Even allowing for difficulties inherent in fluctuations in volume of banking operations, however, the problem of ascertaining costs per unit of business done might not be considered very complex by the cost accountant - at least in theory. There are other elements, however, in the bank's business which present considerably more difficult problems. The most important of these is probably that which centers around the question of reserves. As we have seen in an earlier portion of this volume, every bank is obliged, either by custom or law, or by both, to maintain a certain reserve. For the sake of ease in figuring, we may assume that this reserve is 20 per cent of its outstanding liabilities. Now, when A brings to the bank a deposit in coin amounting to $1,000, the bank establishes in his favor a credit on its books of $1,000, while it places in its cash reserve the $1,000 in coin. It is evident that if the bank must keep a reserve of 20 per cent behind its outstanding deposits, $200 of the coin which is thus received must be maintained permanently on hand in its vault to protect the outstanding credit of $1,000. This means that it has $800 of free cash. It may theoretically lend this $800 to borrowers. Suppose, for the sake of argument, that it does so, how does the position of the bank then stand? It owes A $1,000, while it has lent $800 to B at, say, 6 per cent. If it pays no interest to A it is now the gainer by the transaction by 6 per cent on $800, or at a rate of $48 per annum. From this must be deducted the expense, whatever it may be, which has been found by experience to repre-sent the cost of carrying a deposit account and of paying checks which are customarily drawn upon it. There must also be taken off the expenses involved in making the loan to B, which include an investigation of his credit and a variety of other items, to say nothing of the overhead and fixed-expense charge applicable to all transactions of the bank. After these have been deducted from the $48, a net profit presumably remains. The bank, however, does not do business in this way customarily, but it holds the $800 in its vaults as a reserve. Customers do not habitually borrow in cash, and if they did the bank would soon refuse to do business with them. If the $800 be regarded as a 20-per-cent reserve, it is evident that the bank might credit on its books liabilities equal to five times that amount - that is to say, it could undertake to credit to depositors the sum of $4,000 and yet be in a safe position, because it would have on hand in its vaults the 20-per-cent protection referred to. The basic income upon which interest would have to be figured would not be 6 per cent on $800, but on $4,000, or $240. Deductions as before would have to be made from this profit, covering the loans that had been made in order to get it, and covering also the other items of expense connected with it.

How safe would the bank be in this position? It would have outstanding $5,000 in deposit accounts, or deposit credits, and would have in its vaults $1,000 in coin. The question of its safety would depend largely upon the question whether it was receiving checks from depositors about as fast as it was paying checks drawn on deposit liabilities which it had thus credited. In other words, it could not regard itself as doing a safe business at all unless there was a steady flow of funds into the bank which fully offset the flow of funds out of it. Of course a certain percentage - perhaps a large percentage - of the checks drawn on the $5,000 of deposit accounts would be drawn in favor of persons who would redeposit them in the bank itself, in which case the expense would be simply the maintenance of the bookkeeping department. A good many, however, would be drawn in favor of other banks, and would have to be cashed. If their cashing resulted in loss of specie the bank would soon find itself back at the position in which it could maintain outstanding only an amount of loans equal to the amount of specie - the original $800. But on condition that it keeps expanding its business and gets in as many checks as it pays, it can keep outstanding a volume of loans represented by deposits on which it receives interest. This amount, as we have seen, is conditional upon its keeping up an active, live business with a steady movement of items into and out of the bank.

By this time it is clear that the assignment of costs to each particular unit of cash that comes into the hands of the bank is very difficult. Thus, for instance, in the illustration that we have given we assume that the original depositor paid in $1,000 and received a credit on the bank's books without interest. This cash was then used as a reserve and loans were made thereon, giving rise to deposit liabilities, while finally we saw that the maintenance of these deposits was conditional upon the bank's doing an active collection business. To trace the expense of all of these transactions back to the original deposit of $1,000 in coin, and so to estimate what that deposit was worth to the bank, is practically out of the question. As a result most banks which do anything in the way of cost accounting simply endeavor to ascertain the expense involved in performing certain representative bank transactions, such as paying checks, collecting checks, etc., and they then seek to estimate the worth of any given account to them upon an expense basis. They usually make no distinction of the form in which deposits are made - whether in coin, claims on other banks, or checks on the bank itself. It is enough for them that a credit has been established on their books, and their effort then is to find out about what the current cost of carrying on such a deposit account is. Nevertheless, it is true that underlying every loan that gives rise to a deposit is the item of reserve carried against it. We have seen that in the case of the illustration already given this reserve was 20 per cent. On every outstanding deposit made by the bank, therefore, it would be proper to figure the "tying up" of 20 per cent of the amount of the deposit. For instance, if A borrows from the bank $1,000 at 6 per cent per annum, and if the bank habitually gets a flow of checks which offsets the checks drawn by A, it might be assumed that the profit of the bank was the interest at 6 per cent on $1,000, or $60, minus the expense involved in keeping open a deposit of that amount, minus such assignment of overhead charges as the bank might determine to make. This amount would be only a part of the truth. It would still be true that the bank was obliged to figure upon having to put $200 out of its power to use that sum, since it is obliged to hold that as a reserve. While it does not cost anything directly to employ its capital in this way, the indirect cost is the interest on $200 at the going rate. Every transaction on the part of the bank, then, which involves the creation of a liability involves also the creation of a reserve and results in a corresponding reduction of the bank's available funds, properly giving rise, therefore, to the corresponding element of charge against income.

This may be a very varying charge. The bank may not find it necessary to keep its whole reserve in coin. Under the central banking system it may be able to keep its reserve with some other bank, which results in cutting down the total amount of reserve required, or it may be disposed to invest its reserve partly in very quick paper. Under the old national banking system a large part of the reserves of American banks was carried on interest with city banks. Conditions of these kinds may result in reducing the unit reserve cost of conducting the institution. The result is still further to complicate the cost analysis of the bank's operations and to make it difficult in any given case to ascertain the exact cost of a given transaction.