Bankruptcy Risk or Bankruptcy Cost?

Debt puts pressure on the firm, because interest and principal payments are obligations. If these obligations are not met, the firm may risk some sort of financial distress. The ultimate distress is bankruptcy, where ownership of the firm’s assets is legally transferred from the shareholders to the bondholders. These debt obligations are fundamentally different from equity obligations. Although shareholders like and expect dividends, they are not legally entitled to them in the way bondholders are legally entitled to interest and principal payments.
We show next that bankruptcy costs, or more generally financial distress costs, tend to offset the advantages to debt. We begin by positing a simple example of bankruptcy. All taxes are ignored to focus only on the costs of debt.

EXAMPLE 16.1

Bankruptcy Costs

Knight NV plans to be in business for one more year. It forecasts a cash flow of either €100 or €50 in the coming year, each occurring with 50 per cent probability. The firm has no other assets. Previously issued debt requires payments of €49 of interest and principal. Day NV has identical cash flow prospects, but has €60 of interest and principal obligations. The cash flows of these two firms can be represented as follows:

p. 436For Knight NV in both boom times and recession, and for Day NV in boom times, cash flow exceeds interest and principal payments. In these situations the bondholders are paid in full, and the shareholders receive any residual. However, the most interesting of the four columns involves Day NV in a recession. Here the bondholders are owed €60, but the firm has only €50 in cash. Because we assumed that the firm has no other assets, the bondholders cannot be satisfied in full. If bankruptcy occurs, the bondholders will receive all of the firm’s cash, and the shareholders will receive nothing. Importantly, the shareholders do not have to come up with the additional €10 (= €60 - €50). Corporations have limited liability in Europe and most other countries, implying that bondholders cannot sue the shareholders for the extra €10.¹
We assume that (a) both bondholders and shareholders are risk-neutral and (b) the interest rate is 10 per cent. Because of this risk-neutrality, cash flows to both shareholders and bondholders are to be discounted at the 10 per cent rate.² We can evaluate the debt, the equity, and the entire firm for both Knight and Day as follows:

Note that the two firms have the same value, even though Day runs the risk of bankruptcy. Furthermore, notice that Day’s bondholders are valuing the bonds with ‘their eyes open’. Though the promised payment of principal and interest is €60, the bondholders are willing to pay only €50. Hence their promised return or yield is

Day’s debt can be viewed as a junk bond because the probability of default is so high. As with all junk bonds, Day’s bondholders demand a high promised yield.
Day’s example is not realistic, because it ignores an important cash flow to be discussed next. A more realistic set of numbers might be these:

Why do the bondholders receive only €35 in a recession? If cash flow is only €50, bondholders will be informed that they will not be paid in full. These bondholders are likely to hire lawyers to negotiate, or even to sue the company. Similarly, the firm is likely to hire lawyers to defend itself. Further costs will be incurred if the case gets to a bankruptcy court. These fees are always paid before the bondholders get paid. In this example we are assuming that bankruptcy costs total €15 (= €50 − 35).
p. 437The value of the firm is now €61.36, an amount below the €68.18 figure calculated earlier. By comparing Day’s value in a world with no bankruptcy costs with Day’s value in a world with these costs, we conclude the following:
The possibility of bankruptcy has a negative effect on the value of the firm. However, it is not the risk of bankruptcy itself that lowers value; rather, it is the costs associated with bankruptcy that lower value.
The explanation follows from our pie example. In a world without bankruptcy costs, the bondholders and the shareholders share the entire pie. However, bankruptcy costs eat up some of the pie in the real world, leaving less for the shareholders and bondholders.
Because the bondholders are aware that they would receive little in a recession, they pay the low price of €43.18. In this case, their promised return is

The bondholders are paying a fair price if they are realistic about both the probability and the cost of bankruptcy. It is the shareholders who bear these future bankruptcy costs. To see this, imagine that Day NV was originally all equity. The shareholders want the firm to issue debt with a promised payment of €60 and use the proceeds to pay a dividend. If there had been no bankruptcy costs, our results show that bondholders would pay €50 to purchase debt with a promised payment of €60. Hence a dividend of €50 could be paid to the shareholders. However, if bankruptcy costs exist, bondholders would pay only €43.18 for the debt. In that case, only a dividend of €43.18 could be paid to the shareholders. Because the dividend is smaller with bankruptcy costs, the shareholders are hurt by these costs.

