Balance Sheets and Bank Loans

Introduction

This document examines the changes over time in the balance sheets, and especially the net worth, of all the entities involved in a simple loan scenario. In order to concentrate on the underlying monetary system, this initial analysis will ignore the payment of interest, and the loan will be repaid as a single lump sum at the end of the loan period.

Also note that the scenario does not consider any other creation or destruction of wealth in the meantime, so care must be taken with the interpretation. This point will be addressed further at the end of the scenario.

The scenario involves Mr R., Mr M., Mr Tophat (the owner of a bank), and his bank: Tophat bank. Mr M. wants to buy a house owned by Mr R., and needs a loan to do so. In order to earn the money to repay the loan, he works for Mr R. as a chauffeur for 10 years. Finally, having enough money, he repays the loan.

For more clarity, entries added to each balance sheet since the previous one (for the same entity) are represented like this, and entries removed are represented like this.

The scenario

Initial balance sheets

The initial state.

Mr R.
AssetsLiabilities
Total200,000Total200,000
House200,000
Net worth200,000
Mr M.
AssetsLiabilities
Total0Total0
Net worth0
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,000,000Total1,000,000
Cash1,000,000
Shareholder equity1,000,000

(*) In order to concentrate on the changes in the balance sheets, we will assume here that Mr R.'s car and tent work well enough for his purposes, but are practically worthless to anyone else, and so do not show as assets on his balance sheet. If we wanted to include them, they could just be added to every single balance sheet as assets, with a corresponding increase in Mr R.'s net worth.

Mr M. obtains a loan to buy the house

Mr M. does not have money to buy the house from Mr R., so he must borrow money from Tophat Bank. He signs a loan agreement, by which the bank agrees to provide £200,000 for him to buy the house now, and he agrees to repay the loan in 10 years' time. Mr M. agrees to use the house as security for the loan – if he fails to repay, Tophat Bank can take ownership of the house, and sell it to settle the loan.

The money, as always, is newly-created as a deposit for Mr M. This deposit is a record that the bank owes £200,000 of its assets to Mr M. i.e. it is a liability of the bank, and an asset for Mr M. Mr M. owes £200,000 to Tophat Bank after 10 years, so this is an asset of the bank and a liability of Mr M.

After the loan agreement is signed

Mr R.
AssetsLiabilities
Total200,000Total200,000
House200,000
Net worth200,000
Mr M.
AssetsLiabilities
Total200,000Total200,000
Deposit (Tophat Bank)200,000Loan (Tophat Bank)200,000
Net worth0
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,200,000Total1,200,000
Loan (Mr M.)200,000Deposit (Mr M.)200,000
Cash1,000,000
Shareholder equity1,000,000

Mr M. buys the house from Mr R.

Mr M. now has the funds he needs to buy the house from Mr R. Assume that Mr R. has an account with Tophat Bank too.

After Mr M. has bought the house from Mr R.

Mr R.
AssetsLiabilities
Total200,000Total200,000
House200,000
Deposit (Tophat Bank)200,000
Net worth200,000
Mr M.
AssetsLiabilities
Total200,000Total200,000
Deposit (Tophat Bank)200,000Loan (Tophat Bank)200,000
House200,000
Net worth0
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,200,000Total1,200,000
Loan (Mr M.)200,000Deposit (Mr M.)200,000
Cash1,000,000Deposit (Mr R.)200,000
Shareholder equity1,000,000

The bank now owes £200,000 to Mr R., but it is still Mr M. who owes £200,000 to the bank in the future. However, Mr M. now has the house.

Mr M. works for Mr R. for 1 year

After working for Mr R. for 1 year, Mr M. is paid £20,000.

