Class 12-commerce NCERT Solutions Accountancy Chapter 2 - Reconstitution of a Partnership Firm - Admission of a Partner

Various matters which need to be adjusted at the time of admission of a new partner are as follows:

1. Profit-sharing Ratio: Determining new profit-sharing ratio
2. Goodwill: Valuation and treatment of goodwill
3. Revaluation of Assets and Liabilities: Profits or losses arising from revaluation of assets and liabilities are to be adjusted among old partners in the old ratio
4. Accumulated Profits, Losses and Reserves: Accumulated profits, losses and reserves are distributed among old partners in the old ratio
5. Capital Adjustment: Adjustment of partner's capital (if agreed)

It is necessary to ascertain new profit-sharing ratio for old partners when new partner/s is/are admitted because the old partner of the partnership firm needs to sacrifice the share of profit in favour of the new partner/s and this reduces the share of profit of old partners.

The ratio in which the existing partners of the partnership firm agree to sacrifice their share of profit in favour of the new incoming partner is called sacrificing ratio. Sacrificing ratio is calculated as the difference between old ratio and new ratio of old partners.

Sacrificing Ratio = Old Ratio - New Ratio

It is important to calculate this ratio because the new partner needs to compensate the old partners for sacrificing their share of profit. The new partner compensates the old partner by making payment to them in the form of goodwill which is transferred among the old partners in their sacrificing ratio.

Sacrificing ratio is used on the following occasions:

1. When the existing partners of the partnership firm mutually decide to change the profit-sharing ratio among them.
2. When a new partner is admitted in the partnership firm and the amount brought by him/her as goodwill is transferred between the old partners in their sacrificing ratio.

If goodwill already exists in the books of the old firm before the new partner/s bring in his/her share of goodwill in cash, then the existing goodwill should be written off between the old partners in their old profit-sharing ratio. Journal entry passed for the following:

When a new partner is admitted in the firm, it becomes essential to revalue assets and liabilities of the partnership firm for determining its true and fair value. Revaluation is done because the value of assets and liabilities may have increased or decreased and thus their corresponding figures in the old balance sheet may be either understated or overstated. Also, it may be possible that some of the assets and liabilities are left to be recorded. Hence, to record the increase and decrease in the market value of the assets and liabilities, the revaluation account is prepared and any profits (or losses) linked with this increase or decrease will be distributed between the old partners of the firm in their old profit-sharing ratio.

Revaluation means valuation of assets and liabilities at the time of reconstitution of the firm. The reasons for the revaluation of assets and liabilities at the time of admission of a partner are

1. The book values of assets and liabilities may have changed over a period of time since the firm was doing its operations.
2. The admitted partner may be of the opinion that the firm has exaggerated the value of assets or shown the liabilities at a lower value.
3. Old partners may think that the value of assets has increased over a period of time and are being shown at a lower value.

Accounting Entries in the Books of Accounts:

The following journal entries are recorded in the Revaluation Account on the date of admission of a new partner:

Goodwill is an intangible asset which represents the value of a firm's reputation and its good brand name in the market. A firm earns goodwill by its hardwork and thereby wins the blind trust and faith of customers by fulfilling their demands in both qualitative and quantitative aspects. Positive goodwill helps a firm to earn supernormal profits compared to its competitors which earn normal profits (as their goodwill is zero). In other words, goodwill ensures greater future profits as there will be greater number of satisfied customers in the future. Goodwill is nothing more than the probability that the old customer is retained.

Characteristics of Goodwill

The following are the characteristics of goodwill:

1. Is an intangible asset
2. Is not a fictitious asset
3. Ascertaining the exact value of goodwill is difficult
4. Enhances the future and present earning capacity of a business
5. Helps a firm earn supernormal profits
6. Assists the business to enjoy its upper hand over its competitors

Factors Affecting Goodwill

Important factors which affect the goodwill of a firm:

1. Quality of Products: A company producing best quality or superior quality products in large scale earns more goodwill.
2. Location: If a business is located at easy to reach and convenient place, it provides an access to more number of consumers who will be attracted again and will lead to increase in sales over a period of time. Therefore, in some time, the firm will earn higher goodwill.
3. Efficient Management: Efficient management leads to cost efficiency and increases productivity. Efficient management means superior quality products at lower cost or which can be sold at lesser price. Superior quality at lower price enables a firm to earn higher goodwill.
4. Market Structure: If a firm is operating in a monopoly market with no close substitutes, then there will be more goodwill of the firm.
5. Special Advantages: A firm enjoying privileges such as continuous supply of power, fuel and raw materials at a low price enjoys higher value of goodwill.

