Farm Gate or Kalimati? A Contract Decision with Numbers
Khopasi Vegetable Cooperative has 120 members farming 40 ha of tomato. Members can sell to a village collector at NPR 25/kg at the farm gate, paid in cash the same day. Alternatively the cooperative can truck to the Kalimati wholesale market, 180 km away, where the price today is NPR 42/kg but fluctuates by about ±30% within a season. Transport and loading cost NPR 4.50 per kg harvested, market commission is 8% of gross sale value, packaging in crates costs NPR 1.00/kg, and experience shows 10% of each consignment is unsalable on arrival. Payment from the wholesale market comes 10–15 days after sale. A mid-season survey of 30 randomly selected members recorded a mean yield of 30.0 t/ha with a standard deviation of 6.0 t/ha. The board must decide before signing a season-long contract with the collector.
1. Compare net realisation per kilogram for the two channels, find the break-even Kalimati price, and state a recommendation with its conditions.
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Net realisation, Kalimati channel
- Saleable fraction: 0.90 of every kilogram harvested.
- Gross sale value per kg harvested: 0.90 × 42 = NPR 37.80.
- Less 8% commission: 37.80 × 0.92 = NPR 34.78.
- Less transport and loading NPR 4.50 and crates NPR 1.00 = NPR 5.50.
- Net = NPR 29.28/kg harvested.
Farm gate channel: NPR 25.00/kg, no transport, no commission, no loss, cash on the day. Net = NPR 25.00/kg.
Difference: Kalimati is better by NPR 4.28/kg. At 40 ha × 30 t/ha = 1,200 t, that is about NPR 5.1 million over the season.
Break-even price Set 0.828P − 5.50 = 25.00, where 0.828 = 0.90 × 0.92. So 0.828P = 30.50 and P = NPR 36.84/kg.
Stress test at ±30%
- Low case, NPR 29.40: net = 0.828 × 29.40 − 5.50 = NPR 18.84, i.e. NPR 6.16/kg worse than the collector.
- High case, NPR 54.60: net = NPR 39.71, i.e. NPR 14.71/kg better.
Recommendation Do not sign the whole season away, but do not lock into the collector either. The Kalimati channel is superior on expected value and its downside is bounded by price, not by volume. Propose a split: commit roughly 60–70% of volume to Kalimati and keep the collector as a floor for the remainder, with a clause allowing the cooperative to divert to the collector when the expected Kalimati price falls below about NPR 37/kg. Because 37/kg is close to the seasonal average, the decision depends on price information and timing, not on a single day's quotation.
2. Calculate a 95% confidence interval for mean yield, applying the finite population correction, and explain what it means for the contract decision.
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Calculation
- Sample mean = 30.0 t/ha, s = 6.0 t/ha, n = 30, N = 120.
- Standard error without correction: 6.0 ÷ √30 = 6.0 ÷ 5.477 = 1.095 t/ha.
- Sampling fraction is 30/120 = 25%, well above 5%, so the finite population correction applies: FPC = √((N − n)/(N − 1)) = √((120 − 30)/(120 − 1)) = √(90/119) = √0.7563 = 0.870.
- Corrected standard error = 1.095 × 0.870 = 0.953 t/ha.
- With z = 1.96: margin = 1.96 × 0.953 = 1.87 t/ha.
- 95% CI = 30.0 ± 1.87, i.e. 28.13 to 31.87 t/ha.
Interpretation for the board
- The plausible range for the true mean yield of all 120 members is about 28.1–31.9 t/ha. Scaled to 40 ha, total production is between about 1,125 t and 1,275 t.
- This precision is adequate for a channel comparison: the ±4.28/kg advantage for Kalimati is not sensitive to a yield estimate that varies by ±6%.
- What the interval does not capture is price risk and the loss percentage, which vary far more than yield and matter more to the decision.
- Two cautions: the sample must genuinely be random across members, and a sample of 30 out of 120 is a 25% sample - adequate for a group decision but not for individual farm planning.
- If the board wants a tighter estimate, sample 50 members to cut the standard error by roughly another 25%.
3. What risks does the Kalimati channel carry beyond price, and how would you manage them contractually and operationally?
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Payment delay and cash flow Ten to fifteen days of credit against daily transport and labour costs is the most underrated risk. At 3 t/day and NPR 42/kg, that is roughly NPR 1.9 million tied up at any time. Manage it by negotiating a partial advance, arranging a cooperative overdraft, or staggering consignments so receivables turn over faster.
Quality rejection and commission disputes Wholesale buyers can reject or down-grade a consignment after arrival, and the cooperative has no presence at the market. Manage by sending a member representative with each load, agreeing a grading standard in writing, photographing loads at dispatch, and using an auction receipt as the payment document.
Transport and breakdown A single breakdown in summer heat can destroy a load. Keep a standby transporter, load overnight, and hold the cooler at the collection centre for emergencies.
Volume concentration and counterparty risk Selling everything to one market exposes the cooperative to a single price and a single set of buyers. A 60–70% commitment with the collector as a floor spreads that risk.
Contract terms to insist on with the collector A fixed price with a defined quality grade, payment within 48 hours, a stated minimum volume obligation so the collector cannot simply walk away, and a no-exclusivity clause that lets the cooperative divert to Kalimati when the price justifies it. Without that last clause the collector's NPR 25/kg becomes a ceiling, not a floor.