Reconstitution of a Partnership Firm – Admission of a Partner

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Test your Understanding – I
1. 1. A and B are partners sharing profits in the ratio of 3:1. They admit C for 1/4 share in the future profits. The new profit sharing ratio will be:
(a)
A \dfrac{9}{16}, B \dfrac{3}{16}, C \dfrac{4}{16} ✔
(b)
A \dfrac{8}{16}, B \dfrac{4}{16}, C \dfrac{4}{16}
(c)
A \dfrac{10}{16}, B \dfrac{2}{16}, C \dfrac{4}{16}
(d)
A \dfrac{8}{16}, B \dfrac{9}{16}, C \dfrac{10}{16}
C’s Share
= \dfrac{1}{4}
= \dfrac{1}{4} × \dfrac{4}{4}
= \dfrac{4}{16}
Remaining Share
= 1 - \dfrac{1}{4}
= \dfrac{3}{4}
A’s new share
= \dfrac{3}{4}\text{ of }\dfrac{3}{4}
= \dfrac{9}{16}
B’s new share
= \dfrac{1}{4}\text{ of }\dfrac{3}{4}
= \dfrac{3}{16}
Note: We tried to express all the rations with a consistent denominator value of 16. Also, After finding A’s share, as it is only the option A that has the A’s ratio as \dfrac{9}{16}, we can conclude that option A is the correct answer. We don’t have to find B’s share, especially if we’re solving MCQs.
2. X and Y share profits in the ratio of 3:2. Z was admitted as a partner who sets 1/5 share. New profit sharing ratio, if Z acquires 3/20 from X and 1/20 from Y would be:
(a) 9 : 7 : 4 ✔
(b) 8 : 8 : 4
(c) 6 : 10 : 4
(d) 10 : 6 : 4
X’s old share
{= \dfrac{3}{5}}
Share sacrificed by X
{= \dfrac{3}{5} - \dfrac{3}{20}}
{= \dfrac{9}{20}}
Y’s old share
{= \dfrac{2}{5}}
Share sacrificed by Y
{= \dfrac{2}{5} - \dfrac{1}{20}}
{= \dfrac{7}{20}}
Z’s share
{= \dfrac{3}{20} + \dfrac{1}{20}}
{= \dfrac{4}{20}}
Ratio of Shares
{= \dfrac{9}{20} : \dfrac{7}{20} : \dfrac{4}{20}}
= 9 : 7 : 4
Note: Will little observation, we can conclude that option (a) is the correct answer, as it is the only option that has 9 as the sharing ratio component, especially when solving MCQs.
3. A and B share profits and losses in the ratio of 3 : 1, C is admitted into partnership for 1/4 share. The sacrificing ratio of A and B is:
(a) equal
(b) 3 : 1 ✔
(c) 2 : 1
(d) 3 : 2
Both A and B will be contributing to the sacrifice in profit in the ratio of their old profit sharing ratio. So, the answer will be 3:1

Test your Understanding – II
Choose the correct alternative –
1. At the time of admission of a new partner, general reserve appearing in the old
balance sheet is transferred to:
(a) all partner’s capital account
(b) new partner’s capital account
(c) old partner’s capital account ✔
(d) none of the above.
2. Asha and Nisha are partner’s sharing profit in the ratio of 2:1. Asha’s son Ashish was admitted for 1/4 share of which 1/8 was gifted by Asha to her son. The remaining was contributed by Nisha. Goodwill of the firm in valued at ₹ 40,000. How much of the goodwill will be credited to the old partner’s capital account.
(a) ₹ 2,500 each
(b) ₹ 5,000 each ✔
(c) ₹ 20,000 each
(d) None of the above.
Ashish’s share ratio
{= \dfrac{1}{4}}
Asha’s sacrifice
{= \dfrac{1}{8}}
Nisha’s sacrifice
{= \dfrac{1}{4} - \dfrac{1}{8}}
{= \dfrac{1}{8}}
Asha and Nisha’s Sacrificing ratio
{= \dfrac{1}{8}:\dfrac{1}{8}}
= 1:1
Total Goodwill
= ₹ 40,000
Ashish’s share of Goodwill
{= ₹~40,000 × \dfrac{1}{4}}
= ₹ 10,000
Ashish’s share of goodwill should be distributed to the old partners’ i.e. Asha’s and Nisha’s capital accounts in the ratio of their sacrificing ratio i.e. 1:1 as follows:
Asha
{= ₹~10,000 × \dfrac{1}{2}}
= ₹ 5,000
Nisha
{= ₹~10,000 × \dfrac{1}{2}}
= ₹ 5,000
3. A, B and C are partner’s in a firm. If D is admitted as a new partner:
(a) old firm is dissolved
(b) old firm and old partnership is dissolved
(c) old partnership is reconstituted ✔
(d) None of the above.
4. On the admission of a new partner increase in the value of assets is debited to:
(a) Profit and Loss Adjustment account
(b) Assets account ✔
(c) Old partner’s capital account
(d) None of the above.
5. At the time of admission of a partner, undistributed profits appearing in the balance sheet of the old firm is transferred to the capital account of:
(a) old partners in old profit sharing ratio
(b) old partners in new profit sharing ratio ✔
(c) all the partner in the new profit sharing ratio.

