New Profit-Sharing Ratio and Sacrificing Ratio

When a new partner is admitted, he is given a share out of the profits that used to belong entirely to the existing (old) partners. This means the old partners' own shares must reduce to make room for him — the ratio in which they give up their shares is exactly as important, for accounting purposes, as the new partner's own share.

How the new partner's share can be given

A question usually admits a new partner in one of these ways, and the method of calculating the sacrificing ratio depends on exactly which one is used:

• The new partner acquires his share entirely from one old partner — only that partner's share reduces; the other old partner's share is unaffected.
• The new partner acquires his share equally from the old partners — each old partner sacrifices exactly half of the new partner's share.
• The new partner acquires his share from the old partners in a specified ratio — the new partner's share is divided between the old partners in that stated ratio.
• No acquisition ratio is specified at all — the new partner's share is then assumed to come from the old partners in their OLD profit-sharing ratio, so the sacrificing ratio and the old ratio turn out to be the same.

Worked illustration. P and Q share profits in the ratio 5:3. They admit R, who is given a 1/4th share of future profits, which he acquires entirely from P.

P's share before admission = 5/8. R's share = 1/4 = 2/8, taken entirely from P.

P's new share = 5/8 − 2/8 = 3/8. Q's share is unaffected = 3/8. R's share = 2/8. …