Admission | ISC Class 12 Accounts Notes

This note covers the admission of a new partner into a partnership firm: reconstitution of the firm, the new profit-sharing ratio, the sacrificing and gaining ratios, goodwill (valuation, premium in cash, premium not in cash, hidden goodwill and goodwill already in the books), revaluation of assets and liabilities, reserves and accumulated profits and losses, adjustment of capitals, the balance sheet after admission, and a change in the profit-sharing ratio among existing partners.

What is admission of a partner, and why does it reconstitute the firm?

A partnership is an agreement between two or more persons, called partners, for sharing the profits of a business carried on by all or any of them acting for all. Any change in the existing agreement amounts to reconstitution of the firm. The old agreement ends and a new one begins, with a changed relationship among the members and/or a changed composition. The firm itself continues.

Reconstitution usually takes place through admission of a new partner, change in the profit-sharing ratio (the proportion in which the partners share profits) among existing partners, retirement of a partner, or death of a partner.

Why is a new partner admitted, and who must agree?

When a firm requires additional capital or managerial help or both for the expansion of its business, a new partner may be admitted to supplement its existing resources. Under the Partnership Act 1932, unless the partnership deed (the agreement among the partners) provides otherwise, a new partner can be admitted only when the existing partners unanimously agree.

What does the new partner acquire, and what does he pay?

A newly admitted partner acquires two main rights in the firm: the right to share its assets and the right to share its profits. For these rights he brings an agreed amount of capital, either in cash or in kind.

An established firm may be earning more profits than the normal rate of return (the rate earned in a similar business) on its capital. Then the new partner is required to contribute some additional amount known as premium or goodwill.

It compensates the sacrificing partners, the old partners who give up part of their share, for the loss of their share in the super profits (the excess of actual profits over the normal profits) of the firm.

Which six matters need attention?

These matters require attention at admission.

1. New profit-sharing ratio.
2. Sacrificing ratio.
3. Valuation and adjustment of goodwill.
4. Revaluation of assets and reassessment of liabilities.
5. Distribution of accumulated profits (reserves).
6. Adjustment of partners' capitals.

How is the new profit-sharing ratio calculated?

A new partner acquires his share in profits from the old partners, who sacrifice a share of their profit in his favour. How much each gives up is decided mutually among the old partners and the new partner. If nothing is specified, it may be assumed that he gets it from the old partners in their profit-sharing ratio.

In any case the old partners' shares fall, so the new ratio among all the partners has to be worked out. A ratio such as 3:2 means shares of 3/5 and 2/5.

New share of old partner = Old share − Share surrendered

What are the sacrificing ratio and the gaining ratio?

The ratio in which the old partners agree to sacrifice their share of profit in favour of the incoming partner is called the sacrificing ratio. It matters because the premium for goodwill that the incoming partner pays is shared by the existing partners in this ratio.

Sacrifice = Old share − New share

The ratio is normally clearly given as agreed among the partners: the old ratio, equal sacrifice, or a specified ratio. If nothing is specified about how the new partner acquires his share, it may be assumed to be the old ratio. It is usually the same as the old ratio, but by agreement it can be different.

If the new profit-sharing ratio is given instead, deduct each partner's new share from his old share.

Worked example 1. Rohit and Mohit share profits in the ratio 5:3. They admit Bijoy for a 1/7 share, and the new profit-sharing ratio is 4:2:1. Calculate the sacrificing ratio of Rohit and Mohit.

Working: the new shares are 4/7, 2/7 and 1/7. Rohit's sacrifice = 5/8 − 4/7 = 35/56 − 32/56 = 3/56. Mohit's sacrifice = 3/8 − 2/7 = 21/56 − 16/56 = 5/56.

Answer: the sacrificing ratio of Rohit and Mohit is 3:5.

What is the gaining ratio?

Sometimes an old partner's new share is larger than his old share. He then gains instead of sacrificing, and the ratio in which such partners gain is the gaining ratio.

