LBO Returns: The Money Multiple and the Rate Behind It

A buyout return is measured two ways. The money multiple is money out over money in. The internal rate of return puts a year on it. The worked structure returns Rs 28,80,15,00,000 on Rs 12,00,00,00,000, being 2.40 times over five years and 19.14 per cent a year, and the Rs 16,80,15,00,000 of value created splits four ways and reconciles to the rupee.

The arithmetic is identical in a shop, and the numbers there are small enough to hold in the head, so a shop makes the starting point. A woman buys a small tailoring unit for Rs 20,00,000. She puts in Rs 8,00,000 of her own savings and the unit borrows Rs 12,00,000 against its machines. Five years later she sells the unit for Rs 30,00,000 and the borrowing is down to Rs 4,00,000, so Rs 26,00,000 comes to her. She put in Rs 8,00,000 and took out Rs 26,00,000.

Then comes the harder question. She made three and a quarter times her money. Where did it come from? The unit stitches more garments now, so some of it came from the unit being worth more than she paid. Some came from the borrowing being smaller at the end than it was at the beginning. A smaller borrowing does nothing to the unit and everything to her share of it. Some may have come from tailoring units simply being fashionable to buy this year. And a slice went out of the door on day one, to the lawyer who wrote the sale deed and to the lender who charged an arrangement fee. The four causes are exhaustive, they add back to the whole, and separating them is the difference between knowing what a return was and knowing what it came from.

Everything below is that shop with more zeros. Sthira Capital Partners, an invented buyout firm, has bought Sankalp Industrial Systems Limited, an invented maker of industrial valves, and the return comes apart the same four ways.

How is the return on a buyout actually measured?

By two numbers, and they are not alternatives. The first is the money multipleMoney returned divided by money put in, with no account taken of how long it took.. Take what came back to the buyer at the end and divide it by what the buyer put in at the start. Nothing else enters. In the worked structure, Rs 28,80,15,00,000 came back against Rs 12,00,00,00,000 put in, so the money multiple is 2.40 times.

The second is the internal rate of returnThe annual rate that turns the money in into the money out over the holding period.. The rate asks a different question: at what annual rate would the money put in have had to grow, compounding, to arrive at the money that came out, over the number of years it actually took? Here that rate is 19.14 per cent a year over a five year hold periodThe number of years between completion and exit..

Both are computed from exactly the same three facts: what went in, what came out, and how long it took. The multiple uses two of the three. The rate uses all three. The third fact is the entire difference between the two measures, and it is why printing only one of them withholds something.

There is a household version of this that settles it in one line. Two neighbours each turn Rs 1,00,000 into Rs 2,40,000. One of them took three years and one took eleven. Both can truthfully say they made 2.40 times their money. Nobody would call those the same result, and the only thing separating them is a fact the multiple does not carry.

What does 2.40 times mean over three years, five and seven?

Three quite different things, and the translation between the two measures is a single line of arithmetic. The rate is the money multiple raised to the power of one over the number of years, less one. In this structure the money goes in once at the start and comes out once at the end. Nothing more elaborate is needed for that shape.

The same 2.40 times run through three different hold periods gives 33.89 per cent a year over three years, 19.14 per cent over five, and 13.32 per cent over seven. The money multiple is identical in all three. A multiple with no hold period attached to it is not a return figure at all; it is one half of one.

What exactly goes into the calculator?

Five inputs, all stated in full here. A return figure built on a number the reader has to go and find is not checkable. How the structure was assembled, which lender demanded what, and who holds what after completion are set out separately. The calculator needs only these five.

The entry. Sthira Capital Partners buys the business at 8.50 times Year 0 earnings before interest, tax, depreciation and amortisation (EBITDA) of Rs 2,88,00,00,000. The entry enterprise value is therefore Rs 24,48,00,00,000. Borrowing put in place at entry, Rs 13,00,00,00,000. The sponsor's own equity cheque, Rs 12,00,00,00,000. Fees paid on completion, Rs 52,00,00,000. Hold period, five years.

