Partnership profit allocation with a guaranteed minimum share
A three-partner firm closes its first year on 30 June. Partner A contributed Rs. 800,000 on 1 July, the first day of the year, and remained in the firm throughout. Partner B contributed Rs. 600,000 on the same date and also stayed for the full twelve months. Partner C was admitted on 1 March with Rs. 900,000 and remained until the year end. The deed provides that profit is shared in the ratio of capital multiplied by the number of months each partner's capital was in the firm, that no interest is charged on capital, that no partner drew during the year, and that C is guaranteed a minimum of Rs. 250,000. Any shortfall against that guarantee is to be borne by A and B in the ratio 2:1 and is not recoverable from C in later years. Profit before appropriation for the year was Rs. 1,020,000. The firm's accountant is preparing the appropriation account and the partners are already disputing how the guarantee should be applied.
1. Allocate the Rs. 1,020,000 profit among the three partners under the deed and state the final amount credited to each partner.
Read the worked answer
Work in capital-months, since the deed weights capital by time:
- A: 800,000 × 12 = 9,600,000
- B: 600,000 × 12 = 7,200,000
- C: 900,000 × 4 (March to June) = 3,600,000
- Total = 20,400,000
The ratio simplifies to A : B : C = 9.6 : 7.2 : 3.6 = 8 : 6 : 3 (out of 17).
- A = 1,020,000 × 8/17 = 480,000
- B = 1,020,000 × 6/17 = 360,000
- C = 1,020,000 × 3/17 = 180,000
C's provisional share (180,000) is below the guaranteed Rs. 250,000, so a shortfall of Rs. 70,000 arises. The guarantee is a charge on the other partners, not a deduction from C: A bears 2/3 × 70,000 = 46,666.67 and B bears 1/3 × 70,000 = 23,333.33.
Final credit: A Rs. 433,333.33, B Rs. 336,666.67, C Rs. 250,000. Total Rs. 1,020,000. Note that the guarantee is applied after, not before, the capital-month split - applying it before would wrongly change the base share.
2. B argues the shortfall should be shared in the profit-sharing ratio (8:6) rather than 2:1, calling that 'fairer'. Quantify the effect on B of adopting his reading and state which reading should be applied.
Read the worked answer
Under the deed's 2:1 wording B bears 1/3 × 70,000 = Rs. 23,333.33.
Under B's proposed 8:6 split, B bears 6/14 of the shortfall = 0.42857 × 70,000 = Rs. 30,000. A would bear Rs. 40,000 instead of Rs. 46,666.67.
Adopting B's reading therefore costs B an extra Rs. 30,000 − 23,333.33 = Rs. 6,666.67, and saves A the same amount.
The answer is not a matter of fairness: the deed names an explicit 2:1 ratio for guarantee shortfalls, and an express term displaces any general presumption that shortfalls follow the profit-sharing ratio. B's argument only has force if the deed were silent, which it is not. A candidate who simply says 'the deed governs' without quantifying the Rs. 6,666.67 swing has answered only half the question.
3. Ignoring the guarantee, how many months would C have needed to be in the firm (at the same Rs. 900,000 capital) for C's unguaranteed share to equal exactly Rs. 250,000?
Read the worked answer
Let x be C's capital-months. A and B together contribute 16,800,000 capital-months. C's share is:
1,020,000 × x / (16,800,000 + x) = 250,000
1,020,000x = 250,000(16,800,000 + x) 1,020,000x − 250,000x = 4,200,000,000,000 770,000x = 4,200,000,000,000 x = 5,454,545.45 capital-months
At Rs. 900,000 of capital, that is 5,454,545.45 / 900,000 = 6.06 months.
So C would have needed to be admitted roughly two months earlier (about 1 February instead of 1 March) for the guarantee to be exactly neutral. This is the useful sensitivity: the guarantee only bites because C's capital was at risk for four months, which is short relative to a twelve-month profit pool. A practical corollary is that the Rs. 70,000 cost of the guarantee is effectively the price A and B paid for late admission of capital.