Admission of C to the A and B Partnership
A and B have shared profits 3:2 and had capitals of 12,000,000 FCFA and 8,000,000 FCFA respectively. Their current accounts were A 1,200,000 FCFA credit and B 300,000 FCFA debit. On 1 January 2025 they admitted C for a one-fifth share. C paid 6,000,000 FCFA into the bank, of which 1,500,000 FCFA was for goodwill and the balance for capital. It was agreed that goodwill should not remain in the books. Assets were revalued: land up 2,000,000 FCFA; inventory down 600,000 FCFA; the provision for doubtful debts increased by 300,000 FCFA; and an unrecorded legal fee of 200,000 FCFA was discovered. The old partners continued to share the remaining profits in their old ratio. C expects his capital to equal one-fifth of total capital.
1. Calculate the new profit-sharing ratio and the sacrifice ratio. Show the journal entries for the goodwill paid in cash and for the revaluation.
Read the worked answer
C takes 1/5, leaving 4/5 for A and B in the old ratio 3:2.
A = 3/5 × 4/5 = 12/25; B = 2/5 × 4/5 = 8/25; C = 5/25.
New ratio A:B:C = 12:8:5.
Sacrifice: A gave 3/5 − 12/25 = 3/25; B gave 2/5 − 8/25 = 2/25. Sacrifice ratio A:B = 3:2.
Goodwill paid in cash
| Journal | FCFA |
|---|---|
| Dr Bank | 1,500,000 |
| Cr A Capital (3/5) | 900,000 |
| Cr B Capital (2/5) | 600,000 |
No goodwill account remains, so no goodwill asset is shown.
Revaluation
Gain = 2,000,000 − 600,000 − 300,000 − 200,000 = 900,000 FCFA.
| Journal | FCFA |
|---|---|
| Dr Land | 2,000,000 |
| Cr Revaluation | 2,000,000 |
| Dr Revaluation | 600,000 |
| Cr Inventory | 600,000 |
| Dr Revaluation | 300,000 |
| Cr Provision for doubtful debts | 300,000 |
| Dr Revaluation | 200,000 |
| Cr Accrued legal fees | 200,000 |
| Dr Revaluation | 900,000 |
| Cr A Capital (3/5) | 540,000 |
| Cr B Capital (2/5) | 360,000 |
2. Prepare the partners' capital accounts after C's admission.
Read the worked answer
| Capital accounts | A | B | C |
|---|---|---|---|
| Opening capital | 12,000,000 | 8,000,000 | - |
| Goodwill in cash | 900,000 | 600,000 | - |
| Revaluation gain | 540,000 | 360,000 | - |
| Cash introduced as capital | - | - | 4,500,000 |
| Closing capital | 13,440,000 | 8,960,000 | 4,500,000 |
Total capital = 13,440,000 + 8,960,000 + 4,500,000 = 26,900,000 FCFA.
The current accounts are not part of capital: A has a 1,200,000 FCFA credit current account and B has a 300,000 FCFA debit current account.
3. Evaluate C's claim that his capital equals one-fifth of total capital. Calculate the adjustment needed if the old partners do not withdraw cash.
Read the worked answer
C's capital is 4,500,000 FCFA out of 26,900,000 FCFA, which is 16.7%, not 20%. The reason is that the 1,500,000 FCFA goodwill payment went to the old partners, while C's capital account received only the 4,500,000 FCFA capital portion.
If C is to hold exactly one-fifth, his capital must equal one-quarter of the old partners' capital:
Old partners' capital = 13,440,000 + 8,960,000 = 22,400,000 FCFA.
Required C capital = 22,400,000 ÷ 4 = 5,600,000 FCFA.
Additional cash required from C = 5,600,000 − 4,500,000 = 1,100,000 FCFA.
If C pays the extra 1,100,000 FCFA, total capital becomes 28,000,000 FCFA and C's 5,600,000 FCFA is exactly 20%. Alternatively, if C does not pay more, the old partners would need to withdraw 4,400,000 FCFA to leave old capital at 18,000,000 FCFA; then total capital would be 22,500,000 FCFA and C's 4,500,000 FCFA would be 20%.