Milk Pricing, a Loan Choice and a Bulk Cooler
A milk producers' co-operative pools about 1,200 litres a day from 60 members and sells to a private dairy. The buyer's rate formula is fixed and published: price per litre = (fat % × ₹6.00) + (SNF % × ₹1.50). Three members want to be paid separately today. Ganesh brings 200 litres at 4.0% fat and 8.5% SNF; Ramesh brings 150 litres at 5.5% fat and 9.0% SNF; Sunita brings 80 litres at 3.5% fat and 8.2% SNF. The co-operative is buying a bulk milk cooler costing ₹4,50,000, of which ₹1,50,000 comes as a grant, so it must borrow ₹3,00,000 for two years. Bank A offers 10% per annum simple interest; Bank B offers 9.5% per annum compounded annually. A costing note claims the cooler will cut spoilage from 3.5% to 0.5% of daily volume, and the average realisable price is ₹38 per litre.
1. Calculate each member's payment using the published formula, and explain why the member with the richest milk may still take home less.
Read the worked answer
Formula: rate per litre = (fat × 6.00) + (SNF × 1.50).
Ganesh - 4.0 × 6 = 24.00; 8.5 × 1.5 = 12.75; rate = ₹36.75/L. Payment = 200 × 36.75 = ₹7,350.
Ramesh - 5.5 × 6 = 33.00; 9.0 × 1.5 = 13.50; rate = ₹46.50/L. Payment = 150 × 46.50 = ₹6,975.
Sunita - 3.5 × 6 = 21.00; 8.2 × 1.5 = 12.30; rate = ₹33.30/L. Payment = 80 × 33.30 = ₹2,664.
Why Ramesh earns less than Ganesh. Payment is rate × volume, and a higher rate does not compensate for 50 litres less milk. Ramesh's rate is ₹9.75 higher, but the shortfall of 50 litres costs ₹1,837.50 at his own rate. This is why a co-operative must show both the rate and the volume on the slip: members often read only the rate and conclude they have been cheated.
2. Compare the two loan offers and advise the committee.
Read the worked answer
Bank A - simple interest. Interest = 3,00,000 × 10 × 2 ÷ 100 = ₹60,000. Total repayment = ₹3,60,000.
Bank B - compounded annually. Amount = 3,00,000 × 1.095² = 3,00,000 × 1.199025 = ₹3,59,707.50. Interest = ₹59,707.50.
Comparison. Bank B is cheaper, but by only ₹292.50 over two years - about 0.08% of the principal. That margin is smaller than almost any hidden term.
Advice. The committee should not decide on the quoted rate alone. It must compare the processing fee, whether the fee is deducted upfront (which reduces the effective loan), the penal charge for a late instalment, whether part-prepayment is allowed, the collateral or guarantee demanded, and whether interest is charged on a reducing balance if the loan is repaid in instalments rather than in one bullet payment at the end. A processing fee above ₹300 wipes out Bank B's advantage entirely. Ask both banks to quote the total repayment figure in writing before signing.
3. Test the bulk cooler on the payback calculation. What assumption in the costing note is weakest?
Read the worked answer
Base case. Spoilage falls from 3.5% to 0.5%, a saving of 3% of daily volume. Milk saved = 0.03 × 1,200 = 36 litres/day. Value = 36 × ₹38 = ₹1,368/day.
Payback on the full cost. 4,50,000 ÷ 1,368 = 328.9, i.e. about 329 days (roughly 11 months). Payback on the co-operative's own ₹3,00,000. 3,00,000 ÷ 1,368 = 219 days, about 7.3 months.
Weakest assumption: that the daily volume stays at 1,200 litres and that saved milk is actually sold. In the lean season a co-operative may pool only 800 litres, and spoilage is a percentage of a smaller base. Lean case: 0.03 × 800 = 24 litres × ₹38 = ₹912/day, so the full-cost payback stretches to 4,50,000 ÷ 912 = 493 days (over 16 months).
Also question the 3.5% spoilage figure: if it was measured in the hottest fortnight, it overstates the annual loss. Recalculate with the co-operative's own 12-month records, and check the cooler's running cost - a diesel generator or unstable supply can add a daily expense that the saved milk barely covers.