Do It Yourself
1. A firm’s profits for the last three years are ₹ 5,00,000; ₹ 4,00,000 and ₹ 6,00,000. Calculate value of firm’s goodwill on the basis of four years’ purchase of the average profits for the last three years.
We have,
Average Profit
{= \dfrac{\text{Total Profit of Last 3 years}}{\text{No. of Years}}}
{= \dfrac{₹~5,00,000 + ₹~4,00,000 + ₹~6,00,000}{3}}
{= \dfrac{₹~15,00,000}{3}}
= ₹ 5,00,000
Goodwill
= Average Profits × No. of Years Purchased
= ₹ 5,00,000 × 4
= ₹ 20,00,000
2. A firm’s profits during 2013, 2014, 2015 and 2016 were ₹ 16,000; ₹ 20,000; ₹ 24,000 and ₹ 32,000 respectively. The firm has capital investment of ₹ 1,00,000. A fair rate of return on investment is 18% p.a. Compute goodwill based on three years’ purchase of the average super profits for the last four years.
Normal Profits
{= \text{Firm's Capital} × \dfrac{\text{Normal Rate of Return}}{100}}
{= ₹~1,00,000 × \dfrac{18}{100}}
= ₹ 18,000
Average Profits:
Year
Profit
₹
2013
16,000
2014
20,000
2015
24,000
2016
32,000
Total
92,000
Average Profits
{= \dfrac{\text{Total Profits}}{\text{No. of Years}}}
{= \dfrac{₹~92,000}{4}}
= ₹ 23,000
Super Profit
= ₹ 23,000 – ₹ 18,000
= ₹ 5,000
Goodwill
= ₹ 23,000 × 3
= ₹ 69,000
3. Based on the data given in the above question, calculate goodwill by capitalisation of super profits method. Will the amount of goodwill be different if it is computed by capitalisation of average profits? Confirm your answer by numerical verification.
(a) Calculation of goodwill by Capitalisation of Super Profits method:
Goodwill
{= \text{Super Profits} × \dfrac{100}{\text{Normal Rate of Return}}}
{= ₹~5,000 × \dfrac{100}{18}}
= ₹ 27,778
(b) Calculation of goodwill by Capitalisation of Average Profits method:
Capitalized value
(of average profits)
{= \text{Average Profits} × \dfrac{100}{\text{Normal Rate of Return}}}
{= ₹~23,000 × \dfrac{100}{18}}
= ₹ 1,27,778
Goodwill
= Capitalized Value – Net Assets
= ₹ 1,27,778 – ₹ 1,00,000
= ₹ 27,778
This confirms that the calculation of goodwill by calitalization of super profits method and capitalization of average profits method gives us the same result.
4. Giri and Shanta are partners in a firm sharing profits equally. They admit Kachroo into partnership who, in addition to capital, brings ₹ 20,000 as goodwill for 1/5th share of profits in the firm. What shall be journal entries if:
(a)
no goodwill appears in the books of the firm.
(b)
goodwill appears in the books of the firm at ₹ 40,000.
In the problem, neither the new profit sharing ratio nor the sacrificing ratio are given. So, we consider that the goodwill brought in by the new partner will be distributed amoung the existing partners in the ratio of thier old profit and loss sharing ratio i.e. 1:1
a) Journal entries when no goodwill appears in the books of the firm:
Journal
Date
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
Cash A/c
Dr.
20,000
To Premium for Goodwill A/c
20,000
(Being goodwill brought in by the new partner Kachroo)
Premium for Goodwill A/c
Dr.
20,000
To Giri’s Capital A/c
10,000
To Shanta’s Capital A/c
10,000
(Being Goodwill brought in by the new partner Kachroo distributed among the old partners in their sacrificing ratio)
b) Journal entries when goodwill appears in the books of the firm at ₹ 40,000
In this case, the existing goodwill i.e. should be distributed among the old partners in their profit sharing ratio i.e equally. So, each will get ₹ 20,000
Journal
Date
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
Giri’s Capital A/c
Dr.
20,000
Shanta’s Capital A/c
Dr.
20,000
To Goodwill A/c
40,000
(Being goodwill exising in the books distributed among the old partners in their profit sharing ration)
Cash A/c
Dr.
20,000
To Premium for Goodwill A/c
20,000
(Being Goodwill brought in by the new partner)
Premium for Goodwill A/c
Dr.
20,000
To Giri’s A/c
10,000
To Shanta’s A/c
10,000
(Being the goodwill brought in by the new partner is share amonh the old partners in their sacrificing ratio)
Working Notes:
Goodwill distributed to:
Giri
{= ₹~20,000 × \dfrac{1}{2}}
= ₹ 10,000
Shanta
{= ₹~20,000 × \dfrac{1}{2}}
= ₹ 10,000

Short Answer Questions
1. Identify various matters that need adjustments at the time of admission of a new partner.
The following are the various matters that need adjustments at the time of admission of a new partner.
1.
New Profit sharing ratio.
2.
Sacrificing ratio.
3.
Valuation and adjust of goodwill.
4.
Revaluation of assets and Reassessment of liabilities.
5.
Distribution of accumulated profits (reserves) and
6.
Adjustment of partners’s capitals
2. Why it is necessary to ascertain new profit sharing ratio even for old partners when a new partner is admitted?
When a new partner is admitted, the old partners sacrifice a share of their profit in favour of the new partner. This will change the profit sharing ratio among the old partners depending on how much their are sacrificing to contribute to the profits of the new partner. Due to this fact it is necessary to ascertain new profit sharing ratio even for old partner when a new partner is admitted.
