Partnership Admission: Calculating New Partner's Goodwill Share

When a new partner is admitted to a firm, goodwill is often valued to compensate the existing partners for the future profits the firm is expected to earn. Sometimes, the value of the firm's goodwill is not explicitly given, but it can be implied from the total capital of the firm based on the new partner's capital and profit share compared to the actual total capital.

Understanding Implied Goodwill Calculation

Implied goodwill is calculated by comparing the total capital of the firm as estimated from the new partner's contribution and share, with the actual combined capital of all partners after adjustments. The excess of the estimated total capital over the actual total capital is considered the goodwill of the firm.

Step-by-Step Calculation of D's Share of Goodwill

Let's calculate the share of goodwill for the new partner, D, based on the given information.

1. Determine Total Capital based on D's Share:

   D is admitted for a 1/5th share in profits and brings ₹35,000 as capital. If ₹35,000 represents 1/5th of the total capital of the new firm, the total capital of the firm should ideally be:

   \(\text{Total Capital based on D's Share} = \frac{\text{D's Capital}}{\text{D's Share}}\)

   \(\text{Total Capital} = \frac{₹35,000}{1/5} = ₹35,000 \times 5 = ₹1,75,000\)

2. Determine Actual Total Capital of the Firm:

   The adjusted capitals of the old partners (A, B, and C) are given as ₹40,000, ₹35,000, and ₹30,000 respectively. D's capital is ₹35,000.

   \(\text{Actual Total Capital} = \text{Adjusted Capital of A} + \text{Adjusted Capital of B} + \text{Adjusted Capital of C} + \text{D's Capital}\)

   \(\text{Actual Total Capital} = ₹40,000 + ₹35,000 + ₹30,000 + ₹35,000\)

   \(\text{Actual Total Capital} = ₹1,05,000 + ₹35,000 = ₹1,40,000\)

3. Calculate Total Goodwill of the Firm (Implied Goodwill):

   The difference between the total capital based on D's share and the actual total capital is the implied goodwill of the firm.

   \(\text{Total Goodwill} = \text{Total Capital based on D's Share} - \text{Actual Total Capital}\)

   \(\text{Total Goodwill} = ₹1,75,000 - ₹1,40,000 = ₹35,000\)

4. Calculate D's Share of Goodwill:

   D's share of goodwill is his share of the total goodwill.

   \(\text{D's Share of Goodwill} = \text{Total Goodwill} \times \text{D's Share}\)

   \(\text{D's Share of Goodwill} = ₹35,000 \times \frac{1}{5} = ₹7,000\)

Based on the calculations, D's share of goodwill is ₹7,000.

Here is a summary of the capitals:

Calculation Summary:

Revision Table: Key Concepts in Partnership Admission

Additional Information: Accounting for Goodwill

When a new partner brings in their share of goodwill, it is typically distributed among the old partners in their sacrificing ratio. If the new partner does not bring goodwill in cash, it might be adjusted through their capital account or a new goodwill account might be raised and then written off.

• Goodwill brought in by the new partner is compensation to the old partners for their sacrifice of profit share.
• The method of accounting for goodwill depends on whether the new partner brings their share of goodwill in cash or not, and the policy of the firm regarding maintaining goodwill in the books.
• In this specific problem, the goodwill is calculated based on the total capital implied by the new partner's capital, which is known as the implied goodwill method. The new partner, D, will typically compensate the old partners for his share of this implied goodwill.