The exit. At the end of Year 5, at the same 8.50 times, on Year 5 EBITDA of Rs 4,32,00,00,000. The exit enterprise value is Rs 36,72,00,00,000. Net debt at exit, Rs 7,91,85,00,000. Exit equity is therefore Rs 36,72,00,00,000 less Rs 7,91,85,00,000, being Rs 28,80,15,00,000. How the borrowing fell from Rs 13,00,00,00,000 to Rs 7,91,85,00,000 year by year is worked through separately; here it is an input.

The most important item on the input list is that the entry multipleThe multiple of earnings at which the business was bought. and the exit multiple are both 8.50 times, deliberately. The structure assumes no multiple expansionSelling at a higher multiple than the one paid, which contributes nothing at all in this worked structure. whatever. Holding the two multiples equal is unusual, and it is unusual on purpose. Every rupee of the eventual return then has to come from somewhere a reader can point at.

One more input matters and it is an assumption rather than a fact: the operating case behind the exit was written by the buyer itself. The buyer's case differs from the company's standalone forecast in exactly two named ways and no others. Capital expenditure is held flat at Rs 90,00,00,000 a year rather than rising from Rs 1,34,80,00,000 to Rs 1,54,00,00,000, and the movement in net working capital is held at Rs 12,00,00,000 a year rather than Rs 18,00,00,000. Revenue and EBITDA are unchanged from the standalone forecast. Nothing in this return rests on the buyer assuming the business gets better at selling valves.

Why must the four causes add back to the whole?

Value createdExit equity less the equity originally put in. is Rs 28,80,15,00,000 less Rs 12,00,00,00,000, being Rs 16,80,15,00,000. The Rs 16,80,15,00,000 is the quantity being explained. A decompositionSplitting a return into causes that add back to it exactly. is only worth the name if the causes it names come to that figure exactly, with no residual and no rounding plug.

The four causes do come to that figure, and there are only four. Only four things can move the equity value of a company that has been bought and is being sold again. The business can earn more. The borrowing against it can be smaller. The market can pay a different multiple for the same earnings. And money can leave for something that is not an asset. There is no fifth thing.

Written out, the four are these. One, growth in earnings valued at a constant multiple, Rs 12,24,00,00,000. Two, debt paydownThe reduction in borrowing over the hold period, which converts directly into equity., Rs 5,08,15,00,000. Three, change in the multiple, Rs 0. Four, fees, minus Rs 52,00,00,000. Add them: 12,24,00,00,000 plus 5,08,15,00,000 plus 0 less 52,00,00,000 is Rs 16,80,15,00,000. The sum is the value created to the rupee.

How much of it came from the business earning more?

Most of it, and this is the number that surprises people. EBITDA at Year 0 was Rs 2,88,00,00,000 and at Year 5 it is Rs 4,32,00,00,000, so it grew by Rs 1,44,00,00,000 over the hold. The growth in EBITDA is worth the exit multiple. At 8.50 times, Rs 1,44,00,00,000 of extra EBITDA is Rs 12,24,00,00,000 of extra enterprise value at the moment of sale, and since the borrowing is a separate line, every rupee of it lands on the equity.

The Rs 12,24,00,00,000 is 72.85 per cent of the value created. Nearly three quarters of what the buyer made came from the company earning more, on a case where the buyer assumed no improvement in margin and no improvement in revenue beyond what the company's own forecast already had. The leverage is not what produced most of this return, and the arithmetic says so plainly.

Notice the mechanism. The multiplier lives inside it. A rupee of extra EBITDA is not worth a rupee. A rupee of extra EBITDA is worth whatever multiple the business sells at. The buyer at the far end is paying for the earnings stream and not for one year of it. At 8.50 times, every rupee of EBITDA the business adds is worth eight rupees and fifty paise on the day it is sold. The multiplier cuts both ways: a rupee of EBITDA lost is worth minus eight rupees and fifty paise on the same day.

How much came from repaying the borrowing?

Rs 5,08,15,00,000, being Rs 13,00,00,00,000 at entry less Rs 7,91,85,00,000 at exit. The repayment is 30.24 per cent of the value created, and the mechanism behind it is the simplest of the four.

