Loan Book Economics: What One Rupee of Lending Earns

Loan book economics is what one rupee of a lender's book earns, what that rupee costs to fund, and what is left over at the end for the lender's own money. Trace the funding first. Rukmini Finance Limited, an invented lender, carries Rs 18,000 crore of assets under management funded by Rs 14,400 crore of borrowings and Rs 3,600 crore of net worth, and every line below that split follows from it.

What does one rupee of this book earn once everything has come out of it?

The instrument opens on Rukmini Finance Limited's recorded year, and every figure it shows there is printed again in the table further down: a book of Rs 18,000 crore, net interest income of Rs 1,386 crore standing at 7.70 per cent on it, Rs 450 crore before tax and Rs 337.50 crore after, reading 1.875 per cent against that book and 9.375 per cent against net worth. Six buttons move it somewhere worth seeing. One rebuilds that same 9.375 per cent on net worth out of a book of Rs 36,000 crore yielding 11.50 per cent, where the return per rupee of book halves to 0.9375 per cent and leverage doubles to 10.00 times. One reprices the borrowing by a single point to 9.50 per cent. Interest paid rises to Rs 1,368 crore, a cost of Rs 144 crore that takes 32.00 per cent of the year's profit before tax with it. One raises credit cost to Rs 846 crore, or 4.70 per cent of the book, where profit before tax is exactly nil. One goes a notch past that to Rs 900 crore, leaving a shortfall of Rs 54 crore for the year. One halves the operating line to Rs 270 crore. Profit before tax rises to Rs 720 crore and the return on net worth to 15.00 per cent. At any setting, the panel keeps the wrong reading on screen beside the right one. The amount by which the two differ is where loan book economics lives.

A loan book is not a product with a margin printed on it. A loan book is a pile of somebody else's money lent out at a higher rate than it was raised at, with the lender's own money sitting underneath as the part that absorbs whatever goes wrong. Think of a wholesaler on a market street who buys stock on thirty days of supplier credit and puts a little of his own cash in as well. The load the wholesaler can carry is decided the moment those two amounts are added up, not by how fast the stock moves. A lender works the same way round. The liability decides the business, so the honest way to build the economics is from the funding side down.

What is loan book economics measuring, and on what base?

Loan book economics measures one year of a book that already exists, layer by layer, with every layer divided by the same number. The divisor is Rukmini Finance Limited's assets under managementEverything a lender currently has out on loan, counted together at one date. Every other figure in the stack is divided by that one total. of Rs 18,000 crore. The measure is not a rate on one loan and it is not the profit on a product. The measure is the whole book reduced to a stack of percentages. All of them sit on one base for one year, and that is what lets them add and subtract.

Watch the base. A careful reader loses control of the arithmetic there without noticing. A margin on assets and a cost on borrowings are both honest figures struck on two different numbers, so neither can be added to or subtracted from the other until each has been turned into an amount. A figure struck on a different base does not belong in the same stack, however sensible it looks sitting there. Every figure in this guide divides on Rs 18,000 crore, for one year.

Where does the money come from before any of it is lent?

Rukmini Finance Limited takes no deposits. Every rupee it lends was either borrowed in the market or is its own. Borrowings are Rs 14,400 crore and net worthThe lender's own money in the business: what would be left over for the shareholders if every asset were realised and every liability settled. is Rs 3,600 crore, and those two add to Rs 18,000 crore exactly. There is nothing else on that side of the balance sheet to add. Borrowings are 80.0 per cent of assets under management and net worth is 20.0 per cent, and the two shares reach 100.0 per cent because the funding side is only those two blocks. Borrowings are 4.0 times net worth. Assets under management are 5.0 times net worth, and that second multiple is the one that will matter at the end.

What does one rupee of the book earn, and what does it cost to fund?

The rate Rukmini Finance Limited charges out is 14.50 per cent for the year, and it is charged on the book, so Rs 18,000 crore at that rate brings in Rs 2,610 crore. The rate it is charged is 8.50 per cent for the year, and that one falls on what it borrowed, so Rs 14,400 crore at that rate takes out Rs 1,224 crore. Read those two sentences again and notice what is different about them: the first rate is charged on the whole book, the second is charged only on the borrowed part of it. The two rates are struck on two different numbers, so subtracting one rate from the other does not produce an amount that anybody owes or receives.

Turn each rate into rupees first, then subtract. Rs 2,610 crore less Rs 1,224 crore is Rs 1,386 crore, and that is Rukmini Finance Limited's net interest income for the year, before a single other cost has been taken out of it. Net interest income is the layer every other layer sits on, and it is also the layer where the most common reading error on any lending business is made.

Why is the margin wider than the spread between the two rates?

