Capital structure

This is the half of Apple's story that made it borrow, and the benefit is easy to put a number on. Interest is subtracted before tax is calculated and dividends are not, so a company with debt hands less to the tax authority. Borrow a thousand at 8 percent under a 21 percent tax rate and the tax bill falls by seventeen, every year the debt is outstanding.

Follow that reasoning to the end, though, and it gives an absurd answer. If each euro borrowed creates value at a fixed rate, no firm should ever stop borrowing, and the ideal capital structure would be 100 percent debt. Nobody believes that. The gap between the arithmetic and the world is where the rest of this page lives.

Two things close the gap. The first is that the saving is smaller than the corporate tax rate suggests, because investors pay tax too. Interest lands in a lender's hands as ordinary income, taxed at the top personal rate. Equity returns arrive as dividends and capital gains, taxed more lightly and often deferred for years. Once both levels are counted, the net advantage of debt shrinks a long way toward nothing, and at current rates it can vanish altogether. Governments cap the shield directly as well: the United States and the European Union both now limit deductible interest to roughly 30 percent of operating earnings.

The second is distress, which is worth splitting into two questions that usually get run together. How likely is trouble, and how much value burns if trouble arrives? Volatile earnings answer the first. What the company is made of answers the second. A mortgaged hotel goes through bankruptcy and comes out the other side still a hotel, because the building does not care whose name is on the deed. A research company does not. Its value was its engineers, its half-finished projects, and customers who trusted it would still be there to honour a warranty, and all three walk out of the door. Across firms that did get into trouble, the damage runs to something like a tenth to a fifth of what they had been worth beforehand.

Note which way the causation runs, because it is easy to get backwards. Bankruptcy is not what destroys the value. It is the legal machinery that starts up once the value is already gone, and most of what distress actually costs happens long before any court is involved.

Managers do appear to think in these terms. Asked directly how they set debt levels, two thirds of a sample of Spanish finance chiefs said they aim at a specific target, and three quarters of the companies that have one reported hitting it at least sixty percent of the time. A target that exists in the head of the person deciding is the behavioural claim trade-off theory actually needs, and it is not something any balance sheet can show you.

The predictions are specific. Firms with steady cash flow, tangible assets a lender can seize, and low volatility should borrow more. Profitable firms should borrow more, because they have more taxable profit to shield. Hold on to that last one.

Put yourself on the other side of the table. A company offers to sell you shares. Management knows exactly what those shares are worth and you do not. Would you not wonder why they are selling?

Myers and Majluf (1984) built a theory out of that suspicion. Suppose managers know more about the firm than investors do. A manager who issues shares is more likely to do so when the shares look dear than when they look cheap. Investors work this out, and mark down the price on any announcement of an equity issue. Anticipating the markdown, managers avoid issuing equity whenever they can.

The trap closes from both sides, which is the part that makes the theory bite. Picture two identical companies that both need money. One manager privately believes the shares are worth far more than the market thinks, and will not sell them that cheaply. The other privately believes the opposite and would happily sell, but knows that trying is itself the giveaway: the announcement alone would knock the price down and destroy the advantage. So the optimist issues debt, and the pessimist issues debt too. Even the company that wants to sell shares ends up borrowing instead.

What survives is an order rather than a target. Retained earnings first, because using cash the firm already has reveals nothing. Debt second, because a fixed claim barely moves on private information about how valuable the firm really is. New equity last, and often only under pressure.

That is a genuinely different claim from the previous chapter, not a refinement of it. Trade-off theory says a company has a right answer and gets pulled back toward it. Pecking order says there is no right answer to be pulled toward. What you read off a balance sheet is just the running total of every occasion the firm needed outside money and every occasion it did not. On this account a debt ratio is residue, not policy.

The theory does not fit everyone equally well. It describes large, established firms with easy access to bond markets best, which are exactly the firms for which borrowing is routine. Younger and faster-growing companies issue equity far more often, partly because they must, and partly because a business whose value is mostly future promise is a dangerous thing to load with fixed repayments.

