Admission, Sacrifice Ratio and Capital Adjustment
X and Y share profits 3:2 and have capitals of ₹2,40,000 and ₹1,60,000. On 1 April 2024 they admit Z for 1/5 share. Z brings ₹1,20,000 as capital and ₹30,000 as goodwill in cash. Before admission, the firm revalues: machinery is reduced by ₹20,000, a provision for doubtful debts of ₹5,000 is created, and an unrecorded investment of ₹35,000 is brought into books. The partners agree that after admission all capitals should be in the new profit-sharing ratio and that any cash adjustment should be made. Z argues that the entire goodwill should be credited to X and Y in their old ratio. X claims that because he sacrifices more, he should get more than Y; Y says goodwill should be shared equally because both agreed to admit Z. The accountant also notices that Z’s capital account will not be proportionate after the revaluation and goodwill entries.
1. Compute the sacrificing ratio, the new ratio and the distribution of goodwill. Decide whether Z, X or Y is correct.
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Sacrifice is in the old ratio 3:2 because the deed is silent. Z’s 1/5 is acquired as X 3/25 and Y 2/25. New ratio: X 3/5 − 3/25 = 12/25; Y 2/5 − 2/25 = 8/25; Z 5/25, i.e. 12:8:5. Goodwill of ₹30,000 belongs to the sacrificing partners: X ₹18,000, Y ₹12,000. Z is not credited because Z is the incoming partner paying for the share. Y’s equal-sharing claim is wrong. Z’s statement that the entire goodwill goes to X and Y in old ratio is correct, and X is right that his larger sacrifice gives him ₹18,000 against Y’s ₹12,000.
2. Prepare the revaluation account and partners’ capital accounts, and determine the cash adjustment required to make capitals proportionate.
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Revaluation: loss on machinery ₹20,000; provision for doubtful debts ₹5,000; gain on unrecorded investment ₹35,000; net profit ₹10,000, shared old 3:2: X ₹6,000, Y ₹4,000. Capital after revaluation and goodwill: X = 2,40,000 + 6,000 + 18,000 = 2,64,000; Y = 1,60,000 + 4,000 + 12,000 = 1,76,000; Z = 1,20,000. Total = 5,60,000. New ratio 12:8:5.
Using Z’s agreed capital of ₹1,20,000 for 5/25, total capital = 1,20,000 × 25/5 = ₹6,00,000. Required capitals: X = 6,00,000 × 12/25 = ₹2,88,000; Y = 6,00,000 × 8/25 = ₹1,92,000; Z = ₹1,20,000. Cash to bring: X ₹24,000; Y ₹16,000; Z nil. The revaluation profit is shared in the old ratio because it arises before Z becomes a partner; goodwill is shared only by those who give up a share.