Net interest income of Rs 1,386 crore over assets under management of Rs 18,000 crore is 7.70 per cent for the year. The spread between 14.50 per cent a year and 8.50 per cent a year is 6.00 percentage points. The margin and the spread are not the same number. The gap is 1.70 points, and it is neither a rounding artefact nor a mistake. The gap has a cause that can be computed in two lines.

Line one. If every rupee of the book had been borrowed, the book would earn the spread on all of it: 6.00 per cent of Rs 18,000 crore is Rs 1,080 crore. Line two. Rs 3,600 crore of the book is not borrowed, so the 8.50 per cent a year that would have been paid on that slice is never paid: 8.50 per cent of Rs 3,600 crore is Rs 306 crore. Put the two together. Rs 1,080 crore alongside Rs 306 crore comes to the same Rs 1,386 crore that subtracting the two amounts produced. The panel above closes that reconciliation on nil at every setting. Nothing about the lender's own money is idle: it is out there carrying assets and charging the lender nothing to do so, and that single fact accounts for the entire gap between the margin and the spread.

What comes out of that margin, and in what order?

Two more layers come out, and both of them divide on the same Rs 18,000 crore for the same one year. Operating expenses are Rs 540 crore, or 3.00 per cent of assets under management. The operating line is what it costs Rukmini Finance Limited to run itself: the people, the systems, the collections work, and what is paid to a lending service providerA partner that finds, services or collects loans for a lender while never holding one on its own books. The rules governing such an arrangement sit elsewhere. that sources or services loans on its behalf. Running the business costs that much whether or not a single loan goes wrong. Then credit costWhat a year of lending actually cost, charged in that year's accounts. A separate treatment covers where it comes from and how it differs from the provision recognised on the balance sheet. of Rs 396 crore, or 2.20 per cent of the same base. Credit cost is a charge in this lender's own accounts for the year, and it is a statement about the book, never about anybody who borrowed from it.

Now stack them. 7.70 less 3.00 less 2.20 is 2.50, so profit before taxWhat is left after every operating cost and every charge for the year, but before any tax is taken out of it. is 2.50 per cent of assets under management, which on Rs 18,000 crore is Rs 450 crore. The same stack in rupees runs Rs 1,386 crore less Rs 540 crore less Rs 396 crore. The answer is the same Rs 450 crore. The two routes land together only because no layer switched denominator on the way down, and running both of them is the cheapest check available on any lending stack.

What is left, and what does it become on the lender's own money?

Tax at 25.0 per cent of Rs 450 crore is Rs 112.50 crore, so Rukmini Finance Limited's profit after tax for the year is Rs 337.50 crore. Now divide that one figure twice. Against assets under management of Rs 18,000 crore it is 1.875 per cent. Against net worth of Rs 3,600 crore it is 9.375 per cent. Nothing about the business changed between those two readings. The same rupees of profit met a smaller denominator the second time.

The step between the two readings is leverage, and it is a multiplication rather than a coincidence: assets under management are 5.0 times net worth, and 1.875 per cent times 5.0 is 9.375 per cent. The step is plain arithmetic rather than anybody's named framework. The shape is a return per rupee of assets, multiplied by how many rupees of assets each rupee of the lender's own money is carrying.

Why do the printed figures not reproduce each other?

Rounded figures that refuse to reproduce each other trip careful readers, and the reason almost never gets said out loud. The figures usually reported for a lender like Rukmini Finance Limited are 1.88 per cent on assets under management, 5.0 times leverage, and 9.38 per cent on net worth. Multiplying the first two gives 9.40, not 9.38. Nothing in that multiplication is wrong. The reported limbs are rounded to two places. The reported product was computed from the unrounded ones: 1.875 times 5.0 is 9.375, and 9.375 itself reports as 9.38. Rounding 1.875 up to 1.88 before multiplying is what adds the extra 0.02.

When a printed number cannot be rebuilt out of the numbers printed next to it, what it costs is trust, and trust is dearer than the space two more decimals take up, so the unrounded limb is set beside the rounded one everywhere the split appears. A reader who checks the arithmetic and finds it does not tie has two conclusions available, that the source is wrong or that they are, and most pick the second and stop checking anything after that. The remedy costs nothing: 1.875 and 5.0 and 9.375 printed, with a note beside them of how each is normally rounded.

The whole year on one base, in one table

Interest paid there reads 6.80 per cent against assets under management, not the 8.50 per cent a year charged on the borrowings. Rs 1,224 crore over Rs 18,000 crore is 6.80 per cent, and the 8.50 per cent was struck on Rs 14,400 crore instead. And 14.50 less 6.80 is 7.70, the margin again. Every figure in the third column has been re-expressed on the one base, and only that makes the column subtract cleanly from top to bottom.

What happens to all of it if the lender borrows more against the same net worth?

