Reconstitution of a Partnership Firm: Admission of a Partner | CBSE Class 12 Accountancy Notes

This note covers partnership reconstitution, admission of a partner, new profit sharing and sacrificing ratios, goodwill valuation and adjustment, accumulated profits and losses, revaluation of assets and liabilities, capital adjustments, and changes in the profit sharing ratio among existing partners.

What is reconstitution, and why is a new partner admitted?

Definition: A partnership is an agreement between persons to share the profits of a business carried on by all, or by any of them acting for all. Reconstitution means a change in that existing agreement while the firm continues.

A new agreement changes the relationship among the partners, their composition, or both. A profit sharing ratio expresses partners’ relative shares of profit. Partners often reconstitute a firm through admission, a change in this ratio, retirement, death or insolvency, meaning inability to pay debts, of a partner. A change in agreement does not itself mean that the business stops.

How can the relationship change?

Admission adds a partner when additional capital, the amount invested in the firm, managerial help or both are needed for expansion. Unless otherwise agreed, admission requires the consent of all existing partners. A partnership deed records the partners’ agreement; its provisions matter when deciding the terms of admission.

Retirement means withdrawal of a partner from the firm’s business. It may result from bad health, old age or changed business interests. Death may also lead to reconstitution if the remaining partners decide to continue the business.

What does the incoming partner receive?

The incoming partner acquires rights to share the firm’s assets, its economic resources, and its profits. The partner contributes agreed capital in cash or in kind, meaning through assets other than cash. An established firm may earn more than the normal return on its capital.

In that case, an additional payment called premium for goodwill compensates partners who surrender a share of those excess profits. Goodwill is the monetary value of the advantage created by a business’s reputation, good name and connections.

1. Determine the new profit sharing ratio.
2. Calculate the sacrificing ratio, the ratio of profit shares surrendered by existing partners.
3. Value goodwill and decide its accounting adjustment.
4. Revalue assets to their current values and reassess liabilities, the firm’s obligations, to their correct amounts.
5. Distribute accumulated profits or reserves, earlier profits retained in the business.
6. Adjust partners’ capitals where required.

How is the new profit sharing ratio calculated?

The new profit sharing ratio gives each partner’s share of future profits after reconstitution. The incoming partner obtains a share from the existing partners. The agreement determines both the incoming share and how much each old partner gives up.

If nothing specifies how the incoming partner acquires the share, it may be assumed that the old partners surrender it in their old profit sharing ratio. State this assumption when using it. Where particular sacrifices are given, use those instead.

In the calculations below, 1 represents the whole profit, a fraction represents a share of that whole, and a colon separates the relative parts of a ratio. The signs ×, ÷, −, + and = mean multiplication, division, subtraction, addition and equality respectively; % means per hundred. A slash separates the upper and lower numbers of a fraction.

New share = Old share − Share surrendered

What if the share comes from the old partners in their old ratio?

Worked example 1. Anil and Vishal share profits in the ratio 3:2. They admit Sumit for 1/5 of future profits. Assume he acquires this share from them in their old ratio. Find the new ratio.

Answer: The remaining share is 1 − 1/5 = 4/5. Anil receives 3/5 × 4/5 = 12/25; Vishal receives 2/5 × 4/5 = 8/25. Sumit’s 1/5 equals 5/25. The new ratio is 12:8:5.

How do specific acquisition terms change the result?

A fraction of a partner’s share differs from a fraction of total profits. When Ram and Shyam share 3:2 and surrender 1/4 and 1/3 of their respective shares to Ghanshyam, their sacrifices are 3/20 and 2/15. Their new ratio is 27:16:17.

How does the sacrificing ratio differ from the new ratio?

Definition: The sacrificing ratio is the ratio in which existing partners surrender their shares of profit in favour of the incoming partner. It determines their shares of compensation for goodwill.

Sacrifice = Old share − New share

The new ratio applies to future profits among all partners. The sacrificing ratio applies to goodwill compensation for those giving up profit shares. It is normally clearly agreed, and may equal the old ratio, represent equal sacrifice, or follow a specified ratio.

