Reconstitution of a Partnership Firm

Written and reviewed by Devendra Dubey, Mathematics & Commerce faculty at UniDrill (M.Sc. Mathematics, Osmania University · 10 years teaching). Based on NCERT Accountancy Class XII (Accountancy Part I), Chapter 2.

Why does a new partner pay for a firm he did not build?

Ravi and Meena run Pixel Press, a printing firm that earns ₹60,000 a year more than a similar press would, because schools and law offices have trusted it for ten years. Kabir, a young designer, wants to join for a one sixth share. If he pays only ₹1,00,000 for a share of the machines, he gets a slice of that trusted name for free, and Ravi and Meena lose out. So the old partners ask for a premium for goodwill.

That one situation drives the whole chapter. A new partner joins, so the old deed ends and a new one begins, although the firm itself carries on. Everything the old partners built before the day of admission must be valued, shared among them, and then the books are reset so that Kabir starts fair. Every journal entry in this chapter is an answer to one question: who earned this, the old partners or the new one?

The six adjustments on admission

When a partner is admitted, six things must be settled. Learn them in this order, because NTA asks for the sequence.

The rule to remember. The newcomer pays for what the future will give him (goodwill), and the old partners keep what the past gave them (reserves and revaluation). Steps 4 and 5 use the old ratio. Only the premium uses the sacrificing ratio.

New ratio and sacrificing ratio

The new partner's share must come from somewhere. It comes from the old partners, and how much each gives up is the sacrifice.

$$\text{Sacrificing share} = \text{Old share} - \text{New share}$$

How the newcomer acquires his share decides the arithmetic.

Worked example: three ways to admit a partner. Work out the new ratio and the sacrificing ratio in each case.

Common wrong step. In (b) and (c), writing the sacrificing ratio as the old ratio. That shortcut works only in case (a), where the question is silent. In (c) Rohit holds the larger old share, yet he gives up less than Mohit, so he gets the smaller part of any premium.

Pause and predict: A and B share 3:2. C is admitted for $\tfrac{1}{5}$ share and takes it equally from both. Who sacrifices more, A or B?

Check your answer: Neither. Each gives up $\tfrac{1}{10}$, so the sacrificing ratio is 1:1 even though the old ratio is 3:2. Any premium C brings is split equally.

Goodwill: what it is and what moves its value

Goodwill is the money value of a firm's good name, reputation and business connections, which lets it earn super profits, meaning profits above what an ordinary firm would earn on the same capital. It is an intangible asset. If the firm earns only normal profits, there is no goodwill to pay for.

Goodwill is valued when the profit sharing ratio changes, a partner is admitted, a partner retires or dies, the firm is sold as a going concern, or firms amalgamate.

Valuing goodwill: three methods

The question always states the method. Your job is to apply it without slipping on one input, the capital employed, which means total assets (excluding goodwill and fictitious assets) less outside liabilities.

Average profits method. The firm is worth a few years of its typical profit.

$$\text{Goodwill} = \text{Average profit} \times \text{Number of years' purchase}$$

Use a simple average unless the profits are clearly rising or falling and weights are given. A weighted average multiplies each year by its weight and divides by the total of the weights.

Super profits method. Only the profit above normal earns goodwill.

$$\text{Normal profit} = \text{Capital employed} \times \dfrac{\text{Normal rate of return}}{100}$$

$$\text{Super profit} = \text{Average profit} - \text{Normal profit}$$

$$\text{Goodwill} = \text{Super profit} \times \text{Number of years' purchase}$$

If partners' salaries at market rates are given, either deduct them from the average profit or add them to the normal profit. The super profit comes out the same.

Capitalisation method. Ask what capital the average profit would need to earn at the normal rate, then compare it with the capital the firm really has. There are two forms and they always agree.

$$\text{Goodwill} = \text{Average profit} \times \dfrac{100}{\text{Normal rate}} - \text{Capital employed}$$

$$\text{Goodwill} = \text{Super profit} \times \dfrac{100}{\text{Normal rate}}$$

Worked example: one firm, all four answers. Profits of the last three years were ₹54,000, ₹60,000 and ₹66,000. Capital employed is ₹5,00,000 and the normal rate of return is 10%. Value goodwill at 3 years' purchase wherever it applies.

