Co-Lending Economics: What Each Side Earns on Its Share

The calculator below takes one loan, divides it between a bank and a finance company in whatever share is entered, and shows what each side earns on its own share once that side has paid for the money it put in. The borrower pays one rate to both. So every rupee of difference between the two columns comes from the funding side and nowhere else.

How a shared loanOne loan to one borrower, funded by two lenders in agreed portions, with each lender carrying its portion on its own books. Covered separately. works, how one is put together and why two lenders would want to sit on the same borrower at all, is covered separately. No diagram supplies the arithmetic of who ends up with what.

One fact makes this arithmetic worth a calculator rather than a paragraph. The borrower pays one rate. Not a rate to the bank and a different rate to the finance company: one rate, on one loan, to be divided. Two lenders can therefore hold identical shares of an identical asset, at an identical rate, and come out with different amounts of money, and the reason has nothing whatever to do with the loan. The reason sits entirely on the other side of each lender's balance sheet, in what that lender paid for the money it put in.

Think of two people buying the same sack of rice at the same shop for the same price, then selling it on the same street for the same price. If one of them borrowed the purchase money from a cooperative at a low rate and the other borrowed it from a moneylender at a high rate, the two of them do not end the day with the same amount in hand. The sack was never the difference. The price each paid for the purchase money was.

What does this calculator work out for a shared loan?

Seven things go in, all of them for one stated year: the size of the pool, the rate the borrower pays on it, what each of the two sides pays for its own money, the loss assumed against the pool, the portion of the pool the bank funds, and the portion of that loss the bank carries. The portion that funds a loan and the portion that carries a default are set by different clauses and need not agree, so those last two are separate entries. Eight things come out, four for each side, and the calculator then adds them back up on the face of it.

The drawing above is the output, not the boxes underneath it. The pool is cut at the share entered, the interest it produces is cut in the same place because there is one borrower paying one rate, and each part is cut again into that side's cost of money, its share of the loss and whatever survives both. The last tier is a rate axis carrying the figure for the pool as a whole, a figure that sits between the two sides and is earned by neither.

One limit is worth saying at the top rather than at the bottom. Nothing in this written record says who found the borrower, who will chase the instalments, or what either side charges the other for doing those jobs, so the calculator does not know. The loss is not something it knows either: the loss is assumed, and so is the side that carries it. The calculator multiplies, subtracts and adds back up, and everything it cannot see stays outside it.

What does each side earn before its own funding cost comes off?

Its share of the pool multiplied by the rate the borrower pays. Nothing has to be decided on this line and nothing can go wrong on it. The line is worth pausing on for exactly that reason.

Take the worked default. The pool is Rs 1,000 crore for one stated year. The borrower pays 14.50 per cent a year on it, the yieldThe rate charged to a borrower on a loan, stated for a year. How a lender sets one, and what a lender weighs before setting it, is covered separately. Rukmini Finance Limited earns on its advances in this written record. So the pool throws off Rs 145 crore of interest for the year. Cut the pool in half and each side funds Rs 500 crore, and each side's Rs 500 crore earns Rs 72.50 crore.

Both sides earn exactly the same rupees on this line, by construction, and it is the single most useful fact in the comparison. Equal earnings on that line turn everything that follows into a controlled comparison. The borrower is the same borrower. The rate is the same rate. The share size is the same size. So whatever separates the two lenders further down cannot possibly have come from any of those, and there is only one place left for it to have come from.

The shape of that argument is worth more than the arithmetic. To find what causes a difference, the useful move is not to explain the difference but to hold everything else still until only one thing is left moving. The calculator takes one yield rather than two, and the borrower's rate therefore cannot quietly become part of the answer.

What does each side pay for the money it puts into its share?

One of the two answers is a rate. The other is not, and refusing to pretend otherwise is the most useful habit in the whole subject.

Start with the straightforward one. Rukmini Finance Limited holds no deposits whatever. Its money is borrowed in the market, and the written record states what those borrowings cost outright, at 8.50 per cent a year. Put Rs 500 crore in at that rate and the money costs Rs 42.50 crore for the year. Nothing has to be derived and nothing is in doubt.

Now Suvarna Commercial Bank Limited, where the record is less generous. The record gives interest expended of Rs 11,160 crore for the year and deposits of Rs 1,92,000 crore. One put over the other comes to 5.8125 per cent a year, reported as 5.81. The division is arithmetically correct, and the answer is not the deposit rate.

The record does not split that interest expense by source, and a bank has liabilities that are not deposits, so putting the whole expense over only the deposits can only overstate what the deposits cost. The true figure is at or below 5.8125 per cent a year. Nothing in the record says how much of the Rs 11,160 crore belonged to anything other than deposits, so how far below is unknowable and no honest reading can produce a range either. So the figure is a ceiling on the deposit rate, the deposit rate itself is not knowable from what is written down, and every rupee computed from the ceiling downstream carries that label with it.

