How Leverage Can Increase and Reduce Equity Value

Leverage raises what is left for owners until it stops. Applying the same unchanged cash flows of Sankalp Industrial Systems Limited, invented, at each debt share, the cost of capital falls from 12.750 to 11.850 per cent and firm value tops out at Rs 21,77,80,00,000 under this invented company's own invented cost of debt schedule. Beyond that it turns down.

The awkward idea in this guide lands faster on something that can be walked around, so start with a warehouse on the edge of a small industrial estate. Suppose a household buys one for a hundred lakh rupees and rents it out. The tenant pays what the tenant pays. The roof leaks when it leaks. Now the same purchase, run twice. In the first version the household pays the whole hundred lakh out of savings. In the second it puts in sixty and borrows forty from a bank.

Ask yourself what changed about the warehouse between those two versions, and the honest answer is nothing at all. The same shed, the same tenant, the same rent, the same leak. The change is who has a claim on the rent and in what order. The bank goes first, at a rate written into a document. The household goes second, and takes whatever is left. Everything in this guide is that one move, done to a company instead of a warehouse, and worked out to the rupee.

How can borrowing make a company worth more when the business does not change?

Because the business and the funding are valued by two different mechanisms, and only one of them moves. Firm valueWhat a model says the whole operating business is worth, before deciding who has a claim on it. here is a stream of cash discounted at a rate. The stream comes from the operating business. The rate comes from what the people funding it require. Changing the funding changes only the second one.

Sankalp Industrial Systems Limited, invented, sits today at a debt shareDebt as a proportion of total capital, measured at market values rather than at what the accounts say. of 25.0 per cent, measured at market: Rs 6,00,00,00,000 of borrowing against a market capitalisation of Rs 18,00,00,00,000, giving total capital of Rs 24,00,00,00,000. At that point its weighted average cost of capitalThe blended cost of all funding, weighted by how much of each kind is used. is exactly 12.00 per cent and the discounted cash flow built on it gives a firm value of Rs 21,28,14,00,000. How that 12.00 per cent was assembled, input by input, is covered separately; every figure it produced is restated here.

So the question is narrow and answerable. The business is held perfectly still. Only the mix moves. So what happens to the number at the end? The answer is that firm value rises, keeps rising for a while, tops out, and then falls away, and by a 60 per cent debt share it is below where it would have been with no borrowing at all. Everything that follows is the arithmetic behind that sentence and the several ways a reader can misread it.

What is the one thing that never moves in any of this?

The cash. The entire exercise is meaningless if the cash slips, so being blunt about it matters. The five years of free cash flow to the firm for Sankalp Industrial Systems Limited are Rs 98,00,00,000, Rs 1,16,00,00,000, Rs 1,34,00,00,000, Rs 1,52,00,00,000 and Rs 1,70,00,00,000, and the terminal build sitting behind Year 5 is unchanged too. The five figures are settled elsewhere and are simply carried in.

Not one rupee of that stream moves when the debt share moves. It cannot. Free cash flow to the firm is what the operating business produces before anybody is paid out of it, so how the funding was arranged has already been stripped out of it by construction. The valves still get made. The aftermarket parts still get sold. The tenant still pays the rent.

Only the rate changes, and the rate changes for exactly two reasons: the mix of the two funding sources shifts, and the price of each source shifts as it does. Almost every misreading of a capital structure argument comes from quietly letting the operating numbers drift while the mix moves, and the sentence above is worth holding for that reason. A model that shows revenue improving as leverage rises is not showing what this guide shows.

Why is borrowed money the cheaper of the two after tax?

Two separate reasons stack on top of each other. The first is contractual position. A lender is paid before a shareholder and has recourse if it is not, so a lender accepts less. Sankalp Industrial Systems Limited borrows across three tranches at a blended pre-tax rate of 8.00 per cent. The return required on its equity at the same moment is 14.00 per cent. Six full percentage points of difference, and none of it is mysterious: it is the price of going second.

