Financial Leverage: How Debt Amplifies Equity Returns

Leverage is what a fixed interest bill does to a profit that moves. Sankalp Industrial Systems Limited, invented, earned operating profit of Rs 2,40,00,00,000 and paid Rs 48,00,00,000 of interest, so cover is exactly 5.00 times. A ten per cent move in operating profit becomes a 13.04 per cent move in what each share earns, upwards and downwards alike.

A household makes the idea easier to feel than to define. A schoolteacher earns a salary that arrives on the same day every month. Her husband runs a tiffin service out of the same kitchen, and what it brings in depends on how many offices are ordering that week. The rent on the flat is Rs 18,000/- and it does not care about any of that. The rent is the same in the month the tiffin service does well and the same in the month a large customer moves out of the area.

Now ask a narrow question about that household. If the tiffin takings fall by a tenth, does the money left at the end of the month also fall by a tenth? It does not. The rent took its Rs 18,000/- first, so the whole of the shortfall landed on what was left and the money at the end of the month falls by considerably more. A borrowing company is that same arrangement, done to a business instead of a household, and worked out to the rupee.

What is financial leverage, and where does the amplification actually come from?

Financial leverageThe effect a fixed interest bill has on what is left for the shareholders when profit moves. is the effect of borrowing on what reaches the people who hold the shares. Leverage is not a strategy, not a quality and not a score. Leverage is an arrangement of claims, and the whole of it can be written as a subtraction.

A lender has a fixed claimAn amount that has to be paid whatever kind of year the business turns out to have.. The amount is written into a document before the year begins, and it is the same amount whether the year is good or bad. A shareholder has a residual claimWhatever is left over once every fixed claim ahead of it has been served in full.. Nothing is written down in advance. The shareholder gets whatever survives the subtraction.

So the shareholders' share of a year is a difference between a number that moves and a number that does not. And a difference of that kind always moves by a larger percentage than its moving part does. The whole of financial leverage is that one difference, and everything after it is only arithmetic.

Sankalp Industrial Systems Limited, invented, is a listed manufacturer of industrial valves, precision castings and the aftermarket parts and service that go with them. In Year 0 it earned earnings before interest and tax, EBITEarnings before interest and tax. The operating profit the business produced, measured before the lender and the tax authority are served., of Rs 2,40,00,00,000. The company carried gross debt of Rs 6,00,00,00,000 at a blended 8.00 per cent, a rate covered separately, so the interest bill was Rs 48,00,00,000.

Nothing about the valves or the castings appears anywhere in that arrangement. The lender is served out of operating profit and the shareholders are served out of what is left. Move the operating profit and the second figure moves further, in percentage terms, every single time.

How is it measured, and what does cover of 5.00 times actually mean?

The single number people reach for is interest coverOperating profit divided by the interest charge for the same period.: operating profit divided by the interest charge. For Sankalp Industrial Systems Limited in Year 0 that is Rs 2,40,00,00,000 over Rs 48,00,00,000. The answer is exactly 5.00 times.

Most people stop there and treat 5.00 as a mark out of ten. A mark out of ten is the wrong way to hold the number, and the right way costs one extra sentence. Cover is a distance, not a score. Cover of 5.00 times says that operating profit can fall from Rs 2,40,00,00,000 all the way to Rs 48,00,00,000 before the interest bill uses the whole of it. The fall available is Rs 1,92,00,00,000, being 80.0 per cent.

Put that way, the number starts carrying information a reader can use. Four fifths is a long way down. Four fifths is further down than almost any manufacturing business goes in an ordinary bad year, and the comparison is the whole of what the ratio tells a reader. The ratio does not say the company is well run, it does not say the borrowing was wise, and it says nothing at all about what happens next.

The other thing the distance tells a reader is where the owners run out, and that point arrives earlier than the lender's does. Tax and the minority claim take their share of the last stretch, so owners reach exactly nothing at operating profit of Rs 56,00,00,000, not Rs 48,00,00,000. The fall to that point is 76.67 per cent rather than 80.0 per cent. Both numbers are on the same scale and they are not the same point.

