Calculation of New Profit Sharing Ratio When New Partner is Admitted

NEW PROFIT SHARING RATIO

When a new partner is admitted then the calculation of new profit sharing ratio becomes necessary. The reason behind that is the new partner acquires his share of profit from the old partners. Hence, old partners’ shares reduce.

1.     When only the ratio of new partner is given: In this case in the absence of any other agreement, it is presumed that the old partners will continue to share the remaining profits in the same ratio in which they were sharing before the admission of the new partner.

Example: X, Y and Z are partners in proportion of 3/6, 2/6 and 1/6 respectively. P was admitted in the firm as a new partner with 1/6^th share. Calculate the new profit sharing ratios of the partners.

Solution:

Let total profit be = 1

Share given to P = 1/6

Remaining Share = 1 – 1/6 = 5/6

Now the old partners will share this remaining profit in their old profit sharing ratios. Hence,

X’s share = 3/6 of 5/6 = 5/12

Y’s share = 2/6 of 5/6 = 5/18

Z’s share = 1/6 of 5/6 = 5/36

Thus, the new profit sharing ratio will be

X      :         Y      :        Z      :       P

5/12   :     5/18   :     5/36    :   1/6  =

15       :       10     :       5        :      6

2.     When the new partner purchases his share of profit from the old partners equally : In such cases, the new profit sharing ratio of the old partners can be calculated by deducting the sacrifice made by them from their existing share of profit.

Example: A and B are partners sharing profits and losses in the ratio of 7/12 : 5/12. They admit C as a new partner for 1/6^th share, which he acquires equally from A and B. Calculate the new profit sharing ratios of the partners

Solution:

Share of profits given to C = 1/6

Share acquired by C from A = ½ of 1/6 = 1/12

Share acquired by C from B = ½ of 1/6 = 1/12

Therefore,

A’s new share = 7/12 – 1/12 = 6/12

B’s new share = 5/12 – 1/12 = 4/12

C’s share = 1/6

Hence, new profit sharing ratio will be

A           :          B          :        C

6/12     :         4/12     :        1/6  =

3           :          2          :        1

3.     When new partner purchases his share from the old partners in a particular ratio: In this case, the new profit sharing ratio of the old partners will be ascertained after deducting the sacrifice made by them from their existing share of profit.

Example: X and Y are partners in a firm sharing profits in the ratio of 7 : 5. Z is admitted on 1/6^th share which he takes 1/24^th from X and 1/8^th from Y. Calculate the new profit sharing of the partners.

Solution:

X’s old share = 7/12, out of which he surrenders 1/24^th in favour of Z.

Therefore, X’s new share = 7/12 – 1/24 = 13/24

Y’s old share = 5/12, out of which he surrenders 1/8^th in favour of Z.

Therefore, Y’s new share = 5/12 – 1/8 = 7/24

Z’s share = 1/6

Hence, new profit sharing ratio will be

X            :           Y          :         Z

13/24    :        7/24      :       1/6  =

13          :           7          :         4

4.     When old partners surrender a particular fraction of their share in favour of the new partner: in such case, the new partner’s share is calculated by adding the surrendered portion of share by the old partners.

Example: P and Q are partners in a firm sharing profits and losses in the ratio of 3:2. A new partner R is admitted. P surrenders 1/5^th share of his profit in favour of R and Q 2/5^th share of his profit in favour of R. Calculate the new ratio of the partners.

Solution:

P’s old share = 3/5

P surrenders 1/5^th of 3/5 in favour of R i.e. 1/5 X 3/5 = 3/25

Q’s old share = 2/5

Q surrenders 2/5^th of 2/5 in favour of R i.e. 2/5 X 2/5 = 4/25

P’s new share after surrendering 3/25 in favour of R = 3/5 – 3/25 = 12/25

Q’s new share after surrendering 4/25 in favour of R = 2/5 – 4/25 = 6/25

R’s share is the total of 3/25 from P and 4/25 from Q = 3/25 + 4/25 = 7/25

Therefore, new ratio will be

P           :         Q          :           R

12/25   :       6/25      :        7/25   =

12         :         6           :           7

Sacrificing Ratio & Gaining Ratio

SACRIFICING RATIO

When there is a change in the profit sharing ratio due to any of the reason, one or more of the existing partners have to surrender some of their old share in favour of one or more of other partners. That surrender of profit in ratio is called sacrificing ratio. It is calculated as below:

Sacrificing Ratio = Old Ratio – New Ratio

The main purpose of calculating this is to determine the amount of compensation to be paid by the Gaining partner to the sacrificing partner (usually paid on the basis of proportionate amount of Goodwill).