Gain = New share − Old share

Worked example 2. Ramesh and Suresh share profits in the ratio 4:3. They admit Mohan, and the new ratio of Ramesh, Suresh and Mohan is 2:3:1. Find the gain or sacrifice of each old partner.

Working: the new shares are 2/6, 3/6 and 1/6. Ramesh: sacrifice = 4/7 − 2/6 = 10/42. Suresh: gain = 3/6 − 3/7 = 3/42. Mohan's share = 1/6 = 7/42.

Answer: Ramesh sacrifices 10/42, Suresh gains 3/42 and Mohan receives 7/42. Ramesh's sacrifice equals Suresh's gain plus Mohan's share (3/42 + 7/42), so the whole sacrifice is by Ramesh alone.

What is goodwill, and how is it valued?

Over a period of time, a well-established business develops the advantage of a good name, reputation and wide business connections. This helps it to earn more profits than a newly set up business.

In accounting, the monetary value of this advantage is known as goodwill. It is an intangible asset (an asset without physical existence). In other words, goodwill is the value of the reputation of a firm in respect of the profits expected in future over and above the normal profits.

It is generally observed that a person who pays for goodwill pays for something that puts him in a position to earn super profits compared with other firms in the same industry. Normal profits are the profits at the normal rate of return on the firm's capital. Goodwill exists only when the firm earns super profits. A firm that earns normal profits, or is incurring losses, has no goodwill.

How is goodwill valued?

The need to value goodwill arises on the admission of a new partner, and it may also arise on other changes such as the retirement or death of a partner. It is very difficult to calculate its value accurately, and the value by one method may differ from the value by another. The method may therefore be specifically decided between the existing partners and the incoming partner.

The firm's capital, or net assets, is total assets (excluding purchased goodwill, non-trade investments and fictitious assets, such as the debit balance of the Profit and Loss Account) less outside liabilities, which are its long-term and short-term liabilities to outsiders.

A weighted average, with more weight on recent years, may be used if profits show an increasing or decreasing trend, but only if it is specified.

How is goodwill treated when the new partner pays his share in cash?

The premium for goodwill brought in by the incoming partner is shared by the existing partners in their sacrificing ratio. If the new partner pays the amount directly to the old partners (privately), no entry is passed in the books of the firm.

When the amount is paid through the firm, which is generally the case, entries are passed. In them, A/c stands for account, and a partner's Capital A/c records the capital he has in the firm. Premium for Goodwill A/c receives the premium and is then cleared by transferring it to the sacrificing partners.

Alternatively, the premium is first credited to the new partner's capital account and then transferred from it to the sacrificing partners.

If the partners decide that the premium credited to their capital accounts should be retained in the business, no additional entry is passed. If the premium is paid in kind, the asset account is debited in place of Bank A/c. The Premium for Goodwill A/c is also commonly called Goodwill A/c, with the same result.

Worked example 3. Sunil and Dalip share profits and losses in the ratio 5:3. They admit Sachin for a 1/5 share. Sachin brings ₹20,000 as capital and ₹4,000 as his share of goodwill by cheque, and the sacrificing ratio is the old ratio 5:3. (₹ is the rupee sign.) Give the entries (a) when the goodwill is retained, (b) when it is fully withdrawn and (c) when 50% of it is withdrawn.

Working: Sunil's share of the premium = 4,000 × 5/8 = ₹2,500. Dalip's share = 4,000 × 3/8 = ₹1,500. The bank receives 20,000 + 4,000 = ₹24,000.

Answer: entries 1 and 2 apply in all three cases. In (a) there is no entry 3.

How is goodwill treated when the new partner cannot pay in cash, or when goodwill is already in the books?

What if the new partner does not bring his share of goodwill?

The goodwill not brought by the new partner, wholly or partly, is debited to his current account, a separate account from his capital account. The capital accounts of the sacrificing partners are credited for their respective shares.

