Case 097Sector valuationHard
A lender has a Rs 10,000 crore book on Rs 2,000 crore of equity, an 8% net interest margin, operating costs of 2.5% and credit costs of 1.5% of the book, tax at 25%, cost of equity 15% and growth 10%. Compute ROA, ROE and the justified price-to-book, then redo it with credit costs at 3%.
1The situation
Dhanvaan Finance, an invented non-bank lender to small businesses, has a Rs 10,000 crore loan book funded by Rs 2,000 crore of equity and Rs 8,000 crore of borrowings, so the book is 5x equity. Its net interest margin is 8% of the book, operating costs are 2.5% of the book and credit costs, the provisions for loans that go bad, are 1.5%. Tax is 25%.
Investors want a 15% return on equity and expect the book to grow 10% a year. A fund manager asks you what the shares are worth relative to book value, and what happens to that answer if a bad year takes credit costs to 3%.
2Your task
Build ROA and ROE from the margin, derive the justified price-to-book from ROE, cost of equity and growth, and show why the stress case breaks the formula and what that means.
Quick check
In the base case, what is Dhanvaan's return on equity?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Base: ROA 3.0%, ROE 15%, justified P/B 1.00x, so the equity is worth its book, Rs 2,000 crore. At 3% credit costs ROA falls to 1.88% and ROE to 9.4%, below the 10% growth rate, and the formula gives -0.12x, which is meaningless. A lender earning 9.4% cannot grow 10% without raising equity; with growth cut to 5% the justified P/B is 0.44x, about Rs 875 crore.
Step 1How does a margin on loans become a return on equity?
Walk down the book in percentage points. Net interest margin 8.0, less operating cost 2.5, less credit cost 1.5, leaves 4.0 pre-tax and 3.0 after tax: that is ROA, the return on the Rs 10,000 crore of loans. A shopkeeper who borrows Rs 8 lakh to add to Rs 2 lakh of his own and earns 3% on the full Rs 10 lakh after paying his interest has earned 15% on his own money; leverage multiplies the return on assets. Dhanvaan's book is 5x equity, so ROE is 3.0% x 5 = 15%, which in rupees is Rs 300 crore of profit on Rs 2,000 crore of equity. Note what sits inside the 8%: it is already net of the cost of the Rs 8,000 crore of borrowings, which is why leverage appears only once.
Step 2What price-to-book does that return justify?
Use the one-stage model: price-to-book equals ROE less growth over cost of equity less growth. With ROE 15%, cost of equity 15% and growth 10%, P/B is (15 less 10) / (15 less 10) = 1.00x: a lender earning exactly its cost of equity is worth exactly its book, whatever it grows. That is the sense check: growth adds value only when ROE beats the cost of equity, because growing means retaining profit and reinvesting it at ROE. Here 10% growth needs 67% of profit retained, so the dividend is a third of earnings, and the shareholders are no better or worse off than if the money came back to them.
| ROE | return on equity, ROA times book over equity |
| g | the long-run growth rate of the book and of profit |
| k_e | the cost of equity, 15% |
| P/B | the justified multiple of book value |
Step 3What breaks when credit costs double?
Another 1.5 points of the book is Rs 150 crore of extra provisions. Pre-tax falls from 4.0 to 2.5 points, ROA to 1.88%, ROE to 9.4% and profit to Rs 188 crore, and because 9.4% is below the 10% growth rate, the formula returns -0.12x. A negative multiple is the model telling you the assumptions contradict each other: a lender cannot grow its book 10% a year when it earns 9.4% on equity, unless it retains every rupee of profit and still raises about Rs 12.5 crore of new equity a year. Fix the growth, not the formula. At 5% growth, which 9.4% ROE can fund with 47% paid out, P/B is (9.38 less 5) / (15 less 5) = 0.44x, about Rs 875 crore against Rs 2,000 crore in the base. Doubling credit costs has removed more than half the equity value.
| % of loan book unless stated | Base | Stress |
|---|---|---|
| Net interest margin | 8.00 | 8.00 |
| Operating cost | (2.50) | (2.50) |
| Credit cost | (1.50) | (3.00) |
| Pre-tax | 4.00 | 2.50 |
| ROA after 25% tax | 3.00 | 1.875 |
| ROE at 5x leverage | 15.0 | 9.375 |
| Growth the ROE can fund with no new equity | up to 15% | up to 9.4% |
| Justified P/B at g = 10% | 1.00x | -0.125x (invalid) |
| Justified P/B at g = 5% | 1.00x | 0.44x |
Close with the view and its limit. A lender's multiple lives on its credit costs: 1.5 points of provisions is the difference between book value and 0.44x book, which is why a buyer prices the stress case before the base. The limit is the one-stage model itself: it treats the stress as permanent. If 3% is one bad year and credit costs return to 1.5%, the value lost is roughly one year's extra provisions, Rs 112 crore after tax, not Rs 1,125 crore. The question a fund manager is really asking is whether 3% is the new normal, and that is a question about the loan book, not the formula.
Where candidates lose it
The usual slip is in the leverage: multiplying pre-tax return by 5 and getting a 20% ROE, or applying leverage to the margin before costs. ROE is after-tax ROA times book over equity, and the cost of the borrowings is already inside the net interest margin.
The second is reporting the negative price-to-book as an answer, or quietly dropping the sign. The negative is a flag that ROE has fallen below growth; the honest response is to cut the growth to what the ROE can fund and recompute.
What the interviewer asks next
- Dhanvaan raises Rs 500 crore of equity at 1.0x book. What happens to ROE and to the justified multiple?
- Why do lenders with the same ROE trade at different price-to-book multiples?
- The regulator raises the minimum capital so the book can only be 4x equity. Rework the base case.
- How would you check whether 3% credit costs is a one-year event or the new level?
Company names and figures are illustrative.