Stating a ceiling properly rather than quickly is worth the extra words. A household knows it spent Rs 42,000/- on the whole month and that Rs 28,000/- of the spending was the rent. If someone asks what the groceries cost and the household says Rs 14,000/-, the answer is a ceiling and not a figure: the electricity, the bus fares and the school fees are all sitting inside that Rs 14,000/- too. Saying the ceiling out loud is not a weakness in the answer. The ceiling is the answer, correctly stated.

Rs 500 crore at that ceiling costs the bank Rs 29.0625 crore for the year. The figure is the most its half could be costing rather than what the half costs.

Why does the same loan produce a different spread for each side?

Because the subtraction is different, and only the subtraction is different. Take the identical Rs 72.50 crore and remove each side's own cost of money from it.

The bank keeps 8.6875 per cent a year on its half, printed as 8.69. The finance company keeps 6.00 per cent a year on its half. And 6.00 percentage points is exactly the gap Rukmini Finance Limited works on across its whole book of advances in this record. The agreement is no coincidence: the company charges 14.50 per cent a year and pays 8.50 per cent a year, and 14.50 less 8.50 is 6.00.

The difference between the two, 8.6875 less 6.0000, is 2.6875 percentage points a year, and that number is the funding cost difference and nothing else at all. Checked the other way round it comes to the same thing: 8.50 per cent a year less 5.8125 per cent a year is 2.6875 percentage points. The yield was the same yield, so the yield cancelled. The share was the same share, so the share cancelled. There was only one borrower, so the borrower cancelled.

A shared loan that never goes wrong is not the interesting case, so now assume a loss. Put 1.50 per cent of the pool against the year and Rs 15 crore comes off. Carried one half each, that is Rs 7.50 crore apiece. The bank is left with Rs 35.9375 crore on its share, or 7.1875 per cent a year, and the finance company with Rs 22.50 crore, or 4.50 per cent a year. Carry the same Rs 15 crore three quarters to the bank instead and the bank takes Rs 11.25 crore of it, leaving Rs 32.1875 crore or 6.4375 per cent a year, against the finance company's Rs 26.25 crore or 5.25 per cent a year.

Both sides moved and the figure for the loan as a whole did not move at all. On either carrying it keeps Rs 58.4375 crore on a pool of Rs 1,000 crore, or 5.84375 per cent a year, printed in the calculator as 5.8438. The 5.8438 is the number a reader is likeliest to lift out and quote, and it is the one figure on the whole loan that nobody lending on it earns. The pool's figure is not the bank's 7.1875 or 6.4375, and it is not the finance company's 4.50 or 5.25. The figure belongs to the loan. Two parties can both quote it, both be arithmetically correct, and both be describing money that is not theirs.

The gap is said that way rather than as 8.69 less 6.00. Two figures already rounded, subtracted from each other, produce an answer that looks derived and is not quite: here it happens to land on 2.69 either way, and on a different set of figures it would not. The subtraction comes before the rounding, every time.

What share should be entered, and who decides the share in practice?

Whatever share is actually under examination. The calculator takes anything from nought to a hundred per cent and suggests nothing, and the one half it opens on was chosen for one reason only: halves are the easiest arithmetic in the world to check by hand, and a default that can be verified in the head is a default that earns trust for the entries that cannot.

One half is a legibility choice. Halves are not a convention, a norm or a requirement. Drag it anywhere, nought included, and the drawing shows what happens rather than refusing.

The slider cannot supply the share each side is permitted or obliged to keep. A permitted share is a rule, set by an authority and revised by it. Six separate things about an arrangement of this sort work that way, and each of the six sits with the Reserve Bank of India: what each side must retain, how the loan counts against a lending target set for the bank, what the borrower has to be told about the loan being shared and about who is holding it, what each side must put in its own reporting, the conditions attaching to the rate the borrower may be charged and to how that rate is disclosed, and how each side provides against the loan if it stops paying.

A rule written down from memory stops being merely dated the morning it changes. The rule becomes false, and nothing in the wording marks the change. So a condition of this kind is named below with the address of the authority that sets it, and filled from that source on the day it is needed.

What can a spread on one loan not say about either institution?

Almost everything worth knowing. A reader who has just watched one side keep 8.6875 points and the other keep 6.00 is standing one short step away from a sentence that is not true.

The 8.6875 and the 6.00 describe what happens to one asset sitting on two different balance sheets. The two rates do not describe either business. A rate a year on one loan has no staff in it, no branches, no systems, no tax, no fee income, no credit costWhat a lender sets aside or writes off across its whole book because some borrowers do not repay. Covered separately. beyond whatever was assumed against this one loan, and no borrowed money multiplying whatever is left over a much smaller base of net worthWhat is left of a business once everything it owes has been taken off what it holds. Covered separately.. Every one of those sits between the loan and the institution, and every one of them is missing here.