If he brings part of the premium, only the amount not brought is debited to his current account. For example, if his share of goodwill is ₹50,000 and he brings only ₹20,000, Bank A/c is debited ₹20,000 and Premium for Goodwill A/c is credited ₹20,000. Premium for Goodwill A/c ₹20,000 and his Current A/c ₹30,000 are then debited, and the sacrificing partners' Capital A/cs are credited ₹50,000 in the sacrificing ratio.

What if goodwill already appears in the books?

Goodwill appearing in the books is written off by debiting the old partners' capital accounts in their old profit-sharing ratio and crediting Goodwill A/c. The new value of goodwill is then given effect, either through the premium brought in or through the incoming partner's current account.

Worked example 4. Srikant and Raman share profits and losses in the ratio 3:2. They admit Venkat for a 1/3 share. He brings ₹30,000 as capital and the necessary amount for his share of goodwill.

Goodwill is valued at ₹24,000, and the Goodwill Account stands in the books at ₹12,000 and is to be written off. Nothing is said about how Venkat acquires his share, so the sacrifice is in the old ratio 3:2. Record the entries.

Working: Venkat's share of goodwill = 24,000 × 1/3 = ₹8,000, shared ₹4,800 and ₹3,200. The existing goodwill of ₹12,000 is written off in the old ratio as ₹7,200 and ₹4,800. The bank receives 30,000 + 8,000 = ₹38,000.

Answer: three entries, shown below, with the bank receiving ₹38,000.

Note: Accounting Standard 26 (AS 26), the standard on intangible assets, allows purchased goodwill to be shown as an asset.

It should then be written off as early as possible, and within 10 years if this takes more than one accounting year. Self-generated goodwill is not accounted for and shown as an asset. If it has been debited to a goodwill account, it should be written off in the same financial year. Alternatively, the new partner's current account may be debited and the sacrificing partners credited, with the same effect.

What is hidden goodwill, and how is it found?

Sometimes the value of goodwill is not given at the time of admission. It then has to be inferred from the arrangement of the capitals and the profit-sharing ratio. Goodwill found in this way is called hidden goodwill.

1. Divide the new partner's capital by his share of profits to find the total capital the new firm should have. For a 1/5 share, multiply his capital by 5.
2. Add the capitals of the old partners (after adding any reserves, accumulated profits and revaluation adjustments given) and the capital of the new partner.
3. The difference is the goodwill: Hidden goodwill = Implied total capital − Actual total capital.
4. Multiply the goodwill by the new partner's share of profits to find his share of it, and credit that share to the sacrificing partners in the sacrificing ratio.

Worked example 5. Hem and Nem share profits in the ratio 3:2, and their capitals are ₹80,000 and ₹50,000. They admit Sam for a 1/5 share in the future profits. Sam brings ₹60,000 as capital and acquires his share from Hem and Nem in the old ratio. Find the goodwill of the firm and record the entries (a) if Sam brings his share of goodwill and (b) if he does not.

Working: implied total capital = 60,000 × 5 = ₹3,00,000. Actual total capital = 80,000 + 50,000 + 60,000 = ₹1,90,000. Goodwill = 3,00,000 − 1,90,000 = ₹1,10,000. Sam's share = 1,10,000 × 1/5 = ₹22,000, shared 3:2 as ₹13,200 and ₹8,800.

Answer: goodwill is ₹1,10,000. In (a), Bank A/c is debited ₹82,000 and Sam's Capital A/c ₹60,000 and Premium for Goodwill A/c ₹22,000 are credited. Premium for Goodwill A/c ₹22,000 is then debited, with Hem's Capital A/c ₹13,200 and Nem's Capital A/c ₹8,800 credited. In (b), Bank A/c is debited and Sam's Capital A/c credited ₹60,000, and Sam's Current A/c is debited ₹22,000 with the same credits to Hem and Nem.

How are reserves and accumulated profits and losses treated at admission?