3. What is sacrificing ratio? Why is it calculated?
When a new partner is admitted, the old partners sacrifice a share of their profit in favour of the new partner. The ratio in which these profits are sacrificed is called as sacrificing ratio. It is calculated as
Sacrificing Ratio = Old Ratio – New Ratio.
To compensate the sacrifice of profits made by the existing partners, the new parter brings in goodwill amount. This goodwill amount is distributed among the already existing partners in their sacrificing ratio.
4. On what occasions sacrificing ratio is used?
The following are the occasion in which the sacrificing ratio is used:
1.
When the existing parters mutually agree to change their profit sharing ratio. In this case, few partners sacrifice their profits while the others gain.
2.
When a new partner is admitted into the firm and brings in goodwill share to compensate the sacrifice of the old partners’ profits, the sacrificing ratio is used to calcualted how the goodwill should be distributed among the existing partners.
5. If some goodwill already exists in the books and the new partner brings in his share of goodwill in cash, how will you deal with existing amount of goodwill?
When some goodwill already exists in the books and the new partner brings in his share of goodwill in cash, this existing amount of goodwill is dealt by writing it off among the old partners in their profit and loss sharing ratio.
The following is the corresponding journal entry.
Date
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
Old Partner’s Capital A/c
Dr.
xxxx
To Goodwill A/c
xxxx
(Being existing goodwill written-off by distributing it among the old partners)
6. Why there is need for the revaluation of assets and liabilities on the admission of a partner?
Revaluation of assets and liabilities is needed on the admission of a partner due to the following reasons:
1.
To record the correct value of understated or overstated assets
2.
To bring in the correct value of liabilities into the books after re-assessment.
3.
To record the unrecorded assets and liabilities
The gain or loss on revaluation of the assets and liabilities is transferred to the revaluation account. The balance of the revaluation account is then transferred to the old partners in their old profit sharing ratio. This exercise is carried out to correct the understated or overstated capital of the existing partners and then adjust the firm’s total capital to the fair value. This will also help to calculate the fair value of the capital that the new partner has to bring into the firm.

Long Answer Questions
1. Do you advise that assets and liabilities must be revalued at the time of admission of a partner? If so, why? Also describe how is this treated in the book of account?
Yes. I advise that assets and liabilities must be revalued at the time of admission of a partner. The following are the reasongs
(i)
The book value of assets may be overstated or understated. Revaluation ensures that the fair value of assets is recorded in the books.
(ii)
The liabilities also may be understated or overstated. Revaluation ensures tha the fair value of liabilities is recorded in the books.
(iii)
The unrecorded assets and liabilities are identified and recorded in the books.
The gain or loss on revaluation of the assets and liabilities is transferred to the revaluation account. The balance of the revaluation account is then transferred to the old partners in their old profit sharing ratio. The interpretation of the revaluation account’s balance is as follows:
Credit Balance:
Gain
Debit Balance:
Loss
This exercise is carried out to correct the understated or overstated capital of the existing partners and then adjust the firm’s total capital to the fair value. This will also help to calculate the fair value of the capital that the new partner has to bring into the firm.
The journal entries recorded for revaluation of assets and reassessment of liabilities are as follows:
(i) For increase in the value of an asset
Asset A/c
Dr.
To Revaluation A/c
(Being appreciation in the value of an asset)
(ii) For reduction in the value of an asset
Revaluation A/c
Dr.
To Asset A/c
(Being reduction in the value of an asset)
(iii) For appreciation in the amount of a liability
Revaluation A/c
Dr.
To Liabilities A/c
(Being appreciation in the value of an asset)
(iv) For reduction in the amount of a liability
Liability A/c
Dr.
To Revaluation A/c
(Being reduction in the value of an asset)
(v) For an unrecorded asset
Asset A/c
Dr.
To Revaluation A/c
(Being an unrecorded asset recorded)
(vi) For an unrecorded liability
Revaluation A/c
Dr.
To Liability A/c
(Being an unrecorded liability recorded)
Only one of the following two is recorded:
(vii) For transferring gain on Revaluation if credit balance
Revaluation A/c
Dr.
To Old Partner’s Capital A/c
(Being gain on revaluation transferred to old partners’ capital accounts in their old proift sharing ratio individually)
OR
(vii) For transferring loss on revaluation
Revaluation A/c
Dr.
To Asset A/c
(Being loss on revaluation transferred to old partners’ capital accounts in their old profit sharing ratio individually)
Note that the entries (i), (ii), (iii) and (iv) are recorded only with the amount increase and decrease in the value of assets and liabilities.

2. What is goodwill? What factors affect goodwill?
Definition of Goodwill:
After being in the business for some time, a well-established business will have the following advantages of
●
Good Name
●
Reputation
●
Wide Business Connections
Due to this advantage, a well-established business will be able to earn more profits as compared to a newly setup business. The monetary value of such advantage is called as Goodwill.
(i)
Goodwill is an intangible asset.