Four methods of valuation of goodwill:

1. Average Profit Method: Goodwill is calculated on the average basis of the profits of past few years. The formula for calculating goodwill is

Number of Years Purchase implies number of years for which the firm expects to earn the same amount of profits. Steps to calculate goodwill by the average profit method:

Step 1: Ascertain the total profit of past given years

Step 2: Add Abnormal losses like loss by fire and theft

Step 3: Add All normal incomes if not added previously

Step 4: Less All non-business incomes and all abnormal gains and incomes like speculation and lottery

Step 5: Less All normal expenses if not deducted previously

Step 6: Calculate Average Profit, by dividing the total profit ascertained in Step 5 by number of years

Step 7: Multiply the Average Profit to the Number of Years' Purchases to calculate the Value of Goodwill

Example:

The profits for last 5 years are Rs 2,00,000, 6,00,000, (4,00,000), 10,00,000, 16,00,000. Calculate goodwill on the basis of 4 years purchase.

2. Weight Average Method: Weights are assigned for each year's profit in a manner where higher weights are assigned to the recent year's profit and lower weights are assigned to the past year's profits. The products of the profits and the weights are added and divided by the total weights to calculate Weighted Average Profits. The formula for calculating goodwill by this method is

Steps to Calculate Goodwill by Weight Average Method: 

Step 1: Assign weights to ever year. More recent years with higher weight

Step 2: Multiply the weights with its corresponding year's profits

Step 3: Calculate the total of the products

Step 4: Divide the total of the product by the total of the weights to calculate Weighted Average Profit

Step 5: Multiply the Weighted Average Profit by the number of years purchase

Example:

The profits for the last 5 years are Rs 2,00,000, Rs 6,00,000, Rs (4,00,000), Rs 10,00,000, Rs 16,00,000

Calculate goodwill on the basis of 4 years purchase.

3. Super Profit Method: Here, goodwill is calculated on the basis of excess profit earned by a firm over and above the normal profit earned by its counterparts in the same industry. The excess profit over the normal profit is termed Super Normal Profit. 

Steps to Calculate Goodwill by Super Profit Method:

Step 1: Calculate Average Profit

Step 2: Calculate Average Capital Employed as

Step 3: Calculated Normal Profit by the formula:

Step 4: Calculate Super Normal Profit by the formula:

Super Normal Profit = Average Profit - Normal Profit

Step 5: Multiply the Super Normal Profit by the Number of Years Purchase to calculate goodwill.

4. Capitalisation Method: There are two methods of capitalisation:

a. By capitalisation of Average Profit

b. By capitalisation of Super Profit

a. Capitalisation of Average Profit

Step 1: Calculate Average Profit

Step 2: Calculate Capitalised Value of Average Profit by the following formula:

Step 3: Ascertain Actual Capital EmployedStep 4: Deduct Actual Capital Employed from Capitalised Average Profit to calculate goodwill.

Goodwill = Capitalised Average Profit - Actual Capital Employed

b. Capitalisation of Super Profit

Step 1: Calculate the Capital Employed

Step 2: Calculate Normal Profit by the following formula:

Step 3: Calculate Average Profit

Step 4: Calculate Super Normal Profit by the following formula:

Super Normal Profit = Average Profit - Normal Profit

Step 5: Calculate goodwill by the following formula:

In case a new partner is admitted to the firm, it may be agreed that the capital of all partners should be proportionate to the new profit-sharing ratio. In such cases, the working of new capital of each partner is based on two of the following cases:

1. Capital of the new partner is given
2. 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 partners involves the following steps:

Step 1: Calculate the total capital of the new firm on the basis of capital of the new partner

Step 2: Divide the total capital of the firm by the individual share of profits of partners to ascertain new capital of each partner

Step 3: Ascertain partner's capital balance (credit-debit) after posting all adjustments

Step 4: The new balance as ascertained in Step 2 is written on the credit side of the Partner's Capital Account.