The second reason is the tax charge. Interest is deducted from taxable profit and a dividend is not, so a rupee of interest costs the company less than a rupee. At the company's own assumed effective tax rate of 25.0 per cent, the after-tax cost of debtThe borrowing rate reduced by the tax that is saved because interest is deducted from taxable profit. is 8.00 times 0.75, or exactly 6.000 per cent. The 25.0 per cent is an effective rate this company assumes for itself rather than a statutory rate, and a statutory rate is set by law, differs by country and by year, and applies to a defined kind of profit.

So the arithmetic of the first force is simple and it is close to linear. Every percentage point of the mix moved out of a 14.000 per cent source and into a 6.000 per cent source lowers the blended rate, and a lower rate applied to an unchanged stream produces a higher value. If nothing else happened, more borrowing would always be better and the curve would rise forever. Something else does happen, twice.

What does the lender do as the borrowing grows?

The lender reprices, and it reprices the whole balance rather than only the new part. The cushion underneath the loan has halved, so a lender looking at a company with a quarter of its capital borrowed and a lender looking at the same company with half of it borrowed are looking at two different propositions. Nothing about the valves changed. The position in the queue did.

Sankalp Industrial Systems Limited carries an invented cost of debt schedule, one pre-tax rate for each debt share, and the whole shape of the argument rests on it. Schedule A in the table further down is the one used throughout. Three things about it are worth noticing before anything is built on it.

First, the 0 per cent row is notional. At a zero debt share there is no debt, so its 8.00 per cent is the rate the company would pay on a first rupee rather than a rate it actually pays, and it is excluded from any claim about the shape. Second, read as 0, 10, 20 and 25 the schedule looks non-monotonic: 8.00, then 7.75, then 7.90, then 8.00 again. A general rule that the cost of debt rises with leverage would be contradicted by these first four rows. From the 10 per cent row upward it is strictly monotonic, and that is the honest way to state it. Third, and this is the part that matters: the schedule is essentially flat and carries almost no information below about a 20 per cent debt share, and the shape that decides everything is what happens above 40 per cent, where it climbs from 9.00 to 13.00 per cent.

What happens to what the shareholders require?

The cost of equity rises, the whole way, and this is the half most readers do not expect. Nobody hands shareholders a new contract when a company borrows more. The claim the shareholders hold is what changes. A residual claimThe shareholders' claim on whatever is left over after every fixed claim has been met. is what is left after every fixed claim has been paid, and the more fixed claims there are, the thinner and more variable what is left becomes.

Think about the warehouse again. If the household paid cash, a bad year with the tenant is annoying. If it borrowed forty of the hundred, the bank's number does not move when the rent does, so the same bad year eats a much larger share of what is left after the bank has been paid. The same variability in the rent has become a larger variability in what the household receives. The thinning of the residual claim is the whole idea, and the arithmetic behind it is covered separately.

On the rate side that shows up through the beta. The unlevered betaThe beta of the business itself, with the effect of funding stripped out, taken here as 1.00. of this business is 1.00. ReleveringAdjusting the unlevered beta upward to reflect a given level of borrowing. it means multiplying by one plus 0.75 times the debt to equity ratio at that point, giving the levered betaThe beta of the equity once the company's borrowing has been taken into account.. The identity itself is covered separately and is restated here. At a 25 per cent debt share the debt to equity ratio is one third, so the levered beta is 1.00 times 1.25, giving 1.2500 exactly.

The cost of equityThe return the residual claim has to be capable of producing for the people who hold it. is then the risk-free rate of 7.75 per cent plus the levered beta times a total equity risk premium of 5.00 per cent. At 1.2500 that is 14.000 per cent exactly. At a 60 per cent debt share the levered beta is 2.1250 and the cost of equity is 18.375 per cent. The debt to equity ratio explodes as the equity share shrinks, moving from one third at a 25 per cent debt share to one and a half at 60 per cent, so the second force is not a fixed penalty but an accelerating one. That acceleration is why the curve turns over rather than flattening out.

What do the ten rows actually say?

Here they are in full. At each debt share the beta is relevered off the unlevered 1.00, the pre-tax cost of debt is read from schedule A, the cost of equity is rebuilt on the relevered beta, and the resulting weighted average is applied to the same unchanged cash flow stream and the same terminal build. Operating cash flow does not move. Only the rate does.