So take the two lenders whole and look at what actually comes out. Both of them return 9.375 per cent on equity for the stated year, reported as 9.38, and those two figures are equal on purpose rather than by accident. The two were built to be equal. An identical number arriving with no explanation reads like somebody copied a cell twice, and a reader who decides the number is a typing error has learned nothing from it at all, so the reason is worth saying in plain words.

The equality has a purpose. Suvarna Commercial Bank Limited reaches 9.375 per cent on equity by earning 0.9375 per cent on each rupee of its assets and running assets at 10.0 times its net worth. Rukmini Finance Limited reaches the identical 9.375 per cent by earning 1.875 per cent on each rupee of its assets, exactly double, and running assets at 5.0 times its net worth, exactly half. Half the return per rupee, twice the leverageHow many rupees of assets a business runs for each rupee of its own net worth. Taken apart properly elsewhere; used here only as one of the two limbs., and the same answer arrives twice. Rank these two on return on equity alone and the ranking cannot tell them apart, and they are not the same business in any respect whatever.

A trap sits in plain sight in the last three rows. Look hard at them. Multiplying the reported limbs gives 9.40 per cent on both sides, and 9.40 is not 9.38. Nothing is broken. The reported returns on assets are roundings: 0.9375 rounds to 0.94 and 1.875 rounds to 1.88, and it is only the unrounded figures that tie, at 0.9375 multiplied by 10.0 and 1.875 multiplied by 5.0, both of which give exactly 9.375. The exact 9.375 is what rounds to 9.38. A reader handed 0.94, 10.0 and 9.38 with no note attached will multiply, land on 9.40, and reasonably conclude the arithmetic does not add up. The unrounded limb is therefore printed beside the reported one rather than left in a working file.

The everyday version is exact rather than approximate. A comparison that exact is worth having. Two people each put Rs 1,00,000/- of their own money into a shop and each ends the year Rs 9,375/- better off. One of them carries Rs 10,00,000/- of stock with Rs 9,00,000/- of it borrowed, and that stock returns 0.9375 per cent. The other carries Rs 5,00,000/- with Rs 4,00,000/- borrowed, and returns 1.875 per cent on it. Same answer. Nobody who has stood in both shops would call them the same shop.

What does this calculator not settle?

Which side has the better deal, and it is important to see that this is not modesty. A share of a loan is not the whole of an arrangement, and the parts that are missing are precisely the parts two lenders would spend their time negotiating.

Somebody found this borrower, checked them and signed them up, and that work is originationThe work of finding a borrower, assessing them and getting the loan signed. Somebody does that work and it costs money. Not entered anywhere in this calculator.. Origination costs money and is nowhere in this arithmetic. Somebody will collect the instalments, answer the borrower's calls and chase the ones that come late, and that work is servicingCollecting and administering a loan after it is made, month after month, until it is repaid. Also not entered anywhere in this calculator.. Servicing costs money too and is also nowhere in this arithmetic. If one side does those jobs for both, a fee normally passes between them for it, and the written record states no such fee, so no fee reaches the arithmetic. And when a borrower stops paying, who carries what is a term of the arrangement rather than a consequence of the arithmetic. The loss carrying is a separate entry in the calculator for exactly that reason, rather than something assumed to follow the funding.

Neither way of running a lending business is shown here to beat the other, and the reason for that is structural rather than polite. Higher leverage is not recklessness, and a wider gap between what a lender charges and what it pays is not skill. Each lender here is one institution in one year. The record contains no downturn, no second year and no failure of any kind, so neither of them can be evidence about what its way of doing business achieves. The arithmetic is stated, and what the arithmetic cannot settle is named.

Who actually reaches for this arithmetic, and what for?

Three people, and none of them is trying to decide which lender is better.

A credit officer at the finance company uses it before a conversation rather than after one. If the tool says the bank's half throws off 2.6875 points a year more than its own half does, that is the size of the thing the two sides are actually negotiating over when they talk about who does the origination and the servicing and what that is worth. Knowing the number does not tell anybody what to ask for. The number tells them what order of magnitude the conversation is in, and that is a different and more useful thing.

An analyst reading two lenders' own reporting uses it as a check on a story rather than as a source of one. If a lender's disclosure says its shared loan book earns a wide gap, the analyst can reconstruct roughly what that implies about the cost of the money behind it, and see whether that squares with what the same lender reports about its funding elsewhere. Two numbers that will not sit together are worth a question. The check is the whole use.

And a treasury desk uses it backwards, the most honest use of the three. The desk already knows what its own money costs. The desk wants the yield at which a share of a given size stops being worth having once its own costs are laid against it, and it finds that yield by moving the borrower's rate down until the number it cares about goes where it goes. The calculator prints negative readings for exactly that reason: a tool that refuses to show the bad side of a line is not much use for finding where the line is.