The preceding example showed that bankruptcy costs can lower the value of the firm. In fact, the same general result holds even if a legal bankruptcy is prevented. Thus financial distress costs may be a better phrase than bankruptcy costs. It is worth while to describe these costs in more detail.

Direct Costs of Financial Distress: Legal and Administrative Costs of Liquidation or Reorganization

As mentioned earlier, lawyers are involved throughout all the stages before and during bankruptcy. With fees often in the hundreds of pounds or euros an hour, these costs can add up quickly. Someone once remarked that bankruptcies are to lawyers what blood is to sharks. In addition, administrative and accounting fees can substantially add to the total bill. If a trial takes place, we must not forget expert witnesses. Each side may hire a number of these witnesses to testify about the fairness of a proposed settlement, and their fees can easily rival those of lawyers or accountants.
One of the most well-publicized bankruptcies in recent years concerned Lehman Brothers, at the time one of the biggest banks in the world. This bankruptcy followed large write-downs on subprime mortgage assets and a general collapse in interbank credit in September 2008. Business Week stated:
p. 438The Lehman Brothers bankruptcy is quickly becoming one giant mess.
Scores of hedge funds that had hundreds of millions in cash and other securities parked with Lehman’s prime brokerage operation in London have had their accounts frozen. A number of these hedge funds have filed formal objections with the bankruptcy court and at least one fund, New York-based Bay Harbour Management, is mounting a legal challenge to the court’s hastily-approved sale of Lehman’s brokerage arm to Barclays Capital.
Now a new and even more troubling scenario is arising: legal disputes stemming from the estimated $1 trillion in derivatives transactions that Lehman had entered into on behalf of itself and some of its customers. Already, at least three lawsuits have been filed, alleging that nearly $600 million in collateral posted by some of Lehman’s trading partners in derivatives transactions hasn’t been returned and is in jeopardy of disappearing as the bankruptcy process unfolds.
To date, the most aggrieved of Lehman’s trading partners is Bank of America, which at one time was considering buying Lehman as the investment firm was lurching towards bankruptcy. The Charlotte, NC based lender is seeking to recover nearly $500 million the bank ‘posted as collateral to ‘support derivative transactions between BofA and the respective Lehman Entities’, according to a lawsuit filed in New York State Supreme Court.³
Bankruptcy costs can be absolutely massive with large companies like Lehman Brothers. For example, as of 2008, the direct costs of Enron’s bankruptcy (in 2001) included thousands of jobs, more than $60 billion in market value, $2 billion in pension plans, $7.3 billion in compensation, and at least $30 billion of claims still in courts. Think of the legal fees resulting from all of this ….
A number of academic studies have measured the direct costs of financial distress. Although large in absolute amount, these costs are actually small as a percentage of firm value. White, Altman and Weiss estimate the direct costs of financial distress to be about 3 per cent of the market value of the firm.⁴ Bris, Welch and Zhu find that direct costs are about 8 per cent of pre-bankruptcy assets. However, since the costs are fixed, irrespective of the size of the firm, the proportional costs can be between 20 and 25 per cent for smaller firms.⁵
Of course, few firms end up in bankruptcy. Thus the preceding cost estimates must be multiplied by the probability of bankruptcy to yield the expected cost of bankruptcy. For example, consider a firm that has a 5 per cent probability of going into bankruptcy each year. If the firm declares bankruptcy, the direct costs it incurs amount to 8 per cent of the total value of the firm. The expected bankruptcy cost must be then 0.4 per cent (= 0.05 × 0.08).