Every firm value in that column is stated to the nearest lakh, the same thing as two decimal places of a crore, and none of the ten is carried further than that. For the one row where the record holds a full precision figure, the 25 per cent row, the exact enterprise value is Rs 21,28,13,79,094; the Rs 21,28,14,00,000 in the table is that same number rounded, and on an answer of this size the last few digits carry no information whatever.

Can one row be rebuilt by hand and land on the figure the record holds?

One row can, and doing it once is what makes the other nine worth trusting. The 25 per cent row has to reconcile against something already settled, so it is the row to take. Levered beta 1.2500. Cost of equity 7.75 plus 1.25 times 5.00, being 14.000 per cent. After-tax cost of debt 8.00 times 0.75, being 6.000 per cent. Weighted average 0.75 times 14.00 plus 0.25 times 6.00, being 10.50 plus 1.50, or 12.000 per cent exactly.

The 12.000 per cent is the same weighted average cost of capital the record already holds for this company. Applying it to the unchanged cash flows returns Rs 21,28,14,00,000, and that is the discounted cash flow answer the record already holds too. The row does not approximately agree with the rest of the record. The row lands on it. The landing is the check that the whole table is built on the right basis rather than on a second, quietly different set of assumptions.

Why does the average fall when both of its parts are rising?

A falling average with both of its parts rising is the counter-intuitive core of the whole subject and it is worth slowing down on. Look across the table from the 0 per cent row to the 40 per cent row. The cost of equity rises from 12.750 to 15.250 per cent. The pre-tax cost of debt rises from 8.00 to 9.00 per cent. Both components go up. And the weighted average of them falls, from 12.750 to 11.850 per cent.

Nothing has gone wrong. A weighted average has two moving parts, the values and the weights, and here the weights are moving faster than the values. The share of capital sitting in the cheaper of the two goes from nothing at all to two fifths, and the after-tax gap between the two is enormous: 6.000 per cent against 14.000 per cent at the starting point. Shifting two fifths of the mix across a gap that wide buys more than the two components lose by drifting up a percentage point or two.

And the same sentence explains why the effect runs out. The weight can only shift so far. The two components keep rising, and rising faster the further the mix goes. Past a certain point there is not enough weight left to move to pay for what the moving costs. The turning point arrives at a 40 per cent debt share on this schedule. At that debt share this invented company's modelled firm value tops out under its own invented cost of debt schedule.

How much does the whole effect turn out to be worth?

Less than most readers expect, and the surprise is worth keeping. Moving from the company's current 25.0 per cent debt share to the 40.0 per cent at which this invented company's modelled firm value tops out under this invented schedule adds Rs 49,67,00,000, being 2.33 per cent. Fifteen percentage points of extra leverage, and a business the same model values at Rs 21,28,14,00,000 gains about two per cent.

Two honest routes give two answers on that figure, and the gap between them is worth a note. Computed on the unrounded model values, 2,177.803 less 2,128.138 in crore, the gain is Rs 49,67,00,000. Subtracting the two printed table figures instead gives Rs 49,66,00,000. The first is the figure of record and it is the one printed above; neither number has been nudged to make the subtraction come out. A record that quietly adjusts a locked figure so that two of its own columns agree has stopped being checkable, and losing that is worse than carrying a one lakh rupee rounding difference in the open.

The same modest scale applies at the bottom of the rate. The weighted average falls from 12.000 per cent to 11.850 per cent, a drop of fifteen basis points. Everything that follows about a curve, a turning point and a shape is a story about fifteen basis points and about two per cent of value. The effect is real, it is worth understanding, and it is not the largest lever anybody has.

What happens on the other side of the top?

Firm value falls, and it keeps falling, and it goes further than most readers guess. At a 45 per cent debt share firm value is Rs 21,31,18,00,000, already below the 40 per cent figure and barely above where the company is standing right now. At 50 per cent it is Rs 20,40,58,00,000, below the current position. At 60 per cent it is Rs 17,96,81,00,000.

Put that last figure next to the first row of the table. With no borrowing at all the same company on the same cash flows is worth Rs 19,08,91,00,000. So at a 60 per cent debt share this invented company is worth Rs 1,12,10,00,000 less than a version of itself that had never borrowed a rupee, being 5.87 per cent, on cash flows that are identical to the last decimal. That single comparison ends the comfortable idea that a bit more debt is always at least slightly better than a bit less.