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

Answer: Rohit sacrifices 5/8 − 4/7 = 3/56. Mohit sacrifices 3/8 − 2/7 = 5/56. Their sacrificing ratio is 3:5, although their old ratio was 5:3.

Can an existing partner gain on admission?

Yes. A gain is an increase in a partner’s profit share. Compare individual old and new fractions before deciding who receives compensation. A negative result from old share minus new share indicates a gain rather than a sacrifice.

Ramesh and Suresh originally share 4:3. After Mohan joins, their new ratio is 2:3:1. Ramesh sacrifices 4/7 − 2/6 = 10/42. Suresh gains 3/6 − 3/7 = 3/42, while Mohan receives 1/6, or 7/42.

The whole sacrifice is therefore Ramesh’s: 10/42 equals Suresh’s gain plus Mohan’s share. Admission does not establish that every old partner sacrifices. Calculate each change separately instead of distributing goodwill automatically in the old ratio.

Note: When a ratio is given only between the old partners after admission, first apply it to the remaining profit share. It is not yet the ratio among all partners.

What determines goodwill and the need to value it?

Goodwill measures the financial advantage of reputation and business connections in relation to expected profits above the normal level. It is an intangible asset, an asset without physical existence. It represents anticipated excess earnings rather than a physical resource such as machinery.

Normal profits are the return expected on the capital employed in a similar business. Super profits are profits above that normal return. Goodwill exists when the firm earns super profits; a firm earning normal profits or incurring losses has no goodwill under this explanation.

Which factors affect its value?

Normally, valuation is needed when a business is sold. For a partnership, it may also be needed on a change in profit sharing ratio, admission, retirement, death, dissolution involving sale as a going concern, or amalgamation of firms.

A going concern is a business continuing in operation. Amalgamation combines firms. Dissolution ends the firm. These situations explain why goodwill valuation is relevant beyond the entry of a new partner.

Goodwill is difficult to value accurately because it is intangible. Different methods may produce different amounts, so the existing and incoming partners may specifically agree on the method. The main methods are average profits, super profits and capitalisation.

How do simple and weighted average profits value goodwill?

The symbol ₹ denotes Indian rupees. The average profits method values goodwill at an agreed number of years’ purchase of past average profits. Years’ purchase means the number of years used as the multiplier. Average profits are the total profits of the selected years divided by their number.

Average profit = Total profits ÷ Number of years

Goodwill = Average profits × Years’ purchase

The method assumes that a new business cannot earn profits during its first few years. The buyer of a running business therefore pays for the profits likely to be received during those years. This is the method’s assumption, not an unconditional prediction about every new business.

Worked example 3. A firm earns ₹4,00,000, ₹3,98,000, ₹4,50,000, ₹4,45,000 and ₹5,00,000 in 2013, 2014, 2015, 2016 and 2017 respectively. Value goodwill at four years’ purchase of five years’ average profits.

Answer: Total profits are ₹21,93,000. Average profit = ₹21,93,000 ÷ 5 = ₹4,38,600. Goodwill = ₹4,38,600 × 4 = ₹17,54,400.

When is a weighted average used?

A weight specifies the relative importance assigned to a year’s profit. Multiplying profit by its weight gives the weighted product. Divide the total products by the total weights to calculate the weighted average.

Sometimes, with an increasing or decreasing trend, it is considered better to give recent years higher weights. However, weighted average should be used only if specified. Do not choose it merely because the figures fluctuate.

For these profits and specified weights, weighted average profit is ₹3,48,000 ÷ 15 = ₹23,200. At three years’ purchase, goodwill is ₹69,600. The simple-average calculation assumes no change in the overall profit situation is expected in the future.

Which adjustments come before averaging?

Use adjusted profits where the question specifies corrections. A management cost reduces the relevant annual profits. Expenditure wrongly charged as an expense may need to be treated as an asset cost, with the required depreciation, the reduction in asset value charged against profit, deducted.

For profits of ₹20,200, ₹24,800, ₹20,000 and ₹30,000 in 2012 to 2015, deducting annual management cost of ₹4,800 gives ₹15,400, ₹20,000, ₹15,200 and ₹25,200. Further adjustments must be made before applying weights.

