Case 052Bank economics, fees and riskCore
Two wealth desks merge: Rs 1,200 crore of assets earning 0.9% and Rs 800 crore earning 0.7%. If 20% of the smaller desk's clients leave, what is the combined revenue, and what was each lost client worth?
1The situation
A private bank is folding a smaller wealth desk into its main one. Desk A manages Rs 1,200 crore and earns a revenue yield of 0.9% on it. Desk B manages Rs 800 crore at 0.7%, spread across 200 client families averaging Rs 4 crore each. The integration plan moves desk B's clients onto desk A's price list, and the bank's own experience is that about 20% of a merged desk's clients follow their old relationship manager out of the door.
Assume the clients who leave are average sized, a relationship lasts ten more years on average, and the bank values future revenue at 10% a year.
2Your task
What is the combined revenue after the leavers go, what was each lost client worth, and does the repricing plan pay for itself?
Quick check
Before repricing, how much revenue do the leavers take with them each year?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Combined revenue falls from Rs 16.4 crore to Rs 15.28 crore a year, and each lost client was worth about Rs 2.8 lakh a year, roughly Rs 17 lakh over the relationship. Desk A earns Rs 10.8 crore and desk B Rs 5.6 crore; 40 average clients with Rs 160 crore take Rs 1.12 crore. Repricing the rest to 0.9% adds back Rs 1.28 crore, so the plan nets only Rs 0.16 crore.
Step 1Where does the combined revenue start from?
Start with each desk on its own yield, because the two books are priced differently. Revenue is assets times the revenue yieldAnnual revenue a wealth business earns divided by the client assets it manages, the all-in price of the service. for each desk, added together. Desk A's Rs 1,200 crore at 0.9% earns Rs 10.8 crore; desk B's Rs 800 crore at 0.7% earns Rs 5.6 crore. The blended yield on Rs 2,000 crore is 0.82%, which is the number a merger deck quotes and the one that hides what happens next.
Step 2What do the clients who leave cost?
Think of two neighbourhood clinics merging: some patients were loyal to a doctor, not to a building, and they follow the doctor. Twenty per cent of desk B's clients is 40 families and Rs 160 crore of assets, which at 0.7% is Rs 1.12 crore a year gone. Combined revenue lands at Rs 15.28 crore, 6.8% below the simple sum.
| 4 cr | the average desk B client's assets |
| 0.7% | desk B's revenue yield |
| 6.14 | the value today of Rs 1 a year for ten years at 10% |
That Rs 17 lakh is the budget question hiding in the case. If a retention bonus, a pricing concession or a dedicated banker costs less than about Rs 17 lakh per client kept, it pays for itself. The limit: leavers are rarely average. If the 20% who leave hold 35% of desk B's assets, because big clients are the ones with personal ties to their banker, the loss is Rs 1.96 crore and revenue falls to Rs 14.44 crore.
Step 3Does moving desk B onto desk A's prices pay for itself?
The remaining Rs 640 crore repriced from 0.7% to 0.9% earns an extra Rs 1.28 crore. Repricing plus attrition leaves the merged desk at Rs 16.56 crore, only Rs 0.16 crore above the two desks standing still, so the plan barely breaks even. Solve for the tipping point: 0.9% on what stays must at least match 0.7% on everything, so the plan loses money once more than 22.2% of desk B's assets walk. Price rises are often what makes clients leave, so the two numbers are not independent.
| Scenario | Desk B assets left, Rs cr | Desk B yield | Total revenue, Rs cr |
|---|---|---|---|
| No merger | 800 | 0.7% | 16.40 |
| 20% of assets leave, old price | 640 | 0.7% | 15.28 |
| Big clients leave, 35% of assets | 520 | 0.7% | 14.44 |
| 20% leave, rest repriced | 640 | 0.9% | 16.56 |
Close with the view. The merger adds almost nothing on revenue at 20% attrition; its case has to rest on cost savings, and retaining desk B's larger clients matters more than the new price list. A strong answer asks for the list of desk B's top twenty clients and who covers each one before agreeing to the plan.
Where candidates lose it
The usual error is applying 20% to the combined revenue, Rs 3.28 crore, as if clients of both desks were leaving. The case says the smaller desk; attrition runs at desk B's assets and desk B's lower yield.
The second is stopping at the annual figure. Asked what a client was worth, give the relationship value, about Rs 17 lakh, because that is the number that tells a manager how much to spend keeping one.
What the interviewer asks next
- How does the answer change if the leavers are desk B's largest twenty clients?
- What would you pay a relationship manager to stay for two years?
- Which costs would you expect to fall after the merger, and by how much would they need to fall to justify it?
Company names and figures are illustrative.