The reason is entirely visible in the table. At a 60 per cent debt share the cost of equity has reached 18.375 per cent and the pre-tax cost of debt has reached 13.00 per cent, or 9.750 per cent after tax. The weighted average of those two is 13.200 per cent, higher than the 12.750 per cent the company would have faced with no debt at all. Both components have risen far enough that no amount of reweighting can rescue the average.

Who actually receives the gain, and who bears the loss?

The same people, in both directions, and that is why this guide is titled the way it is. The debt is contracted: a stated amount, at a stated rate, on stated dates. The debt does not participate when firm value rises and does not absorb anything when firm value falls, right up until the moment it is not paid. Every rupee of movement therefore has exactly one place to land.

Under this invented schedule, this company's modelled firm value is highest at a 40.0 per cent debt share. Going there from 25.0 per cent, the Rs 49,67,00,000 of additional firm value belongs to the shareholders. The gain reaches them twice over in a sense. Getting there reduces the share count at the same time, so the same larger residual is spread across fewer holders. Going from 40.0 to 60.0 per cent, the Rs 3,80,99,00,000 of firm value that disappears belongs to the shareholders too, and there is nobody else for it to go to. The two movements together are leverage increasing and reducing equity value, and they are not two mechanisms but one, run forwards and then backwards.

The household version is easier to feel, so go back to the warehouse for a second. If the estate becomes fashionable and the shed becomes more valuable, the bank does not ask for a share of the gain; it asks for its instalment. If the estate empties out and the shed becomes worth less than the loan, the bank still asks for its instalment. The household holds the whole of the upside and the whole of the downside, precisely what it agreed to when it accepted the cheaper money.

Does the reported earnings number agree with any of this?

No, and that disagreement is the sharpest thing here. Earnings per share, run at each point on the same invented schedule, does not top out where firm value does. With earnings before interest and tax (EBIT) held at Rs 2,40,00,00,000, total capital at market held at Rs 24,00,00,00,000, equity moved in and out at the share price of Rs 90.00, interest charged at the schedule rate on the debt at each point, tax at the company's own assumed 25.0 per cent, and the Rs 6,00,00,000 attributable to the minority in Sankalp Coatings Private Limited taken out, the 25 per cent row gives Rs 6.90 exactly, the figure the company reports today, so the ladder is anchored to something already settled.

Now read the rest of it. Earnings per share climbs to Rs 6.9348 at a 30 per cent debt share and then starts falling. At the 40 per cent debt share where this invented company's modelled firm value tops out under this invented schedule, earnings per share is Rs 6.8250, below the Rs 6.90 the company reports today. The move that adds the most modelled firm value is the move that lowers the reported earnings number, and a reader who has quietly been using earnings per share as a proxy for value has just been shown why that does not work. The earnings per share figures are arithmetic on the locked schedule rather than locked figures in their own right, and the same label applies to every difference computed off the table above.

How precisely can that turning point actually be located?

Far less precisely than the table's decimal places suggest, and this is the most important qualification in this guide. Between a 30 and a 45 per cent debt share the weighted average cost of capital moves only from 11.906 to 11.991 per cent. On the printed figures that is a range of eight and a half basis points across fifteen percentage points of leverage. Firm value across the same stretch stays inside Rs 46,62,00,000, being 2.1 per cent of the highest figure.

Look narrower still. Firm value at a 35 per cent debt share is Rs 21,75,27,00,000 and at 40 per cent it is Rs 21,77,80,00,000. The difference between the two is Rs 2,53,00,000 on the printed figures, about one part in nine hundred of the company. Nothing that went into this model is known to one part in nine hundred: not the unlevered beta, not the equity risk premium, not the terminal growth rate, and certainly not what a lender would charge at a debt share the company has never been at.

So the honest statement of the answer is not that the point is 40.0 per cent. The honest statement is that modelled firm value is highest somewhere in a broad band around a 40 per cent debt share, that the table is far more precise than the answer is, and that quoting the figure to one decimal place asserts an accuracy the arithmetic cannot support. A drawing of this curve with a sharp spike on it would be asserting something the record does not contain. The shape drawn above has a visibly flat top and a shaded band across it for exactly that reason.

