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

Valuation of Goodwill - partnership accounting

Valuation of Goodwill

Goodwill is an intangible asset. Therefore it is very difficult to assess the value of it. Its value depends on the seller & purchaser’s mutual agreement. There are different methods of valuing goodwill. Some are discussed as below:

1.     Average Profit Method: This is a very simple method. Goodwill is calculated on the basis of the no. of past years profits. Because past profits indicate as to what profits are likely to accrue in the future. Therefore past profits are averaged. Average of such profits is multiplied by the agreed no. of years to find out the value of goodwill.

Value of Goodwill = Average Profit × Number of Years of Purchase

Some adjustment should be done while calculating the average profit:

·        Abnormal income of a year should be deducted out of the net profit of that year.

·        Abnormal loss of a year should be added back to the net profit of that year.

·        Income from investments should be deducted out of the net profit of that year.

Example: X sold his business to Y. Calculate the value of goodwill taking into consideration the following factors:

·        Goodwill is valued at three years purchase of the average profits of the last four years. Profits of the last four years were as : year 2011 – ₹40,000, year 2012 – ₹58,000, year 2013 – ₹53,000, year 2014 – ₹62,000.

·        Abnormal loss of ₹2,000 due to theft has reduced the profits of the year 2011.

·        Profits for the year 2012 include abnormal profit of ₹4,000.

·        A speculative and lottery profit of ₹5,000 was received during the year 2013 which was included in that year’s profit.

·        Profits of the year 2014 were reduced by ₹10,000 of the depreciation on such a machinery which was destroyed by the fire during the year.

Solution: Valuation of Goodwill

                                                                             ₹                     ₹

              Profit for 2011                             40,000              

Add:     Abnormal Loss                               2,000                42,000

             Profit for 2012                              58,000

Less:    Abnormal Gain                               4,000                54,000

             Profit for 2013                              53,000

Less:    Abnormal Gain                               5,000                48,000

             Profit for 2014                              62,000

Add:     Abnormal Loss                             10,000               72,000

              Total Profit                                                                 2,16,000

Average Profits = ₹ 2,16,000 / 4  = ₹ 54,000

Goodwill at 3 years purchase = ₹ 54,000 × 3 = ₹ 1,62,000       

                       

2.     Weighted Average Profit Method: It is considered better than the simple average profit method because each year’s profit is assigned a weight and highest weightage is given to the latest year. Then the each year’s profit is multiplied by the weight assigned to it and the total of their product is then divided by the total of weights in order to calculate the weighted average profits. Then goodwill is calculated by multiplying the weighted average profit obtained with the no. of year’s purchase agreed.

 

Weighted Average Profit=Total of Products of Profits/Total of Weights

           Goodwill = Weighted Average Profit × No. of Year’s of Purchase 

Example: The profits earned by a firm during the last four years were as follows:

Year ended 31^st March                         Profits (₹)

2009                                                             80,000

2010                                                           1,00,000

2011                                                           1,10,000

2012                                                           1,50,000

Calculate the value of goodwill on the basis of 3 year’s purchase of weighted average profits. Weights to be used 1, 2, 3 and 4 respectively to the profits for 2009, 2010, 2011 and 2012.

Solution: Valuation of Goodwill

Year ended 31^st March                   Profits (₹)             Weight               Products

2009                                                    80,000                     1                         80,000

2010                                                 1,00,000                     2                      2,00,000

2011                                                 1,10,000                     3                      3,30,000

2012                                                 1,50,000                     4                      6,00,000

                                                                                             10                   12,10,000

Weighted Average Profit = 12,10,000 / 10 = ₹ 1,21,000

Goodwill = ₹ 1,21,000 × 3 = ₹ 3,63,000

This method is preferred when the profits over the past 4 or 5 years have been continuously rising or falling.

3.     Super Profit Method: In this method goodwill is calculated on the basis of super profits. Super profit is the profit which a firm earns over normal profit. If it has no excess profit then it will have no goodwill. Goodwill is calculated by multiplying the super profits by a reasonable no. of years purchase.

Normal Profit = Capital Invested × Normal Rate of Return/100

 

Super Profit = Actual or Average Profit – Normal Profit

 

Goodwill = Super Profit × No. of years purchase

Example: A partnership firm earned net profits during the last four years as follows:

Year                                                            Profits (₹)

1                                                                                                                  56,000

2                                                                                                                  64,000

3                                                                                                                  60,000

4                                                                                                                  62,000

The Capital investment in the firm throughout the above mentioned period has been ₹ 3,00,000. Having regard to the risk involved, 15% is considered to be a fair return on capital. Calculate the value of goodwill on the basis of 3 years’ purchase of average super profits earned during the above mentioned 4 years.

Solution: Total Profits of four years=₹56,000+₹64,000+₹60,000+₹62,000

                                                                 = ₹ 2,42,000

Average Profit = ₹ 2,42,000 / 4 = ₹ 60,500

Normal Profit = 3,00,000 × 15 / 100 = ₹ 45,000

Super profit = ₹ 60,500 – ₹ 45,000 = ₹ 15,500

Value of Goodwill = 15,500 × 3 = ₹ 46,500

4.     Capitalisation of Average Profit Method:  In this method, Goodwill is calculated by deducting the actual capital employed from the capitalized value of average profits. First we calculate average profits and then we capitalized it on the basis of normal rate of return.

Capitalized value of Average Profit=Average Profits×100/Normal Rate of Return

Capital Employed = Assets – Liabilities

Goodwill = Capitalized Value of Average Profits – Capital Employed

There will be no goodwill if the actual capital employed in the business exceeds or equals the capitalized value of average profits.

Example: The average profit of a firm is ₹ 48,000. The total assets of the firm are ₹ 8,00,000. Value of other liabilities is ₹ 5,00,000. Average rate of return in the same business is 12%. Calculate the goodwill from capitalization of average profits method.

Solution: Capitalized value of Average profits=₹48,000×100/12=₹4,00,000

Capital employed = ₹ 8,00,000 – ₹ 5,00,000 = ₹ 3,00,000

Goodwill = ₹ 4,00,000 - ₹ 3,00,000 = ₹ 1,00,000

5.     Capitalisation of Super Profit Method: In this method Goodwill is calculated on the basis of super profits. We have to calculate the capital needed for earning of super profits on the basis of normal rate of return. This capitalized value of super profit is actually called the Goodwill.

Super Profit = Average Profit – Normal Profit

Goodwill = Super Profit ×100 / Normal Rate of Return

Example: From the figures given below, calculate goodwill according to the capitalization of super profit method:

(i)                Actual Average Profits = ₹ 72,000

(ii)              Normal Rate of Return = 10%

(iii)            Assets = ₹ 9,70,000

(iv)            Liabilities = ₹ 4,00,000

Solution: Capital Employed = Assets – Liabilities

                                                  = ₹ 9,70,000 - ₹1,00,000 =₹ 5,70,000       

Normal Profit=Capital Employed×Normal Rate of Return/100

                          = ₹ 5,70,000 × 10 / 100 = ₹ 57,000

Super Profit = Average Profit – Normal Profit

                       = ₹ 72,000 - ₹ 57,000 = ₹ 15,000

Goodwill = Super Profit×100/Normal Rate of Return

                 = ₹ 15,000×100/10 = ₹1,50,000