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Difficulty: HardAdmission of a New Partner

Zainab and Babatunde are partners in a haulage enterprise sharing profits and losses in the ratio of 3:23:2. Prior to the admission of Chijioke, their capital balances were ₦400,000\text{₦}400,000 and ₦300,000\text{₦}300,000 respectively. Upon admitting Chijioke to a 15\frac{1}{5} share in the profits, the firm's assets were revalued, resulting in an appreciation of ₦80,000\text{₦}80,000 on machinery and a depreciation of ₦20,000\text{₦}20,000 on inventory. Additionally, goodwill was valued at ₦150,000\text{₦}150,000, and Chijioke brought in his share of goodwill premium in cash to be distributed to the existing partners. What is the updated balance of Zainab's capital account immediately following these admission adjustments?

Answer: 454000 ₦

Answer

The updated balance of Zainab's capital account immediately following the admission adjustments is ₦454,000.
Zainab's capital account begins with ₦400,000. The net gain on revaluation (₦80,000 appreciation minus ₦20,000 depreciation = ₦60,000) is split in the old ratio of 3:2, adding ₦36,000 to her account. The goodwill premium paid by Chijioke is 1/5 of ₦150,000, which equals ₦30,000; Zainab receives 3/5 of this premium (₦18,000). Adding these yields an updated capital balance of ₦454,000.

Step-by-Step Solution

1
Calculate the net gain or loss on revaluation of assets
Net Revaluation Gain = ₦80,000 - ₦20,000 = ₦60,000
Appreciation increases asset value while depreciation decreases it. The net figure represents total gain shared by existing partners.
2
Distribute the net revaluation gain to Zainab using the old profit sharing ratio
Zainab's Share of Revaluation Gain = 3/5 × ₦60,000 = ₦36,000
Revaluation gains belong to existing partners in their old profit sharing ratio.
3
Determine Chijioke's share of goodwill and allocate premium to Zainab
Goodwill Premium = 1/5 × ₦150,000 = ₦30,000; Zainab's Share = 3/5 × ₦30,000 = ₦18,000
The incoming partner pays premium for goodwill proportional to their profit share, which is credited to existing partners in their sacrificing ratio.
4
Sum Zainab's initial capital and all admission credits
Updated Capital Balance = ₦400,000 + ₦36,000 + ₦18,000 = ₦454,000
Capital accounts increase with revaluation gains and goodwill premium credits.

Key Concept

Adjustment of Partner's Capital Account on Admission
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Topics

Admission of a New Partner

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