Indirect Costs of Financial Distress

Impaired Ability to Conduct Business Bankruptcy hampers conduct with customers and suppliers. Sales are frequently lost because of both fear of impaired service and loss of trust. For example, in 2008 many loyal HBOS and Royal Bank of Scotland customers switched to other banks when rumours of the banks’ funding situation spread. These buyers questioned whether they would be able to get access to their money were the banks to fail. Sometimes the taint of impending bankruptcy is enough to drive customers away.
Though these costs clearly exist, it is quite difficult to measure them. Altman estimates that both direct and indirect costs of financial distress are frequently greater than 20 per cent of firm value.⁶ Andrade and Kaplan estimate total distress costs to be between 10 per cent and 20 per cent of firm value.⁷ Bar-Or estimates expected future distress costs for firms that are currently healthy to be 8 to 10 per cent of operating value, a number below the estimates of either Altman or Andrade and Kaplan.⁸ However, unlike Bar-Or, these authors consider distress costs for firms already in distress, not expected distress costs for currently healthy firms.
Cutler and Summers examine the costs of the well-publicized Texaco bankruptcy.⁹ In January 1984 Pennzoil reached what it believed to be a binding agreement to acquire three-sevenths of Getty Oil. However, less than a week later Texaco acquired all of Getty at a higher per-share price. Pennzoil then sued Getty for breach of contract. Because Texaco had previously indemnified Getty against litigation, Texaco became liable for damages.
p. 439In November 1985 the Texas State Court awarded damages of $12 billion to Pennzoil, although this amount was later reduced. As a result, Texaco filed for bankruptcy. Cutler and Summers identify nine important events over the course of the litigation. They find that Texaco’s market value (share price times number of shares outstanding) fell a cumulative $4.1 bil-lion over these events, whereas Pennzoil rose only $682 million. Thus Pennzoil gained about one-sixth of what Texaco lost, resulting in a net loss to the two firms of almost $3.5 billion.
What could explain this net loss? Cutler and Summers suggest that it is probably due to costs that Texaco and Pennzoil incurred from the litigation and subsequent bankruptcy. The authors argue that direct bankruptcy fees represent only a small part of these costs, estimating Texaco’s after-tax legal expenses to be about $165 million. Legal costs to Pennzoil were more difficult to assess, because Pennzoil’s lead lawyer, Joe Jamail, stated publicly that he had no set fee. However, using a clever statistical analysis, the authors estimate his fee to be about $200 million. Thus we must search elsewhere for the bulk of the costs.
Indirect costs of financial distress may be the culprit. An affidavit by Texaco stated that, following the lawsuit, some of its suppliers were demanding cash payment. Other suppliers halted or cancelled shipments of crude oil. Certain banks restricted Texaco’s use of futures contracts on foreign exchange. The affidavit stressed that these constraints were reducing Texaco’s ability to run its business, leading to deterioration of its financial condition. Could these sorts of indirect costs explain the $3.5 billion disparity between Texaco’s drop and Pennzoil’s rise in market value? Unfortunately, although it is quite likely that indirect costs play a role here, there is simply no way to obtain a decent quantitative estimate for them.

Agency Costs

When a firm has debt, conflicts of interest arise between shareholders and bondholders. Because of this, shareholders are tempted to pursue selfish strategies. These conflicts of interest, which are magnified when financial distress is incurred, impose agency costs on the firm. We describe three kinds of selfish strategy that shareholders use to hurt the bondholders and help themselves. These strategies are costly, because they will lower the market value of the whole firm.
Selfish Investment Strategy 1: Incentive to Take Large Risks Firms near bankruptcy often take great chances, because they believe that they are playing with someone else’s money. To see this, imagine a levered firm considering two mutually exclusive projects, a low-risk one and a high-risk one. There are two equally likely outcomes, recession and boom. The firm is in such dire straits that should a recession hit, it will come near to bankruptcy with one project and actually fall into bankruptcy with the other. The cash flows for the entire firm if the low-risk project is taken can be described as follows:

If recession occurs, the value of the firm will be £100; if a boom occurs, the value of the firm will be £200. The expected value of the firm is £150 (= 0.5 × £100 + 0.5 × £200).
The firm has promised to pay bondholders £100. Shareholders will obtain the difference between the total pay-off and the amount paid to the bondholders. In other words, the bondholders have the prior claim on the pay-offs, and the shareholders have the residual claim.
Now suppose that the riskier project can be substituted for the low-risk project. The pay-offs and probabilities are as follows:

p. 440The expected value of the firm is £145 (= 0.5 × £50 + 0.5 × £240), which is lower than the expected value of the firm with the low-risk project. Thus the low-risk project would be accepted if the firm were all equity. However, note that the expected value of the equity is £70 (= 0.5 × 0 + 0.5 × £140) with the high-risk project, but only £50 (= 0.5 × 0 + 0.5 × £100) with the low-risk project. Given the firm’s present levered state, shareholders will select the high-risk project, even though the high-risk project has a lower NPV.
The key is that, relative to the low-risk project, the high-risk project increases firm value in a boom and decreases firm value in a recession. The increase in value in a boom is captured by the shareholders because the bondholders are paid in full (they receive £100) regardless of which project is accepted. Conversely, the drop in value in a recession is lost by the bondholders because they are paid in full with the low-risk project but receive only £50 with the high-risk one. The shareholders will receive nothing in a recession anyway, whether the high-risk or low-risk project is selected. Thus financial economists argue that shareholders expropriate value from the bondholders by selecting high-risk projects.
Selfish Investment Strategy 2: Incentive towards Underinvestment Shareholders of a firm with a significant probability of bankruptcy often find that new investment helps the bondholders at the shareholders’ expense. The simplest case might be a property owner facing imminent bankruptcy. If he took €100,000 out of his own pocket to refurbish the building, he could increase the building’s value by, say, €150,000. Though this investment has a positive net present value, he will turn it down if the increase in value cannot prevent bankruptcy. ‘Why,’ he asks, ‘should I use my own funds to improve the value of a building that the bank will soon repossess?’
This idea is formalized by the following simple example. Consider the firm in Table 16.1, which must decide whether to accept or reject a new project. The first two columns in the table show cash flows without the project. The firm receives cash inflows of £5,000 and £2,400 under a boom and a recession, respectively. Because the firm must pay principal and interest of £4,000, the firm will default in a recession.
Alternatively, as indicated in the next two columns of the table, the firm could raise equity to invest in a new project. The project brings in £1,700 in either state, which is enough to prevent bankruptcy even in a recession. Because £1,700 is much greater than the project’s cost of £1,000, the project has a positive NPV at any plausible interest rate. Clearly, an all-equity firm would accept the project.