A firm may have accumulated profits that have not yet been transferred to the partners' capital accounts. They are usually in the form of general reserve, reserve and/or the Profit and Loss Account. The new partner is not entitled to any share in them. They are transferred to the old partners' capital or current accounts in the old profit-sharing ratio.

Accumulated losses, such as a debit balance of the Profit and Loss Account or deferred revenue expenditure (a revenue expense not yet written off and so carried in the balance sheet), are transferred to the old partners' capital accounts in the old ratio.

Worked example 6. Rajinder and Surinder share profits in the ratio 4:1. When Narender is admitted, the books show a general reserve of ₹20,000 and a debit balance of ₹10,000 in the Profit and Loss Account. Pass the entries.

Working: the reserve is shared 20,000 × 4/5 = ₹16,000 and 20,000 × 1/5 = ₹4,000. The loss is shared 10,000 × 4/5 = ₹8,000 and 10,000 × 1/5 = ₹2,000.

Answer: General Reserve A/c is debited ₹20,000, with Rajinder's Capital A/c credited ₹16,000 and Surinder's Capital A/c ₹4,000. Rajinder's Capital A/c ₹8,000 and Surinder's Capital A/c ₹2,000 are debited, and Profit and Loss A/c is credited ₹10,000.

What if the accumulated balances stay in the balance sheet?

Sometimes the balances are left in the books. A single entry then adjusts the incoming partner's share through his current account, as for goodwill not brought in cash. For each partner the amount is the balance multiplied by his gain or sacrifice. For profits, the gaining partners' accounts are debited and the sacrificing partners' accounts are credited. For losses, the entry is reversed.

Worked example 7. Leela and Meeta share profits and losses in the ratio 5:3. They admit Om, and the new ratio of Leela, Meeta and Om is 5:3:2. A general reserve of ₹16,000 and a credit balance of ₹24,000 in the Profit and Loss Account stay in the books. Pass the single entry.

Working: the balances total 16,000 + 24,000 = ₹40,000. Leela sacrifices 5/8 − 5/10 = 5/40 and Meeta sacrifices 3/8 − 3/10 = 3/40, while Om gains 2/10 = 8/40. Om bears 40,000 × 8/40 = ₹8,000. Leela receives 40,000 × 5/40 = ₹5,000 and Meeta 40,000 × 3/40 = ₹3,000.

Answer: Om's Current A/c is debited ₹8,000, and Leela's Capital A/c ₹5,000 and Meeta's Capital A/c ₹3,000 are credited.

How are assets and liabilities revalued?

At admission it is always desirable to ascertain whether the assets of the firm are shown in the books at their current values. Overstated or understated assets are revalued, and liabilities are reassessed so that they are brought in at their correct values. Unrecorded assets and liabilities, which exist but have not been entered in the books, are also brought in.

The firm prepares a Revaluation Account for this purpose. It is credited with an increase in an asset and a decrease in a liability, because each is a gain. It is debited with a decrease in an asset and an increase in a liability, because each is a loss. Unrecorded assets are credited and unrecorded liabilities are debited. Its final balance goes to the old partners' capital accounts in the old ratio.

Worked example 8. A and B share profits in the ratio 3:2. Their balance sheet shows creditors ₹20,000; capitals of A ₹30,000 and B ₹20,000; cash ₹3,000; debtors ₹12,000; stock ₹15,000; furniture ₹10,000; and plant and machinery ₹30,000.

C is admitted for a 1/6 share, bringing ₹15,000 as capital and ₹5,000 as premium, shared by A and B in their sacrificing ratio 3:2.

Stock is reduced by 10% and plant and machinery appreciated by 10%. Furniture is revalued at ₹9,000. A provision for doubtful debts (an amount set aside for debts that may not be recovered) of 5% is created on debtors, and ₹200 is provided for an electricity bill. An investment of ₹1,000 not in the balance sheet is taken into account, and a creditor of ₹100 who is not likely to claim is written off. Prepare the Revaluation Account and the capital accounts.

