Reconstitution and the new profit sharing ratio

Any change in the agreement between partners reconstitutes the firm: a new partner joining (admission), a change in the profit sharing ratio, a partner leaving (retirement), or a partner's death. The old agreement ends and a new one begins, but the firm continues its business.

A new partner can join only with the consent of all the existing partners (unless the deed says otherwise). He gets two rights: to share the firm's assets, and to share its future profits. In return, he usually brings capital, and often a premium for goodwill.

His share must come from the old partners: when a new partner comes in, someone must give up part of their share. So the first job is to find the new profit sharing ratio. Three cases:

• Nothing is said about how he takes his share: he takes it from the old partners in their old ratio. Their remaining share is divided in the old ratio. For example, if A and B share 3:2 and C gets 1/5, then 4/5 is left: A gets 3/5 × 4/5 = 12/25, B gets 8/25, and C gets 5/25. New ratio 12:8:5.
• He takes given fractions from each partner: each old partner's new share = old share − the fraction given.
• Each old partner surrenders a part of his own share: new share = old share × (1 − the part surrendered), and the new partner's share is the total surrendered.