Admission of a Partner

When a firm needs more capital or managerial skill, it may admit a new partner. On admission, the new partner gets two rights: a share in future profits and a share in the assets of the firm. In return he brings in capital and (usually) a premium for goodwill. The first task is arithmetic: working out the new profit-sharing ratio and the sacrificing ratio.

The new partner's share comes out of the old partners' shares — so the old partners sacrifice. The sacrificing ratio = Old Ratio − New Ratio, and it is the ratio in which the old partners give up profit to the newcomer (and so the ratio in which they receive the goodwill premium).

Common cases:

• New partner's share given, old ratio unchanged between themselves: the old partners sacrifice in their old ratio, so sacrificing ratio = old ratio.
• New partner acquires his share from the old partners in a stated ratio: deduct each old partner's surrender from his old share.

Worked example. A and B share 3:2. C is admitted for 1/5. Remaining share for A and B = 1 − 1/5 = 4/5, shared in their old ratio 3:2. So A = 4/5 × 3/5 = 12/25, B = 4/5 × 2/5 = 8/25, C = 1/5 = 5/25. New ratio = 12:8:5. Here A and B sacrificed in 3:2 (their old ratio). Getting this ratio right is the foundation for the goodwill entry that follows.

Because the new partner will share in future profits built on the firm's reputation, he compensates the old partners for goodwill. AS-26 still bars raising self-generated goodwill in the books, so the treatment depends on how the goodwill is brought.

• Premium brought in cash (premium method) — the new partner brings his share of goodwill in cash. Cash is received and the premium is then credited to the sacrificing partners in their sacrificing ratio:
  Cash/Bank A/c Dr (capital + premium); Premium for Goodwill A/c Dr / To Sacrificing Partners' Capital A/cs (in sacrificing ratio).
• Premium not brought in / brought partly — the new partner's capital is debited for his share of goodwill (a hidden adjustment): New Partner's Capital A/c Dr / To Sacrificing Partners' Capital A/cs.
• Premium withdrawn by old partners — if the old partners take the premium out, an extra entry credits Cash and debits their capitals.

Hidden (inferred) goodwill. Sometimes goodwill is not given but can be worked out from the capitals. Compute the firm's total capital implied by the new partner's capital and share, compare it with the actual combined capital, and the shortfall is the firm's goodwill. For example, if C brings Rs 30,000 for a 1/4 share, the implied total capital = 30,000 × 4 = Rs 1,20,000; if the actual total capital (including C) is Rs 1,00,000, the hidden goodwill = Rs 20,000, and C's share = 20,000 × 1/4 = Rs 5,000, adjusted through capitals. The golden rule throughout: the goodwill premium always goes to the sacrificing partners in their sacrificing ratio.

Just like a change in ratio, admission triggers a revaluation of assets and liabilities and a distribution of accumulated reserves — all belonging to the old partners in the old ratio.

• Revaluation Account — asset increase / liability decrease = gain (credit); asset decrease / liability increase = loss (debit). The net profit or loss is transferred to the old partners in their old ratio (the new partner does not share it).
• Reserves & accumulated profits/losses — distributed to the old partners in the old ratio before admission.

Finally comes capital adjustment. Often the partners agree that capitals should be in the new profit-sharing ratio. Two situations arise:

• New partner's capital is the base — from his capital and share, compute the total capital of the firm, then each old partner's required capital in the new ratio. The difference between actual and required capital is brought in or withdrawn (or transferred to a current account).
• Total capital is given — split it in the new ratio to find each partner's required capital.

For example, if after all adjustments A's actual capital is Rs 70,000 but his required capital in the new ratio is Rs 60,000, the surplus Rs 10,000 is paid to him (or kept in his current account). With revaluation, reserves, goodwill and capital adjustment complete, the new partner is fully admitted and the firm's books reflect the reconstituted partnership — the same machinery that handles retirement next.