The two capitalisation answers match, as they must. If they do not, one input is wrong. Here the average profits method gives the largest figure, because it pays for all the profit, normal or not.

Common wrong step. Including goodwill or a fictitious asset (such as preliminary expenses) in capital employed. That inflates normal profit and shrinks goodwill. A second slip is using a weighted average when no weights are given. With weights 1, 2, 3 the same profits would give (54,000 × 1 + 60,000 × 2 + 66,000 × 3) ÷ 6 = ₹62,000, so use weights only when the question supplies them.

Beyond the textbook. For the exam: use the formula the question names and give one number. In reality: in practice partners treat these formulas as a starting point and then bargain, or call in a valuer. Different industries are priced at different multiples of profit, so there is no single correct goodwill figure. Why it matters: this is why every exam question tells you the method and the years' purchase: it is an agreed figure, not a measured one.

Treating goodwill in the books

Three situations decide the entry. In each one, ask who earned the goodwill.

Why the Current Account, not the Capital Account? Capital stays at the amount the partners agreed to invest. Goodwill that he has not paid in cash is a debt to the old partners, so it sits in his Current Account and can be cleared later out of his drawings or share of profit.

Why is existing goodwill written off? An accounting standard does not allow a firm to carry goodwill it built itself. Goodwill appears only when it is bought, so any goodwill in the books must be removed first. It was built by the old partners, so it goes to them in the old ratio.

Worked example: premium brought in cash. A and B share 3:2. C is admitted for $\tfrac{1}{5}$ share, taking $\tfrac{1}{10}$ from each partner. C brings ₹1,00,000 as capital and ₹40,000 as premium for goodwill. Pass the entries.

Both entries total ₹1,40,000 and ₹40,000 on each side, so they balance. The sacrifice was 1:1 (see the case (b) above), so each partner gets ₹20,000.

Common wrong entry. Sharing the premium in the old ratio 3:2, which gives A ₹24,000 and B ₹16,000. A would be paid for a sacrifice he did not make. If the old partners then withdraw their premium, the entry is Dr Capital A/c, Cr Bank A/c.

Worked example: goodwill not brought, with existing goodwill. A and B share 3:2. The books show goodwill of ₹50,000. C is admitted for $\tfrac{1}{5}$ share, new ratio 5:3:2. Goodwill of the firm is valued at ₹2,00,000 and C does not bring any. Pass the entries.

C's share is $\tfrac{1}{5} \times 2{,}00{,}000 = 40{,}000$. Net effect on A: −30,000 + 20,000 = −10,000. Net effect on B: −20,000 + 20,000 = 0.

Common wrong step. Writing off the old goodwill in the new ratio 5:3:2 (₹25,000, ₹15,000, ₹10,000). That makes C pay for goodwill built before he arrived.

Beyond the textbook. For the exam: goodwill in the books is written off on admission. In reality: the accounting standard on intangible assets allows a business to show only purchased goodwill, for example when it buys another business for more than the value of that business's net assets. Self-generated goodwill never appears in a balance sheet, however strong the brand. Why it matters: this is the reason a firm's famous name does not show up on its balance sheet, and the reason the old goodwill entry is mandatory.

Hidden goodwill

Sometimes no goodwill figure is given. Instead the new partner's capital and share tell you what the whole firm must be worth. If he pays for $\tfrac{1}{5}$ and brings ₹60,000, the firm as a whole is worth five times that. Compare this with what the books actually show.

$$\text{Implied total capital} = \text{New partner's capital} \times \dfrac{1}{\text{His share}}$$

$$\text{Hidden goodwill} = \text{Implied total capital} - \text{Actual total capital after admission}$$

Worked example: finding goodwill from the capitals. Hem and Nem share 3:2 with capitals of ₹80,000 and ₹50,000 (after all adjustments). Sam is admitted for $\tfrac{1}{5}$ share and brings ₹60,000. New ratio is not given.

The entry is Sam's Current A/c Dr ₹22,000, To Hem's Capital A/c ₹13,200, To Nem's Capital A/c ₹8,800. Debit total equals credit total at ₹22,000.

Common wrong step. Leaving Sam's own capital out of the actual total, which gives ₹1,30,000 and a goodwill of ₹1,70,000. Sam's capital is part of the firm after admission, so it belongs in the sum. Use the old partners' capitals after reserves and revaluation have been adjusted.