(ii)
It is the value of the reputation of a firm in respect of the profits expected in future over and above the normal profits
(iii)
It is generally observed that when a person pays for goodwill, he/she pays for something, which places him in the position of being able to earn super profits as compared to the profit earned by other firms in the same industry
In simple words, goodwill can be defined as “the present value of a firm’s anticipated excess earnings” or as “the capitalised value attached to the differential profit capacity of a business”. Thus, goodwill exists only when the firm earns super profits. Any firm that earns normal profits or is incurring losses has no goodwill.
The following are the factors that affect goodwill:
1.
Nature of Business: A business that produces high value added products or has a stable demand is more profitable. So, it has more goodwill.
2.
Location: When hte business is located in a central location or located in a place where the customer traffic is more, it will have more goodwill.
3.
Effective Management: An effectively manged business will have the advantage of high productivity and cost efficiency. This results in high profits. So, such a business will have more goodwill.
4.
Market Location: When the business is monopoly or has limited competition, it helps the business to earn more profits. This results in a higher value of goodwill.
5.
Spacial Advantage: The business that is previliged to avail special advantages like
●
Import Licences
●
Low Rate
●
Assured Supply of electircity
●
Long-term contracts for supply of materials
●
well-known collaborators
●
Patents
●
Trademarks etc.
will have more value of goodwill

3. Explain various methods of valuation of goodwill.
The following are the various methods of valuation of goodwill
1.
Average Profits Method
2.
Super Profits Method
3.
Capitalisation Method
(a)
Capitalisation of Average Profits
(b)
Capitalisation of Super Profits
Each of these methods are explained below:
1. Average Profits Method:
In this method, the goodwill is calculated as the number of ‘years’ purchase of the average profits of the past few years. The following formula is used to calculate the goodwill in this method.
First, the average profits is calculated as
{\text{Average Profits} = \dfrac{\text{Total Profits in the past few years}}{\text{No. of Years}}}
The goodwill is then calculated as
Goodwill = Average Profits × No. Years of Purchase
The following steps are used to calculate the goodwill in this method
(i)
Calculate the total profits of the last given years.
(ii)
Calculate the average Profits
(iii)
Calculate the the product of average profits and the number of years of purchase.
Suppose the profits in four past consecutive years happen to be ₹ 1,00,000, ₹ 1,50,000, ₹ 2,00,000 and ₹ 2,10,000
The average profit is then calculated as:
Average Profits
{= \dfrac{\text{Total Profits in the past 4 years}}{\text{No. of years}}}
{= \dfrac{₹~1,00,000 + ₹~1,50,000 + ₹~2,00,000 + ₹~2,10,000}{4}}
{= \dfrac{₹~6,60,000}{4}}
= ₹ 1,65,000
If the goodwill is considered as three years of purchase of the avaerage profits, then the goodwill can be calculated as
Goodwill
= Average Profits × No. of Years of Purchase
= ₹ 1,65,000 × 3
= ₹ 4,95,000
In a scenario where there is an increasing or decreasing trend in the profis, then weightage is considered under this mehod. Usually a higher weightage is given to the profits earned in the recent years than the profits made in the earlier years. The following are the steps used to calculate the goodwill in this method.
(i)
Multiply profit in each year with the corresponding weight.
(ii)
Calculate the total of the product of the weight and the corresponding profits.
(iii)
Calculate the average Profits dividing the total in step (ii) with the total of the weights.
(iv)
Calculate the the product of average profits and the number of years of purchase.
The weights and the profits made by a company are as 2018 – ₹ 1,00,000, 2019 – ₹ 1,50,000, 2020 – ₹ 2,00,000 and 2021 – ₹ 3,00,000 and the weights are given as 2018 – 1, 2019 – 2, 2020 – 3, 2021 – 4, the calculation is as follows:
Year
Profit
Weight
Product
2018
1,00,000
1
1,00,000
2019
1,50,000
2
3,00,000
2020
2,00,000
3
6,00,000
2021
3,00,000
4
12,00,000
Total
10
22,00,000
Weighted Average Profits
{= \dfrac{\text{Total profits products for past 4 years}}{\text{Weighted Years}}}
{= \dfrac{₹~22,00,000}{10}}
= ₹ 2,20,000
Now, the goodwill for 3 years of purchase can be calculated as:
Goodwill
= Weighted Average Profits × No. of Years of Purchase
= ₹ 2,20,000 × 3
= ₹ 6,60,000
2. Super Profits Method:
In this method, the goodwill is based on the excess profits in the coming years and not the actual profits. This excess of actual profits over the normal profits is termed as Super profits. The following steps are used to calculate the goodwill in this method.