What would a different cost of debt schedule do to the shape?

A different schedule would move the whole curve, and the swap is the test that shows what the 40 per cent figure actually belongs to. Take the identical company. Same five years of cash flow, same terminal build, same unlevered beta of 1.00, same risk-free rate of 7.75 per cent, same total equity risk premium of 5.00 per cent, same assumed tax rate. Change only what a lender would charge at each debt share.

Schedule B in the table above is a second invented schedule for a lender who reprices earlier and harder: 8.00 per cent at no debt, 9.10 at a 25 per cent debt share and 18.00 at 60. Run the same arithmetic on it and modelled firm value tops out at a 25 per cent debt share at Rs 20,63,25,00,000, and the whole hill sits lower than the first one everywhere past the first few rows. Not one cash flow moved, and the answer changed from 40 per cent to 25 per cent. The 40 per cent is therefore a property of the schedule rather than a property of companies.

Both schedules were made up for this walkthrough, and neither is a claim about what any real lender charges anybody. The difference between them is precisely the point. If two invented schedules produce two different answers on identical cash flows, then a real company's answer depends on a real schedule that only its own lenders can supply, and no figure from this guide can substitute for it.

Why does the simple tax-shield answer point the other way?

Because it leaves out both of the forces that make the curve turn, and it is worth seeing exactly how far wrong it goes. The tax shieldThe reduction in a tax bill caused by interest being deducted from taxable profit. is real arithmetic on an assumed rate: interest is deducted, so tax falls. The static tax-shield valueThe simple valuation of that benefit as the tax rate multiplied by the amount borrowed. takes the next step and values the whole benefit as the tax rate times the debt.

Run it here. At the company's own assumed 25.0 per cent rate, Rs 6,00,00,00,000 of borrowing gives Rs 1,50,00,00,000 of shield and Rs 9,60,00,00,000 gives Rs 2,40,00,00,000, an increment of Rs 90,00,00,000 for the move to a 40 per cent debt share. The full model says Rs 49,67,00,000. And at a 60 per cent debt share the static formula claims Rs 3,60,00,00,000 of shield. Modelled firm value has actually fallen to Rs 17,96,81,00,000, which is Rs 3,31,33,00,000 below where it started on the printed figures and Rs 3,31,32,00,000 on the unrounded ones.

The static answer has no turning point at all: it rises in a straight line forever and concludes that a company should be funded entirely by debt, a conclusion no company anywhere acts on. The gap between the two answers is exactly what Modigliani and Miller assumed away. Their argument in The Cost of Capital, Corporation Finance and the Theory of Investment, American Economic Review, 1958, was that in a world with no taxes, no costs of financial distress, no transaction costs, no information asymmetry and free borrowing at one rate for everybody, the mix cannot change what a company is worth. Their later correction admitted the deductibility of interest and produced the rising straight line. Both ideas are used above and both are theirs.

So which of those assumptions does this invented company break? Two of them, visibly. The company does not borrow at one flat rate. Schedule A prices its borrowing differently at every debt share, and that is a lender charging for risk. And its residual claim reprices too, through a beta that is relevered at each point. Put those two back and a straight line becomes a hill. Everything else Modigliani and Miller assumed away, including what distress starts costing long before anything is missed, is covered separately and immediately after this subject, and putting that in as well would push the top of the curve to a lower debt share still.

So what transfers to another company, and what does not?

Three things travel and two do not. The shape travels: on a company whose lenders reprice as it borrows more and whose shareholders reprice alongside them, modelled value rises with leverage, tops out, and then falls away. The reason travels: one force is close to linear and the other accelerates, so the second one wins eventually. And what travels is the method: hold the cash flows perfectly still, move only the rate, and read the consequence.

The 40.0 per cent does not travel, and neither does the Rs 49,67,00,000 nor the Rs 21,77,80,00,000. All three are outputs of one invented schedule belonging to one invented company. Whether a company should borrow more is not settled by a curve at all: it is settled by whether the company can meet the fixed payments through a bad year. The 40.0 per cent is where this invented company's modelled firm value is highest under this invented cost of debt schedule, and it is a band rather than a point even there.