I don’t know what it is about Citigroup that inspires journalists at reputable media outlets to spout unadulerated garbage, but there seems to be a lot of it going around.

Yesterday’s prize went to The Washington Post and David Cho. That prompted a long-time reader to draw my attention to a December 2009 story in The Nation by Zach Carter. And at the heart of this story is the big fat plum that makes them the hands-down winners of today’s prize.

In October and November 2008, Citigroup received more than $45 billion in TARP money, in two installments, in exchange for preferred shares. That package was later restructured. $20 billion was converted into a loan, and $25 billion was converted into common stock.

Then, in December 2009, Citigroup proposed to repay the $20 billion loan by issuing new equity. Their primary motivation was evidently to wriggle out from under the restrictions that an unpaid TARP loan would subject them to, restrictions on executive compensation and bonuses. (Having duly wriggled out, Citigroup went on to announce $25 billion in bonuses.)

Zach Carter’s piece is an outspoken criticism of this repayment proposal. His objections, though, are not to Citigroup’s profligate motivation for the repayment. It’s the “sloppy structuring of Citi’s repayment plan” that “is going to cost the government literally billions of dollars” which has him all worked up.

Taxpayers are getting a raw deal in Citigroup’s plan to repay its bailout funds, but you wouldn’t know it from reading the news. …
[...]
On Monday, Citi said that in order to have enough money to pay off the government’s $20 billion loan, it was going to raise about $20 billion by issuing more shares of common stock. The company’s financial health has improved; it can raise money from the private sector and pay back the taxpayers. Sounds great, right? Wrong.

Taxpayers are getting screwed. Citi’s stock market value at the end of Friday was roughly $90 billion. If Citi issues another $20 billion in common stock, the company does not magically become more valuable. It’s still got the same credit card and mortgage problems it had last week, and the same shaky profit prospects. Since $20 billion is about 22 percent of $90 billion, everybody who owns a stake in Citi’s common stock, including the taxpayers, will see the value of their investment decline in value (sic) by about 22 percent.

How big a deal is this? Well, 22 percent of the government’s $30.7 billion stake is $6.8 billion. That means Citi’s plan to “repay” the government actually ends up costing taxpayers money. Not only will our $5.7 billion profit be wiped out, but the value of our common stock investment will actually drop below what we first paid for it in February.

Of course, Carter’s dire prediction of a 22% decline in the share price never came to pass. That’s because it was pure unadulterated hogwash.

(And he doesn’t seem to realize that, at the time he wrote his article, any decline that was warranted by news of this transaction wouldn’t still be waiting to occur. It would have occurred right when the transaction was announced, not when it was later consummated, but that’s a text for another day. This is, though, one of the most basic facts about how the market works, and someone who doesn’t understand something that basic really shouldn’t be allowed to write about financial markets. Not in a reputable media outlet. Or, at least, not without a finance-knowledgeable editor looking closely over his shoulder, and schooling him along the way. I do, of course, happen to know a very well-qualified person, who would excel at such a job, even if I say so myself, but this post is no place for job applications.)

Returning to the main theme, Zach Carter is invoking one of the great urban legends of corporate finance, the “dilution effect of stock sales”. The notion is that any time you issue new stock you are diluting stockholder wealth — because you’ve increased the number of shares but the company does not magically become more valuable, it still has the same assets, opportunities and problems it had before — and it’s just plain wrong. Moreover, the math that Carter produces — if new equity brings in money equal to 22% of the previous equity value, then the value of the previous equity must decline by 22% — would make anyone acquainted with finance laugh out loud.

Let’s take the math first. What actually happens when a company issues new equity is:

Whether the value of old equity will decline depends entirely on what price the new shares are sold at.

There’s a decline if, and only if, the new shares are sold below the current market price.

If they’re sold at current market value, there’s no decline. (Which is only as it should be. Selling something at fair market value should not destroy wealth.)

In a minute, I’ll lay out a simple example to demonstrate this point. But, first, I want to stress that any claim that the value of the old equity will decline by x% regardless of what price the new shares are sold at is laughable.

Assume that a company has 22.5 billion shares outstanding, and a share price of $4 (for an aggregate equity value of $90 billion). (Those were roughly Citigroup’s numbers when they announced the repayment plan in December 2009.) They now plan to issue new shares worth $20 billion, at the current stock price of $4. This means that they would be issuing 5 billion new shares.

The first thing that happens as a result of the issue is that the company’s assets go up. (If the money is then used to repay debt, both assets and liabilities will go down in step two, but we’ll come back to that later.) That’s where Carter’s simple-minded argument breaks down. It’s not true that the firm has the same assets it had last week. $20 billion in cash just came into the firm; that’s a new asset, in anyone’s book. So the new issue doesn’t just increase the number of shares outstanding, it also increases the asset base. And when the new shares are sold at the current market price, the number of shares and the asset base increase in the same proportion.

Before the issue, we had 22.5 billion shares worth $90 billion. The number of shares goes up to 27.5 billion (a 22% increase). Simultaneously, because the assets went up by $20 billion, the aggregate value of the shares goes up from $90 billion to $110 billion (once again a 22% increase). We end up with 27.5 billion shares worth a total of $110 billion, for an unchanged stock price price of $4.

So, dear Zack, even though the firm raised $20 billion in new equity, and $20 billion is 22% of $90 billion, everybody who owns a stake in Citi’s common stock didn’t see the value of their investment decline by 22%.

So it’s not issuing equity per se that makes the wealth of old stockholders decline.

There will be a decline, though, if the new shares are sold at a discount from the market price. Suppose the new shares are sold at $3.33 instead of $4. Now, to raise $20 billion, the company will have to sell 6 billion shares. We end up with 28.5 billion shares worth an aggregate of $110 billion, and the stock price ends up at $3.86 (a decline of 3.5%).

Nor is the potential decline limited to Zach Carter’s magic number of 22%. If you sell the new shares for $1 each, you end up selling 20 billion shares. The stock price falls to 110/42.5, which is $2.59, a decline of 35%.

Let me now come back and dot some i’s. My simple example ignores what is supposed to happen in step 2: that the $20 billion that was raised will be used to repay an outstanding loan. There’s really no need to construct a second, more complicated example to address this, though.

First of all, Carter’s argument that Citigroup’s repayment plan will “cost the government literally billions of dollars” has nothing to do with the use of the funds. His point is that it’s the new equity issue that will dilute stock value. When you use $20 billion in cash to pay off a $20 billion loan, that should be a value-neutral transaction.*

Secondly, if you focus just on the repayment (since we’ve already dealt with the new issue), here’s what happens. Before repayment of the loan, stockholders in effect own a smaller slice of the assets, because the loan represents a prior claim on part of the cashflows from the assets. Repaying the loan reduces the firm’s asset base (by the $20 billion in cash used for the repayment), but now the stockholders own a larger slice of that reduced asset base. These two effects basically cancel each other out.

Or putting it differently, the company’s assets after the new issue and repayment are exactly the same as they were before the joint transaction. So that part of Carter’s argument is accurate: “the company does not magically become more valuable, it still has the same assets, opportunities and problems it had before”. What he misses is that, because the debt was extinguished, in effect stockholders now own a larger slice of that same asset base. That’s what offsets the increased number of shares.

* This assumes, of course, that $20 billion is not just the amount borrowed but the current market value of the debt. If the debt is actually worth less (perhaps because the government paid more for the debt than it was worth) or more (perhaps because of an improvement in Citigroup’s prospects), that’s a separate issue.