Equity is what is left of the business after the lenders are paid. So if the business is worth the same amount at the end as at the beginning, and the borrowing against it has fallen by Rs 5,08,15,00,000, then the equity is larger by exactly Rs 5,08,15,00,000. Not more, not less, and with no multiple applied to it. Repayment of borrowing converts into equity one rupee for one rupee. A structure can therefore create value for its shareholder without the business being worth a paisa more than the day it was bought.

The tailoring unit again. Her machines are worth the same at the end of five years as at the start. But the loan against them fell from Rs 12,00,000 to Rs 4,00,000, so her share of the same machines rose by Rs 8,00,000. Nothing happened to the machines. Everything happened to the claim ahead of her.

A buyout shows that conversion more plainly than an ordinary company does. In an ordinary company, cash generated is spent, invested, or paid out. Here it is contractually pointed at the borrowing, so the arithmetic of the conversion is visible rather than buried. The mechanics of how that repayment is scheduled and swept are covered separately.

What did the change in the multiple contribute?

Nothing. Rs 0, being 0.00 per cent of the value created. The business was bought at 8.50 times Year 0 EBITDA and sold at 8.50 times Year 5 EBITDA, and a term that measures the effect of the multiple moving is zero when the multiple does not move.

The entry multiple of 8.50 times sits above the 7.78 times at which the same company traded before any of this, and the gap still contributes nothing to the return. The gap is a fact about the price the buyer paid for control. The buyer is on the paying side of that gap, so it is not a source of return to the buyer. The return term is about the multiple at which the business is sold compared with the multiple at which it was bought, and those two are identical.

A structure whose return depends on selling at a higher multiple than it bought at is depending on a judgement made by somebody else, five years later, about a market the buyer does not control. Holding the two multiples equal is what makes this worked example honest: it removes the one term that can flatter a result without anybody having done anything.

Turn the term around and it becomes a warning. Had the same business been sold at 7.50 times rather than 8.50, the exit enterprise value would have been one turn lower on Year 5 EBITDA of Rs 4,32,00,00,000, and the whole of that would have come off the equity. The multiple term is the one an experienced reader looks at first. It is the largest single number in most real splits, and it is the one attributable to nothing the buyer did.

What did the fees cost the return?

Minus Rs 52,00,00,000, being minus 3.09 per cent of the value created. Fees are the only negative term in the four, and the only one that nothing the business does can ever earn back on its own account.

Completion morning makes the term concrete. Look at what happens. The business is worth Rs 24,48,00,00,000 and it carries Rs 13,00,00,00,000 of borrowing, so the equity underneath the sponsor is worth Rs 11,48,00,00,000. The sponsor wrote a cheque for Rs 12,00,00,00,000. The sponsor is Rs 52,00,00,000 behind before a single valve has been sold, and that Rs 52,00,00,000 is exactly the fees: Rs 32,00,00,000 of financing fees and Rs 20,00,00,000 of advisory and other transaction fees.

The fees bought no machine, no order book and no customer. The Rs 52,00,00,000 appears in no valuation of the company at any date. The first Rs 52,00,00,000 of value this structure creates is spent getting back to level, and every return figure in this guide is computed after that hole has been climbed out of.

The household version is a house purchase. A couple buys a flat for Rs 60,00,000 and pays Rs 3,00,000 in stamp duty, registration, brokerage and legal costs. The morning after, the flat is worth Rs 60,00,000 and they have spent Rs 63,00,000. Nobody cheated them. The Rs 3,00,000 was the cost of the transaction rather than the cost of the flat, and the flat has to appreciate by Rs 3,00,000 before they are level.

Does the split reconcile, and what about the rounding?

The split reconciles in rupees, and the rupees are where the check lives. Rs 12,24,00,00,000 plus Rs 5,08,15,00,000 plus Rs 0 less Rs 52,00,00,000 is Rs 16,80,15,00,000, and Rs 16,80,15,00,000 is exit equity less the cheque. Two independent routes to one figure. Any attribution that does not add back to that figure to the rupee is a story about a return rather than a decomposition of one.

