Many factors go into the methods banks use to determine what interest rates they charge on loans. Many other factors go into determining how profitable those loans are, or how readily consumers use them under given conditions. It's tempting to over-simplify this, but the only simple truth is that it's complicated.
Retail banks are essentially in the business of getting money from various sources and then lending the money to consumers. Generally, banks set the interest rates they charge on a loan based on a number of factors:
- The cost of cash. Banks can't literally make money, they essentially have to pay someone else to get the money they then lend out. This may mean borrowing money from a central bank. Or it may mean borrowing it from consumers (basically, paying consumers an interest rate to deposit cash in a savings account or other deposit product). It may also mean borrowing money from other retail banks, or many other sources.
- The cost of risk. Not all borrowers play by the rules. Some borrowers choose to not pay back their loans. That represents a risk of loss, because the bank loses the money they lent (and there is an opportunity cost in that they could have lent that money to someone more trustworthy). Because of this, consumers who represent a greater risk will be charged higher rates.
- The cost of servicing a loan. It can cost a significant amount of money to service a loan. Banks need branches, websites, apps, ATMs, call centers, and other channels to interact with their customers. They need to follow regulations and interact with the government. They need to pay their employees and vendors. They need to operate or pay for access to servers and network infrastructure. And so on.
- Profit. Ultimately, all business is operated in the hopes of making a profit. A bank needs to make money for it's shareholders. Credit unions make money to pay their members.
To get back to your question, you said:
The book mentions something about central bank setting an interest rate vs banks interest rate determined by forces of the market etc which i do not understand.
When people talk about central banks setting interest rates, they are essentially talking (indirectly) about the cost of cash - my first point above. The assumption is that a central bank's rate is the biggest influence on what a bank needs to pay in order to get money to lend to consumers. If I am operating a bank, and I get my cash from a central bank, I need to pay interest to that central bank. If the central bank changes their interest rate, then I will probably need to change my rates to reflect the increased rate I am now paying. Of course, the reality is often more complicated than that, but it's arguable that central bank rates are at least a strong indicator of the cost a retail bank pays to get money to lend out. So, if a central bank lowers their rates, we would expect a retail bank to lower the rates it charges on loans.
That ties into your concern when you mentioned,
However I am not yet convinced why a textbook source is stating that lower interest rates is good for banks.
In a sense, a retail bank will typically change it's rates to match changes in a central bank's rates. So if a central bank drops it's rates, the retail bank will, too. That drop in rate does not mean that the retail bank is making less money. If a central bank is charging 5%, and a retail bank is lending at 6%, the retail bank has a 1% margin. If the central bank drops their rate to 4%, and the retail bank drops their rate to 5%, the retail bank still has the same 1% margin. If they write the same number of loans, their result will largely be the same. However, if more consumers decide to take out loans (maybe there were some people who decided they couldn't afford a 6% loan but they are able to afford a 5% loan), the bank now has a higher volume at the same margin and stands to make more money. That's why a lower central bank rate can be interpreted as good for banks. Effectively, that is the simple answer to your question.
However, as alluded above, the simple answer isn't really the whole truth. more people taking out loans at the lower rate can impact all the other factors mentioned above, too. In other words, a 1% margin at a 5% rate may be very different for a bank than a 1% margin at a 4% rate:
- The cost of cash factor is essentially the reason for the change in retail rates, so it's self explanatory.
- Risk can shift. If you attract more consumers, or different consumers, your risk profile changes. People who did not take a loan at a higher rate because they can barely afford a loan are going to drive up your risk. People who didn't take the higher rate because they were being thrifty and looking for a bargain may actually drive down your risk. This can be incredibly hard to predict even given the level of effort banks put into classifying risk. Lenders often have entire teams of people and/or vendor partners who focus solely on predicting loan performance based on changes in interest rates or economic conditions.
- operating cost can change, too. A change in rates can mean a change in product mix - consumers may hold out on taking out certain types of loans until rates are "good" but may take out other types of loans no matter what. A lender who has lots of different types of loans may find that a change in rates causes some types to shoot up in volume but other types to decrease. If different products have different operating costs, this can change the cost to service the portfolio as a whole. Banks sometimes make some loans to some consumers essentially at a loss (or at least at a questionably small profit margin) because they expect those consumers to be valuable in other ways. A change in economic conditions or a change in central bank rates can throw that off.
- A bank may choose to adjust their profit based on a perceived potential change in the marketplace. If a bank decides that a change will result in a significant increase in lending volume, they may actually be happy to drop their profit because the larger volume will mean they're still making more money. They may need to do this if the change in rates creates a more competitive environment among other lenders.
Of course, banks need to approach this whole problem on a "whole portfolio" level, while a consumer is often approaching it one loan at a time. For a consumer, a change in central bank rates may literally not make a difference. Many consumer loans have fixed rates. If you are two years into paying off a three year auto loan, and it's a fixed rate loan, changes in central bank rates or the rates your retail bank is writing new auto loans at won't impact your current loan. But if you have a loan with a variable rate (as is sometimes the case with certain types of loans), the bank may change the rate you're paying for your loan every time the central bank changes their rate, so a change in central bank rates can directly impact you.