# Computation of New Profit Sharing Ratio and Sacrifice Ratio

When a new partner is admitted, the partner acquires sharing profit from existing partner. The profit sharing ratio in the new firm is decided mutually between the existing partners and the new partner.The incoming partner acquires his/her share of future profits from one or more existing partners. The existing partners sacrifice a share of their profit in favour of the new partner. Hence, the calculation of new profit sharing ratio becomes necessary.

The ratio in which the existing partners agree to sacrifice their share of profits in favour of the incoming partner is called the sacrificing ratio.

The ratio in which all partners including the incoming partner will share the profit and losses in future is known as new profit sharing ratio.

**Note:** Unless specifically given, it is assumed that the old partners sacrifice in the old profit sharing ratio.

Following cases may arise for the calculation of new profit sharing ratio and sacrificing ratio:

**Only the new partnerâ€™s share is given**

In this case, it is presumed that the existing partners continue to share the remaining profit in the same ratio in which they were sharing profits and losses before the admission of the new partner.

Then, the existing partnerâ€™s new ratio is calculated by dividing the remaining share of the profit in their existing ratio.

**Illustration 1**

X and Y are partners sharing profit in the ratio of 3:2. They admit Z as a new partner for 1/5th share in profit. Calculate the new profit sharing ratio and sacrificing ratio.

**Solution:**

Calculation of new profit sharing ratio

Let total profit = 1

New partnerâ€™s share = 1/5

Remaining share = 1 - 1/5 = 4/5

Xâ€™s new share = 3/5 of 4/5 i.e. 12/25

Yâ€™s new share = 2/5 of 4/5 i.e. 8/25

Zâ€™s Share = 1/5

The new profit sharing ratio of X, Y and Z is:

= 12/25: 8/25: 1/5 = = 12:8:5

Xâ€™s sacrifice = 3/5 - 12/25 = (15 - 12)/25 = 3/25

Yâ€™s sacrifice = 2/5 - 8/25 = (10 - 8)/25 = 2/25

Sacrificing ratio = 3 : 2

New Ratio = 12:8:5

Sacrificing ratio of the existing partners is same as their existing ratio.

**If the new partner purchases his/her share of the profit from the existing partner in a particular ratio.**

In this case, the new profit sharing ratio of the existing partners is to be ascertained after deducting the sacrifice ratio agreed from his share.

**Illustration 2**

X and Y are partners sharing profit in the ratio of 5:3. They admit Z as a new partner for 1/6^{th} share in profit. She acquires this share as 1/8^{th} from X and 1/24^{th} share from Y. Calculate the new profit sharing ratio and sacrificing ratio.

**Solution:**

Xâ€™s and Yâ€™s existing ratio is 5:3

Xâ€™s new share = 5/8 - 1/8 = 4/8 or 12/24

Yâ€™s new share = 3/8 - 1/24 = 8/24

Zâ€™s share = 1/8 + 1/24 =4/24

The new profit sharing ratio of X, Y and Z is

12/24 : 8/24 : 4/24

= 12 : 8 : 4 = 3 : 2 : 1

Sacrifice ratio = 1/8 : 1/24 or 3 : 1

New ratio = 3 : 2 : 1

**Existing partners surrender a particular portion of their share in favour of the new partner**

In this case, the sacrificed share of each partner is to be ascertained. This is ascertained by multiplying the existing partnersâ€™ share in the ratio of their sacrifice. The share of the incoming partner is the sum of sacrifice by the existing partners.

**Illustration 3**

X and Y shared profits in the ratio of 5 : 3. Z was admitted as a partner. X surrendered 1/5^{th} of his share and Y, 1/3^{rd} of his share in favour of Z. Calculate the new profit sharing ratio.

**Solution:**

X surrenders 1/5 of his share, = 1/5 x 5/8 = 1/8

Y surrenders 1/3 of his share, i.e., = 1/3 x 3/8 = 1/8

So, sacrificing ratio of X and Y is 1/8 : 1/8 (equal)

Xâ€™s new share = 5/8 - 1/8 = 4/8 and Yâ€™s new share = 3/8 - 1/8 = 2/8

Zâ€™s New share = 1/8 + 1/8 = 2/8

New profit sharing ratio of X, Y and Z is

= 4/8 : 2 / 8 : 2 / 8 or 4 : 2 : 2 or 2 : 1 : 1

Sacrificing ratio = 1 : 1

New ratio = 2 : 1 : 1