The percentage column is a display of the same four rupee figures and carries less information than they do. Computed on the unrounded values the four shares are 72.850638, 30.244323, 0.000000 and minus 3.094962 per cent, which sum to 100 exactly because they are four parts of one whole. Printed to two decimal places the four shares are 72.85, 30.24, 0.00 and minus 3.09, and those four printed figures also sum to 100.00. The three rounding adjustments happen to cancel.

The honest treatment of a percentage column is a real skill, and the cancelling is where it shows. Rounding each share once, from its full value straight to the two places to be printed, gives a fee share of minus 3.09 per cent. Rounding it twice, first to four places, giving minus 3.0950, and then to two, gives minus 3.10, at which point the four printed shares no longer sum to 100.00 and the percentage no longer ties to the rupee figure beside it. Round once, at the end, and never rebuild one printed figure out of another printed figure. If a set of printed shares does come to 99.99 or 100.01, the treatment is to say so and change nothing, because a figure nudged to make a total look tidy has stopped being a check.

Why does the buyer's cheque move rupee for rupee with the price?

Because everything sitting between the entry enterprise value and the sponsor's cheque is a fixed amount, and it can be derived rather than assumed. Take the funding statement for this transaction, built out separately, and rearrange it.

The amount that has to be paid is the entry enterprise value less Rs 4,40,00,00,000, being the price for all the shares, plus Rs 6,00,00,00,000 to repay the borrowing already there, plus Rs 60,00,00,000 for the minority stake, plus Rs 52,00,00,000 of fees. The uses come to the entry enterprise value plus Rs 2,72,00,00,000. The sources other than the sponsor's own cheque are Rs 9,00,00,00,000 of senior term loan, Rs 4,00,00,00,000 of subordinated notes, Rs 1,20,00,00,000 of cash already at the company and Rs 1,00,00,00,000 from selling the assets that sit outside the operating business, being Rs 15,20,00,00,000.

Subtract. Sponsor equity always equals the entry enterprise value less a flat Rs 12,48,00,00,000. The fixed wedgeThe constant difference between the entry enterprise value and the sponsor's equity cheque, made up of borrowing and other sources that do not change with the price. does not move when the price moves. Check it at the struck price: Rs 24,48,00,00,000 less Rs 12,48,00,00,000 is Rs 12,00,00,00,000, which is the cheque exactly.

The consequence is the whole of the next two sections. One turn of entry multiple is one times Year 0 EBITDA of Rs 2,88,00,00,000. Since the wedge is fixed, that entire Rs 2,88,00,00,000 lands on the sponsor's cheque and nowhere else. The seller receives Rs 2,88,00,00,000 more and the buyer funds Rs 2,88,00,00,000 more, from its own pocket, with not a rupee of it borrowed.

What happens to the return as the entry price changes?

The return falls. Everybody expects that much. Almost nobody expects the reason, and the ladder below makes it visible. Six entry multiples from 7.50 to 9.50 times, with the exit held at 8.50 times throughout and every other input untouched.

Read the third column down. The debt package does not change with what the buyer pays, so exit equity is Rs 28,80,15,00,000 at every single row. The numerator of the return never moves at all, and the entire relationship between price and return is a denominator effect.

The denominator effect runs counter to instinct. Instinct says a buyer who pays more gets more, or at least gets something. Here the buyer who pays a turn more gets exactly the same Rs 28,80,15,00,000 back. The exit enterprise value is fixed by Year 5 EBITDA at 8.50 times whatever was paid at the front, and the borrowing put in place at entry is fixed at Rs 13,00,00,00,000 whatever was paid at the front. Only the cheque moves.

The steps are not even, and it pays to notice. Moving up a whole turn from the struck 8.50 to 9.50 times costs 5.02 points of return, from 19.14 to 14.12 per cent, and hands the seller another Rs 2,88,00,00,000. The same turn taken downward, from 8.50 to 7.50 times, is worth 6.72 points, from 19.14 to 25.86 per cent. Half a turn either side of the struck price is worth roughly two and a half to three points. The numerator is constant while the denominator grows, so the rupees move in a straight line and the rate does not.

What is the highest price that still reaches a required return?