Hold Rukmini Finance Limited's net worth at Rs 3,600 crore and let borrowings vary. The book earns 14.50 less 3.00 less 2.20 after both costs, or 9.30 per cent a year on assets. The borrowed part costs 8.50 per cent a year on borrowings. Rearrange those two and profit before tax is 9.30 per cent of net worth plus 0.80 per cent of borrowings. At Rs 3,600 crore and Rs 14,400 crore that is Rs 334.80 crore plus Rs 115.20 crore. The total is Rs 450 crore exactly, the same figure the stack gave.

The second limb is smaller than most readers expect. Each borrowed rupee adds only 0.80 percentage points, being what the book earns after costs less what the borrowing costs, and leverage is nothing more than that thin margin repeated a great many times. A trader who buys at Rs 100/- and sells at Rs 100.80/- is not running a wide business, but a trader doing it four times over on borrowed stock has quadrupled a thin thing rather than found a fat one. A thin margin repeated many times over is the honest picture of a levered lender, and the control below moves it.

Why is the line straight, and what would bend it?

The line is straight because nothing in these figures is allowed to move when borrowings move. The worked year holds Rukmini Finance Limited's cost of borrowings at 8.50 per cent a year and its credit cost at 2.20 per cent of assets under management at every level of borrowing, and it contains one year, no second year and no failure event of any kind. Under those holds the 0.80 point margin on each borrowed rupee cannot change, so the return can only rise by 0.30 points for every Rs 1,800 crore added, seventeen settings in a row.

In an actual funding market a lender that borrows a great deal more against the same net worth is generally asked to pay more for it, and the extra it is asked to pay is what would bend the line downwards at the far end. Nowhere in these figures is there a price for heavier borrowing, and without one there is nothing to bend the line with. The straight line shows the arithmetic of leverage and shows nothing whatever about the behaviour of anybody's funding market, and a reader who does not hear that difference will walk away holding the second thing.

What has to keep happening on the funding side for any of this to hold?

Rukmini Finance Limited takes no depositMoney the public places with a bank, repayable on demand or at an agreed date. Which institutions may accept deposits, and what cover applies to them, is set separately. of any kind, so every rupee of its Rs 14,400 crore of borrowings has a lender on the other side who has to choose, again and again, to keep lending. An advanceA loan a lender has actually paid out and is carrying on its own books, as opposed to one merely sanctioned. made for three years does not care what happens next month. The borrowing that funded it very much does. An asset side that runs for years is funded by a liability side that has to be renewed, so the return the control moves is available only for as long as the funding is. That is a difference in kind rather than in degree.

Picture a shopkeeper who buys stock on supplier credit and sells it over four months. The stock sells at its own pace, but the supplier decides every month whether to keep extending the credit, and a month when the supplier says no does not wait for the stock to clear. RefinancingReplacing a borrowing that is falling due with a new one, so that the money stays in the business rather than having to be repaid out of it. is that same monthly conversation, at the scale of Rs 14,400 crore. None of it appears in the stack above. The stack measures a year that already happened, and that is exactly why the funding side was traced first rather than last.

How does somebody assessing a lender actually use this stack?

Somebody sizing up a finance company, whether they are lending it money, buying its shares or supplying it with loans to fund, reads the stack the same way and in the same order. First they check the base. If the margin is on assets under management and the operating line is on advances and the credit line is on something else again, the stack does not subtract and the conclusion drawn from it is worthless. Second they read the two limbs rather than the return on net worth. On its own, 9.375 per cent says nothing about whether it came from a fat book or a thin book carried many times over.

Third, and this is the habit that separates a real assessment from a ratio comparison, they ask what has to be renewed and how often. A book earning 9.30 per cent after costs and funded at 8.50 per cent is running on a 0.80 point cushion per borrowed rupee, and a funding market that repriced by even half a point would take a large bite out of it. Answering it needs a series of funding costs rather than a single figure, and a series is looked up rather than recalled: the Reserve Bank of India's data site at dbie.rbi.org.in is where such a series is found. One year of one lender says nothing about how that cushion behaves over a cycle.

What none of this settles

Run the same arithmetic on Suvarna Commercial Bank Limited, invented, and it gives 0.9375 per cent on total assets multiplied by 10.0 times leverage, which is also 9.375 per cent on net worth. The two lenders land on exactly the same return on their own money from opposite limbs: half the return per rupee of assets against twice the leverage. The equality is the whole point: rank lenders on return on net worth by itself and two utterly unlike businesses come out indistinguishable. The decomposition is the teaching here; the ratio on its own is not.

A lender that levers further is not thereby reckless, and a lender working a wider spread is not thereby skilful. No verdict on which of the two arrangements is the better business follows from a single year, nothing before it, no cycle, and no episode anywhere in these figures of anything going wrong. An invented lender with a good-looking stack is evidence of arithmetic and of nothing else at all.