Case 031FinancialsCore

Build Nirvela Bank's return on equity from an ROA tree: margin, fees, cost to income, credit cost, tax and leverage. Where is the gap to a peer earning 17%?

The situation

Nirvela Bank is a mid-sized Indian private bank. As a percentage of average total assets, its net interest income is 3.40% and its fees and other income 1.20%. Operating costs are 48% of total income. Loan loss provisions, the credit cost, run at 0.84% of assets. Tax is 25%, and assets are 11 times equity.

Pratika Bank, the peer the market compares it with, earns a 17% return on equity. It has the same net interest margin, fee income, tax rate and leverage, but its cost to income ratio is 45% and its credit cost is 0.47% of assets.

Your task

What is Nirvela's ROE, how much of the gap to Pratika comes from each link, and what would you ask management?

Quick check

Before building the tree: which link do you expect to explain most of the gap?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Nirvela earns an ROE of about 12.8%, and most of the 4.2 point gap to Pratika's 17% is credit cost. Income of 4.60% of assets less costs of 2.21% leaves 2.39%; credit cost of 0.84% leaves 1.55% before tax, a 1.16% ROA, times 11 leverage. Matching Pratika's credit cost would add 3.1 points; matching its costs only 1.1. The question for management is why Nirvela takes more credit risk without earning a higher margin for it.

Step 1Why build the ROE as a chain rather than read it off the income statement?

Think of a shop owner who wants to know why a neighbour earns more. Comparing total profit tells her nothing; comparing profit per Rs 100 of stock, line by line, shows whether the neighbour charges more, spends less or loses less to theft. Expressing every line of a bank's income statement as a percentage of average assets makes each link comparable across banks of any size, and the chain then multiplies up to ROE. This is the DuPont analysisBreaking return on equity into a product of simpler ratios, margin, efficiency and leverage, so the source of a difference can be found. Named after the DuPont company, where it was first used. adapted to a bank.

Bank ROE is a chain: per Rs 100 of assets, Nirvela against its peerNII + feesNirvela4.60Peer4.60less costsNirvela-2.21Peer-2.07C/I 48% vs 45%= pre-provisionNirvela2.39Peer2.53less credit costNirvela-0.84Peer-0.47weakest linkROA, after taxNirvela1.16Peer1.54tax 25%ROE, x 11Nirvela12.8%Peer17.0%same leverageThe ROE gap is 4.2 points. Credit cost explains 3.1 of it, costs explain 1.1.Each 0.10 of assets lost before tax costs 0.10 x 0.75 x 11 = 0.83 points of ROE.
Per Rs 100 of assets Nirvela and Pratika earn the same 4.60 of income, but Nirvela spends 2.21 against 2.07 on costs and loses 0.84 against 0.47 to credit, so its ROA is 1.16% against 1.54% and its ROE 12.8% against 17.0%.
The relationship
ROE=[(NIM+fees)(1−C/I)−credit cost](1−t)×AE=[4.60×0.52−0.84]×0.75×11≈12.8%\text{ROE} = \big[(\text{NIM} + \text{fees})(1 - \text{C/I}) - \text{credit cost}\big](1 - t) \times \frac{A}{E} = \big[4.60 \times 0.52 - 0.84\big] \times 0.75 \times 11 \approx 12.8\%
NIM + feestotal income, % of average assets
C/Icost to income ratio, 48%
credit costprovisions for bad loans, % of assets
ttax rate, 25%
A/Eassets divided by equity, leverage of 11
What it says in wordsReturn on equity is what is left of each rupee of assets after costs, bad loans and tax, multiplied by how many rupees of assets each rupee of equity supports.
Step 2How do you size each link's share of the gap?

Change one link at a time to the peer's value and carry it down the chain. A pre-tax difference of x% of assets becomes x times 0.75 times 11 points of ROE, so every 0.10% of assets is worth about 0.83 points. The cost gap is 2.21 less 2.07, 0.14% of assets, worth 1.1 points. The credit gap is 0.84 less 0.47, 0.37% of assets, worth 3.1 points. Together they close the 4.2 points exactly because nothing else differs.

Closing the gap to 17%: which link is worth fixing?Nirvela ROE today12.8%Cost to income 48% to 45%+1.1Credit cost 0.84% to 0.47%+3.1Peer ROE17.0%
Nirvela's ROE of 12.8% rises by 1.1 points if its cost to income falls to Pratika's 45% and by a further 3.1 points if its credit cost falls to 0.47%, reaching Pratika's 17.0%.
Step 3What does the weak link tell you about the bank?

Here is the part worth sitting with. Nirvela takes more credit losses than Pratika but earns exactly the same net interest margin, so it is carrying extra risk without being paid for it. A bank that lends to riskier borrowers should charge more; one that does not is either mispricing risk or dealing with a one-off problem in a single book. The questions follow: which segment drives the 0.84%, is it falling, and what are fresh slippages and recoveries doing? One lever to reject: raising leverage to 13x would lift ROE to 15.1% on paper while thinning the capital that absorbs those very losses.

Where candidates lose it

The common loss is fixating on cost to income because 48% against 45% looks like a large gap. Three points of income is small on a bank's asset base; the interviewer is checking whether you convert every link into the same unit before ranking them.

The second is forgetting to carry the difference through tax and leverage. Stopping at a 0.37% ROA gap undersells a problem that is worth three points of ROE.

What the interviewer asks next

  • Credit cost is 0.84% of assets and loans are 65% of assets. What is it as a percentage of loans?
  • Nirvela's credit cost falls to 0.60% next year. What is the new ROE?
  • Why do analysts value a bank on price to book, and how does this ROE feed that multiple?

Company names and figures are illustrative.