Table 16.1	Example illustrating incentive to underinvest

p. 441However, the project hurts the shareholders of the levered firm. To see this, imagine that the old shareholders contribute the £1,000 themselves.¹⁰ Assuming that a boom and a recession are equally likely, the expected value of the shareholders’ interest without the project is £500 (= 0.5 × £1,000 + 0.5 × 0). The expected value with the project is £1,400 (= 0.5 × £2,700 + 0.5 × £100). The shareholders’ interest rises by only £900 (= £1,400 - £500) while costing £1,000.
Why does a project with a positive NPV hurt the shareholders? The key is that the shareholders contribute the full £1,000 investment, but the shareholders and bondholders share the benefits. The shareholders take the entire gain if boom times occur. Conversely, the bondholders reap most of the cash flow from the project in a recession.
The discussion of selfish strategy 1 is quite similar to the discussion of selfish strategy 2. In both cases an investment strategy for the levered firm is different from the one for the unlevered firm. Thus leverage results in distorted investment policy. Whereas the unlevered corporation always chooses projects with positive net present value, the levered firm may deviate from this policy.
Selfish Investment Strategy 3: Milking the Property Another strategy is to pay out extra dividends or other distributions in times of financial distress, leaving less in the firm for the bondholders. This is known as milking the property, a phrase taken from real estate. Strategies 2 and 3 are very similar. In strategy 2, the firm chooses not to raise new equity. Strategy 3 goes one step further because equity is actually withdrawn through the dividend.
Summary of Selfish Strategies The distortions just discussed occur only when there is a probability of bankruptcy or financial distress. Thus these distortions should not affect, say, Vodafone because bankruptcy is not a realistic possibility for a diversified blue-chip firm such as this. In other words, Vodafone’s debt will be virtually risk-free, regardless of the projects it accepts. The same argument could be made for nationalized banks, such as the Royal Bank of Scotland, that are protected by the government. By contrast, small firms in risky industries, such as computers, are more likely to experience financial distress and, in turn, to be affected by such distortions.
Who pays for the cost of selfish investment strategies? We argue that it is ultimately the shareholders. Rational bondholders know that when financial distress is imminent, they cannot expect help from shareholders. Rather, shareholders are likely to choose investment strategies that reduce the value of the bonds. Bondholders protect themselves accordingly by raising the interest rate that they require on the bonds. Because the shareholders must pay these high rates, they ultimately bear the costs of selfish strategies. For firms that face these distortions, debt will be difficult and costly to obtain. These firms will have low leverage ratios.
The relationship between shareholders and bondholders is very similar to the relationship between Erroll Flynn and David Niven, good friends and movie stars in the 1930s. Niven reportedly said that the good thing about Flynn was that you knew exactly where you stood with him. When you needed his help, you could always count on him to let you down

16.7 The Pecking-Order Theory

Although the trade-off theory has dominated corporate finance circles for a long time, attention has also been paid to the pecking-order theory.¹⁷ To understand this view of the world, let’s put ourselves in the position of a corporate financial manager whose firm needs new capital. The manager faces a choice between issuing debt and issuing equity. Previously, we evaluated the choice in terms of tax benefits, distress costs, and agency costs. However, there is one consideration that we have so far neglected: timing.
Imagine the manager saying:
p. 450

I want to issue equity in one situation only - when it is overvalued. If the equity of my firm is selling at £50 per share, but I think that it is actually worth £60, I will not issue equity. I would actually be giving new shareholders a gift because they would receive equity worth £60 but would only have to pay £50 for it. More important, my current shareholders would be upset because the firm would be receiving £50 in cash but giving away something worth £60. So if I believe that my equity is undervalued, I would issue bonds. Bonds, particularly those with little or no risk of default, are likely to be priced correctly. Their value is determined primarily by the market-wide interest rate, a variable that is publicly known.
But suppose our equity is selling at £70. Now I’d like to issue equity. If I can get some fool to buy our shares for £70 while the equity is really worth only £60, I will be making £10 for our current shareholders.

Although this may strike you as a cynical view, it seems to square well with reality. Before the United States adopted insider trading and disclosure laws, many managers were alleged to have unfairly trumpeted their firm’s prospects prior to equity issuance. And even today, managers seem more willing to issue equity after the price of their shares has risen than after their shares have fallen in price. Thus timing might be an important motive in equity issuance, perhaps even more important than the motives in the trade-off model. After all, the firm in the preceding example immediately makes £10 by properly timing the issuance of equity. £10 worth of agency costs and bankruptcy cost reduction might take many years to realize.
The key that makes the example work is asymmetric information: the manager must know more about his firm’s prospects than the typical investor does. If the manager’s estimate of the true worth of the company is no better than the estimate of a typical investor, any attempts by the manager at timing will fail. This assumption of asymmetry is quite plausible. Managers should know more about their company than outsiders do because managers work at the company every day. (One caveat is that some managers are perpetually optimistic about their firm, blurring good judgement.)
But we are not done with this example yet; we must consider the investor. Imagine an investor saying:

I make investments carefully because they involve my hard-earned money. However, even with all the time I put into studying shares, I can’t possibly know what the managers themselves know. After all, I’ve got a day job to be concerned with. So I watch what the managers do. If a firm issues equity, the firm was probably overvalued beforehand. If a firm issues debt, it was probably undervalued.