After Mr M. has worked for Mr R. for 1 year

Mr R.
AssetsLiabilities
Total180,000Total180,000
Deposit (Tophat Bank)200,000
180,000
Net worth200,000
180,000
Mr M.
AssetsLiabilities
Total220,000Total220,000
House200,000Loan (Tophat Bank)200,000
Deposit (Tophat Bank)20,000
Net worth0
20,000
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,200,000Total1,200,000
Loan (Mr M.)200,000Deposit (Mr R.)200,000
180,000
Cash1,000,000Deposit (Mr M.)20,000
Shareholder equity1,000,000

Mr M. has produced a service, which Mr R. has consumed. In exchange Mr R. pays Mr M. some money (say via a cheque, which directs Tophat Bank to transfer ownership of a specified level of deposits from Mr R. to Mr M.). Mr R. has consumed more than he produced this year, so his net worth has decreased. Mr M.'s net worth has increased because he has produced more than he has consumed.

Mr M. works for Mr R. for a second year

After working for Mr R. for another year, Mr M. is due to be paid another £20,000. Suppose that this time, Mr R. pays Mr M. by cash. The result is the same as paying by cheque, but we can verify that by examining every stage of the process.

Mr R. withdraws cash to pay Mr M.

Mr R. withdraws £20,000 in bank notes from the bank.

Mr R. withdraws cash to pay Mr M.

Mr R.
AssetsLiabilities
Total180,000Total180,000
Deposit (Tophat Bank)180,000
160,000
Cash20,000
Net worth180,000
Mr M.
AssetsLiabilities
Total220,000Total220,000
House200,000Loan (Tophat Bank)200,000
Deposit (Tophat Bank)20,000
Net worth20,000
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,180,000Total1,180,000
Loan (Mr M.)200,000Deposit (Mr R.)180,000
160,000
Cash1,000,000
980,000
Deposit (Mr M.)20,000
Shareholder equity1,000,000

Mr R. has simply replaced one asset (£20,000 of his deposit with Tophat Bank) with another (£20,000 cash). The withdrawal of cash does not affect Tophat Bank's net worth because its liabilities (deposits) are reduced by the same amount as its assets (cash).

Mr R. pays Mr M. in cash

Mr R. hands the £20,000 of bank notes to Mr M.

Mr R. pays Mr M. in cash

Mr R.
AssetsLiabilities
Total160,000Total160,000
Deposit (Tophat Bank)160,000
Cash20,000
Net worth180,000
160,000
Mr M.
AssetsLiabilities
Total240,000Total240,000
House200,000Loan (Tophat Bank)200,000
Deposit (Tophat Bank)20,000
Cash20,000
Net worth20,000
40,000
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,180,000Total1,180,000
Loan (Mr M.)200,000Deposit (Mr R.)160,000
Cash980,000Deposit (Mr M.)20,000
Shareholder equity1,000,000

Mr M.'s net worth has now increased, because he has produced more than he has consumed. Similarly, Mr R.'s net worth has decreased because he has consumed more than he has produced.

Mr M. pays the cash in at the bank

Mr R. pays the £20,000 of bank notes into his account at Tophat Bank.

Mr M. deposits the cash at Tophat Bank

Mr R.
AssetsLiabilities
Total160,000Total160,000
Deposit (Tophat Bank)160,000
Net worth160,000
Mr M.
AssetsLiabilities
Total240,000Total240,000
House200,000Loan (Tophat Bank)200,000
Deposit (Tophat Bank)20,000
40,000
Cash20,000
Net worth40,000
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,200,000Total1,200,000
Loan (Mr M.)200,000Deposit (Mr R.)160,000
Cash980,000
1,000,000
Deposit (Mr M.)20,000
40,000
Shareholder equity1,000,000

Again, there is no change to the net worth of Tophat Bank as a result of Mr M. paying the cash into his account at the bank. Its liabilities (deposit) are increased by the same amount as its assets (cash).

Cash vs cheque payments

Examining the balance sheets, it is clear that the result of payment via cash is identical to the payment via cheque – a given amount of deposit is transferred from Mr R. to Mr M.

Mr M. works for Mr R. for a tenth year

The process is identical for each of the ten years. The net result is that £20,000 of deposit is transferred each year from Mr R. to Mr M. After ten years, the loan is ready to be repaid.

