Determination of New Profit Sharing Ratio

The new or incoming partner is entitled to the share of future profits & losses of the firm. Therefore, there will be a change in the existing profit sharing ratio of the old partners since the new partner will acquire his/her share from the existing share of old partners. The new or incoming partners may acquire the share from the old partner in the following ways;

  1. In their old profit-sharing ratio
  2. In a particular ratio or surrendered ratio
  3. In a particular fraction from some of the partners

Let us discuss in detail;

  1. When a new partner acquires his share from old or existing partners in their old profit sharing ratio;

In this situation, the share of the new partner is given & it is assumed that the new partner has acquired his share from old partners in their old profit sharing ratio. Old partners continue to share the balance profits & losses in their old profit-sharing ratio. Unless otherwise agreed, the profit-sharing ratio of the existing partners remains unchanged & the new profit sharing ratio is determined by deducting new or incoming partner’s share from 1 & then dividing the balance in old profit sharing ratio of the old partners.

  1. When share of the New partner is given & new ratio of Old Partners is also given;

In this case, the new partner’s share is deducted from 1 & the balance is divided among old partners in their new ratio. Hence, there is a new profit-sharing ratio for all the partners.

  1. When New or Incoming Partner acquires his share from old or existing partners in a particular ratio;

In such a case, the new or incoming partner acquires a part of share of profits from one partner & a part of share of profits from another partner. The existing partner’s share will change to the extent of share sacrificed on admission of new partner.

  1. When new or incoming partner acquires his shares by surrender of particular fraction of their shares by the old or existing partners;

In such a case, the shares surrendered by the old partners in favor of the new partners are added & it becomes the share of the new partner. The shares surrendered by the old partners is deducted from their respective share to determine old partner’s share in the reconstituted firm. 

The Concept of Sacrificing Ratio

Sacrificing ratio can be explained as the ratio in which existing or old partners sacrifice their share of profits in favor of the new or incoming partner. It can also be defined as the ratio in which the new partner is given a share by the existing partners. This share can be given by all the partners equally or by some of the partners in agreed share. Sacrificing ratio determines the compensation that new partner should pay to the old partners for the share of profits sacrificed by them. The following can be the situations under which sacrificing ratio is determined;

  1. When the share of new or incoming partner is given without giving the details of the sacrifice made by the old or existing partners

In this situation, there is no change in the profit sharing ratio of old partners because it is assumed that the partners make sacrifices in their old profit sharing ratio & for that reason sacrificing ratio is always in the old profit sharing ratio.

  1. When the old ratio of old or existing partners & new ratio of all the partners are given

In this case, the sacrificing ratio is the difference between the old ratio & the new ratio.

  1. When new or incoming partner acquires the share by surrendering a particular fraction of shares by old partners

In such a case, the shares surrendered by the old partner in favor of the new partner are added & it becomes the share of the incoming or new partner. The shares so surrendered by the old partner is deducted from his old share to find out his share in the reconstituted firm.

New Profit Sharing Ratio

When new partner is admitted he acquires his share in profits from the old partners. In other words, on the admission of a new partner, the old partners sacrifice a share of their profit in favour of the new partner. But, what will be the share of new partner and how he will acquire it from the existing partners is decided mutually among the old partners and the new partner. However, if nothing is specified as to how the new partner acquires his share from the old partners; it may be assumed that he gets it from them in their profit sharing ratio. In any case, on admission of a new partner, the profit sharing ratio among the old partners will change keeping in view their respective contribution to the profit sharing ratio of the incoming partner. Hence, there is a need to ascertain the new profit sharing ratio among all the partners. This depends upon how does the new partner acquires his share from the old partners for which there are many possibilities. Let us understand it with the help of the following Revisions.

Revision 1

Anil and Vishal are partners sharing profits in the ratio of 3:2. They admitted Sumit as a new partner for 1/5 share in the future profits of the firm. Calculate new profit sharing ratio of Anil, Vishal and Sumit.

Solution

Sumit’s share = 1/5

Remaining share  =  1 – 1/5 = 4/5

Anil’s new share       = 3/5 × 4/5 =12/25

Vishal’s new share   =   2/5 × 4/5 = 8/25

New profit sharing ratio of Anil, Vishal and Sumit will be 12:8:5.

Note: It has been assumed that the new partner acquired his share from old partners in old ratio

Revision 2

Akshay and Bharati are partners sharing profits in the ratio of 3:2. They admit Dinesh as a new partner for 1/5th share in the future profits of the firm which he gets equally from Akshay and Bharati. Calculate new profit sharing ratio of Akshay, Bharati and Dinesh.

Solution

Dinesh’s share = 1/5 or 2/10

Akshay’s share = 3/5 – 1/10 = 5/10

Bharti’s share = 2/5 – 1/10 = 3/10

New profit sharing ratio between Akshay, Bharati and Dinesh will be 5:3:2.

Revision  3

Anshu and Nitu are partners sharing profits in the ratio of 3:2. They admitted Jyoti as a new partner for 3/10 share which she acquired 2/10 from Anshu and 1/10 from Nitu. Calculate the new profit sharing ratio of Anshu, Nitu and Jyoti.

