Fisher's Separation Theorem

Fisher's Separation Theorem...like, you have to keep your tuna way from your marlin.

Er...not quite.

The Separation Theorem was first proposed by economist Irving Fisher. Nothing to do with seafood. It has to do with corporate decision-making.

So...a bit about how running a big corporation works. A corporation has two sets of bosses. You've got the owners. And you've got the managers. In small companies, these are often the same people. The guy who owns the sneaker repair pagoda at the mall probably owns 100% of the stock...and works full time as the manager. And probably as the only employee, too. But in large corporations, a separation comes into play. There are shareholders: the people who own the stock. And there are the managers: people like the CEO, the CFO and the COO...the people who run the company day-to-day.

There can be overlap. Managers often own stock. But for the most part, the roles operate separately. Fisher's Separation Theorem deals with the fact that a corporation, as run by the managers, acts separately from the wishes of its shareholders. The best thing for the company is often different than the best thing for shareholders. Each entity (the shareholders and the corporate managers) responds to different forces and thinks differently about the best uses of the company's money.

The Fisher Separation Theorem says that these differences don't really matter, at least in terms of making corporate decisions. The theory states that a corporation should maximize its present value, regardless of what its shareholders want.

You run Treat Not Trick Inc., a company that makes tiny x-ray devices to check Halloween candy for razor blades. You made $10 million in profit last year. You have two fundamental choices. You can use that money to invest in the business. Things like expanding your x-ray mine or running an R&D project to make a better Caramel Density Offsetter. Or you can give the money to shareholders in the form of dividends. Which means giving them cash as a reward for holding your stock.

So what do your shareholders think you should do with your $10 million in profit? Well, one of your shareholders, Polly Favor, is sitting pretty. Her other investments are going well. Her second trust fund just vested, and she miraculously just won the national lottery in Mozambique. She doesn't need the money. She tells you to invest the full $10 million in the company. Meanwhile, another shareholder, Artie Lootflush, isn't doing so well. He got divorced last year and owes a lot of child support...both to his ex-wife and to his former mistress. Meanwhile, his other investments have all gone south, and he lost a ton of money in an unsuccessful attempt to rig the, uh...national lottery of Mozambique.

He really needs the money. He asks you to turn the full $10 million in profit into dividends. The Fisher Separation Theorem suggests that you'll ignore them both. That you'll figure out what projects make sense to invest in and commit whatever profit is needed to run those programs. Whatever's left over, you'll give as a dividend. So your staff crunches the numbers and decides that, if you buy another Ray Excreter for $1 million, it will have a return on investment of 25% next year. Meanwhile, if you invest $4 million in developing a new product for checking Valentine's Day candy for poison, it will show a return of 15%.

Every other possible project has an expected return of 7% or less. Meanwhile, your nerd crew determines that the capital markets will return 8% over the coming year. Which means that, if you borrow money, you'll have to pay 8% interest on the loan. Or, if you loan money out, you'll get a return of 8%. So there’s your cutoff. If you can't get more than 8%, you might as well just loan the money out...or give it to your shareholders as a dividend. So that's what you do. You invest $1 million in a Ray Excreter. It has a 25% return…meaning it gets you $1.25 million by the end of the year.

You also invest $4 million in the Valentine's Day Poison Prevention Project...the V-D 3P, as you call it. You expect it to return 15%...meaning you'll wind up with $4.6 million from that by the end of the year. You invested $5 million of your $10 million in high-yield projects. You have $5 million left. You give that 5 mil out in dividends. Polly is a little disappointed, because she wanted you to keep the money and invest it. But she takes the extra money you give her and loans it out at 8% interest. It therefore gives her the same return as she would have gotten from keeping the money with the company. You already invested in all your high-return projects.

The best the company could have done with that money is earn 8% interest in the capital market...the same thing that Polly's going to do with it. It doesn't matter whether she has the money, or the company keeps it. Meanwhile, Artie is bummed. He needed the extra money...bad. But he still has access to the money he needs. He can go into the capital market and borrow it at 8% interest...he can just give Polly a call and borrow it from her.

Okay, but how is Artie going to pay the money back? Well, the company that he invests in took $5 million and turned it into $5.85 million in a year. That's the $1 million it invested at a 25% return, and the $4 million it invested at a 15% return. Blended together, that's a 17% return on the investment...much more than the 8% interest rate he has to pay on the loan. So next year, come dividend time, he'll get that additional amount paid out, which he can use to pay down the debt. Unless the company can invest it at a higher rate than the vanilla capital market rate. At which point Artie will just roll over his loan for another year and let the company earn a higher return again.

That's the math behind the Fisher Separation Theorem. The company will take as much profit as it needs to run its high-return projects...anything more than it could get by just loaning the money out at interest. Anything else goes to the shareholders. The shareholders stay happy because they can just use the capital markets to make up the difference. If they wanted less money, they can loan out the extra. If they wanted more, they can borrow what they need.

Meanwhile, if the company needs more money, it can borrow as well. Say that, next year, you bring in $7 million in profit. The capital markets are paying 8% again. But you have $10 million in projects that can make more than 15% return. For that extra $3 million, you'll borrow the funds at 8% interest and pay it back when it returns at least 15%. Borrow at 8%. Earn 15%. You end up on the plus-side in the end. In that year, shareholders won't get any dividends. All the money, plus extra that's been borrowed, gets invested in the company.

But the shareholders don't mind, because they can also borrow money if they need it. Meanwhile, the money invested with you makes an above-market return. A key here is that it makes no difference how the firm's investments are financed, whether by debt, cash, or stock. And if things get too bad for Artie, he can always sell his stock in Treat Not Trick Inc. The sale will give him plenty of money for child support...and for the legal costs related to the charges of lottery-tampering he faces in Mozambique...