(i)
Calculate the average profit
(ii)
Calculate the normal profit on the capital employed on the basis of normal rate of return using the formula
{\text{Normal Profits} = \dfrac{\text{Firm's Capital × \text{Normal Rate of Return}}}{100}}
(iii)
Calculate the super profits by deducting normal profis from the average profits
(iv)
Calculate the goodwill by multiplying the super profits by the given number of years of purchase
For example, the normal rate of return in a business is 15% p.a. and a business has earned ₹ 20,000, ₹ 24,000, ₹ 25,000 and ₹ 27,000 in the past four years with capital ₹ 1,00,000, then the goodwill for a 3 year purchase can be calculated as follows:
Normal Profits
{= \text{Firm's Capital} × \dfrac{\text{Normal Rate of Return}}{100}}
{= ₹~1,00,000 × \dfrac{15}{100}}
= ₹ 15,000
Average Profits
{= \dfrac{\text{Total Profits in the past 4 years}}{\text{No. of Years}}}
{= \dfrac{₹~20,000 + ₹~24,000 + ₹~25,000 + ₹~27,000}{4}}
{= \dfrac{₹~96,000}{4}}
= ₹ 24,000
Super Profits
= Average Profits – Normal Profits
= ₹ 24,000 – ₹ 15,000
= ₹ 9,000
Goodwill
= Super Profits × No. of Years of Purchase
= ₹ 9,000 × 3
= ₹ 27,000
3. Capitalization method → (a) Capitalization of Average Profits:
In this method, the value of the goodwill is calculated by deducting the actual firm’s capital (net assets) in the business from the capitalized value of the average profits on the basis of normal rate of return. The following are the steps in this method:
(i)
Calculate the average profits based on the past few years performance
(ii)
Capitalize the average profis on the basis of the normal rate of return. This will give us the capitalized value of average profits as follows: {\text{Average Profits} × \dfrac{100}{\text{Normal Rate of Return}}}
(iii)
Calculate the actual firm’s capital (net assets) by deducting outside liabilities from the total assets (excluding goodwill and fictious assets) as Firm’s Capital = Total Assets (excluding goodwill) – Outside Liabilities
(iv)
Calculate the value of goodwill by deducting the net assets from the capitalized value of average profits i.e (ii) – (iii)
If a firm has ₹ 1,00,000 as average profits during the past few years and the normal rate of return is 15% p.a. on a similar business and the net assets of the firm are 8,00,000, calculate the goodwill.
Capitalized value of average profits
{= \text{Average Profits} × \dfrac{100}{\text{Normal Rate of Return}}}
{= ₹~1,00,000 × \dfrac{100}{10}}
= ₹ 10,00,000
Goodwill
= Capitalized Value – Net Assets
= ₹ 10,00,000 – ₹ 8,00,000
= ₹ 2,00,000
3. Capitalization method -> (b) Capitalization of Super Profits:
In this method, the value of goodwill is calculated by capitalising the super profits directly. In this method we dont’ have to calcuate the capitalized value of average profits. The following are the steps in this method:
(i)
Calculate the capital of the firm as Firm’s Capital = Total Assets (excluding goodwill) – Outside Liabilities
(ii)
Calculate the normal profits on the capital employed.
(iii)
Calculate the average profits for the past few years.
(iv)
Calculate the super profits by deducting the normal profits from average profits.
(v)
Multiply the super profits by the required rate of return multipler as below
{\text{Goodwill} = \text{Super Profits} × \dfrac{100}{\text{Normal Rate of Return}}}
The profits of a firm in the past five years are ₹ 10,000, ₹ 15,000, ₹ 4,000, ₹ 6,000 and ₹ 5,000. The normal rate of return in a similar business is 8% p.a.. The capital of the firm is ₹ 1,00,000. The goodwill of the firm can be calculated as follows:
Total Profits
= ₹ 10,000 + ₹ 15,000 + ₹ 4,000 + ₹ 6,000 + ₹ 15,000
= ₹ 50,000
Average Profits
{= \dfrac{\text{Total Profits}}{\text{No. of Years}}}
{= \dfrac{₹~50,000}{5}}
= ₹ 10,000
Normal Profits
{= \text{Firm's Capital} × \dfrac{\text{Normal Rate of Return}}{100}}
= {₹~1,00,000 × \dfrac{8}{100}}
= ₹ 8,000
Super Profits
= ₹ 10,000 – ₹ 8,000
= ₹ 2,000
Goodwill
{= \text{Super Profits} × \dfrac{100}{\text{Normal Rate of Return}}}
{= ₹~2,000 × \dfrac{100}{8}}
= ₹ 25,000

4. If it is agreed that the capital of all the partners should 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.
If it is agreed that the capital of all the partners should be proportionate to the new profit sharing ratio, we can work out the new capital of each partner in the following two scenarios:
(a)
When the capital of the new partner is given.
(b)
When the capital of the firm is specified.
(a) When the capital of the new partner is given:
When the capital of the new partner is given, the following steps are used to calculate the new capital of the existing partners.
(i)
The old capitals are adjusted for
●
Goodwill
●
Reserves
●
Revaluation of Assets and Liabilities
(ii)
Considering the new partner’s capital as the base, the new capital of the firm is calculated.
(iii)
New Capitals of the old partners are calculated as per the new profit sharing ratio.
(iii)
The capitals thus obtained are compared with their old capitals
(iv)
The partner whose capital falls short, will bring in the necessary amount to cover the shortage and the partner who has a surplus, will withdraw the excess amount of capital.
A and B are partners sharing profits in the ratio of 2:1. C is admitted into the firm for 1/4 share of profits. C brings in ₹ 20,000 in respect of his capital. The capitals of old partners A and B, after all adjustments relating to goodwill, revaluation of assets and liabilities, etc., are ₹ 45,000 and ₹ 15,000 respectively.
