Limited Liability Revisited

by Michael S. Rozeff
by Michael S. Rozeff

Judging from my e-mails and from Gary North’s able, useful and correct follow-up article, my first article on limited liability missed the mark. This article takes the discussion further. Without boring you with a rehash, it also puts right, at least I hope so, whatever mistakes and appearances of mistakes cropped up in the earlier article.

This time I’ll show more precisely what limited and unlimited liability mean in regard to financing a company. I’ll show how they are linked and how they can be converted one into the other financially. I’ll argue that neither civilization nor the corporation will fall to pieces if there is no State around that has a limited liability law. I’ll explain some reasons why limited liability has value in terms of financing a company. Paradoxically, this does not mean that corporations or anyone else require a State’s limited liability law. Free persons in a free and stateless society can create limited liability on their own and at will by agreement or contractually. There are also ways to create limited liability by financial operations.

Free persons frequently want to create homemade limited liability on their own, and there are good reasons to do so. Therefore, for the State to outlaw limited liability is both unjust, taking away what belongs to individuals, and also thwarts mankind’s legitimate proclivities. Outlawing limited liability is clearly inconsistent with freedom.

Freedom is also inconsistent with a State’s imposing limited liability by statute on every corporation and disallowing it for other business forms. If unincorporated businesses such as partnerships and proprietorships must have unlimited liability and simultaneously must face different tax and other rules than corporations, then their freedom is diminished. This is because they have to choose a package of business features (liability, tax and regulatory). This was the case in the United States until 1977. In that year Wyoming passed a Limited Liability Company Act that allowed limited liability without being a corporation. After the IRS changed its rulings concerning taxation, this business form caught on.

Despite the fact that the LLC has limited liability, lenders often demand personal loan guarantees. This procedure converts what lenders view as a high-risk loan that they do not wish to extend into a lower-risk loan that they are willing to make. In other words, by private agreement lenders and borrowers convert a limited liability form into an unlimited liability form, wholly or partially. That is, by varying the loan risk and default contingencies, the amount of loan exposure to unlimited liability can be altered on a sliding scale. We will see that conversions in both directions are possible. This flexibility arises from the alternatives open within financial contracting. Such financial flexibility illustrates that individuals can control risks without State interference.

In my first article, I wrote: "A real free market does not allow one person to damage another person with impunity. For this reason, there can be no limited liability in a free market..." Damaging others with impunity by breaking laws or agreements is wrong, and for such acts one should be exposed to liability. However, the stand-alone phrase (without the qualifier "for this reason" and without reference to damage with impunity) that "there can be no limited liability in a free market" is false. Limited liability is certainly possible in a free market by agreements that intentionally and voluntarily allow some acts to go unpunished. That means that all affected parties understand and agree to the situation. Free market limited liability does not refer to a situation in which the State defines or imposes limited liability in such a way that persons damaged by a corporation’s actions are unable to obtain redress, or a situation where the State limits the forms of business organization.

The notion that a free society is a "full liability" society does not mean to me that voluntary limited liability is disallowed by the State. It means that one must face the consequences of one’s illegitimate acts against others. It is a term meant to contrast with a situation in which the State arbitrarily limits liability and prevents injured parties from obtaining justice. Perhaps the term "full liability" is too confusing to be used properly in this way.

As mentioned above, the State via IRS rulings and other regulations was able to constrain many businesses from forming the equivalent of the LLC by their using purely financial means. The IRS constantly strives to render tax shelters inoperative. Therefore, financial methods do not provide unlimited flexibility to undo all of the State’s strictures. However, both individual investors and corporations have the ability to create limited liability from unlimited liability, and to transform unlimited liability into limited liability. They can do this by contract, guarantees, insurance and other control devices and sometimes by financial maneuvers. This can be done in a variety of ways without the State being involved. It can happen in a free society or in a society with a State. The complexity and subtlety of these issues are reflected in the lengthy venture capital agreements that can run to hundreds of pages.