Asked directly, managers describe this ladder almost rung for rung. In a survey of 140 Spanish finance chiefs, retained earnings came out as the most important source of funding, bank debt a close second, and issuing shares second from last, behind both money borrowed from other companies in the same group and ordinary supplier credit. The theory predicts an ordering, and the ordering is what the people doing it report.

Now the useful part. Pecking order predicts that profitability is negatively related to leverage: a profitable firm funds itself and pays debt down. Trade-off theory predicts the opposite sign on the same variable. Two theories, one coefficient, opposite directions. The data can referee.

Utilities sit at the top: the median utility funds about 45 percent of itself with debt. Regulated, predictable revenue and physical assets a lender can seize make borrowing cheap for them. Real estate follows at 40 percent for the same reason in a purer form, since there the asset is literally the collateral. At the other end, information technology and health care sit at 6 and 7 percent, because the assets are intangible, the cash flows are promised to nobody, and what a lender would repossess in a default is mostly people who would already have left.

That ordering is not a quirk of this sample. Brealey and Myers publish the same table built from a different data vendor, a different decade and book rather than market equity, and the two ends agree: utilities near the top, pharmaceuticals, software and semiconductors at the very bottom. Two independent measurements landing in the same order is worth more than either one alone.

The middle of the table agrees far less, and every level here is lower than in the textbook version. Both have the same cause. This page measures equity at market value rather than book value, and listed companies are usually worth more than their accounts say, so the denominator is bigger and each ratio comes out smaller. It also reshuffles any sector whose market value has run well ahead of its books. Communication services is the clearest case: it reads as one of the most indebted sectors on book equity and a middling one here, because the modern definition of that sector is dominated by a few enormous and very lightly indebted platform companies.

The overlap matters more than the ordering anyway. The middle half of almost every sector runs through the middle half of almost every other one. A sector label narrows the guess, and then leaves most of the work undone.

Solvency is the single strongest input. A firm's Altman Z, its earnings volatility and its asset tangibility all move predicted leverage in the direction trade-off theory requires, and they do so independently of one another. Three separate distress proxies agreeing is worth more than any one of them being large.

Pecking order splits in a way that is more interesting than a clean pass or fail. Its mechanism survives: analyst disagreement, the standard proxy for what managers know and investors do not, is positive and significant exactly as Myers and Majluf require, and accumulated retained earnings carry the negative sign it predicts. Its most famous prediction does not survive at all.

That prediction is that profitable firms borrow less, and it is close to the most reliable finding in this literature. Here they borrow more, with a coefficient that is both large and highly significant. The figure below is the reason not to believe it. The effect halves and halves again as book equity thickens, and measured against market equity it cannot be told apart from zero. Buybacks and write-offs shrink book equity, and a shrunken denominator raises book leverage for exactly the firms that are most profitable. An artefact of the measure rather than a fact about firms, but an artefact this panel could not scrub out.

The tax result deserves a note, because it reads as a disappointment and is not one. Adding the corporate tax rate barely moves the model. Part of the reason is that the corporate rate is the wrong quantity to be using at all, which chapter 08 takes apart: it ignores that shareholders are taxed a second time, and that some countries hand the company's tax straight back to them. Measured properly the effect is there and correctly signed, and it is still small. Once investors' own taxes are netted off, the advantage of borrowing is a thin margin rather than the headline rate, and a thin margin is hard to see in a panel where a hundred other things are moving at once.

The people who make the decision say the same thing. Asked to rate nine considerations when setting a debt level, Spanish finance chiefs put tax saving eighth, at 1.36 out of 4. Financial flexibility came first at 2.62, access to debt second, and the risk of insolvency comfortably ahead of tax at 1.91. So three unrelated kinds of evidence agree: a textbook argument about personal taxes, a model that barely twitches when tax rates are added, and a survey of the managers themselves. The tax shield is real, and it is not what is driving the decision.