A ₹6,000 plant repair on 1 September 2014 is to be capitalised, meaning included in asset cost. Add it back to 2014 profit and deduct ₹200 depreciation at 10% for four months. The following year’s depreciation is ₹580 on the remaining ₹5,800.

Closing stock is inventory at a year’s end; it becomes the next year’s opening stock. Correcting a ₹2,400 overvaluation of 2013 closing stock reduces 2013 profit and increases 2014 profit. Final adjusted profits are ₹15,400, ₹17,600, ₹23,400 and ₹24,620.

With specified weights 1, 2, 3 and 4, the weighted products total ₹2,19,280. Dividing by total weights of 10 gives ₹21,928. Goodwill at three years’ purchase is ₹65,784.

How do super profits and capitalisation value goodwill?

The super profits method focuses on the buyer’s benefit above a normal return. Capital employed means the firm’s capital used in business. For this calculation, it includes partners’ capital and reserves and surplus, but excludes goodwill and fictitious assets.

Fictitious assets are debit balances such as deferred expenditure rather than real assets. Reserves and surplus represent profits retained in the business. The normal rate of return is the expected percentage return in a similar business.

Normal profit = Capital employed × Normal rate of return ÷ 100

Super profit = Average profit − Normal profit

Goodwill = Super profits × Years’ purchase

1. Calculate average profit for the specified period.
2. Calculate normal profit on the firm’s capital using the normal rate.
3. Subtract normal profit from average profit to obtain super profit.
4. Multiply super profit by the agreed years’ purchase.

Worked example 4. Capital employed is ₹5,00,000. Profits in 2011 to 2015 are ₹40,000, ₹50,000, ₹55,000, ₹70,000 and ₹85,000. The normal return is 10%. Value goodwill at three years’ purchase of super profits.

Answer: Average profit is ₹3,00,000 ÷ 5 = ₹60,000. Normal profit is ₹5,00,000 × 10 ÷ 100 = ₹50,000. Super profit is ₹10,000. Goodwill is ₹10,000 × 3 = ₹30,000.

What does capitalisation mean?

Capitalisation converts a profit amount into its equivalent capital value at a given return. Under capitalisation of average profits, calculate that value and subtract actual net assets. Net assets equal assets excluding goodwill and fictitious assets, less outside liabilities, including short-term and long-term obligations.

Capitalised value = Average profits × 100 ÷ Normal rate of return

Goodwill = Capitalised value − Net assets

Alternatively, capitalise super profits directly: Goodwill = Super profits × 100 ÷ Normal rate of return. With the same underlying data, the two capitalisation methods give exactly the same goodwill.

For average profits of ₹1,00,000, a normal return of 10% and net assets of ₹8,20,000, capitalised value is ₹10,00,000 and goodwill ₹1,80,000. Alternatively, normal profit is ₹82,000; super profit ₹18,000 capitalised at 10% also gives ₹1,80,000.

How is goodwill recorded when the new partner pays cash?

The incoming partner’s share of goodwill equals the firm’s goodwill multiplied by the profit share acquired. When paid through the firm, it is credited to the sacrificing partners in their sacrificing ratio. A private payment directly to old partners requires no entry in the firm’s books.

In the entries below, A/c means account, Dr. means debit and Cr. means credit. A journal entry records accounts debited and credited for a transaction. A partner’s capital account records capital and the adjustments made to it.

Worked example 5. Sunil and Dalip share profits and losses 5:3. Sachin joins for 1/5 and brings ₹20,000 capital and ₹4,000 goodwill by cheque. Assume sacrifice in the old ratio. Record receipt and distribution with goodwill retained in business.

Answer: Debit Bank ₹24,000; credit Sachin’s Capital ₹20,000 and Premium for Goodwill ₹4,000. Then debit Premium for Goodwill ₹4,000; credit Sunil’s Capital ₹2,500 and Dalip’s Capital ₹1,500.

What if the old partners withdraw the premium?

If the premium remains in the business, no additional withdrawal entry is needed. If Sunil and Dalip withdraw it fully, debit their capital accounts ₹2,500 and ₹1,500 and credit Bank ₹4,000. Their credited shares determine the respective withdrawals.