To explain what limited liability and unlimited liability mean financially and to illustrate their transformations, I go to the other extreme and use the simplest possible example. Complications do not alter the basic conclusions. The dollar values chosen are self-consistent in a way common to financial analysis. They are not selected at random, and they can’t be altered at random without running into contradiction. In particular, there are no "free lunches" allowed, or easily spotted profits.

For simplicity, the risk-free rate of interest (the Treasury bill rate, say) is set at 0 percent. Do not be alarmed; this doesn’t affect the conclusions at all. To simplify, we look at stocks and bonds for which only two things can happen in the future. They can either go up to a single value or down to a single value. To maintain the no free lunch market, any dollar of cash flow in the up state always has a present worth of $0.35 and any dollar of cash flow in the down state always has a present worth of $0.65. Money is worth more in the down state because it represents hard times and there is less income, but the conclusions would not be altered if we changed these numbers as long as we use them consistently. There are some other simplifications that I will not spell out.

Suppose there is a company whose current market value is $128.50 and that in the future (at some one time), the value can either rise to $200 or fall to $90. There is a good state and a bad state of the world, like boom or bust. To check the arithmetic, notice that the present value of 128.50 = 0.35(200) + 0.65(90).

Let us imagine that the company is an unlimited liability company financed by both stocks and bonds. If its liability is unlimited, then the bonds have no risk. The bondholders can always recover their money because they can assess the company owners personally.

That’s worth repeating because it’s so uncommon. Unlimited stockholder liability means that the company’s bonds have no risk of loss even if the company goes bankrupt. The bondholders will take what’s owed them from the personal assets of the stockholders. A stockholder can lose more than his initial investment.

I posit that the risk-free debt of this company is now worth $100. This means that next period it pays off $100 no matter whether the stock rises or falls. This is because the debt has no risk – it surely pays off $100 – and because the interest rate is 0.

The unlimited liability stock has to be worth $28.5 because 100 + 28.5 = 128.50; market value is preserved. This stock pays off $100 in the good state, because the firm’s total payoff in boom times is $200 = $100 + $100. In the bad state, the stock is bankrupt. The bondholders take the $90 worth of firm assets. The stockholders dig into their pockets to pay the other $10 that they owe. That’s their personal liability. The payoffs of the stock are thus $100 in the good state and –$10 in the bad state. That negative sign is what unlimited liability is all about. Owning the unlimited liability stock creates a stockholder liability or payout in the bad state.

Now I will show how to convert this position into a limited liability position using only financial actions. There are many possibilities. The target I choose is a capital structure in which there is a risky bond that pays off $100 in the good state and $90 in the bad state. These bonds are worth $93.5, because 93.5 = 0.35(100) + 0.65(90). In the good state, they pay off at par of $100, but in the bad state they pay off only $90, which is all that the company is worth. In other words, the assets of the bankrupt company go to the risky bondholder but he does not get back all his initial investment of $93.5.

These risky bonds have a higher yield than the 0 rate of the risk-free bonds, but we do not need to work out what it is.

In this risky bond case, the stock now has limited liability. The stock receives $100 in the good state and $0 in the bad state because the risky bondholders get the $90 in the bad state. This limited liability stock is worth $35, which is $6.50 more than the unlimited liability stock. The overall value of the company is still $128.50. However, this value is split up in a different way between the bondholders and the stockholders.

An owner of the risk-free bond can convert it into the risky bond as follows. Sell off $9.0909 of the $100 worth of the risk-free bond. From the $9.0909, take enough money ($2.5909) to buy 0.09091 of the unlimited liability stock. This operation leaves the person with $6.50 left over, which he pockets. But it’s fair compensation for now owning a risky bond.

Wait! Where’s the risky bond he is supposed to own? It’s there because the future cash flows of this combined risk-free bond + unlimited liability stock position give cash flows in the future identical to the risky bond. In the good state, the owner has $90.909 cash flow from the risk-free bond and 0.09091(100) = $9.091 cash flow from the stock. They add up to $100, the same as the risky bond. In the bad state, the owner has $90.9091 cash flow from the risk-free bond and must pay out 0.09091(10) = $0.9091 on the stock. He nets $90, the same as the risky bond. These steps have replicated the risky bond out of the risk-free bond and the unlimited liability stock.