What exactly is the multiplier, and why does the tax rate not appear in it?

There is a number that predicts every row of everything that follows, and it takes one subtraction and one division to find. Take operating profit. Subtract the interest. Divide the first by the second. For Sankalp Industrial Systems Limited that is Rs 2,40,00,00,000 over Rs 1,92,00,00,000. The answer is exactly 1.25.

The 1.25 has a name, the degree of financial leverageThe multiplier: how many percentage points profit after interest moves for each percentage point operating profit moves., and what it means is plain. Every one per cent move in operating profit becomes a 1.25 per cent move in what is left after interest, in whichever direction the operating profit went. A 10 per cent rise becomes 12.50 per cent. A 10 per cent fall becomes 12.50 per cent the other way. A 50 per cent collapse becomes 62.50 per cent.

Now the part that surprises people. The company's own assumed effective tax rate of 25.0 per cent does not appear in that ratio anywhere. It cannot. A flat rate multiplies the figure before tax and the figure after tax by the same 0.75, and a factor that appears on the top and the bottom of a fraction cancels out of it. At an assumed rate of 30.0 per cent the multiplier is still 1.25.

The cancellation matters more than it looks. The amplification is a property of the borrowing and of nothing else. The amplification is not a tax effect, not an accounting effect and not a feature of how the numbers happen to be presented. Take the borrowing away and the amplification goes with it.

What happens to what owners get when operating profit falls by a tenth?

Guess before reading on. The gap between what people expect and what the arithmetic does is what makes the question worth asking.

Here is the reported year first, so there is something to move away from. Operating profit Rs 2,40,00,00,000. Interest Rs 48,00,00,000, leaving profit before taxWhat is left once interest has been paid and before the tax charge is taken off. of Rs 1,92,00,00,000. Tax at the company's own assumed effective rate of 25.0 per cent, Rs 48,00,00,000. Profit after tax Rs 1,44,00,00,000. Then Rs 6,00,00,000 comes out for the minority interestThe part of a consolidated subsidiary that belongs to somebody outside the group. in Sankalp Coatings Private Limited, invented, of which the group holds 75.0 per cent. The subtraction leaves Rs 1,38,00,00,000 attributable to owners, and on 20,00,00,000 shares that is earnings per shareProfit attributable to owners divided by the number of shares in issue. of Rs 6.90.

Now take a tenth off the top. Operating profit Rs 2,16,00,00,000. Interest is contracted and does not move, so profit before tax is Rs 1,68,00,00,000. Tax Rs 42,00,00,000. Profit after tax Rs 1,26,00,00,000. Less the same Rs 6,00,00,000 for the minority, held flat here as an assumption of this illustration, leaving Rs 1,20,00,00,000 and Rs 6.00 a share.

Operating profit fell 10 per cent and earnings per share fell 13.04 per cent. The fall is thirty per cent further than a guess of a tenth would put it. Profit after tax fell 12.50 per cent, exactly the 1.25 multiplier at work. Earnings per share fell a little further still, and the reason for that extra step is worth its own section further down.

The last column is doing something the other columns cannot. Cover falls from 5.00 times to 4.50, to 4.00, to 3.50, to 2.50. Cover is the company's distance to the point where interest is exactly covered, and the distance shrinks in the same years the earnings figure shrinks. The two things move together, and that turns out to matter a great deal more than the percentages do.

Is the rise the mirror image of the fall, or is the fall worse?

Almost everyone answers this wrongly, and they answer it wrongly in the same direction. Leverage gets taught as a downside risk, so readers arrive expecting the downward half of the table to be steeper than the upward half.

