Question

If it is agreed that the capital of all the partners be proportionate to the new profit sharing ratio, how will you work out the new capital of each partner? Give examples and state how necessary adjustments will be made.

Answer 1

When a new partner is admitted, sometimes it is agreed that the capital of all the partners should be proportionate to the new profit sharing ratio. The calculation of the new capital of each partner depends on the following situations:
1) When the capital of the new partner is given
2) When the total capital of the firm is given.

1) When the capital of the new partner is given
In this situation, the calculation of the new capital of all the partners involves the following steps:
Step 1: The total capital of the new firm is calculated on the basis of new partner’s capital.
Step 2: The new capital of each partner is calculated by dividing the total capital of the firm by their individual new profit share.
Step 3: After posting all adjustments and items in the Partners’ Capital Account, calculate credit minus debit side of the old Partners’ Capital Account.
Step 4: The new capital ascertained in the Step 2 is written as ‘Balance c/d’ on the credit side of the Partner’s Capital Account.
Step 5: If the amount ascertained in Step 2 (New capital) exceeds the capital amount ascertained in Step 3 (Old Capital), then it is termed as ‘Deficit’ and the difference amount is to be brought in by the old partners. On the contrast, if the amount ascertained in the Step 2 (New Capital) is lesser than the capital amount ascertained in the Step 3 (old Capital), then it is termed as ‘Surplus’ and the difference amount is returned to the old partners.
Let us understand the above steps with the help of an example.
A and B are partners sharing profit and loss equally. They agree to admit C for `1/3rd`  share in profit. C brings Rs 50,000 as capital. The old capitals of A and B are Rs 60,000 and Rs 40,000 respectively, at the time admission of C.
Step 1:
The total capital of the new firm on the basis of C = 50,000 x `3/1` = Rs. 1,50,000.
Step 2:
A’s new capital = 1,50,000 x `1/3` = Rs. 50,000
B’s share in new firm = 150,000 x `1/3` = Rs. 50,000
Step 3:

	A	B
New Capital	50,000	50,000
Less: Existing Capital	(60,000)	(40,000)
Withdrawal (deposit)	10,000	(10,000)

2) When the total capital of the new firm is given:
When the capital of new partner is not mentioned then his/her capital is ascertained on the proportionate basis of total capital of the firm. The amount ascertained is to be brought in by the new partner in the form of his/her portion of capital. In order to ascertain the proportionate capital of the new partner, the following steps are to be followed.
Step 1: Ascertain the total old capital of the old partners (after making all adjustments)
Step 2: Ascertain the total capital of the new firm by multiplying the total of old capitals of the old partners (ascertained in the Step 1) with reciprocal of total share of old partners. That is,

Total Capital of New Firm = Total Capital of the Old Partners x Reciprocal of the Combined New Share of the Old Partners

Step 3: Calculate New Capital of each partner on the basis of Total Capital ascertained in Step 2. That is, multiplying the Total Capital by the new profit sharing ratio individually for all the partners (including the new partner). 
Let us understand the above steps with the help of an example.
X and Y are partners in a firm sharing profit and loss equally. They agree to admit Z for `1/3rd` share in profit and decided to share future profit and loss equally. X’s capital is Rs 2,00,000 and Y’s capital is Rs 1,50,000. Z brings sufficient capital for his share in profit. 
Step 1: Calculation of Total Capital of Old Partners (after all adjustments)

The total capital of the old partners = Rs 2,00,000 + Rs 1,50,000 = Rs 3,50,000
Step 2: Calculation of Total Capital of New Firm
Total Capital of New Firm = Total Capital of the Old Partners x Reciprocal of the Combined New Share of the Old Partners

Total Capital of New Firm = 3,50,000 x `3/2` = Rs. 5,25,000

Step 3: Calculation of New Capital of Each Partner
X's (New) Capital = 5,25,000 x `1/3` = Rs. 1,75,000

Y's (New) Capital = 5,25,000 x `1/3` = Rs. 1,75,000.

Z's Capital = 5,25,000 x `1/3` = Rs. 1,75,000.