Working: stock falls 10% of 15,000 = ₹1,500. Plant and machinery rise 10% of 30,000 = ₹3,000. Furniture falls ₹1,000. The provision is 5% of 12,000 = ₹600.

Answer: the profit on revaluation is ₹800, shared ₹480 to A and ₹320 to B. The closing capitals are A = 30,000 + 3,000 + 480 = ₹33,480, B = 20,000 + 2,000 + 320 = ₹22,320 and C = ₹15,000.

How are the partners' capitals adjusted?

At admission the partners sometimes agree that their capitals should be proportionate to their profit-sharing ratio. If the capital of the new partner is given, it can be used as the base for the new capitals of the old partners. These are compared with the old partners' capitals after all adjustments for goodwill, reserves and revaluation. The partner whose capital falls short brings in the shortage, and the partner with a surplus withdraws the excess.

Total capital = New partner capital ÷ His share, and Required capital = New share × Total capital.

If the partners agree, a shortage or an excess can instead go to the partner's current account. Sometimes the total capital of the firm is clearly specified, and each partner's capital, including the new partner's, is then his share applied to that total.

Worked example 9. A and B share profits in the ratio 2:1. C is admitted for a 1/4 share and brings ₹20,000 as capital. After all adjustments, the capitals of A and B are ₹45,000 and ₹15,000. Capitals are to be in the new profit-sharing ratio, with a shortage brought in and an excess withdrawn.

Working: nothing is said about how C acquires his share, so he takes it from A and B in the old ratio 2:1. The remaining share is 3/4, so A has 2/3 of 3/4 = 2/4 and B has 1/3 of 3/4 = 1/4. The new ratio is 2:1:1. C's ₹20,000 for a 1/4 share gives a total capital of 20,000 × 4 = ₹80,000. A needs 2/4 of 80,000 = ₹40,000 and B needs 1/4 of 80,000 = ₹20,000.

Answer: A has ₹45,000 against ₹40,000 and withdraws ₹5,000: A's Capital A/c is debited and Cash A/c credited ₹5,000. B has ₹15,000 against ₹20,000 and brings in ₹5,000: Cash A/c is debited and B's Capital A/c credited ₹5,000.

How is the new partner's capital found from the old partners' adjusted capitals?

The base can also be turned round. Ashoo and Rahul share profits in the ratio 5:3, and Gaurav is admitted for a 1/5 share. After all adjustments, Ashoo's capital is ₹45,000 and Rahul's is ₹35,000, and Gaurav is to contribute capital proportionate to his share.

The old partners' capitals total ₹80,000 and they hold the other 4/5 of the profits, so the total capital is 80,000 ÷ 4/5 = ₹1,00,000. Gaurav's capital is 1/5 of 1,00,000 = ₹20,000.

How is the balance sheet prepared after admission?

After the adjustments, the new balance sheet is prepared in horizontal format, with liabilities on the left, assets on the right and the same total on each side. Cash or bank rises by the capital and premium brought in. Revalued assets appear at their new values, provisions are deducted from debtors, and closed balances such as reserves and written-off goodwill disappear.

Worked example 10. A and B share profits in the ratio 2:1. C is admitted for a 1/4 share, bringing ₹30,000 as capital and ₹12,000 as goodwill. The capitals of A and B are to be adjusted in the profit-sharing ratio by opening current accounts. The old balance sheet shows creditors ₹8,000; bills payable ₹4,000; general reserve ₹6,000; capitals of A ₹50,000 and B ₹32,000; cash in hand ₹2,000; cash at bank ₹10,000; debtors ₹8,000; stock ₹10,000; furniture ₹5,000; machinery ₹25,000; and building ₹40,000.

The building is valued at ₹45,000, the machinery at ₹23,000, and a provision for bad debts of 6% is created on debtors. Prepare the new balance sheet.

