Introduction:
Goodwill is an intangible asset that represents the reputation, customer loyalty, and brand value of a business. It is an important factor in determining the value of a business. When a new partner is admitted into a partnership, it is crucial to distribute the goodwill among the old partners. This is done to ensure fairness, transparency, and to maintain the financial equilibrium of the partnership.

Reasons for distributing goodwill:
1. Recognition of past efforts: Goodwill is generated through the collective efforts of all partners, including the old partners who have been a part of the business before the admission of the new partner. By distributing the goodwill, the old partners are acknowledged for their contributions in building and maintaining the reputation of the business.

2. Sharing the value of the business: Goodwill represents the value of the business beyond its tangible assets. By distributing the goodwill, the old partners are sharing the value they have created with the new partner. This helps in creating a sense of ownership and alignment among all partners.

3. Fairness and equality: Distributing goodwill ensures fairness and equality among the partners. It prevents any undue advantage or disadvantage to any partner. Each partner should have an equal opportunity to benefit from the goodwill of the business.

4. Financial balance: Goodwill has a financial value, and distributing it helps in maintaining the financial equilibrium of the partnership. It ensures that the new partner contributes an amount equivalent to their share of the goodwill, thereby maintaining the overall financial stability of the partnership.

5. Reflecting market value: Distributing goodwill at the time of admission of a new partner helps in reflecting the market value of the business accurately. Goodwill is often considered in the valuation of a business, and distributing it ensures that the new partner is acquiring a fair share of the business's market value.

Conclusion:
Distributing goodwill among the old partners at the time of admission of a new partner is important for recognizing past efforts, sharing the value of the business, ensuring fairness and equality, maintaining financial balance, and reflecting the market value of the business. It is a fair and transparent way to incorporate a new partner into the partnership and maintain the harmonious functioning of the business.