Partnership Profit Sharing and a Working-Capital Loan Choice
A trading firm has three partners. In the year just ended, A contributed ₹4,00,000 for the full 12 months, B contributed ₹6,00,000 but kept it invested for only 9 months, and C joined at the start of the fifth month with ₹8,00,000, which stayed in the business for the remaining 8 months. Distributable profit was ₹4,15,000, and the deed provides no salaries or interest on capital, so profit is shared strictly in the ratio of capital × time. Separately, the firm must borrow ₹5,00,000 for 18 months. Bank P offers 12% per annum compounded quarterly; financier Q offers 13% per annum simple interest. The accountant says the bank is cheaper 'because 12 is less than 13'. Next year the partners expect the same ₹4,15,000 profit, with A and B keeping the same capital and duration. C wants his share to be exactly one-third of the profit and asks how much capital he should deploy for his 8-month period.
1. Compute each partner's share of the ₹4,15,000 profit for the year. Does C's existing 8-month capital already give him a one-third share?
Read the worked answer
Convert each capital into unit-months (₹ × months):
- A: 4,00,000 × 12 = 48,00,000
- B: 6,00,000 × 9 = 54,00,000
- C: 8,00,000 × 8 = 64,00,000
Ratio = 48 : 54 : 64 = 24 : 27 : 32, total 83 parts.
Profit per part = 4,15,000 ÷ 83 = ₹5,000.
- A = 24 × 5,000 = ₹1,20,000
- B = 27 × 5,000 = ₹1,35,000
- C = 32 × 5,000 = ₹1,60,000
Check: 1,20,000 + 1,35,000 + 1,60,000 = ₹4,15,000.
C's share is 1,60,000 ÷ 4,15,000 = 38.55%, which is already above one-third (33.33%). The common assumption that joining later automatically means a smaller share is wrong here, because C's capital is the largest and is in for 8 months.
2. Compare the two borrowing options over the full 18 months and evaluate the accountant's reasoning.
Read the worked answer
Bank P: quarterly rate = 12%/4 = 3%; 18 months = 6 quarters. Amount = 5,00,000 × (1.03)^6 = 5,00,000 × 1.194052 = ₹5,97,026. Interest = ₹97,026.
Financier Q: simple interest = 5,00,000 × 13% × 1.5 = ₹97,500.
Bank P is cheaper, but only by ₹474 (about 0.5% of the interest). The accountant's conclusion is right, but the reason is wrong: nominal rates cannot be compared when compounding frequencies differ. The correct comparison is on an effective basis.
Effective annual rate, P = (1.03)^4 − 1 = 12.55%, versus 13% for Q. Over 18 months, P costs 19.405% of principal against 19.5% for Q.
The decision is therefore sensitive to small changes: if Q had quoted 12.4% simple, its interest would be ₹93,000 and Q would win. The firm should also weigh non-price terms such as collateral, prepayment penalties and processing fees before choosing.
3. C wants his share to be exactly one-third of the ₹4,15,000 profit next year, with A and B unchanged. What capital should C deploy for 8 months, and is this a sensible objective?
Read the worked answer
Let C's capital be K lakh, giving unit-months 8K lakh. A and B together have 48 + 54 = 102 lakh unit-months.
For a one-third share: 8K ÷ (102 + 8K) = 1/3 24K = 102 + 8K 16K = 102 K = 6.375
So C should deploy ₹6,37,500 for 8 months (51 lakh unit-months), not more.
Check: C's units = 51; total = 102 + 51 = 153; 51/153 = 1/3, giving profit of ₹1,38,333.
The result is counter-intuitive: to hit exactly one-third, C must reduce capital by ₹1,62,500 from ₹8,00,000, because 64/166 = 38.55% is above one-third. Reducing capital costs him ₹21,667 of profit (1,60,000 − 1,38,333). 'Exactly one-third' is a vanity target, not a value-maximising one; if C wants maximum absolute income he should keep ₹8,00,000 and negotiate on other grounds.