When we look at both issuers and investors, we see a kind of poker game, with each side trying to outwit the other. What should the issuing firm do in this poker game? Clearly, the firm should issue debt if the equity is undervalued. But what if the equity is overvalued? Here it gets tricky, because a first thought is that the firm should issue equity. However, if a firm issues equity, investors will infer that the shares are overvalued. They will not buy them until the share price has fallen enough to eliminate any advantage from equity issuance. In fact, it can be shown that only the most overvalued firms have any incentive to issue equity. Should even a moderately overpriced firm issue equity, investors will infer that this firm is among the most overpriced, causing the shares to fall more than is deserved. Thus the end result is that virtually no one will issue equity.¹⁸
This result, that essentially all firms should issue debt, is clearly an extreme one. It is as extreme as (a) the Modigliani–Miller (MM) result that, in a world without taxes, firms are indifferent to capital structure, and (b) the MM result that, in a world of corporate taxes but no financial distress costs, all firms should be 100 per cent debt-financed. Perhaps we in finance have a penchant for extreme models!
But just as we can temper MM’s conclusions by combining financial distress costs with corporate taxes, we can temper those of the pure pecking-order theory. This pure version assumes that timing is the financial manager’s only consideration. In reality, a manager must consider taxes, financial distress costs and agency costs as well. Thus a firm may issue debt only up to a point. If financial distress becomes a real possibility beyond that point, the firm may issue equity instead.

Rules of the Pecking Order

p. 451The previous discussion presented the basic ideas behind the pecking-order theory. What are the practical implications of the theory for financial managers? The theory provides the following two rules for the real world.
Rule 1: Use Internal Financing For expository purposes, we have oversimplified by comparing equity to riskless debt. Managers cannot use special knowledge of their firm to determine whether this type of debt is mispriced, because the price of riskless debt is determined solely by the market-wide interest rate. However, in reality, corporate debt has the possibility of default. Thus, just as managers tend to issue equity when they think it is overvalued, managers also tend to issue debt when they think it is overvalued.
When would managers view their debt as overvalued? Probably in the same situations when they think their equity is overvalued. For example, if the public thinks that the firm’s prospects are rosy but the managers see trouble ahead, these managers would view their debt - as well as their equity - as being overvalued. That is, the public might see the debt as nearly risk-free, whereas the managers see a strong possibility of default.
Thus investors are likely to price a debt issue with the same scepticism that they have when pricing an equity issue. The way managers get out of this box is to finance projects out of retained earnings. You don’t have to worry about investor scepticism if you can avoid going to investors in the first place. So the first rule of the pecking order is this:
Use internal financing.
Rule 2: Issue Safe Securities First Although investors fear mispricing of both debt and equity, the fear is much greater for equity. Corporate debt still has relatively little risk compared with equity, because if financial distress is avoided, investors receive a fixed return. Thus the pecking-order theory implies that if outside financing is required, debt should be issued before equity. Only when the firm’s debt capacity is reached should the firm consider equity.
Of course, there are many types of debt. For example, because convertible debt is more risky than straight debt, the pecking-order theory implies that managers should issue straight debt before issuing convertibles. So, the second rule of pecking-order theory is this:
Issue the safest securities first.

Implications

A number of implications associated with the pecking-order theory are at odds with those of the trade-off theory.