Alternatively, receipt can initially be credited to the incoming partner’s capital account. Debit that account for the goodwill amount and credit the sacrificing partners. This transfers the premium to its intended recipients while retaining the separately agreed incoming capital.

Existing goodwill appearing in the books is written off on admission. Debit the old partners’ capital accounts in their old profit sharing ratio and credit Goodwill. This removes the previous asset balance; it differs from distributing the incoming premium in the sacrificing ratio.

How are unpaid and hidden goodwill adjusted?

When goodwill is not brought in cash, fully or partly, debit the incoming partner’s current account for the unpaid amount and credit the sacrificing partners’ capital accounts. A current account records partner adjustments separately from the capital account.

If existing goodwill appears in the books, first write it off against the old partners in their old profit sharing ratio. The adjustment for the incoming partner’s unpaid premium then compensates sacrificing partners in their sacrificing ratio.

For a goodwill share of ₹50,000 with ₹20,000 brought in cash, debit Bank ₹20,000 and credit Premium for Goodwill ₹20,000. Then debit Premium for Goodwill ₹20,000 and the incoming partner’s Current Account ₹30,000; credit sacrificing partners’ capital accounts ₹50,000 in total.

Why is valuation separate from recognising an asset?

Accounting Standard 26, dealing with intangible assets, does not permit internally generated goodwill to be recognised as an asset. Internally generated goodwill is goodwill developed within the business. Purchased goodwill may be accounted for as an asset, subject to its accounting treatment.

Thus, valuing goodwill for compensation does not mean retaining self-generated goodwill in the balance sheet. A balance sheet presents the firm’s assets, liabilities and capital balances. Adjusting partners’ accounts gives effect to compensation without showing self-generated goodwill as an asset.

How is hidden goodwill inferred?

Hidden goodwill is goodwill inferred from agreed capital and profit shares when its value is not stated. Determine the total capital implied by the new partner’s contribution, then subtract the actual combined capitals, including the incoming capital.

Worked example 6. Hem and Nem share profits 3:2 and have capitals of ₹80,000 and ₹50,000. Sam joins for 1/5 and brings ₹60,000 capital. Calculate hidden goodwill and adjust Sam’s unpaid share, assuming sacrifice in the old ratio.

Answer: Implied total capital is ₹60,000 × 5 = ₹3,00,000. Actual combined capital is ₹1,90,000. Goodwill is ₹1,10,000 and Sam’s share ₹22,000. Debit Sam’s Current Account ₹22,000; credit Hem’s Capital ₹13,200 and Nem’s Capital ₹8,800.

If Sam instead brings the premium, Bank is debited ₹82,000, with credits of ₹60,000 to his capital and ₹22,000 to Premium for Goodwill. The premium is then transferred to Hem and Nem in the same ₹13,200 and ₹8,800 amounts.

How are accumulated balances and revaluation treated?

Accumulated profits are earlier profits not yet transferred to partners’ accounts, usually held as general reserve or a credit balance of Profit and Loss Account. The incoming partner has no share in them. Transfer these amounts to the old partners in their old profit sharing ratio.

Accumulated losses, including a debit Profit and Loss balance, are charged to old partners in the old ratio. Deferred revenue expenditure is expenditure carried forward instead of being fully charged immediately; such an existing balance is similarly transferred to old partners.

Rajinder and Surinder share 4:1. On Narender’s admission, General Reserve is ₹20,000 and the Profit and Loss debit balance is ₹10,000. Debit General Reserve ₹20,000; credit Rajinder ₹16,000 and Surinder ₹4,000. Debit their capitals ₹8,000 and ₹2,000; credit Profit and Loss ₹10,000.

What passes through the Revaluation Account?

Revaluation brings assets to current values; reassessment corrects liability amounts. The Revaluation Account collects the resulting gains and losses, including unrecorded assets and liabilities. Its balance belongs to the old partners in their old ratio.