Total Share
= 1
C’s share
{= \dfrac{1}{4}}
Remaining share
{= 1 - \dfrac{1}{4}}
{= \dfrac{3}{4}}
A’s new share
{= \dfrac{3}{4} × \dfrac{2}{3}}
{= \dfrac{6}{12}}
B’s new share
{= \dfrac{3}{4} × \dfrac{1}{3}}
{= \dfrac{3}{12}}
C’s share
{= \dfrac{1}{4} × \dfrac{3}{3}}
{= \dfrac{3}{12}}
New Ratio
{= \dfrac{6}{12} : \dfrac{3}{12} : \dfrac{3}{12}}
= 2:1:1
C’s Capital
= ₹ 20,000
Total Capital
{= ₹~20,000 × \dfrac{4}{1}}
= ₹ 80,000
A’s new Capital
{= ₹~80,000 × \dfrac{2}{4}}
= ₹ 40,000
B’s new Capital
{= ₹~80,000 × \dfrac{1}{4}}
= ₹ 20,000
The capital of A and B after all adjustments have been made, are ₹ 45,000 and ₹ 15,000 respectively. Hence, A will withdraw ₹ 5,000 (₹ 45,000 – ₹ 40,000) from the firm whereas B will contribute additional amount of ₹ 5,000 (₹ 20,000 – ₹ 15,000). The journal entries will be :
Date
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
A’s Capital A/c
Dr.
5,000
To Cash A/c
5,000
(Being excess capital withdrawn by A)
Cash A/c
Dr.
5,000
To B’s Capital A/c
5,000
(Being deficiency made good by additional amount brought in by B)
(b) When the capital of the firm is specified
When the total capital of the firm is given, the following steps are used to calculate the new capital of the existing partners. In this case, it is agreed that the capital of each partner should be proportionate to his share in profits
(i)
The old capitals are adjusted for
●
Goodwill
●
Reserves
●
Revaluation of Assets and Liabilities
(ii)
Each partner’s new capital (including the new partner’s capital to be brought by him) is calculated on the basis of his share in profits.
(iii)
The capitals thus obtained are compared with their old capitals
(iv)
The partner whose capital falls short, will bring in the necessary amount to cover the shortage and the partner who has a surplus, will withdraw the excess amount of capital.
For instance, consider the following scenario.
A, B and C are partners in a firm sharing profits the ratio of 3:2:1. D is admitted into the firm for 1/4 share in profits, which he gets as 1/8 from A and 1/8 from B. The total capital of the firm is agreed upon as ₹ 1,20,000 and D is to bring in cash equivalent to 1/4 of this amount as his capital. The capitals of other partners are also to be adjusted in the ratio of their respective shares in profits. The capitals of A, B and C after all adjustments are ₹ 40,000, ₹ 35,000 and ₹ 30,000 respectively.
Calculation of new profit sharing ratio:
A’s new share
{= \dfrac{1}{2} - \dfrac{1}{8}}
{= \dfrac{4 - 1}{8}}
{= \dfrac{3}{8}}
B’s new share
{= \dfrac{1}{3} - \dfrac{1}{8}}
{= \dfrac{8 - 3}{24}}
{= \dfrac{5}{24}}
C’s share
{= \dfrac{1}{6}}
D’s share
{= \dfrac{1}{4}}
New Ratio
{= \dfrac{3}{8} : \dfrac{5}{24} : \dfrac{1}{6} : \dfrac{1}{4}}
{= \dfrac{9}{24} : \dfrac{5}{24} : \dfrac{4}{24}} : \dfrac{6}{24}
= 9 : 5 : 4 : 6
Calculation of required capitals of all the partners:
A’s Capital
{= ₹~1,20,000 × \dfrac{9}{24}}
= ₹ 45,000
B’s Capital
{= ₹~1,20,000 × \dfrac{5}{24}}
= ₹ 25,000
C’s Capital
{= ₹~1,20,000 × \dfrac{4}{24}}
= ₹ 20,000
D’s Capital
{= ₹~1,20,000 × \dfrac{6}{24}}
= ₹ 30,000
Hence, A will bring in ₹ 5,000 (₹ 45,000 – ₹ 40,000), B will withdraw ₹ 10,000 (₹ 35,000 – ₹ 25,000), C will withdraw ₹ 10,000 (₹ 30,000 – ₹ 20,000) and D will bring in ₹ 30,000. Alternatively, the current accounts can be opened and the amounts to be brought in or withdrawn by A, B and C will be transferred to their respective current accounts subject to the agreement among the partners. The journal entries in this regard will be recorded as follows:
Books of A, B, C and D
Journal
Date
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
Cash A/c
Dr.
5,000
To A’s Capital A/c
5,000
(Being Deficiency made good by additional amount brought in by A)
B’s Capital A/c
Dr.
10,000
C’s Capital A/c
Dr.
10,000
To Cash A/c
20,000
(Being excess amounts withdrawn by B and C)
Cash A/c
Dr.
30,000
To D’s Capital A/c
30,000
(Being Cash brough in by D as Capital)
Alternatively, for entries (2) and (3) above shall be
Books of A, B, C and D
Journal
Date
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
A’s Current A/c
Dr.
5,000
To A’s Capital A/c
5,000
(Being Deficience in A’s Capital transferred to A’s current Account)
B’s Capital A/c
Dr.
10,000
C’s Capital A/c
Dr.
10,000
To B’s Current A/c
10,000
To C’s Current A/c
10,000
(Being excess capital of B and C transferred to their current account)

5. Explain how will you deal with goodwill when new partner is not in a position to bring his share of goodwill in cash.
When new partner is not in a position to bring his share of goodwill in cash, we deal with the goodwill as described below. Note that there’re two possibilities that require to be considered while dealing with this scenario.