Working: nothing is said about how C acquires his share, so the sacrifice is in the old ratio 2:1 and the new ratio is 2:1:1. The goodwill of ₹12,000 is shared ₹8,000 and ₹4,000. The building rises ₹5,000, while the machinery falls ₹2,000 and the provision is 6% of 8,000 = ₹480. The profit is 5,000 − 2,480 = ₹2,520, shared ₹1,680 and ₹840. The reserve of ₹6,000 is shared ₹4,000 and ₹2,000.

C's ₹30,000 for a 1/4 share gives a total capital of ₹1,20,000, so A needs 2/4 = ₹60,000 and B needs 1/4 = ₹30,000.

Answer: the new balance sheet totals ₹1,44,520 on each side.

What happens when only the profit-sharing ratio of existing partners changes?

Sometimes the partners change their profit-sharing ratio without any admission or retirement. Some then gain share in future profits and others lose part of theirs.

The gain and loss in the value of goodwill are adjusted by crediting the sacrificing partners and debiting the gaining partners with appropriate amounts, as for a new partner. Revaluation, transfer of accumulated profits and losses to the capital accounts in the old ratio, and adjustment of capitals to the new ratio are done as on admission.

Worked example 11. Dinesh, Ramesh and Suresh share profits and losses in the ratio 3:3:2 and decide to share equally in future. Goodwill is valued at ₹90,000 (4½ years' purchase of an average profit of ₹20,000) and is not to appear in the books. Find the adjustment for goodwill.

Working: Dinesh's share changes from 3/8 to 1/3, a sacrifice of 1/24. Ramesh also sacrifices 1/24. Suresh's share changes from 2/8 to 1/3, a gain of 2/24.

Answer: Suresh pays 90,000 × 2/24 = ₹7,500, and Dinesh and Ramesh each receive 90,000 × 1/24 = ₹3,750. Suresh's Capital A/c is debited ₹7,500, and Dinesh's Capital A/c and Ramesh's Capital A/c are each credited ₹3,750.

Glossary

• Reconstitution — Any change in the existing partnership agreement, such as admission of a partner, which ends the old agreement and begins a new one.
• Sacrificing ratio — The ratio in which the old partners agree to sacrifice their share of profit in favour of the incoming partner. Each sacrifice is old share minus new share.
• Gaining ratio — The ratio in which partners gain share of profit when a partner's new share is more than his old share. Each gain is new share minus old share.
• Goodwill — The monetary value of the advantage of good name, reputation and wide business connections; an intangible asset that exists only when the firm earns super profits.
• Premium for goodwill — The additional amount an incoming partner brings to compensate the sacrificing partners for their loss of share in super profits. It is shared in the sacrificing ratio.
• Super profits — The excess of actual profits over normal profits. Goodwill exists only when the firm earns them.
• Years' purchase — The number of years of profit paid for in valuing goodwill; three years' purchase of an average profit means multiplying it by 3.
• Hidden goodwill — Goodwill that is not given in the problem and is inferred from the new partner's capital, his share of profits and the actual capitals of the partners.
• Revaluation Account — The account that records gains and losses from revaluing assets and reassessing liabilities. Its balance goes to the old partners' capital accounts in the old ratio.
• Current account — A partner's account kept apart from his capital account. Amounts such as goodwill not brought in cash are debited or credited to it.

Common errors and misconceptions

• Misconception: The new partner shares in the reserves and accumulated profits already in the books. Correct: He is not entitled to any share. They are transferred to the old partners' capital accounts in the old profit-sharing ratio.
• Misconception: The sacrificing ratio is the old ratio in every question. Correct: It is usually the same as the old ratio, but by agreement it can be different. If the new ratio is given, find old share minus new share.
• Misconception: The premium for goodwill is shared by all partners, including the new partner. Correct: It is shared by the existing partners in their sacrificing ratio, because they give up share.
• Misconception: The profit on revaluation is shared in the new ratio or credited to the new partner. Correct: It belongs to the old partners and is credited to their capital accounts in the old ratio.
• Misconception: If the new partner brings no goodwill in cash, no entry is needed. Correct: His current account is debited for the amount not brought and the sacrificing partners' capital accounts are credited.
• Misconception: Goodwill already in the books can stay as an asset after admission. Correct: It is written off by debiting the old partners' capital accounts in their old ratio.