A credit balance represents revaluation profit: debit Revaluation and credit old partners’ capitals. A debit balance represents loss: debit their capitals and credit Revaluation. For changes in already recorded assets and liabilities, enter the increase or decrease, not the entire revised value.

Debtors owe the firm money; creditors are owed money by the firm. A provision for doubtful debts is an allowance for debts that may not be collected. Creating or increasing it produces a revaluation loss by reducing the value recoverable from debtors.

How are partners’ capitals made proportionate to their shares?

Sometimes partners agree to make capitals proportionate to their new profit shares. If the incoming partner’s capital is specified, use it to calculate the firm’s total required capital. Then apply each partner’s new fraction to that total.

Total capital = Incoming capital ÷ Incoming profit share

Compare required capital with each old partner’s balance after all adjustments for goodwill, accumulated balances and revaluation. A deficiency requires an additional contribution; an excess is withdrawn. The agreement may instead provide for transfers to current accounts.

Worked example 7. A and B share profits 2:1. C receives 1/4 and brings ₹20,000 capital. A and B have adjusted capitals of ₹45,000 and ₹15,000. Assume C acquires the share in the old ratio and capitals must match new shares.

Answer: The new ratio is 2:1:1. Total capital is ₹20,000 ÷ 1/4 = ₹80,000. Required capitals are A ₹40,000, B ₹20,000 and C ₹20,000. A withdraws ₹5,000; B contributes ₹5,000.

What if total capital is already agreed?

Use the agreed total directly. A, B and C share 3:2:1. D joins for 1/4, acquiring 1/8 each from A and B. Total capital is agreed at ₹1,20,000. Adjusted capitals of A, B and C are ₹40,000, ₹35,000 and ₹30,000.

The new ratio is 9:5:4:6. Required capitals are A ₹45,000, B ₹25,000, C ₹20,000 and D ₹30,000. A contributes ₹5,000; B and C withdraw ₹10,000 each; D brings ₹30,000.

Subject to agreement, A’s deficiency can instead be debited to A’s Current Account and credited to A’s Capital. B’s and C’s excesses can be debited to their capital accounts and credited to their current accounts. These transfers adjust capital balances without those cash movements.

How do the adjustments lead to a revised balance sheet?

A complete admission problem connects the ratios, goodwill, revaluation, accumulated balances and final capitals. Work through each adjustment before preparing the revised balance sheet. Keep incoming capital distinct from premium, and cash transactions distinct from transfers between partners’ accounts.

What information is needed?

A and B share profits 2:1. Their balance sheet at 31 March 2017 contains creditors ₹8,000, bills payable of ₹4,000, general reserve ₹6,000 and capitals A ₹50,000, B ₹32,000. Bills payable are obligations recorded through accepted bills.

Assets are 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. Stock is inventory held by the business. The original balance sheet totals ₹1,00,000 on each side.

C joins for 1/4, bringing ₹30,000 capital and ₹12,000 goodwill in cash. Building is valued at ₹45,000, machinery at ₹23,000, and a 6% provision is required on debtors. A’s and B’s capitals must match the new ratio, with differences transferred to current accounts.

How are the working amounts calculated?

1. Assuming C acquires the share in the old ratio, the new ratio is 2:1:1 and the sacrificing ratio 2:1.
2. Allocate C’s ₹12,000 premium: A receives ₹8,000 and B ₹4,000.
3. Revaluation gains are ₹5,000 on building; losses are ₹2,000 on machinery and ₹480 for doubtful debts. Profit is ₹2,520, allocated ₹1,680 to A and ₹840 to B.
4. Transfer general reserve: A receives ₹4,000 and B ₹2,000. Their adjusted capitals become ₹63,680 and ₹38,840.
5. Total required capital is ₹1,20,000. Required capitals are A ₹60,000, B ₹30,000 and C ₹30,000.
6. Transfer A’s excess ₹3,680 and B’s excess ₹8,840 to their current accounts by debiting their capitals and crediting their current accounts.

What balances appear after admission?

Cash in hand becomes ₹44,000 after receiving C’s ₹42,000. Cash at bank remains ₹10,000. Debtors are shown at ₹7,520 after the ₹480 provision. General reserve and revaluation profit have been transferred to the partners.