It is worth holding the model against what the literature already settled. Rajan and Zingales found four characteristics that moved leverage in every one of the seven countries they examined: size and asset tangibility upward, profitability and the market's valuation of the firm downward. Three of those four are inputs here and all three carry the expected sign, with size and margin ranking second and third by weight. The fourth is deliberately absent. A market-to-book ratio contains the firm's market capitalisation, which is also the denominator of the thing being predicted, so feeding it in would let the model read part of the answer off its own inputs.

Chapter 17 of the same textbook sets a second test of that kind, and one input here fails it far more quietly. Modigliani and Miller's second proposition says a share's beta is the beta of the underlying business plus a term in debt over equity: refinance a company without touching a single thing it does and its beta rises regardless. A beta is therefore not a measurement of business risk. It is business risk multiplied by the quantity this model exists to predict.

Both channels turn out to be visible in the panel, working against each other. Beta's raw correlation with borrowing is minus 0.04, which is nothing at all, while earnings volatility, measured before any interest is paid, gives minus 0.23. Hold business risk, size, tangibility, sector and year fixed and beta rises with borrowing at plus 0.26, with a t statistic of 12. The mechanical channel is real, and it had been quietly cancelling out the economic one. It is also much flatter than the identity on its own would give, which is what noise in an estimated beta does to a slope, and it reverses outright in energy, in health care, and among the most volatile quarter of firms. Beta stays, because dropping it costs roughly six thousandths of R squared averaged over four rolling origins, but it is the one input on this page that is partly an output, and its slider now says so. The same suspicion fell on net margin, which is struck after interest and so contains borrowing by construction, and that one came back clean: the gap between net and operating margin tracks borrowing at minus 0.03, and only the most indebted tenth of firms widens it appreciably.

The input that outranks all four of them is a bankruptcy-risk score. That is not on Rajan and Zingales's list, and it is the clearest single piece of evidence on this page for trade-off theory: the variable the model leans on hardest is a direct measure of how close a firm is to the thing trade-off theory says sets the limit.

The model explains roughly four fifths of the variation in leverage across firms it has never seen, in a year it was not trained on. That is higher than the published benchmark, and the reason is not that this model is better.

Amini and co-authors ran this same family of models over 128,000 company-years of American data and report out-of-sample R squared of about 0.40 for a linear model, rising to 0.55 for boosting and 0.56 for a random forest. The distance between their 0.56 and the 0.79 here is mostly a difference in the question. They predict next year's leverage from this year's figures, deliberately lagging every input so nothing is used before it was public knowledge. This page predicts the same year it observes, which is a genuinely easier problem. They also scale debt by the market value of all assets rather than by debt plus equity. Read 0.79 as a description of this task, not as a score against theirs.

Two further caveats keep the number honest. Predicting the levelof leverage is easier than it sounds, because leverage is highly persistent: last year's value is a strong predictor of this year's all by itself. And predicting the change from prior information is close to impossible here, because the fundamentals that explain where a firm sits explain almost nothing about where it moves next. That is a limit of this panel rather than of the question. With 47 years of data and a framework built for the purpose, the same authors do recover movement toward a target, and find the typical firm closing about half of its gap within a year.

There is a third caveat and it is the one worth holding on to. That four fifths is the score on one particular year. Run the same design across ten different test years, training on the four years before each one, and it averages about three points lower. 2025 was a kind year to be tested on. The number is real, but it is a single draw rather than a promise.

Feeding it more history does not fix that, which is worth saying because the instinct is always to give a model more. Training on fifteen years instead of four makes it measurably worse, and the loss grows with every extra year of history added. Nor is it a question of volume: hand the model the same number of rows drawn from across fifteen years and it still does worse than the same number drawn from the last four. What a balance sheet said about a company's borrowing in 2013 is simply less true today.

Which raises the awkward question of how long any of this stays fresh. Train a model, then test it one, two, three, four and five years later. It gives up about five points in the first year past the data it learned from, then roughly settles. The model on this page learned from figures up to 2024, so a reader arriving in 2026 is already on the second row below, not the first.