If you skipped the arithmetic, it showed that a risk-free bond and an unlimited liability stock can be converted into a risky bond by selling off some of the risk-free bond and investing in the stock. If we start out with a risky bond and a limited liability stock, we can reverse the procedure. We can convert a limited liability position into an unlimited liability position.

That extra $6.50 is the value of the shareholder’s right in a limited liability company to place or put the $90 of assets into the hands of the risky bondholders. Limited liability gives shareholders the right to walk away from the company in bankruptcy and let the bondholders take the assets, but that right is not free. It costs $6.50. This right is an instance of a put option. The risk-free bondholders have issued this put option (indirectly via their financial actions) and collected $6.50 for it. In return, if things go badly the stockholders have the right to "put" the company’s assets to them.

By the same token, the unlimited liability shareholders have in essence bought this put option for $6.50. This option converts their position into one of limited liability. To see this, start out with an unlimited liability position and convert it into a limited liability position by selling off some of the shares and lending. In this example, sell off 0.09091 shares for $2.5909 and lend $9.0909, which costs a net amount of $6.50. In the good state, the shareholder has 0.9091($100) = $90.91 from the remaining shares and $9.0909 from the loan, which total $100. In the bad state, he has $9.0909 from the loan and must pay out 0.9091($10). These add to $0. The resulting cash flows of $100 in the good state and $0 in the bad state are identical to those of a limited liability share.

The conversion requires the shareholders to spend $6.50 of their own money, which is the present value of the $10 they would otherwise have to pay in bankruptcy. There is no free lunch, but it is possible to change from unlimited to limited liability. To do the reverse, we can convert the limited liability stock into unlimited liability stock by borrowing and buying the limited liability shares.

By financial operations that do not directly involve any put option but mimic a put option, one can convert risky debt into risk-free debt or the reverse, and one can convert limited liability stock into unlimited liability stock or the reverse.

To sum up, risk-free debt + unlimited liability stock has the same value as risky debt + limited liability stock, or $100 + $28.50 = $93.5 + $35. Limited liability stock is worth more than unlimited liability stock because the limited liability stockholders can put the assets to the risky bondholders. The risky debt is worth less than the risk-free debt by the same amount, because the risk-free debtholders have written this put option.

Limited liability involves an ability to cut off damages when something bad happens. That can be done by insurance. A put option is a type of insurance against losses when the stock declines.

Although these conversions are possible financially without making contractual changes, they are uncommon. However, they serve to illustrate what’s really involved in a limited liability stock, they show that financial freedom can sometimes negate State constraints, and they give some idea of orders of magnitude of the effects. In practice, the ability to make contracts makes it even more possible for investors and companies to create all sorts of mutually desirable financial securities or other limited liability situations. As complex as real-world situations can be, they often can be broken down into simpler pieces involving various kinds of options that pay off under various contingencies. The example provides a taste of what free market contracting can come up with.

Let’s apply what we have gone through to the real world. Today’s corporations have risky debt and limited liability. Many large corporations have high-grade debt that is close to risk-free. If they somehow lost the limited liability feature, the stock values would not alter much. Many companies have lower-grade debt, and that means that the limited liability option contributes more to their stock values. If they suddenly lost limited liability, the bonds would gain in value and the stocks would lose in value. Overall market value would probably decline temporarily because the financial structure had been disrupted and it would take time for everyone to adjust and revamp the features of securities. But the decline need not be monstrous because the bonds gain what the stocks lose. Furthermore, despite the fact that the illustration used was very simple, the values selected were representative of the real world. For this firm, which was very heavily indebted, having nearly 78 percent debt, the limited liability option value of $6.50 was 23 percent of the stock’s value and only 5 percent of the firm’s value. For companies with lower financial leverage, limited liability option values will be even lower. Doomsday predictions that capitalism and corporations will collapse if the State and its limited liability law are not around are faulty. By the same token, it is highly unlikely that the State’s role in limited liability is the main source of corporation value or success. However, limited liability is preferable to unlimited liability for reasons to be outlined shortly.