There is no target amount of leverage. According to the trade-off model, each firm balances the benefits of debt, such as the tax shield, with the costs of debt, such as distress costs. The optimal amount of leverage occurs where the marginal benefit of debt equals the marginal cost of debt.
By contrast, the pecking-order theory does not imply a target amount of leverage. Rather, each firm chooses its leverage ratio based on financing needs. Firms first fund projects out of retained earnings. This should lower the percentage of debt in the capital structure, because profitable, internally funded projects raise both the book value and the market value of equity. Additional projects are funded with debt, clearly raising the debt level. However, at some point the debt capacity of the firm may be exhausted, giving way to equity issuance. Thus the amount of leverage is determined by the happenstance of available projects. Firms do not pursue a target ratio of debt to equity.
p. 452
Profitable firms use less debt. Profitable firms generate cash internally, implying less need for outside financing. Because firms desiring outside capital turn to debt first, profitable firms end up relying on less debt. The trade-off model does not have this implication. Here the greater cash flow of more profitable firms creates greater debt capacity. These firms will use that debt capacity to capture the tax shield and the other benefits of leverage.
Companies like financial slack. The pecking-order theory is based on the difficulties of obtaining financing at a reasonable cost. A sceptical investing public thinks an equity is overvalued if the managers try to issue more of it, thereby leading to a share price decline. Because this happens with bonds, only to a lesser extent, managers rely first on bond financing. However, firms can issue only so much debt before encountering the potential costs of financial distress.
Wouldn’t it be easier to have the cash ahead of time? This is the idea behind financial slack. Because firms know that they will have to fund profitable projects at various times in the future, they accumulate cash today. They are then not forced to go to the capital markets when a project comes up. However, there is a limit to the amount of cash a firm will want to accumulate. As mentioned earlier in this chapter, too much free cash may tempt managers to pursue wasteful activities.

Growth and the Debt–Equity Ratio
Although the trade-off between the tax shield and bankruptcy costs (as illustrated in Fig. 16.1) is often viewed as the ‘tandard model’ of capital structure, it has its critics. For example, some point out that bankruptcy costs in the real world appear to be much smaller than the tax subsidy. Thus the model implies that the optimal debt/value ratio should be near 100 per cent, an implication at odds with reality.¹⁹
Perhaps the pecking-order theory is more consistent with the real world here. That is, firms are likely to have more equity in their capital structure than implied by the static trade-off theory, because internal financing is preferred to external financing.
There is another approach that implies significant equity financing, even in a world with low bankruptcy costs. This idea, developed by Berens and Cuny,²⁰ argues that equity financing follows from growth. To explain the idea, we first consider an example of a no-growth firm. Next, we examine the effect of growth on firm leverage.

No Growth
Imagine a world of perfect certainty²¹ where a firm has annual earnings before interest and taxes (EBIT) of €100. In addition, the firm has issued €1,000 of debt at an interest rate of 10 per cent, implying interest payments of €100 per year. Here are the cash flows to the firm:

The firm has issued just enough debt so that all EBIT are paid out as interest. Because interest is tax-deductible, the firm pays no taxes. In this example the equity is worthless, because shareholders receive no cash flows. Since debt is worth €1,000, the firm is also valued at €1,000. Therefore the debt-to-value ratio is 100 per cent (= €1,000/€1,000).
Had the firm issued less than €1,000 of debt, the corporation would have positive taxable income and, consequently, would have ended up paying some taxes. Had the firm issued more than €1,000 of debt, interest would have exceeded EBIT, causing default. Consequently, the optimal debt-to-value ratio is 100 per cent.

Growth
p. 453Now imagine another firm where EBIT are also €100 at date 1 but are growing at 5 per cent per year.²² To eliminate taxes, this firm also wants to issue enough debt so that interest equals EBIT. Because EBIT are growing at 5 per cent per year, interest must also grow at this rate. This is achieved by increasing debt by 5 per cent per year.²³ The debt, EBIT, interest and taxable income levels are these:

Note that interest on a particular date is always 10 per cent of the debt on the previous date. Debt is set so that interest is exactly equal to EBIT. As in the no-growth case, the levered firm has the maximum amount of debt at each date. Default would occur if interest payments were increased.
Because growth is 5 per cent per year, the value of the firm is²⁴

