Admitting a partner to the Amal and Nadia printing partnership
Amal and Nadia have run a printing partnership for twelve years, sharing profits 3:2. At 31 December 2024 their capital accounts stood at €90,000 and €60,000, and their current accounts at €12,000 credit and €5,000 debit respectively. On 1 April 2025 they admitted Omar, who paid €70,000 in cash for a one-quarter share of profits; Amal and Nadia continue to share the remaining three-quarters in the ratio 3:2.
Before Omar's admission the partners agreed a revaluation: premises were revalued upwards by €40,000, inventory was written down by €6,000 because of obsolete stock, and an allowance for doubtful debts of €4,000 was created. Goodwill was agreed at €100,000, but the partners do not want goodwill to remain in the statement of financial position.
The profit for the year ended 31 December 2025 was €180,000. Because the partnership's sales are heavily concentrated in the last quarter, Nadia argues that splitting the year's profit by time is unfair to her and Amal.
1. Prepare the partners' capital accounts to show each balance on 1 April 2025, and state the new profit-sharing ratio.
Read the worked answer
New ratio: Omar takes 1/4, leaving 3/4 to Amal and Nadia in 3:2. Amal = 3/4 x 3/5 = 9/20; Nadia = 3/4 x 2/5 = 6/20; Omar = 5/20. So the ratio is Amal 9 : Nadia 6 : Omar 5.
Revaluation gain: +40,000 - 6,000 - 4,000 = €30,000, shared in the old ratio 3:2: Amal €18,000, Nadia €12,000.
Goodwill of €100,000: raised in the old ratio (Amal €60,000, Nadia €40,000), then written off in the new ratio 9:6:5 (Amal €45,000, Nadia €30,000, Omar €25,000).
| Capital accounts | Amal € | Nadia € | Omar € |
|---|---|---|---|
| Balance 31 December 2024 | 90,000 | 60,000 | - |
| Share of revaluation gain 3:2 | 18,000 | 12,000 | - |
| Goodwill raised 3:2 | 60,000 | 40,000 | - |
| Goodwill written off 9:6:5 | (45,000) | (30,000) | (25,000) |
| Cash introduced | - | - | 70,000 |
| Balance 1 April 2025 | 123,000 | 82,000 | 45,000 |
Total capital is €250,000, which equals the old capital of €150,000 plus the €30,000 revaluation gain plus Omar's €70,000. The goodwill entries cancel out overall, as they must, because no goodwill is to be carried as an asset.
Current accounts are not affected by the admission and remain at €12,000 credit for Amal and €5,000 debit for Nadia.
2. Explain why goodwill is adjusted on admission, and what would go wrong for Amal and Nadia if the €100,000 were instead left in the statement of financial position as an asset.
Read the worked answer
Goodwill exists because the partnership has built up a customer base, a reputation and a trained workforce over twelve years. Omar is buying a quarter of that established business, not a quarter of the net assets alone.
The principle. Each partner must end up with capital equal to what they have actually put in or earned. Omar pays €70,000; he must receive capital of €70,000, no more and no less.
If goodwill is raised and written off immediately (the method used here), the net effect on Omar is a €25,000 debit (his 5/20 share of €100,000) and his capital becomes 70,000 - 25,000 = €45,000. That €25,000 has effectively been paid to Amal and Nadia in the old 3:2 ratio: Amal gains 60,000 - 45,000 = €15,000 and Nadia gains 40,000 - 30,000 = €10,000. This is exactly right, because they built the goodwill.
If goodwill stayed in the books as an asset, total capital would be €350,000 and Omar's €70,000 would buy him 1/4 x 350,000 = €87,500 of capital. Amal and Nadia would have given away €17,500 of value they had created, and Omar would be sharing in goodwill he never paid for. In later years he would also receive a quarter of the profits earned on that goodwill.
Practical objections to carrying goodwill. Goodwill is subjective and can fall in value without warning; writing it off amounts to admitting it cannot be realised separately from the business. Raising and writing off on admission records the adjustment once, cleanly, and leaves the statement of financial position free of an unverifiable intangible.
3. Calculate the appropriation of the €180,000 profit on a time basis and evaluate Nadia's claim that the time basis is unfair to her and Amal.
Read the worked answer
Time apportionment. Three months (1 January to 31 March) at the old 3:2 ratio; nine months (1 April to 31 December) at the new 9:6:5 ratio.
Pre-admission: 180,000 x 3/12 = €45,000
- Amal 3/5 = €27,000
- Nadia 2/5 = €18,000
Post-admission: 180,000 x 9/12 = €135,000
- Amal 9/20 = €60,750
- Nadia 6/20 = €40,500
- Omar 5/20 = €33,750
| Total share | € |
|---|---|
| Amal (27,000 + 60,750) | 87,750 |
| Nadia (18,000 + 40,500) | 58,500 |
| Omar | 33,750 |
| Total | 180,000 |
Is Nadia right? No - on her own facts she has the argument the wrong way round. The time basis assumes profit is earned evenly, at €15,000 a month. If sales and profit are concentrated in the last quarter, then the nine months after 1 April contain more than €135,000 of profit, and the three months before contain less than €45,000.
Omar therefore receives 25% of a post-admission profit that is actually larger than €135,000, yet he is credited with only €33,750, which is 18.75% of the annual profit. The time basis under-rewards Omar and over-protects Amal and Nadia.
Better approaches. Either compute the actual profit for the three months to 31 March and the nine months to 31 December from the ledger, which removes the assumption altogether, or agree an alternative in the new partnership agreement - for example a salary to Omar for running the sales side, with the residual shared in the profit ratio.
Whatever is agreed, it should be written into the partnership agreement before the year end, not argued about afterwards.