The arithmetic turns around here and becomes useful to somebody deciding something. Instead of asking what a price produces, fix the answer and solve for the price. A buyer with a required returnA rate the buyer has decided it needs, which turns a valuation into a ceiling on a price. of 20.00 per cent a year over a five year hold can work out the most it can pay in three steps.

Step one. Exit equity is Rs 28,80,15,00,000 and that does not move with the price, as the ladder has just shown. Step two. Discount it back five years at 20.00 per cent: divide by 1.20 to the fifth, which is 2.48832, giving Rs 11,57,47,00,000 rounded to the nearest crore. Rs 11,57,47,00,000 is the most the cheque can be. Step three. The cheque is always the entry enterprise value less that amount, so add the fixed wedge of Rs 12,48,00,00,000. The maximum entry multipleThe highest price at which a structure still reaches a stated required return. is an entry enterprise value of Rs 24,05,47,00,000, being 8.3523 times Year 0 EBITDA, printed as 8.35 times.

Two things fall out of that and both are worth carrying. The first is a check on the wedge itself. The wedge was derived from the funding statement, not assumed, and it reproduces two separately locked figures: the Rs 12,00,00,00,000 cheque at 8.50 times, and this Rs 24,05,47,00,000 ceiling from the Rs 11,57,47,00,000 present value. A relationship that regenerates two known answers from two different directions has earned some trust.

The second is that a required 20.00 per cent over five years is the same statement as a required money multiple of 2.48832 times, printed 2.49 times. Raising 1.20 to the fifth gives exactly that figure. The two measures at the top of this guide are two spellings of one requirement.

Now compare with what happened. The deal was struck at 8.50 times, being Rs 24,48,00,00,000. The struck price sits Rs 42,53,00,000 above the ceiling, or 1.77 per cent above it, or about a seventh of a turn. The overshoot is the entire reason the structure returns 19.14 per cent rather than 20.00, and a small overshoot produces a small shortfall.

The word maximum invites the wrong reading, so be precise about the ceiling. The ceiling is not an estimate of the value of the business. The ceiling is not a view about the company at all. The ceiling is an arithmetic limit. Given a return this buyer has decided it needs, and given this structure, that is the most it can hand over. A different buyer with a different requirement, or the same buyer with a different funding structure, gets a different ceiling on the same company. A buyer's number is a ceiling on a price derived from a required return, and reading it as a valuation of the business is a category error.

Both forms are printed, so one precision note. The exact ceiling is 8.3523 times. The printed 8.35 times is a shade below the true ceiling, and a lower price gives a slightly higher rate. With the control above set there, the cheque is Rs 11,56,80,00,000 and the rate reads 20.01 per cent rather than 20.00. Both figures are correct; they differ because one is rounded for display. Every identity in this guide is computed on the unrounded value and every printed figure is rounded once at the end.

What does a return figure not tell anybody?

Nearly everything a reader wants to know. A return figure does not say the price was a sensible one. The figure does not say the structure was well judged. Nor does it say a similar result is available, likely, or repeatable. The 19.14 per cent is arithmetic on an invented structure over an invented five years, on an operating case the buyer wrote for itself, and it is not typical of anything.

The operating case is the limitation most easily forgotten. The Rs 28,80,15,00,000 of exit equity rests on Year 5 EBITDA of Rs 4,32,00,00,000 and on an exit at 8.50 times, and both are assumptions inside the return rather than observations behind it. A change in either changes every figure in this guide. The two lines the buyer did move, capital expenditure and the working capital movement, are both lines the buyer proposed to manage rather than lines somebody independent verified.

And a return figure says nothing whatever about the company as an object. Neither Rs 24,48,00,00,000 nor Rs 24,05,47,00,000 says whether Sankalp Industrial Systems Limited is cheap or expensive. A price paid and a value are different quantities. The ceiling computed above is a property of one buyer's requirement and one funding structure. Two buyers with different requirements looking at the same company produce two different ceilings, and neither of them is the value of the business.

The arithmetic gives a discipline instead. The discipline forces every rupee of a result to be attributed to a named cause, makes the causes add back, and makes visible which of them the person presenting the result was relying on. Attribution is a small thing to be able to do, and it is worth more than the headline figure it decomposes.