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Difficulty: MediumAdmission of a New Partner

Bello and Kabir are partners in a trading firm sharing profits and losses in the ratio of 4:14:1. They admit Danladi into the partnership, giving him a 16\frac{1}{6} share of future profits. The goodwill of the firm is valued at ₦120,000\text{₦}120,000, and Danladi brings in his required share of goodwill in cash. What is the amount of goodwill premium (in Naira) to be credited to Kabir's capital account?

Answer: 4000 ₦

Answer

The amount of goodwill premium credited to Kabir's capital account is ₦4,000.
The total goodwill of the firm is ₦120,000\text{₦}120,000. Danladi's 16\frac{1}{6} share of goodwill is 16×₦120,000=₦20,000\frac{1}{6} \times \text{₦}120,000 = \text{₦}20,000. This premium is shared between Bello and Kabir in their sacrificing ratio of 4:14:1. Therefore, Kabir receives 15×₦20,000=₦4,000\frac{1}{5} \times \text{₦}20,000 = \text{₦}4,000.

Step-by-Step Solution

1
Determine the new partner's share of goodwill
Danladi's share of goodwill = 16×₦120,000=₦20,000\frac{1}{6} \times \text{₦}120,000 = \text{₦}20,000
The incoming partner pays a premium for goodwill proportional to their share of future profits.
2
Apportion the goodwill premium to the existing partners
Kabir's share = 15×₦20,000=₦4,000\frac{1}{5} \times \text{₦}20,000 = \text{₦}4,000
Goodwill premium brought in cash by a new partner is credited to existing partners in their sacrificing ratio (which equals their old profit-sharing ratio of 4:14:1 when no new ratio among old partners is specified).

Key Concept

Valuation and distribution of goodwill premium upon admission of a new partner
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Admission of a New Partner

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