Step 5: Calculate Surplus or Deficit. If the new capital (Step 2) exceeds the old capital (Step 3), then it is termed 'Deficit' and the difference amount is to be brought in by the old partners. If the new capital is lesser than old capital, then it is termed 'Surplus' and the difference amount is returned to the old partners.

Example:

L and M are partners sharing profit and loss equally. They agree to admit N for  share in profit. N brings Rs 25,000 as capital. The old capitals of L and M are Rs 30,000 and Rs 20,000, respectively, at the time admission of N.

Step 1: The total capital of the new firm on the basis of N's Capital

Step 2:

Step 3:

2. When the total capital of the new firm is given: When the capital of the new partner is not mentioned, his/her capital is ascertained on the proportionate basis of total capital of the firm. The capital ascertained is to be brought in by the new partner in form of his/her portion of capital. 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: Multiply the total of old partner's capital (Step 1) with reciprocal of total share of old partners to ascertain the total capital of the new firm

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

Step 3: Calculate new capital of each partner on the basis of total capital. This is done by multiplying the Total Capital by the new profit-sharing ratio individually for all partners including the new partner.

Example:

A and B are partners in a firm sharing profit and loss equally. They agree to admit C for  share in profit and decided to share future profit and loss equally. A's capital is 4,00,000 and B's capital is 3,00,000. C 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. 4,00,000 + Rs. 3,00,000 = Rs. 7,00,000

Step 2: Calculation of Total Capital of New Firm

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

Step 3: Calculation of New Capital of Each Partner

When a new partner enters a partnership firm, the old partner sacrifices his share for him, so it is the duty of the new partner to give goodwill in cash or in any other way to the old partner. In case the new partner is not in a position to bring his share of goodwill in cash, then a goodwill account is adjusted through the old Partner's Capital Account. The New Partner's Capital Account or Current Account is debited with his/her share of goodwill and partners who sacrifice their share in favour of the new partner are credited in their sacrificing ratio.

Also, according to Para 16 of Accounting, Standard 10, goodwill is recorded in the books only when some consideration in money or money's worth has been paid for it. It is mandatory to follow this practice. For admission, retirement. death or change in profit-sharing ratio among existing partners, a Goodwill Account cannot be raised as no consideration is paid for it.

The following are journal entries recorded in the books of accounts if a new partner is not able to bring goodwill in cash.

Two methods for the treatment of goodwill at the admission of a new partner include

1. Premium Method
2. Revaluation Method

Any of the two methods can be adopted, but before that it is necessary that if any goodwill already appears in the old books of the firm, then first, that should be written off among all the old partners in their old profit-sharing ratio. The following journal entry is passed to distribute the goodwill:

Treatment of Goodwill

1. Premium Method: It is used when the new partner pays his or her share of goodwill in cash. The accounting treatment under this depends on the situation and scenarios which include

 i. If the new partner privately pays his/her share of goodwill to the old partners: No accounting treatment is required to be done as the goodwill is privately paid.

 ii. When the new partner brings his/her share of goodwill in cash and the goodwill is retained in the business.

 Accounting Entries

 iii. If the new partner partly brings his/her share of goodwill

2. Revaluation Method: This method is adopted when the new partner is not able to bring goodwill in cash at all. 

The profits or losses which have accumulated over the years and have not been credited or debited to the partners capital account are called accumulated or undistributed profits or losses. In case a new partner is admitted to the partnership firm, then all the past accumulated profits or losses and the reserves are to be distributed among all the old partners in their old profit-sharing ratio. This is because these profits and losses are attributable to the hardwork and labours of the old partners, and consequently, the old partners are liable to bear losses, if any. The new partner is not entitled to a share in these profits/losses as he/she was not part of such efforts or hard earned profits/losses and accordingly is not responsible for the past performance of the business.