(a)
Goodwill does not exist in the books and
(b)
Goodwill exists in the books
(a) Goodwill does not exist in the books:
When goodwill does not exist in the books, sacrificing partners are credited with their share of goodwill and new partner is debited by the amount of goodwill not brought by him. The journal entry in this case is:
Incoming (New) Partners Current A/c
Dr.
To Sacrificing Partners Capital A/c
(individually)
(Account of goodwill not brought in by new partner)
Sometimes the new partner brings part of premium for goodwill in cash. In such a situation, new partners current account will be debited by the amount not brought by new partner.
(b) Goodwill exists in the books :
Goodwill appearing in the books will be written-off by debiting old partners’ capital accounts in their old profit sharing ratio. Thereafter new value of goodwill will be given effect by crediting sacrificing partners’ capital accounts and debiting new partners’ current account.
The journal entries will be as follow:
(i) When the valve of goodwill appears in the books and is written-off
Partners capital A/c (old)
(In profit sharing ratio)
Dr.
To Goodwill A/c
(Goodwill appearing in the books written-off)
(ii) For new value of goodwill:
Incoming partners’ current A/c
Dr.
To Sacrificing partners’ capital A/c.
(In sacrificing ratio individually)
6. Explain various methods for the treatment of goodwill on the admission of a new partner?
The pre-requisite before treating the goodwill on the admission of a new partner is to write off the exising goodwill among the existing partner in their old profit sharing ratio. The corresponding journal entries are as blow.
Old Partners’ Capital A/c
Dr.
To Goodwill A/c
Goodwill written off among the existing partners in their profit sharing ratio.)
Once the existing goodwill (if any) is written-off, the various methods for the treatment of goodwill on the admission of a new partner are explained below.
1.
Premium Method
2.
Revaluation Method
1. Premium Method: When this method is followed, the new partner has to pay the goodwill in cash. This occurs under the following two scenarios:
a.
Goodwill is paid privately in cash by the new partner to the existing partners: As the payment is done privately, it will not be recorded in the books of account.
b.
When the new parnerer brings his/her share of goodwill in cash and the goodwill is retained in the business: In this scenario, the following entries are made in the books of accounts.
i.
When the goodwill is brought in cash by the new partner
Cash/Bank A/c
Dr.
To Premium for Goodwill A/c
(Being goodwill brought in by the new partner)
ii.
Goodwill brought in by the new partner is distributed among the old partners (When the goodwill is retained in the business)
Premium for Goodwill A/c
Dr.
To Sacrificing Partner’s Capital A/c
(Being goodwill brought in by the new partner is distributed among the old partners in their respective sacrificing ratio)
iii.
Old partners withdraw the new partners’ share of goodwill
Sacrificing Partner’s Capital A/c
Dr.
To Cash A/c
(Being amount of goodwill is withdrawn by the old partners)
c.
When the new partner brings his/her share of goodwill partially: In this scenario, the following entries are made in the books of accounts.
i.
When the goodwill is brought in cash:
Cash/Bank A/c
Dr.
To Premium for Goodwill A/c
(Being goodwill brought in cash by the new partner)
ii.
Goodwill brought in by the new partner is distributed among the old partners (When the goodwill is retained in the business): Goodwill brought in cash by the new partner(s) is distributed among the existing partners. For the rest of the goodwill (not brought in cash by the new partner) the new partner’s capital account is debited and existing partners’ capital accounts are credited.
Goodwill A/c
Dr.
New Partner’s Capital A/c
Dr.
To Sacrificing Partner’s Capital A/c
(Being share good new partner’s goodwill is distributed among the existing partners in their respective sacrificing ratio)
2. Revaluation Method: When the new partner is not able to bring in the goodwill in the form of cash: In this case, the new partners capital account is debited with an amount equal to goodwill and distributed among the existing partners in their respective sacrificing ratios. The following are the corresponding entries in the books of accounts
New Partner’s Capital A/c
Dr.
To Sacrificing Partner’s Capital A/c
(Being share of new partner’s goodwill is distributed among the existing partners in their respective sacrificing ratio)
Note: As per the Para 16 of Accounting Standard 10, we need to record the goodwill in the books of accounts only when the new partner brings in the goodwill in an equivalent worth of money or money’s worth. This is mandatory. When a new partner is admitted or any of the existing partner(s) retire/dead or if there is a change in the profit sharing ratio among the existing partners, the goodwill account cannot be raised as no consideration is paid for it.

7. How will you deal with the accumulated profits and losses and reserves on the admission of a new partner?
At the time of admission of a new partner, there might be accumulated profits that are not yet transferred to capital accounts of the existing partners. These accumulated profits are usually in the form of general reserve, reserve and/or Profit and Loss Account. As these accumulated profits are earned before the admission of a new partner, only the existing partners are entitled to share them. The new partner is not entitled to have any share in these profits. So, these accumulated profits are distributed among the existing partners in the ratio of their old profit sharing ratios. It is not only for the accumulated profits, if there are any accumulated losses in the form of a debit balance of profit and loss account and/or deferred revenue expenditure appearing in the blanace sheet of the firm, it should also be distributed among the existing partners in the ratio of their old profit sharing ratio.
The treatment of the accumulated profits and losses is as follows:
1.