Here is the whole ladder, run to the same four distances in each direction so that nothing is hidden by the choice of rows. Interest is held at Rs 48,00,00,000 in every line because it is contracted, and the minority claim is held at Rs 6,00,00,000 as a stated assumption of this illustration. Every row is one year's reported figures recomputed at another level of operating profit.

The two halves are identical to the last decimal, and there is no version of this arithmetic in which they are not. Down 10 gives 12.50 and up 10 gives 12.50. Down 50 gives 62.50 and up 50 gives 62.50. On earnings per share it is 13.04 against 13.04 and 65.22 against 65.22. Calling the multiplier a constant means exactly this: the same constant sits on both sides of the reported year.

If the symmetry feels wrong, the feeling is pointing at something real and is worth examining rather than dismissing. The consequence is what is not symmetric, and the consequence is taken up below once the arithmetic is settled. But the arithmetic itself has no preference for either direction, and an account that showed only the upward ladder would have taught half a subject and the comfortable half.

Why does earnings per share move 13.04 per cent when profit after tax moves 12.50?

Because there are two fixed claims in this structure and not one, and the second is easy to miss. Interest of Rs 48,00,00,000 is the loud one. The Rs 6,00,00,000 attributable to the minority in Sankalp Coatings Private Limited is the quiet one, and in this illustration it is held flat across every row.

Held flat, it behaves exactly like interest. The minority claim comes off after the tax charge and before anything reaches the owners of the parent, and it does not move when the parent's operating profit moves. A fixed claim is a fixed claim whoever happens to hold it. So a group with minority interests carries slightly more amplification than its interest cover on its own would suggest.

The arithmetic is easy to check. Profit attributable to owners is 0.75 times operating profit, less Rs 42,00,00,000, once both fixed claims and the tax charge are accounted for. Every extra rupee of operating profit adds 0.75 of a rupee for owners, and the base it is added to is Rs 1,38,00,00,000 rather than Rs 1,44,00,00,000. 0.75 times Rs 2,40,00,00,000 divided by Rs 1,38,00,00,000 is 1.304348. The 13.04 per cent comes from there. On profit after tax the base is Rs 1,44,00,00,000 and the same sum gives exactly 1.25.

One assumption departs from what would really happen, and it deserves stating plainly. Holding the minority claim at Rs 6,00,00,000 while the parent's operating profit swings by half is not realistic. The subsidiary's own profit would move as well, and the amount attributable to the minority would move with it. The Rs 6,00,00,000 is a reported figure for the reported year alone, and every other row holds it flat as an assumption.

How far can operating profit fall before interest stops being covered?

All the way down to Rs 48,00,00,000, a fall of 80.0 per cent. At that point profit before tax is nil and there is no tax charge. The minority claim is still standing there whether or not anything is left to pay it out of, so profit attributable to owners is minus Rs 6,00,00,000.

Walk the last part of that distance slowly. Nobody draws that part. At operating profit of Rs 96,00,00,000 cover is 2.00 times, owners get Rs 30,00,00,000 and Rs 1.50 a share. At Rs 72,00,00,000 cover is 1.50 times, owners get Rs 12,00,00,000 and Rs 0.60 a share. At Rs 56,00,00,000 cover is 1.17 times and owners get exactly nothing. At Rs 48,00,00,000 cover is 1.00 times and owners are Rs 6,00,00,000 short.

Notice how quickly the last stretch goes. Between cover of 2.00 times and cover of 1.17 times, operating profit falls by Rs 40,00,00,000, being 41.7 per cent of where it started that stretch, and the whole of what owners were getting disappears. The multiplier is doing what a multiplier does: as the denominator shrinks, the same rupees of movement become larger and larger percentages. At cover of 2.00 times the multiplier is 2.00. At cover of 1.50 times it is 3.00. At cover of 1.17 times it is about 7.00.

Two things do not follow from those numbers. A level of borrowing is a distance and not a verdict, so cover of 5.00 times is not in itself safe and no other level is in itself unsafe. And what happens at cover below 1.00 times belongs elsewhere: what starts costing a company money long before a payment is actually missed is covered separately.

