Pricing a Development Loan with a Subsidy Component
A national development finance institution (DFI) is designing a USD 10 million line of credit to on-lend to smallholder coffee cooperatives through three participating commercial banks. The DFI's mandate is to increase access to finance in rural areas where commercial banks perceive high risk. The DFI can raise funds at 4% and must cover its own operating costs, which add roughly 2% to the cost of funds. The participating banks will on-lend at a margin of 5%. A commercial bank would normally charge smallholder cooperatives 22–25% because of perceived default risk, lack of collateral, and high transaction costs. The government has offered a partial credit guarantee covering 50% of losses on the portfolio, but only if the DFI prices the on-lending rate at or below 15% to end borrowers. The DFI's board is split: some directors want full cost recovery, others want the lowest possible rate.
1. Calculate the indicative end-borrower rate under a full-cost-recovery approach and assess whether the 15% guarantee condition can be met without a subsidy.
Read the worked answer
Full-cost-recovery build-up:
- Cost of funds: 4%
- DFI operating cost: 2%
- DFI on-lending rate to participating banks: 6% (before any margin or risk premium)
- Participating bank margin: 5%
- Indicative end-borrower rate: 6% + 5% = 11% (before credit risk and transaction costs)
But this understates the true cost. The 11% excludes:
- Expected credit losses on smallholder lending (historically high, perhaps 5–10%)
- Transaction costs of many small loans (origination, monitoring, collection in rural areas)
- The DFI's own risk capital and any return the board requires
Adding a realistic risk and transaction-cost allowance of, say, 6–8% pushes the end-borrower rate to 17–19%, above the 15% guarantee threshold.
Conclusion: Pure full-cost recovery with realistic risk pricing does not meet the 15% condition. To reach 15% the DFI must either (a) accept a lower return / subsidise the risk premium, (b) use the guarantee to reduce the risk premium the banks charge, or (c) reduce transaction costs through portfolio aggregation. The guarantee itself is a subsidy - it transfers 50% of loss risk to the government - so the question is how to allocate that benefit.
2. Propose a pricing and risk-sharing structure that meets the 15% condition while preserving the DFI's sustainability. Show the arithmetic.
Read the worked answer
Proposed structure:
- DFI on-lending rate to banks: 5% (cost of funds 4% + 1% partial operating recovery; the DFI accepts a 1% operating subsidy, justified by its access mandate)
- Participating bank margin: 4% (reduced from 5% because the guarantee lowers their risk)
- Expected credit loss borne by banks after the 50% guarantee: assume gross expected loss of 8%; with 50% cover, the banks' net expected loss is 4%
- End-borrower rate: 5% + 4% + 4% = 13%, comfortably under the 15% cap.
Why this works:
- The guarantee is doing the heavy lifting - it converts an 8% expected loss into a 4% net loss, which is what allows the banks to lend at a margin they would otherwise reject.
- The DFI accepts a 1% operating shortfall, which is a transparent, budgeted subsidy rather than an open-ended one.
- The 15% cap leaves 2% headroom for transaction costs and a small risk buffer, so the structure is not fragile.
Sustainability safeguard: The DFI should set a portfolio-level loss trigger - if actual losses exceed 10%, the pricing is reviewed. It should also require the banks to report monthly so the DFI can verify that the subsidy is reaching borrowers rather than being absorbed as extra margin.
3. The board asks how the DFI should measure whether this intervention is achieving its development mandate rather than just subsidising banks. What indicators and safeguards should be used?
Read the worked answer
Development additionality indicators:
- Reach: number of cooperatives and smallholders financed, disaggregated by size, gender, and region - and crucially, the share that had no prior access to formal credit (additionality).
- Depth: average loan size and whether smallholders (not just large cooperatives) are being reached.
- Pricing pass-through: verified end-borrower rates versus the 15% cap - audit a sample of loan contracts, not just bank reports.
- Outcomes: yield/income changes, repayment rates, and whether borrowers graduate to commercial lending without the guarantee.
Safeguards against subsidy capture:
- Capped bank margin written into the participation agreement, with clawback if the bank charges above the agreed spread.
- Ring-fencing: the DFI line must be traceable to specific loans, not commingled with the bank's general book.
- Independent verification of end-borrower rates and borrower characteristics (sample audits).
- Sunset and graduation: the guarantee and subsidised pricing taper over time as the banks build experience and loss data, so the intervention does not become permanent.
- Loss-sharing discipline: banks retain a meaningful first-loss or pari-passu share so they keep skin in the game and do not relax credit standards.
Reporting: a quarterly development-effectiveness report to the board comparing actuals against these indicators, with a decision point on whether to scale, adjust, or exit.