Exam-style questions with model answers

Q1. What is the sacrificing ratio? How is it calculated when the new profit-sharing ratio is given? [2 marks]

1. The sacrificing ratio is the ratio in which the old partners agree to sacrifice their share of profit in favour of the incoming partner. It is used to share the premium for goodwill that he brings.
2. When the new profit-sharing ratio is given, each old partner's sacrifice is his old share minus his new share, and the sacrificing ratio is the ratio of these sacrifices.

Q2. Why is a Revaluation Account prepared when a new partner is admitted, and in what ratio is its balance shared? [2 marks]

1. The assets of the firm may be overstated or understated, liabilities may need reassessment, and some assets or liabilities may be unrecorded. The Revaluation Account brings them to correct values by recording each gain and loss.
2. Its final balance, a net gain or a net loss, is transferred to the capital accounts of the old partners in their old profit-sharing ratio.

Q3. Amit and Viney share profits and losses in the ratio 3:1. When Ranjan is admitted, the Profit and Loss Account shows a debit balance of ₹40,000. Record the journal entry for it and state who bears the loss. [3 marks]

1. The debit balance is an accumulated loss. The new partner has no share in it, so it is borne by the old partners in their old ratio 3:1.
2. Amit bears 40,000 × 3/4 = ₹30,000 and Viney bears 40,000 × 1/4 = ₹10,000.
3. Journal entry: Amit's Capital A/c debited ₹30,000 and Viney's Capital A/c debited ₹10,000; Profit and Loss A/c credited ₹40,000.

Q4. Rajesh and Mukesh are equal partners. They admit Hari, and the new profit-sharing ratio of Rajesh, Mukesh and Hari is 4:3:2. Goodwill is valued at ₹36,000. Hari cannot bring his share of goodwill in cash, and the partners decide not to show goodwill in the balance sheet. Calculate the sacrificing ratio and pass the journal entry. [4 marks]

1. The old shares are 1/2 each and the new shares are 4/9, 3/9 and 2/9. Rajesh's sacrifice = 1/2 − 4/9 = 1/18. Mukesh's sacrifice = 1/2 − 3/9 = 3/18.
2. The sacrificing ratio of Rajesh and Mukesh is 1:3.
3. Hari's share of goodwill = 36,000 × 2/9 = ₹8,000. It is shared 1:3 as ₹2,000 to Rajesh and ₹6,000 to Mukesh.
4. Journal entry: Hari's Current A/c debited ₹8,000; Rajesh's Capital A/c credited ₹2,000; Mukesh's Capital A/c credited ₹6,000. No goodwill account is opened.

Q5. A, B and C share profits in the ratio 3:2:1. D is admitted for a 1/4 share, which he gets as 1/8 from A and 1/8 from B. The total capital of the new firm is agreed at ₹1,20,000, and D brings 1/4 of it in cash. The capitals of A, B and C are to be in their new profit-sharing ratio. After all adjustments, the capitals of A, B and C are ₹40,000, ₹35,000 and ₹30,000. Calculate the new capitals and state the cash adjustments. [5 marks]

1. New shares: A = 3/6 − 1/8 = 9/24; B = 2/6 − 1/8 = 5/24; C stays at 1/6 = 4/24; D = 1/4 = 6/24. The new ratio is 9:5:4:6.
2. Required capitals on ₹1,20,000: A = ₹45,000; B = ₹25,000; C = ₹20,000; D = ₹30,000.
3. A has ₹40,000 against ₹45,000 needed, so A brings in ₹5,000.
4. B has ₹35,000 against ₹25,000 and C has ₹30,000 against ₹20,000, so B and C each withdraw ₹10,000.
5. D brings ₹30,000 in cash as capital. If the partners agree, the amounts for A, B and C can instead be transferred to their current accounts.