One more thing this made visible, and it answers a question worth asking: are companies gradually converging on some shared idea of the right amount to borrow? They are not. Over the same decade the spread between them widened, measurably so, while the model's typical error stayed flat at about ten points. The gap between the most and least indebted firms is growing, and the ability to pin any single one of them is not improving. If managers were all quietly adopting the same textbook, this is not what it would look like.

Two of their findings carry over directly. The first is that the relationship between leverage and its drivers is genuinely curved rather than straight, which is the reason this page runs a tree ensemble instead of a regression: they show that bolting squared and cubed terms onto a linear model does not recover what the tree models find on their own. The second is that the two exercises lean on the same variables. Their best model ranks market-to-book, industry median leverage, cash, the Altman Z score, profitability, stock returns and firm size at the top. Five of those seven sit near the top here as well. The two that do not are market-to-book and past stock return, both left out of this model deliberately, because each contains the market capitalisation that sits in the denominator of the thing being predicted.

The shipped model is also not the best one available. A boosted ensemble small enough to run in a browser gives up very little, but a random forest at the same size gives up a great deal, which is why this page serves boosting rather than the forest the original coursework used.

Interest is deductible and the cost of equity is not. That asymmetry, the debt bias described by De Mooij (2012), pushes firms above the leverage their fundamentals alone would imply, and it makes downturns worse by loading more firms with fixed obligations at the moment cash flow falls.

But the size of that subsidy is not the corporate tax rate, which is the number everyone reaches for, including an earlier version of this page. A company pays tax on its profit, and then the shareholder pays tax again on what reaches them. Borrowing only avoids the first of those. So what matters is what happens to the company-level slice, and countries answer that differently.

Australia answers it in the way that makes the point. There, tax the company has already paid is credited back to shareholders against their own bill, so the company layer is not really a separate levy at all. Skipping it by borrowing gains nobody anything. Germany, and most countries, do not do this: the company slice is gone for good and avoiding it is worth real money. Near enough the same headline rate of thirty percent, and a completely different reason to borrow.

Measuring the subsidy properly instead of reaching for the headline rate changes what the data says. Using the statutory corporate rate, the effect of tax on borrowing here cannot be told apart from zero. Using what a euro of interest actually shelters once shareholder credits are netted off, a positive effect appears, and it holds up when each country is compared against its own past rather than against its neighbours. It is small: countries with a meaningfully larger effective subsidy carry roughly one point more debt.

Small is the right answer and it is what the theory predicted. Once investors' own taxes are counted, the advantage of borrowing is a thin margin rather than the headline rate. A page that found a large effect here would be a page to distrust.

What makes the measurement possible is countries changing their minds. The United Kingdom raised its corporate rate from 19 to 25 percent in 2023, and the United States cut its combined rate from about 39 to 26 percent in 2018. Following the same firms through those changes is what separates a tax effect from everything else that differs between one country and another. It is also why this part of the work needed fifteen years of data, even though the model itself is better off with four.

Policy already targets this margin. The EU anti-tax-avoidance directive caps net interest deductions at 30 percent of EBITDA, and allowance-for-corporate-equity proposals go the other way by giving equity a deduction of its own. Both need the same thing to be evaluated: an estimate of the leverage a firm would carry on its fundamentals, which is what a conditional model like this one provides.

This panel was rebuilt for exactly that question, and the answer is instructive about method. Country is plainly not irrelevant: what firms in the same country do is the fourth heaviest input in the model. Yet comparing tax rates across countries finds nothing, because a country's tax rate travels in company with its legal system, its banks, its disclosure rules and its investor base, and a cross section cannot pull those apart. The effect only appears with the predicted sign when the same firms are followed through real reforms, such as the United Kingdom moving from 19 to 25 percent in 2023. Getting a usable number out of a policy question turns out to depend less on the model than on finding a change worth watching.