Mr M. has been paid for 10 years' work

Mr R.
AssetsLiabilities
Total0Total0
Deposit (Tophat Bank)160,000
Net worth0
Mr M.
AssetsLiabilities
Total400,000Total400,000
House200,000Loan (Tophat Bank)200,000
Deposit (Tophat Bank)40,000
200,000
Net worth200,000
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,200,000Total1,200,000
Loan (Mr M.)200,000Deposit (Mr R.)160,000
Cash1,000,000Deposit (Mr M.)40,000
200,000
Shareholder equity1,000,000

It is interesting to compare this situation to that immediately after the loan was made. The only difference is that Mr M. now has a house that he did not have before, and Mr R. no longer has the house that he had at the time.

Mr M. repays the loan

Mr M. has repaid the loan

Mr R.
AssetsLiabilities
Total0Total0
Net worth0
Mr M.
AssetsLiabilities
Total200,000Total200,000
House200,000Loan (Tophat Bank)200,000
Deposit (Tophat Bank)200,000
Net worth200,000
Mr Tophat
AssetsLiabilities
Total1,100,000Total1,100,000
Shares (Tophat Bank)1,000,000
Cash100,000
Net worth1,100,000
Tophat Bank
AssetsLiabilities
Total1,200,000Total1,200,000
Loan (Mr M.)200,000Deposit (Mr M.)200,000
Cash1,000,000
Shareholder equity1,000,000

Mr M. repays the loan by allowing his deposit to be destroyed. This is a transfer of wealth from Mr M. to Tophat Bank, in that Mr M. was owed £200,000 of Tophat Bank's assets, and no longer is. However, there is also a equal transfer of wealth from Tophat Bank to Mr M., in that the loan is also extinguished, meaning that Mr M. no longer owes £200,000 to the bank. There is no net transfer of wealth, just as there was none when the loan was initially made. There is, however, less money than there was – the deposit has been destroyed.

Conclusions

  1. The only changes in net worth in the scenario are when Mr M. provides a service for Mr R., and Mr R. pays with his money (consuming his saved wealth) instead of producing as much value as he consumes.
  2. Every other interaction between the different entities in the scenario has no effect on any entity's net worth. Specifically, the net worth of Mr Tophat is completely unaffected, and the shareholder equity in Tophat Bank is constant throughout the scenario.
  3. Contrary to the assertions of some monetary reformers, there is no free lunch for the bank directly from its ability to create money(*). The money which it creates (in the form of deposits) are its liabilities: the bank owes that value of its assets to the entity in whose account the deposit is held. The value of the deposit comes from the bank's asset which was created at the same time, namely the loan i.e. the promise of the borrower to pay money to the bank. (As explained in the earlier document on the money life cycle, this value is underwritten by the bank, so if the borrower fails to repay, the bank's owner(s) must pay on the borrower's behalf).

(*) The bank does however get the ability to charge interest on the money which it creates. And the more loans which it makes, the more interest it can receive. However, as discussed in money life cycle document, this interest must compensate for any defaults by borrowers, and pay both the costs and profits of running the banking business, practically identically to premiums in the insurance business. A bank making more risky loans is practically identical to an insurance company issuing more risky policies, leading to a higher chance of losses for shareholders.

Constant total net worth? No.

In this scenario, the total net worth is a constant £1,300,000, which could be taken as suggesting that total net worth is constant, only being transferred between entities. However, this is actually artificial – purely a result of this scenario concentrating on the interactions directly related to the loan and its repayment.

As mentioned in the earlier document on balance sheets, an entity's net worth is constantly increasing and decreasing as it produces and consumes wealth respectively. Mr R. would be very foolish to consume his entire saved wealth in purchasing chauffeur services from Mr M. without producing something of value in the meantime, otherwise he will face a sudden solvency crisis at the end of the 10 years. In a realistic scenario, it is to be hoped that Mr R. would use his skills, labour, and any capital which he has at his disposal in order to create something of value which would maintain his net worth.