Pause and predict: A firm has a General Reserve of ₹50,000 and a debit balance in the Profit and Loss A/c of ₹10,000. A and B share 3:2, and C is being admitted. How much is credited to A, net?

Check your answer: ₹24,000. The net amount to share is 50,000 − 10,000 = ₹40,000, and A's share in the old ratio is $\tfrac{3}{5} \times 40{,}000$. Using the new ratio would give C a share of profits he did not help earn.

Accumulated profits and losses

General Reserve and the credit balance of the Profit and Loss A/c are profits the old partners earned, so they are credited to the old partners' Capital A/cs in the old ratio. Debit balances of the Profit and Loss A/c, and fictitious assets like preliminary expenses, are losses and are debited to them the same way.

Revaluation of assets and liabilities

Before the newcomer joins, assets and liabilities are restated to current values, so that he buys into the firm at fair worth. A Revaluation Account collects every change. Remember one rule and the rest follows: an increase in an asset or a fall in a liability is a gain (credit), and the opposite is a loss (debit).

The balancing figure is transferred to the old partners in the old ratio. A gain is credited to their capitals, and a loss debited. If the revised values are not to be shown in the books, a Memorandum Revaluation Account is used instead. The gain or loss is first shared in the old ratio and then reversed in the new ratio, which leaves the books unchanged.

Worked example: the whole admission on one page. P and Q share 3:2. The balance sheet on 1 April is below. R is admitted for $\tfrac{1}{5}$ share (new ratio 12:8:5, the old ratio applied to the remaining $\tfrac{4}{5}$). R brings ₹2,00,000 as capital and ₹60,000 as premium for goodwill. Land is to be raised by ₹50,000, stock reduced by ₹12,000 and machinery by ₹18,000, and a provision of ₹8,000 for doubtful debts is to be created. Prepare the Revaluation Account, the Capital Accounts and the new Balance Sheet.

Revaluation Account. The total of each side is ₹50,000.

Capital Accounts (the entries are all credits, so only the closing balances are totalled).

Balance Sheet after admission.

The sacrificing ratio here is 3:2 because the new ratio was found by the old ratio, so the premium of ₹60,000 is shared 36,000 and 24,000.

Common wrong step. Sharing the reserve of ₹70,000 in the new ratio 12:8:5. R would get ₹14,000 of profit earned before he joined, and P and Q would lose ₹14,000 between them.

Adjusting the capitals

Partners may agree that capitals should match the profit shares. The base is the capital of the partner whose figure is fixed, usually the newcomer's.

A partner whose actual capital is short brings cash (or his Current A/c is debited). A partner whose capital is in surplus withdraws cash (or his Current A/c is credited).

Worked example: bringing capitals into line. A and B share 2:1. C is admitted for $\tfrac{1}{4}$ share and brings ₹20,000 as capital. New ratio from the old ratio is 2:1:1. After all other adjustments A's capital is ₹52,000 and B's is ₹12,000. Adjust the capitals.

Common wrong step. Taking the average of the old capitals as the base. The base must be the figure that is fixed, here C's ₹20,000.

Change in profit sharing ratio among the old partners

No one is admitted, but the same adjustments are needed. Some partners gain share and some sacrifice. Gainers compensate sacrificers for the goodwill, and the share each pays or receives is its gain or sacrifice multiplied by the goodwill.

Worked example: three partners become equal. A, B and C share 3:2:1 and decide to share equally. Goodwill is valued at ₹1,20,000.

C's gain is paid for: $\tfrac{1}{6} \times 1{,}20{,}000 = 20{,}000$. Entry: C's Capital A/c Dr ₹20,000, To A's Capital A/c ₹20,000. B is not part of the entry at all.

Common wrong step. Debiting all three partners or crediting B. B's share did not change, so B is neither a gainer nor a sacrificer.

Exam traps

Formula and format sheet

60-second revision

Where this chapter connects

This chapter builds on Accounting for Partnership: Basic Concepts, where the profit sharing ratio, Capital and Current Accounts and goodwill first appear. The gaining ratio, the mirror image of what you learned here, is the core of Retirement or Death of a Partner. The Revaluation Account returns, in a different form, in Dissolution of a Partnership Firm.