Nick Rowe presents a very simple example to demonstrate how a commercial bank might appear to be insolvent when you look at its balance sheet, but could still have a sizable net worth:
I start a bank. I have zero capital. I borrow $100 and lend $100. What is the net worth of my bank?
Looking at the balance sheet, the answer is simple and obvious: assets $100, liabilities $100, net worth = assets minus liabilities = $0.
But looking at the income statement we may get a very different answer. If I borrow at 3%, lend at 5%, and have no administrative costs, my bank earns $2 profit per year, which discounted at 5% gives a Net Present Value of $40, so my bank is worth $40.
So if the bank still has a positive net worth from an income statement perspective, what is to keep other investors from bidding for its assets if it becomes balance-sheet insolvent? To what extent does the market adapt to the realities of discounting the expected net revenues on the income-statement?
Is the problem with balance-sheet insolvency more of a regulatory problem? Or are we actually observing serious cases of income-statement insolvency in some/many financial institutions, especially in the US?
Good questions John. I don't know the answers, but that's not going to stop me trying...
Example 1. I get ill, with some non-contagious disease, and can no longer run my bank. I sell the whole bank as a going concern, for anything between $0 and $40 (depending on how competitive the market is). In effect, the "assets" include not just the assets on the balance sheet, but my customer base (the depositors are an "asset", even though the deposits are a liability.
Example 2. I get ill, and so do all the other bankers (it's contagious). So nobody wants to run my bank, even though it's profitable. I wind up the bank and end up with $0.
Example 3. Interest rates on loans rise to 10% the day after I started the bank lending at 5% and borrowing at 3%. My assets are now only worth $50 on the market (they were perpetual loans). There are now two equilibria. If a sunspot appears (not the global warming kind, but a purely irrelevant event) the depositors fear there will be a run on my bank. Each depositor runs to withdraw his money first. After $50 has been withdrawn, I run out of funds to repay depositors. So their belief is self-fulfilling. If there is no sunspot, the depositors believe my bank will stay in business. And since it continues to earn $5 and pay $3 every year, it does stay in business, so their belief is also self-fulfilling. Would anybody (with deeper pockets) buy my bank if there were a sunspot? Only if they thought that by doing so they could flip my bank into the other equilibrium (and if so, they would pay up to $20).
Example 4: 20% of my loans go bad the day after I start the bank. Again, there are two equilibria, one with a bank run and one without. Somebody with deeper pockets might buy my bank, for up to $20, if they thought they could flip my bank into the non-run equilibrium.
I think the last few months have been a mixture of 3 and 4, only it has affected the whole banking system, so there's nobody around with deep pockets, except the govt. (i.e. the taxpayer). In a couple of cases, I think the regulators have closed banks that look insolvent from a balance sheet perspective, but were possibly solvent on the income statement. Dunno.
Posted by: Nick Rowe | December 04, 2008 at 02:02 PM