Bank unit economics: is a loan worth making?
Judge a loan book by its return on equity after interest, costs, credit losses, tax, and capital, and compare branch and digital costs.
Industry brief, with a one-minute summary: Retail and commercial bankingKey takeaways
- Judge a loan by its return on the capital it uses, after funding cost, running cost, and expected losses.
- After a loan calculation, name the variable that moves the answer most.
- The unit in banking is usually one loan book (all the loans of one product) or one customer.
Key idea
Judge a loan by its return on the capital it uses, after funding cost, running cost, and expected losses. A high interest rate means nothing if the losses and the capital needed are high too.
The unit in banking is usually one loan book (all the loans of one product) or one customer. The steps are always the same: interest earned, minus funding cost, minus operating cost, minus expected credit losses, minus tax, then divide by the equity the bank must hold. Compare the result with the cost of equity, which is the return shareholders expect (often about 10 to 15 percent, higher in riskier markets).
Worked case
Return on equity of a personal loan book in India
The prompt
A private bank in India plans a new personal loan book of INR 1,000 crore. The loan rate is 14 percent a year and the bank's funding cost is 7 percent. Operating costs are 2 percent of the loan balance each year, and expected credit losses are 3 percent a year. Tax is 25 percent. The bank must hold equity equal to 12 percent of the loans. What return on equity does the book earn, and is it worth doing if the cost of equity is 14 percent?
The structure
- Return on equity of the loan book
- Net interest income = loans x (loan rate minus funding cost)
- Minus operating costs and expected credit losses
- Minus tax
- Divide by the equity the bank must hold
Working it through
1. Net interest income
The spread is 14 minus 7, which is 7 percent of INR 1,000 crore.
Net interest income (INR crore):1,000 × (0.14 - 0.07) = 702. Operating costs
2 percent of the loan balance.
Operating costs (INR crore):1,000 × 0.02 = 203. Credit losses
3 percent of the loan balance is expected to go bad each year.
Credit losses (INR crore):1,000 × 0.03 = 304. Profit after tax
Profit before tax is 70 minus 20 minus 30, which is 20. Keep 75 percent after tax.
Profit after tax (INR crore):(70 - 20 - 30) × 0.75 = 155. Equity needed
12 percent of the loans.
Equity (INR crore):1,000 × 0.12 = 1206. Return on equity
Profit after tax divided by equity.
ROE (percent):15 ÷ 120 × 100 = 12.5
The recommendation
The bank should not launch the book as designed, because it earns about 12.5 percent on equity, below the 14 percent cost of equity. First, after INR 70 crore of net interest income, credit losses of INR 30 crore are the biggest cost. Second, cutting expected losses from 3 to 2.5 percent through better underwriting adds INR 5 crore before tax and lifts ROE to about 15.6 percent, above the bar. The risk is that losses on unsecured loans can double in a downturn. As a next step, test the underwriting model on past loan data before launch.
Risks: This simplified model ignores that equity itself funds part of the loans, which slightly lowers funding cost; In a downturn, credit losses on unsecured loans can double; Prepayments shorten the life of loans and reduce income.
After a loan calculation, name the variable that moves the answer most. For unsecured loans it is usually credit losses. For mortgages it is usually the spread between the loan rate and the funding cost, because losses are low but margins are thin.
A bank in Singapore has average interest-earning assets of SGD 50 billion. In the year it earned SGD 2.4 billion of interest and paid SGD 1.4 billion of interest. What is its net interest margin, in percent?
Branches versus digital
A branch has high fixed costs: rent, staff, security, and cash handling. A mobile app has a high build cost but a very low cost for each extra transaction. That is why banks move simple transactions to digital channels and keep branches for advice, complex products, business customers, and customers who prefer to meet in person. Closing a branch saves cost, but some customers may leave, and deposits and loan sales can fall. A good answer counts both sides.
A branch in Germany costs EUR 600,000 a year to run and handles 100,000 transactions. If all these transactions moved to the app at an extra cost of EUR 0.50 each, how much would the bank save a year, in EUR? (Ignore any lost customers.)
A new credit card product charges 30 percent interest a year. What should you check before calling it very profitable?
Sources for this lesson (2)
- Bank for International Settlements: Basel III framework overview (official)
- Recognized public explanations of case-interview concepts and frameworks
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