Admitting a Partner: Who Sacrificed What, and Who Pays for the Old Goodwill
A and B are partners sharing profits 3:2, with capitals of ₹1,50,000 and ₹1,00,000. Their balance sheet carries goodwill of ₹50,000, created when a partner retired two years ago and never written off. On 1 April they admit C for a 1/5 share of future profits. C brings ₹80,000 as capital and ₹40,000 as premium for goodwill, both in cash. The firm's goodwill is agreed at ₹2,00,000. The admission deed says only that C 'acquires his share equally from A and B'. A clerk proposes: (i) credit the ₹40,000 premium to A and B in 3:2; (ii) leave the existing ₹50,000 goodwill on the balance sheet; (iii) treat C's ₹80,000 as his capital without checking it against his profit share. B objects to point (i) but can give no better reason than 'it feels wrong'. The new profit-sharing ratio has not yet been written down.
1. Work out the sacrificing ratio and the new profit-sharing ratio, and distribute the premium for goodwill.
Read the worked answer
Old shares: A 3/5 = 6/10, B 2/5 = 4/10. C takes 1/5 = 2/10, half from each, so A gives 1/10 and B gives 1/10. New shares: A 6/10 − 1/10 = 5/10; B 4/10 − 1/10 = 3/10; C 2/10. New ratio 5:3:2. The sacrificing ratio is therefore 1:1, not 3:2. Premium for goodwill follows the sacrificing ratio, so ₹40,000 is credited A ₹20,000 and B ₹20,000. The clerk's 3:2 split would give A ₹24,000 and B ₹16,000 - A over-credited by ₹4,000 and B under-credited by the same amount. Check the total against the valuation: C's share of goodwill is 1/5 × ₹2,00,000 = ₹40,000, exactly what he brought, so there is no shortfall. B's instinct was right; the test is always 'who gave up what', never 'what was the old ratio'.
2. What should be done with the existing ₹50,000 goodwill, and why?
Read the worked answer
Write it off against the old partners' capitals in the old ratio 3:2 - A ₹30,000, B ₹20,000 - before C is admitted. Reason: goodwill already sitting in the books at admission is the written-up value of the old firm's reputation, an asset C has not paid for. If it stays, C's capital account effectively acquires a 1/5 interest in value he did not fund, and A and B would later withdraw against what they already owned. There is also a double-counting problem: C's premium is being paid for the firm's current goodwill of ₹2,00,000, so leaving the old ₹50,000 on the balance sheet records the same reputation twice. After the write-off, A stands at ₹1,50,000 − ₹30,000 = ₹1,20,000 and B at ₹1,00,000 − ₹20,000 = ₹80,000; the premium then takes them to ₹1,40,000 and ₹1,00,000.
3. Is C's capital consistent with his profit share? Show the check and advise the partners.
Read the worked answer
Use C's contribution as the test of the whole capital structure. C pays ₹80,000 for 2/10, which implies firm capital of ₹80,000 × 10/2 = ₹4,00,000. On that basis A should hold 5/10 = ₹2,00,000 and B 3/10 = ₹1,20,000. They actually hold ₹1,40,000 and ₹1,00,000 - short by ₹60,000 and ₹20,000 - while C sits exactly on the line. The firm is under-capitalised relative to C's entry price. Three defensible fixes: A and B bring in the shortfall in cash (₹60,000 and ₹20,000); an undervalued asset such as land is revalued, with the gain going to the old partners only; or it is agreed that C has paid a premium for a share of future profits and part of his ₹80,000 is recorded accordingly. What is not acceptable is the clerk's third proposal - leaving the imbalance unexplained in the capital accounts.