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# Computation of Sacrificing Ratio in case of Admission of a Partner

• Last Updated : 06 Sep, 2022

Sacrificing Ratio is the ratio in which the old partners sacrifice their share of profit and loss in the firm for the new partner admitted. During the time of admission of new partners, there is a change in the profit sharing ratio. There is a change in the profit sharing ratio because the new partner’s share in future profit and loss is given from the existing or old partners’ share in profit and loss of the firm. The share given to the new partner is given by the old partners equally from all partners, in the agreed ratio, or wholly by one partner.

Sacrificing ratio is calculated to determine the compensation the new partner shall pay to the sacrificing partner(s) for the part of the share sacrificed by him in form of a premium for goodwill. The ratio in which the existing partners sacrifice or forgo their share of profit for the new partner is the sacrificing ratio.

Sacrificing Ratio = Old Ratio – New Ratio

#### Case 1: When the old and new ratios both are given:

Under this method, the ratio of the old partner’s share in profit and loss of the firm is given and the new profit sharing ratio of the firm is given after the admission of the new partner.

#### Steps to calculate new profit sharing ratio:

To calculate the sacrifice ratio of the old partners the new ratio of profit sharing is deducted from the old ratio.

Illustration:

M and N are partners sharing profit and loss in the ratio of 5:4. Q is admitted into the firm as a partner. They decided to share future profit and loss in the ratio of 4:3:2. Calculate the sacrificing ratio.

Solution:

Sacrificing ratio = Old ratio – New ratio

M’s old share =

M’s new share =

M’s sacrificing share = M’s old share – M’s new share

=

N’s old share =

N’s new share  =

M’s sacrificing share = N’s old share – N’s new share

=

Sacrificing ratio =

= 1:1

#### Case 2: When the share of a new partner is given with the old profit sharing ratio:

Under this method, new profit sharing is determined by calculating the remaining share by deducting the new partner’s share from 1 and dividing the remaining share in the old profit sharing ratio among the old partners. The profit-sharing ratio will remain the same among the old partners under this situation.

#### Steps to calculate new profit sharing ratio:

Step 1: Let the total profit be 1.

Step 2: Calculate the remaining share of the old partners by deducting the new partner’s share from the total share.

Step 3: Distribute the remaining share among the old partners in the old profit-sharing ratio of the old partners.

Step 4: Sacrificing ratio of the old partners is calculated by deducting the new ratio from the old ratio.

Illustration:

Ajay and Atul are partners sharing the profit and loss of the firm in the ratio of 3:2. Anuj is admitted to the firm who got   ratio in the profits. Calculate the new profit sharing ratio and sacrificing ratio.

Solution:

Let the total profit be 1

Therefore, Remaining Profit = 1 –

New share of Ajay =

New share of Atul =

Share of Anuj =

New Profit-Sharing Ratio = 9:6:5

Sacrificing Ratio of Ajay =

Sacrificing Ratio of Atul =

Sacrificing Ratio = 3:2

#### Case 3: When an old partner shares the balance at a fixed ratio:

Under this method, the new partner acquires his share of future profit and loss of the firm from the old partners in the agreed ratio. Old partners share the balance of profits in a fixed proportion. New profit sharing is determined by deducting the new partner’s share from 1 and dividing the remaining share in the fixed proportion among the old partners. The new profit-sharing ratio of the old partners is in a fixed proportion.

#### Steps to calculate new profit sharing ratio:

Step 1: Let the total profit be 1.

Step 2: Calculate the remaining share of the old partners by deducting the new partner’s share from the total share.

Step 3: Distribute the remaining share among the old partners in a fixed proportion.

Step 4: Sacrificed ratio of the old partners is calculated by deducting the new ratio from the old ratio.

Illustration:

P and Q are partners sharing the profit and loss of the firm in the ratio of 6:3. R is admitted to the firm as the new partner for a   share. P and Q decided to share future profit and loss in the ratio of 2:1. Calculate the new ratio and sacrificing ratio.

Solution:

Let the total profit be 1.

Share of P and Q =

( this will be shared among P and Q in a 4:3 ratio)

P’s New Share =

Q’s New Share =

P and Q share =

R’s share =

New profit sharing ratio of P, Q, and R =

= 4:2:3

Sacrificing ratio = Old ratio – New ratio

P’s old share =

P’s new share =

P’s sacrificing share = P’s old share – P’s new share

=

Q’s old share =

Q’s new share =

Q’s sacrificing share = Q’s old share – Q’s new share

Sacrificing ratio =

= 2:1

#### Case 4: When an old partner sacrifices a fixed part of his share for a new partner:

Under this method, the new partner acquires his share of profits in the future, a part of the share from one partner and another part of the share from another partner. In the new profit sharing ratio of the firm, the share of the new partner is a part of the share of the old partners surrendered.

#### Steps to calculate new profit sharing ratio:

Step 1: Calculate the share surrendered by the old partner in favour of the new partner by multiplying the share contributed with the old share in profit.

Step 2: Calculate the new share of old partners by deducting the share surrendered from the old profit sharing ratio.

Step 3: Add the shares surrendered by the old partners in favour of the new partner to calculate the new partner profit sharing ratio.

Illustration:

G and H are partners in the firm sharing profit and losses in a ratio of 3:2. J is admitted as the new partner. G surrenders   of his share and H surrenders   of his share for the new partner, J. Calculate the new profit sharing ratio.

Solution:

G’s share =

G surrender in favor of J =

So, G’s new share =

=

H’s share =

H’s surrender in favor of J =

=

So, H’s new share =

=

J acquires =

=

New profit sharing ratio of G, H, and J =

= 9:4:7

Sacrificing ratio = Old ratio – New ratio

G’s old share =

G’s new share =

G’s sacrificing share = G’s old share – G’s new share

=

H’s old share =

H’s new share  =

H’s sacrificing share = H’s old share – H’s new share

=

=

Sacrificing ratio = 3/20:4/20

=3:4

#### Case 5: When only one partner sacrifices his part for the new partner:

Under this method, the share of a new partner is the share contributed by one partner. One of the old partners contributes a part of his share entirely to the new partner in future profits. The new share of that old partner who contributed his share to the new partner is determined by deducting the share contributed by him from the old profit sharing ratio.

#### Steps to calculate new profit sharing ratio:

Step 1: Deduct the share contributed to the new partner from the old partner’s share of profit and loss, to calculate the new share of the old partner.

Step 2: The new partner’s share in future profits and losses in the firm is entirely the share contributed by the old partner.

Step 3: Sacrificed ratio is the part of the share sacrificed by the old partner to the new partner.

Illustration:

C and D are partners in the firm sharing profit and loss in the ratio of 5:3. F is admitted as the new partner in the firm. F acquires his share of profit and loss in the firm from C. He acquires  share from C. Calculate the new ratio and sacrificing ratio.

Solution:

Calculation of new profit sharing ratio:

C’s share after giving  to F = C’s old share – C’s sacrificed share

=

C’s new share =

New profit sharing ratio =

#### Calculation of Sacrificing ratio:

Sacrificing ratio = Old ratio – New ratio

C’s old share =

C’s new share =

C’s sacrificing share = C’s old share – C’s new share

=

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