What changes when existing partners revise their profit sharing ratio?

Reconstitution can occur without admission or retirement. Some partners gain a share of future profits while others sacrifice. Any goodwill compensation is adjusted by debiting gaining partners and crediting sacrificing partners with the appropriate amounts.

Gain = New share − Old share

The gaining ratio expresses the relative increases in profit shares. Calculate each partner’s old and new fractions to establish who gains and who sacrifices. Multiply each gain or sacrifice by the firm’s goodwill to find the corresponding adjustment.

How is the goodwill adjustment made?

Dinesh, Ramesh and Suresh change from 3:3:2 to equal sharing. Dinesh and Ramesh each sacrifice 3/8 − 1/3 = 1/24. Suresh gains 1/3 − 2/8 = 2/24. Thus, Suresh compensates the other two equally.

Their five annual profits are ₹14,000, ₹17,000, ₹20,000, ₹22,000 and ₹27,000. Goodwill is valued at four and a half years’ purchase of average profit. Total profit ₹1,00,000 gives average profit ₹20,000 and goodwill ₹90,000.

Debit Suresh’s Capital ₹7,500, calculated as ₹90,000 × 2/24. Credit Dinesh’s and Ramesh’s capital accounts ₹3,750 each, calculated as ₹90,000 × 1/24. Goodwill is adjusted through their accounts rather than retained as an asset.

A change in ratio may also involve revaluation of assets and liabilities and transfer of accumulated profits and losses in the old ratio. Capitals are adjusted to the new ratio if specified. These adjustments follow the same principles used on admission.

Glossary

• Reconstitution — A change in the partnership agreement while the firm continues its business.
• New profit sharing ratio — The ratio in which all partners share future profits after reconstitution.
• Sacrificing ratio — The ratio in which existing partners surrender profit shares to an incoming partner.
• Gaining ratio — The relative proportions in which partners acquire additional shares of future profits.
• Goodwill — Monetary value of reputation and business advantages associated with expected earnings above normal profits.
• Premium for goodwill — The incoming partner’s contribution compensating sacrificing partners for their loss of super profit shares.
• Years’ purchase — The agreed number of years used to multiply average profits or super profits.
• Normal profit — The expected return on capital employed at the normal rate for similar business.
• Super profit — The excess of average profit over the normal return on the firm’s capital.
• Capitalisation — Conversion of profits into an equivalent capital value using the normal rate of return.
• Hidden goodwill — Goodwill inferred from the incoming partner’s capital contribution and agreed share in profits.
• Revaluation Account — The account collecting gains and losses from revised assets and liabilities on reconstitution.
• Accumulated profits — Earlier undistributed profits belonging to old partners in their old profit sharing ratio.
• Current account — A partner’s account used for adjustments kept separate from the capital account.

Common errors and misconceptions

• Misconception: Admission ends the firm’s business. Correct: The agreement changes and the firm continues under its reconstituted partnership.
• Misconception: Sacrificing ratio must equal old ratio. Correct: Calculate sacrifice from old and new shares unless the acquisition terms already specify it.
• Misconception: Every old partner sacrifices on admission. Correct: An old partner may gain; compare each partner’s old and new fractions.
• Misconception: Weighted average may be chosen whenever profits change. Correct: Use weighted average only if it is specified.
• Misconception: The incoming partner pays the firm’s entire goodwill. Correct: The premium corresponds to the share of goodwill acquired by that partner.
• Misconception: Existing goodwill is written off in the new ratio. Correct: Debit old partners in their old ratio; distribute incoming premium in sacrificing ratio.
• Misconception: Revaluation profit belongs to every partner after admission. Correct: Transfer it to old partners in their old ratio.
• Misconception: Capital adjustments use original capital balances. Correct: First complete goodwill, reserves and revaluation adjustments, then compare adjusted and required capitals.

Exam-style questions with model answers

Q1. What two main rights does a newly admitted partner acquire? [2 marks]

1. The partner acquires the right to share in the assets of the partnership firm.
2. The partner also acquires the right to share in the profits of the partnership firm.

