Case 040Bank economics, fees and riskCore
A private bank relationship holds Rs 40 crore across advisory, custody and a loan, with Rs 12 lakh of cost to serve. Is it profitable, and which lever moves it most?
1The situation
The Wadekar relationship at an invented private bank has Rs 40 crore with the bank. Rs 15 crore is in an advisory mandate at a fee of 0.8% a year. Rs 20 crore sits in custody, holding shares the family manages itself, at 0.1% a year. The bank has also lent the family Rs 5 crore against securities, earning a net interest margin of 1.5% a year.
The relationship manager's time, the service team, reporting and systems cost the bank an estimated Rs 12 lakh a year to serve this family. Ignore the capital the bank must hold against the loan for the first pass.
2Your task
Is the relationship profitable, and by how much? Of the levers available, which moves the profit most, and what does that say about how a private bank should look at a client?
Quick check
Custody is half of the Wadekar assets. Roughly what share of the revenue does it bring?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Yes: revenue is Rs 21.5 lakh and profit Rs 9.5 lakh a year, before the capital held against the loan. Advisory brings Rs 12.0 lakh, lending Rs 7.5 lakh and custody only Rs 2.0 lakh, though custody is half the assets. The biggest lever is moving custody money into advice: Rs 5 crore moved adds Rs 3.5 lakh. The product mix, not the Rs 40 crore total, decides profitability.
Step 1Why is the asset total the wrong place to start?
A restaurant that fills every table with people ordering only tea is busy, not profitable. Private bank revenue is assets times the fee on each product, so two clients with the same assets can earn the bank very different amounts. The Wadekars bring Rs 40 crore, but half of it pays 0.1% because the family runs it themselves. Start from each line's fee, not from the headline.
Step 2Which lever moves profit most?
Price each lever in rupees rather than arguing about it. Moving Rs 5 crore from custody to advice adds Rs 3.5 lakh, because each rupee moves from 0.1% to 0.8%; that beats growing the loan by Rs 2 crore, raising the advisory fee, or trimming costs. It is also the lever that serves the family, if they want the advice: it only works if the bank earns the mandate by being useful, not by pushing.
| Lever | Extra profit a year, Rs lakh |
|---|---|
| Move Rs 5 crore from custody to advised | 3.5 |
| Grow the loan by Rs 2 crore | 3.0 |
| Raise the advisory fee by 0.1 point | 1.5 |
| Cut cost to serve by 10% | 1.2 |
Step 3What does the comparison with an all-custody client show?
Put the same Rs 40 crore entirely in custody at 0.1% and revenue is Rs 4.0 lakh against Rs 12 lakh of cost: a loss of Rs 8.0 lakh a year. A large relationship can lose money, and a smaller one with advice and lending can make more; banks that rank clients by assets alone misread both. Two limits to state: cost to serve is an allocation and can be argued, and the loan uses bank capital, so its true profit is lower than the margin suggests.
Where candidates lose it
The common miss is multiplying Rs 40 crore by an average fee, say 0.5%, and calling it Rs 20 lakh of revenue. The answer happens to land close, but the method hides the point of the case: the mix decides everything.
The second is pushing the loan as the lever because the margin is highest. Lending carries credit risk and needs capital; a stronger answer puts the advisory conversion first and names the capital cost of the loan.
What the interviewer asks next
- The bank holds capital of 10% of the loan at a 14% cost of equity. What does the loan really earn?
- The family says the custody fee is too high. How do you respond?
- How would you set a minimum profitable size for a new relationship?
Company names and figures are illustrative.