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The Limited Liability Paradox


A puzzle is presented for the reader's consideration.

Stocks, which represent ownership in a company, cannot trade below 0. In the event of bankruptcy, stockholders do not have to pay the company’s creditors; liability is limited. Now imagine that you buy shares of a penny stock, XYZ, for $0.01. Then XYZ “finds” $15 per share (perhaps XYZ wins a surprising, long-forgotten lawsuit). It seems that XYZ should trade at $15.01. First, adding $15 of cash per share should add $15 of value to each share. Second, the company could pay the $15 as dividends and then be back with a $0.01 stock, and surely that is worth $15.01.

Now imagine company ABC, which, let us stipulate, trades at $10, which is its fair value. ABC has $15 per share of cash (it’s worth noting that these assumptions would most likely mean that ABC has a good deal of debt/liabilities). ABC’s management then goes off the rails and literally burns the $15 of cash per share, or so the press reports. A picture of the CFO wielding a flamethrower hits the front pages of the Wall Street Journal and the Financial Times. Stocks cannot trade below 0; perhaps ABC trades at $0.01. But hold on – a few days later ABC announces that the burning-of-the-cash was a hoax. ABC is a $0.01 stock that has “found” $15 per share. At what price should ABC trade? We saw from XYZ that ABC should trade at $15.01. However, surely pretending to burn money cannot add value to a stock, and so ABC should again trade at $10 (let us ignore the loss of confidence in management that such CFO behavior may bring about). Should ABC trade at $15.01 or $10? This is the “limited liability paradox” because if liability were not limited, an investment worth $10 that took a $15 loss would be worth -$5, meaning that people would have to be paid $5 to assume ownership, and there would be no paradox. What is the way out of this paradox?

Those who like puzzles and paradoxes may want to pause reading as we now turn to the way out of the paradox. Notice that company ABC was initially assumed to have more cash per share ($15) than share value ($10). This can happen, but as noted, would mean that a company would have a lot of debt. To see the way out of the paradox, let’s move from per share considerations to the consideration of a whole company. Imagine a company that has a market cap of $1 billion. Perhaps it is a cruise company. Then let the company borrow $1.5 billion to build a new cruise ship. The company has a market cap of $1 billion and cash of $1.5 billion. Now, covenants and laws would likely prevent the following, but if the company could return all of the $1.5 billion to owners (shareholders), then the market cap would be $1.5 billion. To put the point bluntly, if owners could appropriate $1.5 billion from creditors, the market cap would immediately rise 50% ($1 billion to $1.5 billion).

Let me suggest some surprising conclusions that flow out of this analysis. First, the value of a company depends, in part, on the board’s/management’s intentions (one might think of Hilary Putnam and ants drawing Winston Churchill). All of the facts about a company cannot determine the value of the company in the absence of whether or not the board intends to appropriate bondholder’s wealth. To make this concrete, imagine that our cruise company is having a board battle. One slate wants to run the company for a sustainable future and use the $1.5 billion to build another cruise ship; now the company is worth $1 billion. Another slate wants to hire lawyers and return the $1.5 billion to owners via rapid special dividends; if possible, now the company is worth (close to) $1.5 billion.

Second, in light of these considerations, how seriously can we take the idea that companies should be maximizing shareholder value? Pushed to its logical conclusion, this would seem to imply that companies should be working hard to appropriate bondholder wealth. It may be that the main factor preventing this occurrence, in the public markets, is management’s self-interest. What board member or C-level executive wants to run their company into bankruptcy and ruin their reputation to maximize shareholder value? But the point is this: If companies should be maximizing shareholder value, then they need to work harder at appropriating bondholder wealth.

Third, let us swing around 180 degrees and ask: Are companies currently in the process of appropriating bondholder wealth? Over the past 10 years or so, non-financial corporate debt has gone up some $5 trillion and the return to shareholders in the form of dividends and buybacks is of a similar order. It is not impossible that we have a spell of bond market carnage. It may then be worth viewing a simplified capital structure as follows, where a top layer is added:

     Stockholders (pre-bankruptcy via dividends and buybacks)

     Bondholders (post-bankruptcy)

     Stockholders (post-bankruptcy)

One may worry that these points are merely academic, but I think that that criticism misses the mark. Think of Pitney Bowes (PBI) and imagine the following. In the next downturn, the Fed takes rates to close to 0% across the curve and engages in QE, taking the balance sheet to $10 trillion. At the same time, the MMT crowd pushes through massive fiscal spending. The world finds that inflation is not dead. With delay, but recognizing its necessity, the Fed gets us to a place where the 10-Year moves from 0% to 7%. PBI, I suggest, will have no hope of rolling over its debt, and will declare bankruptcy. Bondholders who take a massive haircut will be angry, if they think of it, at the massive return of capital to stockholders that transpired over the life of the company (this return to stockholders presently runs at something like $100 million a year, which is well over 10% of market cap). Stockholders and bondholders may be less aligned than people suspect.