Question

A bank has deposits of 400 dollar. It holds reserves of 50 dollar. It has purchased government bonds worth 70 dollar. It has made loans of 500 dollar. Set up a T-account balance sheet for the bank, with assets and liabilities, and calculate the bank's net worth.

Short answer

The bank has total assets of 620 dollars, comprised of 50 dollars in reserves, 70 dollars in government bonds, and 500 dollars in loans. Its total liabilities are 400 dollars in deposits. The T-account balance sheet is as follows: | Assets | Liabilities | |-------------------------------|-------------------------------| | Reserves: 50 dollars | Deposits: 400 dollars | | Government Bonds: 70 dollars | | | Loans: 500 dollars | | | Total Assets: 620 dollars | Total Liabilities: 400 dollars| The bank's net worth can be calculated as total assets (620 dollars) minus total liabilities (400 dollars), resulting in a net worth of 220 dollars.

Step-by-step solution

List the assets

The bank has three types of assets: 1. Reserves: 50 dollars 2. Government bonds: 70 dollars 3. Loans: 500 dollars

Calculate total assets

To calculate the total assets, add the reserves, government bonds, and loans together: Total assets = Reserves + Government bonds + Loans Total assets = \(50 + 70 + 500 = 620\) dollars

List the liabilities

The bank has one type of liability: 1. Deposits: 400 dollars

Calculate total liabilities

In this case, the total liabilities equal the deposits value: Total liabilities = Deposits Total liabilities = 400 dollars

Set up the T-account balance sheet

Create a T-account balance sheet with assets on the left side and liabilities on the right side: | Assets | Liabilities | |-------------------------------|-------------------------------| | Reserves: 50 dollars | Deposits: 400 dollars | | Government Bonds: 70 dollars | | | Loans: 500 dollars | | | Total Assets: 620 dollars | Total Liabilities: 400 dollars|

Calculate the bank's net worth

To calculate the bank's net worth, subtract the total liabilities from the total assets: Net worth = Total assets - Total liabilities Net worth = \(620 - 400 = 220\) dollars The bank's net worth is 220 dollars.

Key concepts

Banking Reserves

Banking reserves are a critical component of a bank's financial health and are the portion of depositors' balances that banks have on hand as cash. This cash is usually stored in the bank's vaults or at the central bank. Reserves are important because they are used to meet the demand for withdrawals and to manage liquidity risks. For instance, in our exercise example, the bank holds reserves of 50 dollars.

These reserves signify the liquid assets the bank has immediately available to facilitate customer withdrawals and payments. Notably, there are two types of reserves: required and excess. Required reserves are the minimum amounts that banks must hold by regulation, while any reserves over this minimum are considered excess. Banks often receive little to no interest on funds held as reserves, which is why they strive to keep reserves low enough to be safe but high enough to be profitable.

Government Bonds

Government bonds represent loans made by investors to the government. They are considered a safe investment with a relatively low interest rate yield. When a bank like the one in our exercise purchases government bonds, worth 70 dollars in this case, these bonds contribute to the bank's assets. They are an investment and form part of the bank's strategies to earn interest.

Since government bonds are backed by the government, they are seen as low-risk investments compared to other assets. For banks, having government bonds in their asset portfolio also provides benefits such as relatively stable returns and the ability to sell these bonds in the open market if liquid funds are urgently needed.

Bank Liabilities

Bank liabilities mainly comprise funds that a bank owes to others, which principally include deposit accounts, such as the 400 dollars in deposits mentioned in the exercise. These deposits form the bank's obligation to give back the money to depositors on demand or after an agreed period. In addition to deposits, other bank liabilities can include borrowings, loans from other financial institutions, and any other financial obligations.

Managing liabilities is crucial for a bank's operations because it affects the bank's ability to lend, invest, and, more importantly, meet withdrawal requests by customers. The totality of these liabilities is an integral part of the balance sheet equation where the total assets must equal the sum of liabilities and bank net worth.

Bank Net Worth

The bank's net worth, often referred to as the bank's equity or capital, is the value that remains after subtracting liabilities from assets. It essentially reflects what the bank owns minus what it owes. In our scenario, the bank's net worth is calculated by subtracting the total liabilities (400 dollars) from the total assets (620 dollars), which equals 220 dollars. This figure of 220 dollars represents the owner's equity in the bank.

This net worth is an indicator of the bank's financial strength and stability. A positive net worth suggests that the bank has more assets than liabilities and is in good financial health. Conversely, a negative net worth would mean the bank is potentially in financial distress and could be at risk of insolvency if the trend continues.