Accounting Treatment of Accumulated Profits and Losses

After revaluation of assets and liabilities has been done for the newly constituted partnership firm, all the assets and liabilities appear at their current market values including any unrecorded asset or liability in the Balance Sheet. This is evident from the example given below:

X, Y and Z were partners in a firm sharing profits in the ratio of 3:2:1, respectively. The Balance Sheet of the firm on 31^st March 2015 stood as follows:

Y retired from the firm on the above date subject to the following conditions:

Goodwill of the firm be valued at Rs 9,000. Machinery would be depreciated by 10% and Motor Van by 15%. Stock would be appreciated by 20% and Building by 10%. The provision for doubtful debts would be increased by Rs 975. Liability for workmen compensation to the extent of Rs 825 would be created.

It was agreed that X and Z would share profits in the future in the ratio of 3:2, respectively.

Revaluation Account, Capital Account and Balance Sheet of the new firm:

Note: Gain Ratio = 3:7

Let new firm profit = 1

Remaining share of A and B in the new firm

= 1- C's share

New Ratio = Old Ratio × Remaining Share

Let new firm profit = 1

Remaining share of A, B and C in new firm

= 1 - D's share

New Ratio = Old Ratio × Remaining Share

New Ratio = Old Ratio - Sacrificing Ratio

D admits for share in the new firm, which he taken from A.

Here only A will sacrifice.

New Ratio = Old Ratio - Sacrificing Ratio

New Ratio = Old Ratio - Sacrificing Ratio

New Ratio = Old Ratio - Sacrificing Ratio

New Ratio = Old Ratio - Sacrificing Ratio

New Ratio = Old Ratio - Sacrificing Ratio

Sacrificing Ratio = Old Ratio × Surrender Ratio

New Ratio = Old Ratio - Sacrificing Ratio

Gopi's Share = Radha's Sacrificing Ratio + Rukmani's Sacrificing Ratio

 Sacrificing Ratio = Old Ratio × Surrender Ratio

New Ratio = Old Ratio - Sacrificing Ratio

Sacrificing Ratio = Old Ratio -New Ratio

Note: Answer given the book is different. However, as per the solution sacrificing ratio is 3:5.

Let the New Firm Profit =1

Combined share of Rao and Swami in the new firm

New Ratio = Combined Share of Rao and Swami × Proportion of Rao and Swami in the Combined Share

Sacrificing Ratio = Old Ratio -New Ratio

= Rs.2,08,000

Capital Employed = Rs.2,00,000

Actual Profit = 48,000

Normal Rate of Return = 15%

= Rs.30,000

Super profit = Actual Profit - Normal Profit

=48,000 - 30,000

= Rs.18,000

Goodwill = Super Profit × Number of Years Purchase

=18,000 × 3

= Rs.54,000

Average Super profit = Actual Profit - Normal Profit

=60,000 - 50,000

= Rs.10,000

Goodwill = Super Profit × Number of Years Purchase

=10,000 × 3

= Rs.30,000

Normal Rate of Return =20%

Goodwill = Capitalised Value - Capital Employed

=7,50,000 - 5,00,000

= Rs.2,50,000

Alternative Method

Super profit = Actual Profit - Normal Profit

=1,50,000 - 1,00,000

=Rs 50,000

Goodwill = Capitalised Value - Capital Employed

=10,00,000 - 8,20,000

= Rs.1,80,000

Alternative Method

Capital Employed = Assets - External Liabilities

= 10,00,000 - 1,80,000

= Rs.8,20,000

Super profit = Actual Profit - Normal Profit

=1,00,000 - 82,000

= Rs.18,000

Sacrificing Ratio = Old Ratio -New Ratio

Goodwill of the firm = Rs.20,000

Sacrificing Ratio = Old Ratio -New Ratio

Note:

1. According to AS - 10 Goodwill can be shown in the book if money and money value is paid for it. Here, no money or money value has been paid for Goodwill. Hence, Goodwill cannot be raised to Rs.40,000.
2. Sacrificing Ratio will be equal to old ratio because new and sacrificing ratio is not given, if sacrificing and new ratio is not given it is assumed that old partners sacrificed in their old ratio.

Sacrificing Ratio = Old Ratio -New Ratio

Working Notes:

1. Sacrificing Ratio = Old Ratio -New Ratio

Sacrificing Ratio between Amar and Akbar= 1:3.

Kanwar admitted for 1/4 share of profit.

New Firm's Goodwill = Rs.80,000

Kanwar' s Share of Goodwill = 80,000 × 1/4 = 20,000