Solution

Jyoti’s share = 3/10

Anshu’s new share =  3/5 – 2/10 = 4/10

Nitu’s new share = old share – share surrendered

= 2/5 – 1/ 10 = 3/10

The new profit sharing ratio between Anshu, Nitu and Jyoti will be  4 : 3 : 3

Revision 4

Ram and Shyam are partners in a firm sharing profits in the ratio of 3:2. They admit Ghanshyam as a new partner. Ram sacrificed 1/4 of his share and Shyam 1/3 of his share in favour of Ghanshyam. Calculate new profit sharing ratio of Ram, Shyam and Ghanshyam.

Solution

Ram’s old share = 3/5

Share sacrificed by Ram = ¼ of 3/5 = 3/20

Ram’s new share = 3/5 – 3/20 = 9/20

Shyam’s old share = 2/5

Share sacrificed by shyam = 1/3 of 2/5 = 2/15

Shyam’s new share = 2/5 – 2/15 = 4/15

Ghanshyam’s new share =   Ram’s sacrifice + Shyam’s Sacrifice

= 3/20 + 2/15 = 17/60

New profit sharing ratio among Ram, Shyam and Ghanshyam will be 27:16:17

Revision 5

  

Das and Sinha are partners in a firm sharing profits in 4:1 ratio. They admitted Pal as a new partner for 1/4 share in the profits, which he acquired wholly from Das. Determine the new profit sharing ratio of the partners.

  

Solution

Pal’s share = 1/4

Das’s new share = old share – share surrendered = 4/5 – ¼ = 11/20

Sinha’s new share = 1/5

The new profit sharing ratio among Das, Sinha and Pal will be 11:4:5.

Sacrificing Ratio

The ratio in which the old partners agree to sacrifice their share of profit in favour of the incoming partner is called sacrificing ratio. The sacrifice by a partner is equal to : Old Share of Profit  – New Share of Profit

As stated earlier, the new partner is required to compensate the old partner’s for their loss of share in the super profits of the firm for which he brings in an additional amount as premium for goodwill. This amount is shared by the existing partners in the ratio in which they forgo their shares in favour of the new partner which is called sacrificing ratio.

The ratio is normally clearly given as agreed among the partners which could be the old ratio, equal sacrifice, or a specified ratio. The difficulty arises where the ratio in which the new partner acquires his share from the old partners is not specified. Instead, the new profit sharing ratio is given. In such a situation, the sacrificing ratio is to be worked out by deducting each partner’s new share from his old share. Look at the Revisions 6 to 8 and see how sacrificing ratio is calculated in such a situation.

Revision  6

Rohit and Mohit are partners in a firm sharing profits in the ratio of 5:3. They admit Bijoy as a new partner for 1/7 share in the profit. The new profit sharing ratio will be 4:2:1. Calculate the sacrificing ratio of Rohit and Mohit.

Solution

Rohit’s old share  = 5/8

Rohit’s new share = 4/7

Rohit’s sacrifice  = 5/8 – 4/7 = 3/56

Mohit’s old share = 3/8

Mohit’s new share  = 2/7

Mohit’s sacrifice  = 3/8 – 2/7 = 5/56

Sacrificing ratio among Rohit and Mohit will be 3:5.

Revision 7

Amar and Bahadur are partners in a firm sharing profits in the ratio of 3:2. They admitted Mary as a new partner for 1/4 share. The new profit sharing ratio between Amar and Bahadur will be 2:1. Calculate their sacrificing ratio.

Solution

Mary’s share  = 1/4

Remaining share = 1 – ¼ = 3/4

 

This 3/4 share is to be shared by Amar and Bahadur in the ratio  of 2:1.

Therefore,

Amar’s new share  = 2/3 of ¾  = 6/12 or 2/4

Bahadur’s new share = 1/3 of ¾ = 3/12 or 1/4

New profit sharing ratio of Amar, Bahadur and Mary will be 2:1:1.

Amar’s sacrifice = 3/5 – 2/4 = 2/20

Bahadur’s sacrifice  = 2/5 – ¼ = 3/20

 

Sacrificing ratio among Amar and Bahadur will be 2:3.

Revision 8

Ramesh and Suresh are partners in a firm sharing profits in the ratio of 4:3. They admitted Mohan as a new partner. The profit sharing ratio of Ramesh, Suresh and Mohan will be 2:3:1. Calculate the gain or sacrifice of old partner.

Solution

Ramesh’s old share             = 4/7

Ramesh’s new share            = 2/6

Ramesh’s sacrifice               = 4/7 – 2/6 = 10/42

Suresh’s new share             = 3/6

Suresh’s old share               = 3/7

Suresh’s gain                       = 3/6 – 3/7 = 3/42

Mohan’s share                     = 1/6 0r 7/ 42

Ramesh’s sacrifice               =   Suresh’s gain+Mohan’s gain

= 3/42 + 7/42 = 10/ 42

In this case, the whole sacrifice is by Ramesh alone.