To Distribute Accumulated Profits and Reserves
Profit and Loss A/c
Dr.
General Reserves A/c
Dr.
Reserve Fund A/c
Dr.
Workmen’s Compensation Fund A/c
Dr.
Contingency Reserve A/c
Dr.
To Old Partner’s Capital A/c
(Being accumulated profits and reserves distributed among the existing partners in their old profit sharing ratio)
2.
To Distribute Accumulated Losses
Old Partner’s Capital A/c
Dr.
To Profit and Loss A/c
(Debit Balance)
To Deferred Advertisement Expenses A/c
To Preliminary Expenses A/c
(Being accumulated losses distributed among the existing partners in their old profit sharing ratio)

8. At what figures the value of assets and liabilities appear in the books of the firm after revaluation has been due. Show with the help of an imaginary balance sheet.
1.
When a new partner is admitted into the firm, it is always desirable to ascertain whether the assets are shown in the books of the firm at their current values. If it is found that the assets are overstated or understated, they are revalued.
2.
Similarly, reassessment of the liabilities is also done to ensure that the liabilities are brought into the books at their correct value.
3.
Sometimes, there may also be some unrecorded assets and liabilities of the firm. These also have to be brought into the books of the firm.
Due to the above reasons, the firm has to prepare the revaluation account. The gain or loss on revaluation on each asset and liability is transferred to this account and finally its balance is transferred to the capital accounts of the old partners in their profit sharing ratio. This implies that the revaluation account is credited with increase in the value of each asset and decrease in liabilities. This is because such an increase in the value of the asset or decrease in the liability is a gain. Similarly, the revaluation account is debited with decrease in the value of the asset and increase in its liabilities as it is a loss.
Similarly, unrecorded assets are credited and unrecorded liabilities are debited in the revaluation account. If the revaluation account finally shows a credit balance then it it indicates net gain and if there is a debit balance then it indicates that there is a net loss.
This gain or loss is transferred to the existing partners accounts in their old profit sharing ratio.
The following is the imaginary balance sheet of A and B who share profits in the ratio of 3:2
Balance Sheet of A and B as on April 1, 2021.
Liabilities
Amount
₹
Assets
Amount
₹
Sundry Creditors
20,000
Cash in hand
3,000
Capitals
Debtors
12,000
A
30,000
Stock
15,000
B
20,000
50,000
Furniture
10,000
Plant and Machinery
30,000
70,000
70,000
On that date C is admitted into the partnership on the following terms:
1.
C is to bring in ₹ 15,000 as capital and ₹ 5,000 as premium for goodwill for \dfrac{1}{6} share.
2.
The value of stock is reduced by 10% while plant and machinery is appreciated by 10%.
3.
Furniture is revalued at ₹ 9,000.
4.
A provision for doubtful debts is to be created on sundry debtors at 5% and ₹ 200 is to be provided for an electricity bill.
5.
Investment worth ₹ 1,000 (not mentioned in the balance sheet) is to be taken into account.
6.
A creditor of ₹ 100 is not likely to claim his money and is to be written off.
Record journal entries and prepare revaluation account and capital account of partners.
Books of A, B and C
Journal
Date
2015
Particulars
L.F.
Debit
Amount
₹
Credit
Amount
₹
Apr 01
Bank A/c
Dr.
20,000
To C’s Capital A/c
15,000
To Goodwill A/c
5,000
(Being Cash brought in by C as capital and goodwill/premium)
02
Goodwill A/c
Dr.
5,000
To A’s Capital A/c
3,000
To B’s Capital A/c
2,000
(Being Premium divided between A and B in their sacrificing ratio of 3:2)
03
Revaluation A/c
Dr.
3,100
To Stock A/c
1,500
To Furniture A/c
1,000
To Provision for Doubtful Debts A/c
600
(Revaluation in the value of assets on revaluation)
04
Plant and Machinery A/c
Dr.
3,000
Investment A/c
Dr.
1,000
To Revaluation A/c
4,000
(Being increase in the value of the assets on revaluation
05
Revaluation A/c
Dr.
200
To Outstanding Electricity A/c
200
(Being Amount provided for outstanding electricity bill)
06
Sundry Creditors A/c
Dr.
100
To Revaluation A/c
100
(Being amount not likely to be claimed by the creditors written off)
07
Revaluation A/c
Dr.
800
To A’s Capital A/c
480
To B’s Capital A/c
320
(Being profit on revaluation of assets and re-assessment of liabilities transferred to A and B in their old profit sharing ratio)
Particulars
Amount
₹
Particulars
Amount
₹
To Stock A/c
1,500
By Plant and Machinery A/c
3,000
To Furniture A/c
1,000
By Investments A/c
1,000
To Provision for Doubtful Debts A/c
600
By Sundry Creditors A/c
100
To Outstanding Electricity A/c
200
Profit on Revaluation transferred:
To A’s Capital A/c
480
To B’s Capital A/c
320
4,100
4,100
Date
2017
Particulars
J.F.
A
₹
B
₹
C
₹
Date
2017
Particulars
J.F.
A
₹
B
₹
C
₹
Apr01
Balance c/d
33,480
22,320
15,000
Apr 01
Balance b/d
30,000
20,000
Bank
15,000
Goodwill
3,000
2,000
Revaluation
(Profit)
480
320
33,480
22,320
15,000
33,480
22,320
15,000