Q2. Anil and Vishal share profits 3:2. Sumit is admitted for 1/5, acquired from them in their old ratio. Calculate the remaining share, each old partner’s new share and the new ratio. [4 marks]

1. Sumit receives 1/5 of total profits, leaving 1 − 1/5 = 4/5 for the old partners.
2. Anil’s new share is 3/5 of the remaining 4/5, which equals 12/25 of total profits.
3. Vishal’s new share is 2/5 of the remaining 4/5, which equals 8/25 of total profits.
4. Sumit’s share is 5/25. Therefore Anil, Vishal and Sumit share future profits in the ratio 12:8:5.

Q3. Rohit and Mohit share profits 5:3. Bijoy joins for 1/7, and the new ratio is 4:2:1. Calculate each old partner’s sacrifice and the sacrificing ratio. [3 marks]

1. Rohit’s old share is 5/8 and his new share is 4/7. His sacrifice is 5/8 − 4/7 = 3/56.
2. Mohit’s old share is 3/8 and his new share is 2/7. His sacrifice is 3/8 − 2/7 = 5/56.
3. The sacrificing ratio is 3/56:5/56, or 3:5. This ratio determines how the two old partners share goodwill compensation for their surrendered shares.

Q4. A firm’s capital employed is ₹5,00,000. Its five annual profits are ₹40,000, ₹50,000, ₹55,000, ₹70,000 and ₹85,000. Normal return is 10%. Calculate goodwill at three years’ purchase of super profits. [4 marks]

1. Total profits are ₹3,00,000. Dividing by five gives average annual profit of ₹60,000 for the specified period.
2. Normal profit is the expected return on capital: ₹5,00,000 × 10 ÷ 100 = ₹50,000.
3. Super profit is average profit less normal profit, so ₹60,000 − ₹50,000 gives an excess of ₹10,000.
4. Goodwill is super profit multiplied by the agreed years’ purchase: ₹10,000 × 3 = ₹30,000.

Q5. Sunil and Dalip share profits 5:3. Sachin joins for 1/5, acquired in that old ratio, bringing ₹20,000 capital and ₹4,000 goodwill by cheque. Give the sacrifice basis, distribution and entries when the premium is retained, then the additional entry if it is fully withdrawn. [5 marks]

1. The sacrificing ratio is 5:3 because Sachin acquires his share from Sunil and Dalip in their old ratio. Use this ratio to distribute the premium.
2. Sunil receives ₹4,000 × 5/8 = ₹2,500. Dalip receives ₹4,000 × 3/8 = ₹1,500 as compensation for their respective sacrifices.
3. For receipt, debit Bank ₹24,000; credit Sachin’s Capital ₹20,000 and Premium for Goodwill ₹4,000, separating the two components.
4. For distribution, debit Premium for Goodwill ₹4,000; credit Sunil’s Capital ₹2,500 and Dalip’s Capital ₹1,500. Retention requires no further entry.
5. If fully withdrawn, debit Sunil’s Capital ₹2,500 and Dalip’s Capital ₹1,500; credit Bank ₹4,000 for the total payment.

Q6. A and B share profits 3:2 and admit C. Stock ₹15,000 falls by 10%; machinery ₹30,000 rises by 10%; furniture ₹10,000 is revalued at ₹9,000. Create a 5% doubtful-debt provision on debtors ₹12,000. Recognise an unpaid electricity bill ₹200 and an unrecorded investment ₹1,000. Write off a creditor ₹100 who is not likely to claim payment. Show the revaluation gains, losses, profit and allocation. [6 marks]

1. Stock falls by ₹1,500 and furniture by ₹1,000. Debit Revaluation for both reductions because they decrease asset values.
2. The doubtful-debt provision is ₹12,000 × 5 ÷ 100 = ₹600. Debit Revaluation ₹600 and credit the provision account.
3. The unpaid electricity bill creates a liability of ₹200. Debit Revaluation and credit Outstanding Electricity for this amount.
4. Machinery increases by ₹3,000 and the unrecorded investment adds ₹1,000. Debit the respective assets and credit Revaluation ₹4,000 in total.
5. Writing off the creditor produces a ₹100 gain. Total gains are ₹4,100; total losses are ₹3,300, giving revaluation profit of ₹800.
6. Transfer the profit in the old ratio 3:2. Debit Revaluation ₹800; credit A’s Capital ₹480 and B’s Capital ₹320.

