On Friday, National Australia Bank reported a $830 million write-down on their assets. As this news article, More NAB bad debt revealed reported,

National Australia Bank’s senior management has been castigated by banking analysts after the bank released a fresh $830 million writedown of its investments in US housing mortgages.

The stock market reacted by plunging 3.5% at the time of writing. Will there be more? We will leave it to the mainstream media chatter to talk about it. Meanwhile, we will show you how a write down will affect the bank’s balance sheet. For this, we continue a simplified bank balance sheet from Introduction to banking corporate accounting:

Asset: $98.50 (Loans), $10.50 (Cash)
Liabilities: $105 (Deposits)
Equity: $4

Let’s say 2% of a bank’s non-performing assets is being written down. That means $1.97 of the asset will be gone. In that case, the asset part will look like this:

Asset: $96.53 (Loans), $10.50 (Cash)

But what about the liabilities and equity side of the balance sheet? The liabilities side remains intact because they represent the saver’s deposit. Therefore, it will be the equity side that gets deducted:

Equity: $2.03

The balance sheet now looks like this:

Asset: $96.53 (Loans), $10.50 (Cash)
Liabilities: $105 (Deposits)
Equity: $2.03

In one write-down the bank’s capital ratio gets reduced to 2.03/96.53 = 2.10%. It’s reserve ratio is still 10%. Will it get into trouble? As we explained before in Banking for dummies,

At its very core, a bank borrows money at lower interest rates and lends them out at higher interest rates. Its borrowings are its liabilities while its lendings are its assets. When you deposit your money into the bank, your money is the bank?s liability but your asset. In accounting technicalities, your money goes into the bank?s balance sheet as an asset with a corresponding liability.

Let’s say the bank pays 9.5% interest rates to its depositors (liabilities) and receives 10% interest rates from its loans (assets)- assuming interests-only payments. That means it will have to pay $105 * 9.5% = $9.975 to its depositors and receives $9.653 from its loans. In this case, the bank is in trouble.

Or let’s say banking regulations says that the capital ratio cannot go below 4%. Currently, it is at 2.10%, which means it is in trouble. It has to either sell its assets or raise cash (via equity raising) to bring the ratio up again.

No matter what, the bank’s profit will fall.

Today, we will go deeper in depth on corporate accounting for banks. Without a proper understanding of this, it will impair our ability to appreciate a bank’s financial position. Back in Banking for dummies, we explained that

At its very core, a bank borrows money at lower interest rates and lends them out at higher interest rates. Its borrowings are its liabilities while its lendings are its assets. When you deposit your money into the bank, your money is the bank?s liability but your asset. In accounting technicalities, your money goes into the bank?s balance sheet as an asset with a corresponding liability.

Today, we will go deeper into that.

First, we will introduce the basics of accounting:

Assets = Liabilities + Equity

So, let’s say you deposit $100 into the bank. In this case, the highly simplified bank’s balance sheet will be:

Assets: $100 (Cash)
Liabilities: $100 (Deposits)
Equity: $0

In this example, the bank is losing money because it is borrowing $100 from you which it has to pay interests on. But its $100 of cash is sitting there idle. Therefore, the bank has to lend out, say $90 at a higher interest rate than it borrows the cash from you. The balance sheet will now look like this:

Asset: $90 (Loans), $10 (Cash)
Liabilities: $100 (Deposits)
Equity: $0

Let’s say it pays 5% p.a. interest rates on deposits and receives 10% p.a. interest rates on its loans. At the end of the first year, the bank balance sheet will be (assuming interest-only payments on loans):

Asset: $90 (Loans), $19 (Cash)
Liabilities: $105 (Deposits)
Equity: $4

Now, there are 2 ratios that you need to understand. First, government regulations require that banks keep a certain ratio between equity and risky loans (in the assets) that it makes out to others. We shall call this the capital ratio. In this example, the capital ratio is 4 (Equity)/90 (Loans), which gives 4.44%. That is, its leverage is 22.5 times. There is another ratio called the reserve ratio, which is the ratio of cash and deposits. In this example, the reserve ratio is 19 (Cash)/105 (Deposits), which gives 18%.

Now, let us assume that the reserve ratio has to be, by law, a minimum of 10%. In that case, this bank has an excess reserve of 8% (see 363 tons of US dollars to Iraq?how much money will eventually be multiplied into the economy?). It can lend out an additional $8.50 to give a balance sheet of:

Asset: $98.50 (Loans), $10.50 (Cash)
Liabilities: $105 (Deposits)
Equity: $4

In this case, its reserve ratio is $10.50/$105, which gives 10%. Its capital ratio is 4/98.5, which gives 4.06% (leverage of 24.6 times).