What does the same arithmetic look like with no debt at all?

The same company with no borrowing at all is the control experiment. Removing the one variable under examination shows what is left.

Take the same Sankalp Industrial Systems Limited, the same valves, the same castings, the same aftermarket business, the same Rs 2,40,00,00,000 of operating profit, and give it no borrowing at all. There is no interest, so profit before tax is the whole Rs 2,40,00,00,000. Tax at the assumed 25.0 per cent is Rs 60,00,00,000. Profit after tax is Rs 1,80,00,00,000. Less the same Rs 6,00,00,000 for the minority, Rs 1,74,00,00,000 reaches the owners, and on 20,00,00,000 shares that is Rs 8.70.

Now take the same tenth off the top. Operating profit Rs 2,16,00,00,000. Tax Rs 54,00,00,000. Profit after tax Rs 1,62,00,00,000. The fall is exactly 10 per cent, not 12.50, and the multiplier on profit after tax is exactly 1.00. The unleveredFunded entirely by shareholders, with no borrowing and therefore no interest bill at all. version of the company does not amplify anything.

Put the two side by side and something small and rather beautiful falls out. In the borrowed version profit after tax fell from Rs 1,44,00,00,000 to Rs 1,26,00,00,000. In the unborrowed version it fell from Rs 1,80,00,00,000 to Rs 1,62,00,00,000. Both fell by exactly Rs 18,00,00,000. The fall in operating profit was the same and the tax charge took a quarter of it either way, so the same rupees left in both cases. Only the base they were a proportion of differed.

One more figure deserves precision. The Rs 6,00,00,000 minority claim is still a fixed claim even when there is no lender, so on earnings per share the unlevered multiplier is not quite 1.00 either: it is 1.034483. Earnings per share falls from Rs 8.70 to Rs 7.80, being 10.34 per cent rather than 10.00. The interest was doing most of the amplifying, but it was never doing all of it.

Why does the same company amplify more as it borrows more?

Because two things get worse at once, and they multiply rather than add. The amount borrowed rises, and the rate charged on it rises as well, so the interest bill grows faster than the borrowing does. A larger interest bill is a larger fixed claim, a larger fixed claim leaves a smaller remainder, and the multiplier is operating profit divided by that remainder.

Sankalp Industrial Systems Limited carries its own invented cost of debt schedule, one contracted rate for each level of borrowing, and every figure below is arithmetic on that schedule. Total capital at market is Rs 24,00,00,00,000, being equity of Rs 18,00,00,00,000 and borrowing of Rs 6,00,00,00,000, so the company sits at a 25 per cent debt share today.

At a 40 per cent debt share the borrowing would be Rs 9,60,00,00,000 at 9.00 per cent, so interest would be Rs 86,40,00,000, cover would fall to 2.78 times and the multiplier would rise to 1.56. At a 60 per cent debt share the borrowing would be Rs 14,40,00,00,000 at 13.00 per cent, interest would be Rs 1,87,20,00,000, cover would be 1.28 times and the multiplier would be 4.55. The multiplier did not grow gently across that range. The steps ran 1.25, then 1.56, then 4.55, and the last one is worth more than everything before it.

The reason the curve bends the way it does is worth naming rather than leaving as a shape. Between a 25 and a 40 per cent debt share the rate moves only from 8.00 to 9.00 per cent. Between 40 and 60 it moves from 9.00 to 13.00 per cent, at the same time as the amount borrowed rises by half again. Multiply the two effects together and the interest bill more than doubles. The operating profit it is taken out of has not moved at all.

The whole shape belongs to one invented cost of debt schedule and one invented company, so it is not a general answer about what borrowing costs anybody. Setting the blended rate against what a company is worth is covered separately. The relationship does turn somewhere, and two things are true about the turn: the curve is close to flat near the bottom, so the point where it turns is far less precise than a table of it would imply, and the whole shape depends on the same invented schedule. Buying a company largely with borrowed money is this same arithmetic taken to its limit, and that is covered separately too.