Q6. A and B share profits in the ratio 2:1, with capitals of ₹1,80,000 and ₹1,50,000. Their assets include sundry debtors ₹60,000, stock ₹40,000, plant ₹1,00,000 and buildings ₹1,50,000. C is admitted for a 1/4 share, bringing ₹1,00,000 as capital and ₹60,000 as goodwill, which A and B share in the old ratio. Plant is raised to ₹1,20,000 and buildings appreciate by 10%. Stock is overvalued by ₹4,000. A provision of 5% is created on debtors. Creditors are unrecorded to the extent of ₹1,000. Find the profit on revaluation and the new capitals. [6 marks]

1. Losses on revaluation: stock ₹4,000, provision 5% of 60,000 = ₹3,000, and unrecorded creditors ₹1,000, a total of ₹8,000.
2. Gains: plant 1,20,000 − 1,00,000 = ₹20,000 and buildings 10% of 1,50,000 = ₹15,000, a total of ₹35,000.
3. Profit on revaluation = 35,000 − 8,000 = ₹27,000, shared 2:1 as ₹18,000 to A and ₹9,000 to B.
4. Goodwill of ₹60,000 is shared 2:1 as ₹40,000 to A and ₹20,000 to B.
5. Capital of A = 1,80,000 + 40,000 + 18,000 = ₹2,38,000. Capital of B = 1,50,000 + 20,000 + 9,000 = ₹1,79,000.
6. Capital of C = ₹1,00,000, so the three capitals total 2,38,000 + 1,79,000 + 1,00,000 = ₹5,17,000.

Key takeaways

• On admission the incoming partner acquires his share of profits from the old partners. The old partners' new shares are found by deducting each surrender from the old share.
• The sacrificing ratio is old share minus new share for each old partner. If nothing is specified it may be assumed to be the old ratio, though by agreement it can be different. A partner whose new share is more than his old share gains.
• The premium for goodwill is shared by the old partners in the sacrificing ratio. If it is paid privately no entry is passed, and if it is not brought in cash the new partner's current account is debited.
• Goodwill already in the books is written off to the old partners' capital accounts in the old ratio. Goodwill not given in a problem can be inferred as hidden goodwill from capitals and shares.
• Reserves and accumulated profits and losses belong to the old partners, and so does the balance of the Revaluation Account. Both go to the old partners' capital accounts in the old ratio.
• When capitals must match the new ratio, the new partner's capital is normally the base. A partner with a shortage brings in cash and a partner with an excess withdraws it.

Test yourself

In what ratio do the old partners share the premium for goodwill?

They share it in their sacrificing ratio, the ratio in which they give up their shares of profit to the new partner.

Which account is debited if the new partner does not bring his share of goodwill?

His current account is debited for the amount not brought. The capital accounts of the sacrificing partners are credited in the sacrificing ratio.

A and B share profits 3:1, and C is admitted for a 1/4 share taken from them in the old ratio. What is the new ratio?

A = 3/4 of 3/4 = 9/16, B = 1/4 of 3/4 = 3/16 and C = 4/16. The new ratio is 9:3:4, and the sacrificing ratio of A and B is 3:1.

A new partner brings ₹60,000 as capital for a 1/5 share. What total capital for the firm does this imply?

60,000 × 5 = ₹3,00,000. If the actual total capital is ₹1,90,000, as for Hem, Nem and Sam, the hidden goodwill is ₹1,10,000.

What happens to a general reserve when a new partner is admitted?

The new partner has no share in it. It is transferred to the old partners' capital accounts in their old profit-sharing ratio.

Ashoo and Rahul have adjusted capitals of ₹45,000 and ₹35,000 and hold 4/5 of the profits. What capital must Gaurav bring for his 1/5 share?

Their capitals total ₹80,000 for 4/5, so the total capital is ₹1,00,000. Gaurav's 1/5 share needs ₹20,000.