# Banking Profit and Loss

## Computing Banking Profit and Loss

To understand how banking profit and loss is calculated we need to identify the sources of revenues and related expenses.

One of the main sources of a bank’s revenue comes from loans.

Let’s take an example to understand how a bank’s loan revenue is computed

### Bank Revenues

The rate at which bank’s charge for loans will vary with the risk profile of each customer. However, let us assume the average rate we earn on loans is 15%.

If the total amount of loans disbursed is \$25 million then ideally we could earn 15% of 25 million.

However, in reality, some loans go bad. Let’s assume we have an good credit department and 95% of our loans are repaid. Of the 5% defaulted we were able to recover 80%. So given our default rate of 5% and recovery rate of 80% the realised rate on loans is

= [ average contractual rate x (1-default rate) ] – [(1-recovery rate) x default rate]

= (15% x 0.95) – (20% x 0.05)

= 13.25%

This realised yield times our loan amount gives us our total revenues from loans

= 13.25% x 25 = \$3.3125 million

### Bank Expenses

The bankâ€™s costs would be costs on the deposits called the variable costs and costs of office premises, furniture, computers etc.

The cost of deposits would also include explicit interest, which is the rate at which the bank advertises to mobilize deposits. There are also implicit interest costs of deposits such as offering free checking, free ATM transactions etc. If the explicit costs are 4% and implicit costs are 2% the total costs of deposits are 6%. Assuming fixed costs are \$0.5 million let’s compute the bankâ€™s profitability.

= (loans x realised yield) – (deposits x deposit cost) – FC

= (25 x 13.25) – (20 x 6%) – 0.5

= 3.3125 – 1.2 – 0.5 = \$1.6125 million

The bankâ€™s return on equity would therefore be =

profit/equity = 1.6125/10 x 100 = 16.125%

Banks can improve their return on equity by either increasing their profits or lowering equity. Increasing profits can be achieved by increasing revenues reducing costs. Reducing equity is risky as banks could face bankruptcy.

Lets summarise the risks and rewards of each variable in a table

 Strategy Risks Increase revenue Increase Loan amount by increasing Deposits increasing deposits will incur higher deposit rates Increase Loan amount by decreasing Reserves Minimum reserve requirement by the central bank? Deposit clearing will become an issue Increase Loan Interest Rates customers will move to competitor banks. Bad Loans will increase Lower Costs Lower deposits Cannot do without lowering loans – not a good idea Lower deposit rates customers will shift to other banks Lower Fixed Costs

Since we are concerned with amounts of loans and deposits in the system lets focus on these two parameters and their constraints. We need to understand the relationship between loans, deposits and reserves and their constraints since in our discussion on central banks these are the three areas central banks are concerned with.

Banks can increase their loan amounts by either increasing their deposits or lowering their reserves. Let’s look at both

#### Improving the Bank’s Profitability

Increasing deposits – Banks borrow to lend and earn a spread between their lending rates and borrowing rates. The more they borrow the more they can lend. Banks can increase deposits by making them more attractive ie increasing the deposit rates (explicit deposit rate) or providing extra free facilities (increasing implicit rates).

This makes deposits more expensive and reduced the spreads banks earn. Banks cannot simultaneously increase their lending rates as customers will migrate to other banks. Bad loans will also increase as customers with good credit ratings will source cheaper loans elsewhere. Therefore increasing deposits without squeezing margins is not easy.

Reducing Reserves – Another source of funds

Reducing Reserves – Assume a bank has 5 million in reserves earning zero interest at the central bank. If the bank reduces its reserves at Central Bank to 4 million, it can increase its loan amount by \$1 million.

Given the effective rate of return on loans is 13.25% as computed above – this translates to 13.25% x \$1 million in profits or \$132,500 improving ROE to 17.45%.

This is great for banks! We can reduce the bankâ€™s reserves to increase its ROE substantially.

Unfortunately, in reality, it’s not so simple. Central banks placeÂ a legal reserve requirement on all banks.

Assuming central bank’s place a reserve requirement of 10% of checking deposits and 0% of regular deposits. Therefore the required reserves can fall to 10% of \$20 million making that \$2 million. The rest can be utilised to improving profits.

Most central banks around the world require banks to hold reserves as part of liquidity management. Some central banks require that banks hold reserves in two forms – highly liquid reserves in the form of deposits at the central bank called cash reserves and at a specific ratio of net deposits sometimes called the cash reserve ratio or the CRR.

The other form is also liquid but not as liquid as cash in the form of government securities called Statutory Reserve Ratio or SLR. We can go deeper into this later but for now, let’s understand that besides statutory requirements there are more practical reasons for banks holding reserves.

### Related Topics

Banking Basics

Financial Accounts of the US or Flow of Funds

Banking Loans, Deposits and Reserves

Fractional Reserve Banking

Central Bank’s Monetary Policy

Bank Profitability

Technical Analysis

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