GAINING RATIO

When profit sharing ratio changes between the partners, then one or more existing partners gain some portion of other partners’ share of profit. This ratio of gain of profit is known as gaining ratio. It can be calculated as follows:

Gaining Ratio = New Ratio – Old Ratio

Example:  A and B were partners in a firm sharing profits in the ratio of 5:3. With effect from 1^st April, 2012 they agreed to share profits equally. Calculate the individual partner’s gain or sacrifice due to change in ratio.

Solution:

Old Ratio of A and B = 5 : 3

New Ratio of A and B = 1: 1

Sacrifice or Gain:

A = 5 / 8 – 1 / 2 = 10 – 8 / 16 = 2 / 16 = 1 / 8 (Sacrifice)

B = 3 / 8 – 1 / 2 = 6 – 8 / 16 = 2 /16 = 1 / 8 (Gain)

A has sacrificed 1 / 8^th share whereas B has gained 1 / 8^th share.

Reconstitution of a Partnership Firm

Reconstitution of a Partnership Firm

It means building partnership in a new way. If there is a change in the partnership agreement, it brings to an end of the existing partnership and a new agreement comes into force, because partnership is the result of an agreement between persons for a business. This change also changes the relationship of partners. In that case partnership continues with reconstitution. It may happen due to following circumstances:

·        When partners decide to change their profit sharing ratio.

·        When a new partner is admitted to the firm.

·        When an existing partner decides to take retirement from the firm.

·        When a partner dies.

·        When two or more firms decide to amalgamate.

In all these cases, the profit sharing ratio of partners changes from their existing ratio. Firm continues its business but with a different agreement. Let’s discuss in detail.

Change in the Profit Sharing Ratio among the existing Partners

Sometimes the existing partners decide to change their profit sharing ratio. This change results in sacrifice or gain for partners. Some partners may acquire extra share in Profit i.e. gain and some partners may have to lose their share i.e. sacrifice. The reasons for change in profit sharing ratio can be change in capital contribution, active participation in the management of business of the firm etc.in that case equity is maintained among the partners. So it is necessary to make some adjustments in assets & liabilities, profit & losses etc.

Some adjustments which are required at that time are:

·        Determination of Sacrificing or Gaining ratio

·        Accounting for Goodwill

·        Accounting treatment of Reserves and Accumulated Profits

·        Accounting for Revaluation of Assets & Liabilities

·        Adjustment of Capitals

When a new partner is admitted to the firm:

Admission of a new partner into the existing firm is possible only when all the existing partners are ready for it. It is one of the modes of reconstitution of the firm. A new partnership deed is prepared at that time because the old one comes to an end. Due to following reasons a new partner is needed into the business:

·        When more capital is needed for the expansion of the business.

·        When a competent and experienced person is needed for the efficient running of the business.

·        To encourage a capable employee by taking him into the partnership.

·        To increase the Goodwill and reputation of the business by taking a reputed and renowned person into partnership.

At the time of admission, the new partner also brings his share of goodwill along with his capital. Therefore, old partners have to sacrifice a share of their profits in favour of the new partner. New partner gets a share in the future profits of the firm.

Some adjustments are needed at the time of the admission of a new partner. These are:

·        Calculation of new profit sharing ratio of the partners

·        Accounting treatment of goodwill

·        Accounting treatment for revaluation of assets and liabilities

·        Accounting treatment of reserves and accumulated profits

·        Adjustment of capitals on the basis of new profit sharing ratio