If the arithmetic is symmetric, why is the bad year not the mirror of the good one?

Because the percentages are mirror images and the consequences are not, and this is the part of the subject that the tables genuinely cannot show.

Go back to the ladder and read the two 50 per cent rows against each other. Up 50 per cent: profit after tax rises 62.50 per cent, earnings per share reaches Rs 11.40, cover improves to 7.50 times. Down 50 per cent: profit after tax falls 62.50 per cent, earnings per share drops to Rs 2.40, cover falls to 2.50 times. Identical arithmetic. Nothing like an identical year.

In the good year the company has more cash than it planned for and a wider distance to its interest bill than it planned for. Nothing needs deciding. In the bad year, cover of 2.50 times is the figure a lender looks at when a facility comes up for renewal, and the working capital facility that Sankalp Industrial Systems Limited draws on is renewed annually. So the company can find itself repricing its borrowing in precisely the year its profits are least able to carry a higher rate. The good year hands the company an option. The bad year hands it a conversation.

The household with the tiffin service knows this without any arithmetic at all. A good month means a little more in the tin at the end of it. A bad month means the rent still has to be found on the first, and it has to be found out of a smaller number, and the landlord is not interested in the average of the two months. Symmetric percentages, asymmetric weeks.

There is a second asymmetry sitting underneath the first, and it is about who is watching. A 62.50 per cent rise in profit after tax gets attributed to management. A 62.50 per cent fall gets attributed to the market, or the cycle, or a customer. The same Rs 48,00,00,000 produced both, so neither attribution is right, and only one of them tends to get corrected.

Does leverage make a business better, or only make its results move more?

Only the second, and that is the distinction the arithmetic establishes.

Look at what changed between the borrowed version of Sankalp Industrial Systems Limited and the unborrowed one. Not the valves. Not the castings. Not the aftermarket parts and service. Not a customer, not a plant, not a rupee of revenue and not a point of operating margin. Operating profit is measured before the lender is served and has no idea whether there is a lender at all, so it was Rs 2,40,00,00,000 in both versions.

The change was in who has a claim on that operating profit and in what order. Leverage rearranges the claims on a result. Leverage does not improve the result. That statement is the practical edge of the argument Modigliani and Miller set out in The Cost of Capital, Corporation Finance and the Theory of Investment in the American Economic Review in 1958: in a world without taxes and frictions, how a company is funded does not change what the underlying business is worth, because the funding decides how the cash is divided and not how much of it there is. Their later correction admitted the deductibility of interest, which does put a real difference back in. The deduction is arithmetic on an assumed rate rather than an improvement in anything the company does.

For a reader of results the point is narrower and blunter. When earnings per share rises 13.04 per cent on operating profit up 10 per cent, the extra 3.04 percentage points were produced by two numbers standing still. No decision taken during the year produced them. And the same two numbers, standing just as still, will produce a 13.04 per cent fall the moment operating profit goes the other way.

So what travels from all of this, and what does not?

Three things travel to any company anywhere and two do not. The mechanism travels: a fixed claim ahead of a residual one always amplifies, in both directions, by a factor equal to the whole divided by the remainder. Cover read as a distance travels too, and it turns a ratio into a sentence that means something. And the refusal travels: amplification is not improvement, so a levered result has to be divided by its multiplier before it can be compared with anything.

None of the rupee figures travels. The Rs 48,00,00,000, the 5.00 times, the 1.25, the 13.04 per cent and the Rs 6.90 belong to one invented company in one invented year, and every one of them is arithmetic on four starting figures. No verdict travels either. The arithmetic settles what a fixed claim does to a moving profit, and it settles nothing about how much a company ought to borrow. A level of borrowing is defended by the distance behind it and the price paid for it, and neither of those is the multiplier.