The equity at date 0 is the difference between the value of the firm at that time, €2,000, and the debt of €1,000. Hence equity must be equal to €1,000,²⁵ implying a debt-to-value ratio of 50 per cent (= €1,000/€2,000). Note the important difference between the no-growth and the growth example. The no-growth example has no equity; the value of the firm is simply the value of the debt. With growth, there is equity as well as debt.
We can also value the equity in another way. It may appear at first glance that the shareholders receive nothing, because the EBIT are paid out as interest each year. However, the new debt issued each year can be paid as a dividend to the shareholders. Because the new debt is €50 at date 1 and grows at 5 per cent per year, the value of the shareholders’ interest is

the same number that we obtained in the previous paragraph.
As we mentioned earlier, any further increase in debt above €1,000 at date 0 would lower the value of the firm in a world with bankruptcy costs. Thus, with growth, the optimal amount of debt is less than 100 per cent. Note, however, that bankruptcy costs need not be as large as the tax subsidy. In fact, even with infinitesimally small bankruptcy costs, firm value would decline if promised interest rose above €100 in the first year. The key to this example is that today’s interest is set equal to today’s income. Although the introduction of future growth opportunities increases firm value, it does not increase the current level of debt needed to shield today’s income from today’s taxes. Because equity is the difference between firm value and debt, growth increases the value of equity.
The preceding example captures an essential feature of the real world: growth. The same conclusion is reached in a world of inflation but with no growth opportunities. Thus the result of this section, that 100 per cent debt financing is suboptimal, holds whether inflation or growth opportunities are present. Furthermore, high-growth firms should have lower debt ratios than low-growth firms. Most firms have growth opportunities, and inflation has been with us for most of this and the previous centuries, so this section’s example is based on realistic assumptions.²⁶
1. We mentioned in the last chapter that, according to theory, firms should create all-debt capital structures under corporate taxation. Because firms generally employ moderate amounts of debt in the real world, the theory must have been missing something at that point. We stated in this chapter that costs of financial distress cause firms to restrain their issuance of debt. These costs are of two types: direct and indirect. Lawyers’ and accountants’ fees during the bankruptcy process are examples of direct costs. We mentioned four examples of indirect costs:
  1. Impaired ability to conduct business
  2. Incentive to take on risky projects
  3. Incentive towards underinvestment
  4. Distribution of funds to shareholders prior to bankruptcy
2. Because financial distress costs are substantial, and the shareholders ultimately bear them, firms have an incentive to reduce costs. Protective covenants and debt consolidation are two common cost reduction techniques.
3. Because costs of financial distress can be reduced but not eliminated, firms will not finance entirely with debt. Figure 16.1 illustrates the relationship between firm value and debt. In the figure, firms select the debt–equity ratio at which firm value is maximized.
4. Signalling theory argues that profitable firms are likely to increase their leverage, because the extra interest payments will offset some of the pre-tax profits. Rational shareholders will infer higher firm value from a higher debt level. Thus investors view debt as a signal of firm value.
5. Managers owning a small proportion of a firm’s equity can be expected to work less, maintain more lavish expense accounts, and accept more pet projects with negative NPVs than managers owning a large proportion of equity. Because new issues of equity dilute a manager’s percentage interest in the firm, such agency costs are likely to increase when a firm’s growth is financed through new equity rather than through new debt.
6. The pecking-order theory implies that managers prefer internal to external financing. If external financing is required, managers tend to choose the safest securities, such as debt. Firms may accumulate slack to avoid external equity.
7. The market timing theory suggests that there is no pecking order or trade-off of capital structure choices. Observed debt ratios are simply a function of past market to book valuations and the timing of funding requirements. Firms will have more equity if they needed funding when market to book valuations were high. Conversely, if financing was required during low market to book periods, debt will tend to dominate.
8. Berens and Cuny argue that significant equity financing can be explained by real growth and inflation, even in a world of low bankruptcy costs.
9. Debt–equity ratios vary across industries. We present three factors determining the target debt–equity ratio:
  1. Taxes: Firms with high taxable income should rely more on debt than firms with low taxable income.
  2. Types of assets: Firms with a high percentage of intangible assets such as research and development should have low debt. Firms with primarily tangible assets should have higher debt.
  3. Uncertainty of operating income: Firms with high uncertainty of operating income should rely mostly on equity.