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Difficulty: Very hardAdmission of a New Partner

Ade and Musa are partners in a trading firm sharing profits and losses in the ratio of 3:23:2. Their capital account balances are ₦80,000\text{₦}80,000 and ₦50,000\text{₦}50,000 respectively. On 1st January, they admit Zainab into the partnership for a 15\frac{1}{5} share of profits, bringing the new profit-sharing ratio among Ade, Musa, and Zainab to 2:2:12:2:1. Zainab brings in ₦40,000\text{₦}40,000 as capital and ₦10,000\text{₦}10,000 as premium for goodwill in cash. On admission, the firm's assets are revalued, resulting in a net revaluation profit of ₦10,000\text{₦}10,000. What is the balance of Ade's capital account immediately after the admission of Zainab?

  1. ₦96,000Answer
  2. B
    ₦92,000
  3. C
    ₦94,000
  4. D
    ₦90,000

Answer

The adjusted balance of Ade's capital account after admission is ₦96,000.
Ade's initial capital is ₦80,000. Upon Zainab's admission, the sacrificing ratio between Ade and Musa is calculated as Old Share minus New Share. Ade's sacrifice is 3/5 - 2/5 = 1/5, while Musa's sacrifice is 2/5 - 2/5 = 0. Because Ade made the entire sacrifice of 1/5, he is entitled to 100% of Zainab's ₦10,000 goodwill premium. Furthermore, the net revaluation gain of ₦10,000 is distributed in the old profit-sharing ratio (3:2), giving Ade 3/5 of ₦10,000 = ₦6,000. Summing these credits to Ade's capital gives ₦80,000 + ₦6,000 + ₦10,000 = ₦96,000.

Step-by-Step Solution

1
Calculate the Sacrificing Ratio of the old partners.
Ade's Sacrifice = 35−25=15\frac{3}{5} - \frac{2}{5} = \frac{1}{5}; Musa's Sacrifice = 25−25=0\frac{2}{5} - \frac{2}{5} = 0. Sacrificing ratio is 1:01:0 (entire sacrifice borne by Ade).
Goodwill premium brought in cash by an incoming partner must be shared strictly among sacrificing partners in their sacrificing ratio.
2
Allocate the Net Revaluation Profit to the existing partners.
Ade's share = 35×₦10,000=₦6,000\frac{3}{5} \times \text{₦}10,000 = \text{₦}6,000; Musa's share = 25×₦10,000=₦4,000\frac{2}{5} \times \text{₦}10,000 = \text{₦}4,000.
Revaluation gains or losses occurring prior to admission belong strictly to old partners and must be shared in their old profit-sharing ratio.
3
Allocate the Goodwill Premium paid by the new partner.
Ade receives ₦10,000\text{₦}10,000; Musa receives ₦0\text{₦}0.
Since Musa did not sacrifice any share of profit upon Zainab's admission, Ade is entitled to the full goodwill premium.
4
Compute Ade's final adjusted capital balance.
Ade's Capital = ₦80,000+₦6,000 (Revaluation Gain)+₦10,000 (Goodwill Premium)=₦96,000\text{₦}80,000 + \text{₦}6,000\ \text{(Revaluation Gain)} + \text{₦}10,000\ \text{(Goodwill Premium)} = \text{₦}96,000.
Ade's capital account is credited with both his share of revaluation profit and the goodwill premium.

Key Concept

Accounting treatment of revaluation gain and goodwill premium upon admission of a new partner.
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Topics

Admission of a New Partner

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