Allocating ₹24 Lakh Between Individual and Group Loans at a Barpeta Branch
A microfinance branch in Barpeta has ₹24,00,000 of fresh funds to lend this quarter and must split them between individual loans and group loans. Individual loans are ₹20,000 each at 18% simple interest for one year. Branch records for 400 such loans show 48 written off, and on a written-off loan only 40% of principal is recovered and no interest. Group loans are ₹15,000 per group of five members with joint liability, also at 18% simple interest for one year; of 300 group loans in the records, 15 defaulted as a whole, again with 40% of principal recovered and no interest. Appraisal and follow-up cost ₹400 per individual loan and ₹150 per group loan; these costs are incurred whether or not the loan is repaid. Ninety-six group loans are ready for disbursement this quarter. Individual applicants are plentiful and unlimited. The branch manager, under pressure to grow the loan book, argues that individual loans should dominate because 18% is earned on a larger ticket.
1. Compute the expected profit per loan and per rupee lent for each product, net of appraisal cost.
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Individual loan (₹20,000). Default rate = 48/400 = 12%, so repayment probability = 0.88. If repaid: interest earned = 20,000 × 0.18 = ₹3,600 (a gain). If defaulted: recovery is 40% of 20,000 = ₹8,000, so the loss of principal is 20,000 − 8,000 = ₹12,000; no interest. Expected profit before cost = 0.88(3,600) + 0.12(−12,000) = 3,168 − 1,440 = ₹1,728. After appraisal cost: 1,728 − 400 = ₹1,328 per loan, i.e. 1,328/20,000 = 6.64% of the amount lent.
Group loan (₹15,000). Default rate = 15/300 = 5%, so repayment probability = 0.95. If repaid: 15,000 × 0.18 = ₹2,700. If defaulted: recovery 6,000, loss 9,000. Expected profit = 0.95(2,700) + 0.05(−9,000) = 2,565 − 450 = ₹2,115. After cost: 2,115 − 150 = ₹1,965 per loan, i.e. 13.10% of the amount lent.
The manager is looking at the wrong number. The group loan earns less in rupees per loan but almost twice as much per rupee deployed, because the default rate is far lower and the appraisal cost is shared across five members.
2. Recommend how to allocate the ₹24,00,000, supporting the answer with expected profit figures for the plausible alternatives.
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The group product earns more per rupee, so fill the group quota first, then place the remainder in individual loans.
Option A - all group (not feasible beyond ₹14.4 lakh). 96 × 15,000 = ₹14,40,000 placed. Profit = 96 × 1,965 = ₹1,88,640. The other ₹9,60,000 stays idle.
Option B - all individual. 24,00,000/20,000 = 120 loans. Profit = 120 × 1,328 = ₹1,59,360.
Option C - group quota first, balance to individuals. 96 group loans = ₹14,40,000; remaining ₹9,60,000 gives 48 individual loans. Profit = 1,88,640 + (48 × 1,328 = 63,744) = ₹2,52,384.
Option C beats B by ₹93,024 and beats A by ₹63,744. The marginal logic is simple: moving ₹1 from an individual loan to a group loan raises expected profit, so the switch should continue until either the group quota or the funds run out - here the quota binds at 96 loans.
The manager's 'bigger ticket' argument confuses volume with return. Note also that if the group default rate rose only from 5% to 8%, expected group profit would fall to 0.92(2,700) − 0.08(9,000) − 150 = 2,484 − 720 − 150 = ₹1,614, still above the individual product but no longer by a wide margin - so the recommendation is sensitive to that estimate.
3. The group loans are concentrated in two villages that depend on the same jute and vegetable crop. How should this affect the allocation and the manager's reporting?
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The expected-value calculation assumes defaults are independent. They are not. If a flood or a price collapse hits both villages, the 96 group loans fail together, not one at a time. The branch would then lose 96 × 9,000 = ₹8,64,000 on group lending alone, plus up to 48 × 12,000 = ₹5,76,000 on the individual book - about ₹14,40,000, or 60% of the whole ₹24 lakh.
The expected profit of ₹2,52,384 is a good central estimate but it describes the average over many comparable quarters; it says nothing about the worst quarter, which is what actually threatens a branch.
Recommended safeguards.
- Cap group exposure per village - for example no more than half the group book in either village - so one local shock cannot take out the full ₹14.4 lakh.
- Verify that the 5% default rate was estimated over a period that included at least one bad season. Fifteen defaults out of 300 loans is a reasonable sample size, but only if the years were representative.
- Report both the expected profit and the 'all group loans default' loss to the regional office, not the expected figure alone.
- Keep the individual loans diversified across more villages and occupations, since they are the branch's diversification leg rather than its yield engine.
In short, take the ₹2,52,384 plan but overlay a concentration limit; the statistics justify the higher group share, and the correlation justifies capping it.