines how future profits and goodwill write-offs are allocated among all partners.
4
Debit all partners' capital accounts to write off goodwill in the new profit-sharing ratio (2:1:12:1:1).
Emeka's debit for goodwill write-off = ₦60,000×24=₦30,000\text{₦}60,000 \times \frac{2}{4} = \text{₦}30,000.
When goodwill is not to be retained in the books, it must be written off against all partners' capital accounts in the new ratio.
5
Compute Emeka's final capital balance.
Final Capital = ₦150,000−₦10,000+₦40,000−₦30,000=₦150,000\text{₦}150,000 - \text{₦}10,000 + \text{₦}40,000 - \text{₦}30,000 = \text{₦}150,000.
Combining the initial capital balance with net debit and credit adjustments yields the updated capital balance.

Key Concept

Accounting for Admission of a New Partner: Revaluation of Assets and Treatment of Goodwill (Raised and Written Off)
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Admission of a New Partner

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