Q7. A and B share profits 2:1. C joins for 1/4, acquired in that old ratio, and contributes ₹20,000 capital. After all other adjustments A’s capital is ₹45,000 and B’s ₹15,000. Capitals must match new profit shares, with cash settlement of differences. Calculate required capitals and adjustment entries. [5 marks]

1. After C receives 1/4, A and B share the remaining 3/4 in the ratio 2:1. The new ratio is therefore 2:1:1.
2. C’s ₹20,000 corresponds to 1/4 of total capital. The firm’s required capital is consequently ₹20,000 ÷ 1/4 = ₹80,000.
3. Required capitals are A ₹80,000 × 2/4 = ₹40,000, B ₹20,000 and C ₹20,000, matching their respective new profit shares.
4. A has excess capital of ₹45,000 − ₹40,000 = ₹5,000. Debit A’s Capital ₹5,000 and credit Cash ₹5,000 for withdrawal.
5. B has a deficiency of ₹20,000 − ₹15,000 = ₹5,000. Debit Cash ₹5,000 and credit B’s Capital ₹5,000 for the additional contribution.

Q8. Hem and Nem share profits 3:2 with capitals ₹80,000 and ₹50,000. Sam joins for 1/5, acquired in their old ratio, bringing ₹60,000 capital but no goodwill premium. Infer firm goodwill, calculate Sam’s share and give its adjustment entry. [4 marks]

1. Sam’s ₹60,000 for a 1/5 share implies total capital of ₹60,000 × 5 = ₹3,00,000.
2. Actual combined capital is ₹80,000 + ₹50,000 + ₹60,000 = ₹1,90,000. Hidden goodwill is the difference, ₹1,10,000.
3. Sam’s share of that goodwill is ₹1,10,000 × 1/5 = ₹22,000, which he has not brought in cash.
4. Debit Sam’s Current Account ₹22,000; credit Hem’s Capital ₹13,200 and Nem’s Capital ₹8,800 in their sacrificing ratio of 3:2.

Key takeaways

• Admission changes the partnership agreement while the firm continues; the incoming partner acquires rights in assets and future profits.
• Calculate new shares from the agreed acquisition terms, and calculate sacrifice by subtracting each old partner’s new share from the old share.
• Goodwill valuation may use average profits, super profits or capitalisation; weighted average is used only when specified.
• Distribute the incoming goodwill premium in the sacrificing ratio, but write off existing goodwill in the old profit sharing ratio.
• Unpaid goodwill is debited to the incoming partner’s current account and credited to sacrificing partners’ capital accounts.
• Accumulated profits, accumulated losses and revaluation results belong to the old partners in their old profit sharing ratio.
• Complete goodwill, reserves and revaluation adjustments before comparing actual capital balances with the capitals required by the agreement.
• A change in ratio among existing partners requires goodwill compensation from gaining partners to sacrificing partners, with other adjustments where applicable.

Test yourself

What assumption may be made if acquisition of the incoming share is unspecified?

It may be assumed that the incoming partner obtains the share from old partners in their old profit sharing ratio.

What is the formula for an old partner’s sacrifice?

Subtract the partner’s new profit share from the old profit share.

When should a weighted average be used for goodwill?

Use weighted average only if it is specified, applying the stated weights to the respective years’ profits.

How is normal profit calculated?

Multiply capital employed by the normal percentage rate of return and divide by one hundred.

What entry records goodwill paid privately to old partners?

No entry is passed in the firm’s books for goodwill paid directly and privately to old partners.

Who receives the balance of general reserve on admission?

The old partners receive it through their capital or current accounts in their old profit sharing ratio.

Which side of Revaluation receives an unrecorded liability?

Debit Revaluation Account and credit the relevant liability account for the amount recognised.

How may capital differences be settled without cash movement?

Subject to agreement, transfer excess capital or capital deficiency to the respective partners’ current accounts.