Two Loan Offers for a Lac-Craft Unit: Which One Is Actually Cheaper?
Twelve women of a self-help group in Khunti district run a lac-craft unit. Their own corpus, built from ₹500 monthly contributions over eight months, is ₹48,000. They must buy a processing machine costing ₹1,20,000 and have two loan offers on the table.
Offer A (public sector bank): ₹1,20,000 at 10% per annum simple interest, repaid in 24 equal monthly instalments, no processing fee.
Offer B (small finance bank): ₹1,20,000 at 9% per annum compounded annually, repaid as a single lump sum of principal plus interest after two years; a 1% processing fee on the sanctioned amount is deducted from the disbursement.
Unit figures: one machine processes 60 pieces a day over 24 working days a month and cannot exceed 1,440 pieces a month. Material costs ₹42 for every piece produced, including pieces later rejected. Rejects run at 5%. Sold pieces fetch ₹70 each, plus ₹3 each for transport. Six members work full time and each is paid ₹4,000 a month. A seventh worker would add no output, because the machine is already at capacity.
1. Which offer actually costs the group less, and which should the group accept? Show the arithmetic and weigh the non-price factors.
Read the worked answer
Offer A (simple interest). Interest = 1,20,000 × 10/100 × 2 = ₹24,000. Total repayment ₹1,44,000, i.e. an instalment of ₹6,000 a month.
Offer B (compound interest plus fee). Amount = 1,20,000 × (1.09)² = 1,20,000 × 1.1881 = ₹1,42,572. Processing fee = 1% of 1,20,000 = ₹1,200, deducted upfront, so the group actually receives ₹1,18,800. True cost = 1,42,572 − 1,18,800 = ₹23,772.
So B is cheaper by only ₹228 over two years, about 0.16%. Convert it to a comparable rate: 23,772 ÷ 1,18,800 = 20.01% over two years, i.e. roughly 10% a year simple - the advertised 9% is neutralised by the upfront fee and by compounding. The 'cheaper' offer is not cheaper in any meaningful sense.
Recommendation: take Offer A, for reasons that are not about price:
- The difference of ₹228 is inside the margin of error of any projection.
- A leaves ₹1,176 surplus each month (see next task), so a fixed ₹6,000 instalment is serviceable. B demands a lump sum of ₹1,42,572 in month 24; the equivalent sinking fund is 1,42,572 ÷ 24 = ₹5,941 a month - barely less than A's instalment, but it depends entirely on the group's own discipline and on not dipping into the fund.
- B also needs ₹1,200 from the corpus on day one, since the machine costs the full ₹1,20,000.
A rule for the group: compare loans on cash actually received and cash actually paid back, never on the quoted rate.
2. Work out the monthly surplus under Offer A. Then choose between (i) hiring a seventh worker at ₹4,000 a month and (ii) spending ₹1,500 a month on quality checks that cut rejects from 5% to 2%. Justify with numbers.
Read the worked answer
Present position (5% rejects).
- Produced: 1,440; rejected 72; sold 1,368.
- Revenue: 1,368 × 70 = ₹95,760.
- Material: 1,440 × 42 = ₹60,480 (charged on every piece produced, so rejects already cost material).
- Wages: 6 × 4,000 = ₹24,000. Transport: 1,368 × 3 = ₹4,104.
- Total cost ₹88,584 → net ₹7,176 a month. After the ₹6,000 instalment, surplus is ₹1,176.
Option (i): seventh worker. Output is capped at 1,440 by the machine, so revenue does not move; only cost rises by ₹4,000. Net falls to ₹3,176 - less than the instalment. The hire creates a monthly deficit of ₹2,824. Reject.
Option (ii): quality checks. Rejects fall to 2%: 1,440 × 0.02 ≈ 29 rejected, 1,411 sold.
- Revenue: 1,411 × 70 = ₹98,770. Transport: 1,411 × 3 = ₹4,233.
- Costs: 60,480 + 24,000 + 4,233 + 1,500 = ₹90,213.
- Net ₹8,557 - an improvement of ₹1,381 a month, and surplus after instalment rises to ₹2,557.
Decision: option (ii). The reasoning is marginal analysis: output is machine-constrained, so extra labour cannot earn anything, while reducing rejects raises the number of saleable pieces from the same material and machine time. Two caveats to state: the gain holds only if buyers absorb the extra 43 pieces a month (check orders first), and the ₹1,500 must actually be spent on inspection before finishing, not after.
3. The small finance bank's field officer says: 'At 9% against 10%, our offer is obviously cheaper; the processing fee is a small formality.' How would you answer him in a short explanation a panchayat member could follow?
Read the worked answer
Say it in cash terms, not rate terms:
- 'You sanction ₹1,20,000 but hand over ₹1,18,800, because you keep ₹1,200 as a fee. We pay interest on the full ₹1,20,000.'
- 'Over two years your interest is ₹22,572. Add the ₹1,200 you kept and our extra payment is ₹23,772 on money we actually got of ₹1,18,800.'
- 'That is 20 paise of cost for every rupee received over two years - about 10 paise a year. Your 9% and the other bank's 10% come to the same thing.'
So the honest statement is not that the fee is a formality but that it converts a 9% loan into roughly a 10% loan. Once the two offers are priced identically, the decision must be made on repayment structure: monthly instalments that match monthly sales versus one lump sum in month 24. The group's monthly surplus is ₹7,176, so it can carry instalments; it cannot easily produce ₹1,42,572 on a single date.
A useful habit for the group: ask every lender for (a) the net amount credited to the account, (b) the total amount to be repaid, (c) the dates of repayment - and compare only those three numbers.