Chen, Okafor and Duarte: Admitting a Partner When Goodwill Has Never Been Recorded
Chen and Okafor have traded for eight years as a design partnership, sharing profits 3:2 after interest on capital at 5% and an annual salary of $18,000 to Okafor. At 1 January 2025 their capital accounts were $120,000 and $80,000 and their current accounts $15,400 credit and $3,200 debit respectively. On that date they admitted Duarte, who paid $100,000 into the business bank account for a 25% share; the remaining 75% continues to be shared between Chen and Okafor in their old ratio. Goodwill of $90,000, agreed by the partners, has never been recorded. The premises were revalued upwards by $40,000 and equipment downwards by $12,000; these valuations are not yet in the books. Profit for 2025 before interest, salary and any goodwill write-off is expected to be $150,000. Duarte asks whether the $100,000 was a fair price.
1. Show the entries for goodwill and the revaluation on Duarte's admission and calculate the capital balance of each partner immediately after admission.
Read the worked answer
New profit-sharing ratio: Duarte takes 1/4; Chen and Okafor share the remaining 3/4 in 3:2, giving Chen 45%, Okafor 30% and Duarte 25% = 9 : 6 : 5.
1. Raise goodwill (the old partners created it)
Dr Goodwill 90,000 Cr Capital - Chen 54,000 Cr Capital - Okafor 36,000
2. Revaluation (gains and losses belong to the old partners alone)
Dr Premises 40,000 Cr Equipment 12,000 Cr Capital - Chen 16,800 Cr Capital - Okafor 11,200
Net gain $28,000 split 3:2.
3. Write off goodwill in the new ratio, because the new firm cannot carry goodwill against a partner who has just bought in
Dr Capital - Chen 40,500 Dr Capital - Okafor 27,000 Dr Capital - Duarte 22,500 Cr Goodwill 90,000
Capital balances after admission
| Chen | Okafor | Duarte | |
|---|---|---|---|
| Opening | 120,000 | 80,000 | - |
| Goodwill raised | 54,000 | 36,000 | - |
| Revaluation | 16,800 | 11,200 | - |
| Cash introduced | - | - | 100,000 |
| Goodwill written off | (40,500) | (27,000) | (22,500) |
| Closing capital | 150,300 | 100,200 | 77,500 |
Total capital = $328,000, which agrees with opening capital $200,000 + revaluation $28,000 + cash $100,000. Current accounts are unaffected by the admission and remain at $15,400 credit and $3,200 debit.
2. Prepare the appropriation account for 2025, assuming profit before interest, salary and goodwill is $150,000 and that interest is calculated on the post-admission capital balances.
Read the worked answer
Appropriation account for the year ended 31 December 2025
| $ | |
|---|---|
| Profit before interest on capital and salary | 150,000 |
| Interest on capital: Chen 5% × 150,300 | (7,515) |
| Interest on capital: Okafor 5% × 100,200 | (5,010) |
| Interest on capital: Duarte 5% × 77,500 | (3,875) |
| Salary - Okafor | (18,000) |
| Residual profit to share 9 : 6 : 5 | 115,600 |
| Partner | Interest | Salary | Share of residual | Total |
|---|---|---|---|---|
| Chen | 7,515 | - | 52,020 | 59,535 |
| Okafor | 5,010 | 18,000 | 34,680 | 57,690 |
| Duarte | 3,875 | - | 28,900 | 32,775 |
| 16,400 | 18,000 | 115,600 | 150,000 |
Presentation point: these amounts are credited to the partners' current accounts, not to capital. Interest on capital and salary are appropriations of profit, not expenses, so they are not deducted in arriving at profit for the year and do not appear in the statement of profit or loss. Only the residual $115,600 is a genuine share of profit; the $16,400 and $18,000 are simply reallocations between partners. If the partners had instead intended interest to be charged on opening balances before admission, the figures above would change, so the basis must be stated in the partnership agreement.
3. Advise Duarte on whether $100,000 was a fair price for a 25% share, and explain how the answer would differ if the partners used the bonus (no goodwill account) method.
Read the worked answer
What the price implies
$100,000 for 25% puts an implied value of $400,000 on the whole firm. Before Duarte's cash the net assets, including the agreed $90,000 goodwill, were $120,000 + $80,000 + $28,000 + $90,000 = $318,000. Duarte's 25% of that is $79,500, so he paid $20,500 above his share of net assets (or $18,000 above his $82,000 capital under the bonus method). On a net-asset basis he has overpaid; the premium compensates Chen and Okafor for eight years of built-up custom, staff and location that the balance sheet cannot show.
Earnings view: Duarte's expected 2025 income is $32,775, a return of 32.8% on $100,000, and the implied price/earnings multiple is about 2.7 (400,000 ÷ 150,000). On that measure the price looks generous to Duarte, not to the existing partners - unless the $150,000 is a one-off peak.
The alternative method: under the bonus method no goodwill account is raised. Total capital becomes $228,000 + $100,000 = $328,000 and Duarte is credited with 25% = $82,000; Chen's capital is $147,600 and Okafor's $98,400, because the $18,000 excess paid by Duarte is a bonus to the old partners. The goodwill method instead leaves Duarte with $77,500 and writes the goodwill off in the new ratio - arithmetically different but conceptually the same bargain, with Duarte acquiring a share of unrecorded reputation.
Advice: the price is defensible only if the 2025 profit level is sustainable and if the partnership agreement protects him - a salary for his work, interest on his capital, a fair share on dissolution, and clear rules on what happens if goodwill is later impaired. He should ask to see three years of accounts and the customer list before signing.