Banks earn money by borrowing from depositors at low interest rates and lending to individuals and businesses at high interest rates. As banks grow, they split into functional divisions that either generate deposits or make loans. To measure the profitability of each division, banks use transfer pricing. For example, if a deposit costs 5%, a loan earns 8%, and the transfer price is 6%, then the deposit division earns 1% times the size of the deposit, and the loan division earns 2% times the size of the loan. Normally, loans and deposits of shorter maturities (less than one year) earn and pay lower interest rates, while those of longer maturities (more than one year) pay higher interest rates. This is illustrated in the following table, which shows four types of customers: those who want one- and five-year loans, and those who want one- and five-year deposits. Assume equal numbers of each consumer type, and each wants to borrow or deposit $100,000.

a. If the bank sets a single transfer price between the deposit and the loan divisions, what is the profit-maximizing transfer price or range of prices and what is the bank's maximum profit?

b. Do you see any problem with this kind of performance evaluation scheme? (Hint: What happens to bank profit if one-year rates rise?) How can the bank solve the problems by changing its performance evaluation scheme?