For the State suddenly to end limited liability would accomplish little. It would shift stockholder wealth to bondholders, but that would be reversed over time as new provisions were voluntarily instituted. The State’s role in limited liability might conceivably be brought to an end by honoring the existing bondholder contracts. Corporations desiring limited liability when issuing new debt could then easily insert provisions that made explicit that the shareholders were not personally liable for debts of the company. Robert Hessen makes this well-known point in an article that Walter Block pointed out to me.

In a free society, limited liability by agreement would very likely be just as prevalent as today. One reason is that we do not routinely see investors or corporations intentionally carrying out the necessary financial operations to create unlimited liability securities. But there are other important reasons. The first of these is that an unlimited liability stock creates a situation where what any one person may need to pay depends upon what everyone else can pay. There may be some shareholders who cannot pay an assessment, and then the burden falls on other shareholders. This means that shareholders have to monitor the wealth positions of other shareholders. This is quite impossible for a large corporation with many shareholders, or at any rate introduces avoidable monitoring costs. Score one for limited liability.

As a firm approaches default, the unlimited liability stockholders have an incentive to dump their shares even more because they know that they face a payment in default. This can create even more downward pressure on the stock and contribute to the firm’s movement toward bankruptcy. Score two for limited liability.

Related to the preceding is that if shareholders create a downward run, new buyers will be reluctant to buy because they do not want to be assessed. The stock may lose its liquidity. Score three for limited liability.

Under unlimited liability, the value of the company depends on its particular shareholders and what their wealth is. This disrupts the important role of stock market prices in transmitting information about the values of the underlying investments of the firm. It makes market values depend more greatly on the financing methods of the firm, which are usually of secondary importance. Score four for limited liability.

Another point is that a shareholder, even a passive shareholder, who owns a portfolio of unlimited liability companies faces high costs of monitoring all the positions because he has to be concerned about assessments occurring. Finally, bankruptcies occur in clusters when the bad state of the world occurs. In such a situation, just when times are bad and one’s income is low or threatened, a stockholder may in addition be faced with paying debtors because of bankruptcies. This introduces a risk that is undesirable. It will make investors in unlimited liability companies demand higher returns to compensate for the risk. This raises a company’s cost of capital. Score five and six for limited liability.

If the State’s role in limited liability falls by the wayside for whatever reason, we can expect both investors and companies rapidly to re-establish it on their own. Those who want capital and those who supply capital are already reaching complex agreements that go far beyond the issue of whether there is limited liability or not. The dangers that lurk here are more from inept legislation, taxation, and judicial rulings that wreck finely-tuned financial engineering mechanisms that have been designed to create wealth. Surely some of these financial methods go wrong too, in which case individuals are hurt and incur losses. However, there are many ways open to individuals to spread these risks and lower the fallout from any given incident. By contrast, when the State blunders, there is systemic risk that is hard to avoid.

While this article dealt with some financial cases, it did not address wrongdoings for which damages are sought, or torts. Some of these liabilities, such as in the tobacco and asbestos cases, have been very large. Lawyers, judges and juries seem to have gone completely haywire in these and other like cases in which bartenders are held responsible for a person’s driving or a restaurant is held responsible for a person’s clumsiness. There are serious incentive and/or other problems for such perverse results to have occurred. One can also imagine catastrophes caused by companies or individuals in which liabilities are so large that they wipe out the entire market value of a corporation or wipe out more than an individual person’s net worth. What happens then? There are serious problems and issues here too. These matters will have to be grist for another day’s mill.

October 4, 2005

Michael S. Rozeff [send him mail] is the Louis M. Jacobs Professor of Finance at University at Buffalo.

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