Principles of Bank Valuation  749 Note that we could further refine the tree by allocating the operating ex- penses to the product lines, represented by the different asset and liability categories. This is worth doing if there is enough information on the operating costs incurred by each product line and the equity capital required for each. Economic Spread vs. Net Interest Income The spread analysis helps to show why a bank’s reported net interest income does not reveal the value created by the bank and should be interpreted with care. For example, out of ABC Bank’s 2019 net interest income after taxes of $20.2 million, only $10.3 million represents true value created (the economic spread of $8.2 million on loans plus $2.2 million on deposits minus a rounding difference, as shown in Exhibit 38.10). The remaining $9.9 million is income but not value, because it is offset by the following two charges shown in the exhibit: 1. The matched-capital charge, amounting to $4.2 million for ABC in 2019, is the income that would be required on assets and liabilities if there were no maturity mismatch and no economic spread. In that case, all assets and liabilities would have identical duration (and risk) to deposits, so that their return would equal kD (the MOR on deposits) and net interest income would equal equity times kD. This component of net interest income does not represent value; it only provides share- holders the required return on their equity investment in a perfectly matched bank.13 13 The cost of capital for the bank’s equity would then also equal kD, because it is the value-weighted average of the cost of capital of all assets and liabilities. EXHIBIT 38.10  ABC Bank: Net Interest Income and Value Creation $ million 2019 Description Net interest income (after tax) 20.2 (1 – T ) (L × rL – D × rD ) Matched-capital charge 4.2 (L – D ) kD = (L × eL × kD ) Mismatched-capital charge 5.7 L × (kL − kD ) Economic spread (after tax) 10.3 = (1 – T ) L (rL – kL) – T × L × eL × kD – T × L (kL – kD) + (1 – T ) D (rD – kD) SBT = 11.2 TPE = –1.3 TMM = –1.7 SBT = 2.2             For loans: 8.2              For deposits: 2.2 750  Banks 2. The mismatched-capital charge, amounting to $5.7 million of ABC’s net interest income, arises from the difference in the duration of ABC’s assets and deposits. To illustrate, when a bank borrows at short maturity and invests at long maturity, it creates income. The income does not represent value when the risks of taking positions on the yield curve are taken into account. The mismatched-capital charge represents the component of net interest income required to compensate shareholders for that risk.14 Complications in Bank Valuations When you value banks, significant challenges arise in addition to those dis- cussed in the hypothetical ABC Bank example. In reality, banks have many in- terest-generating business lines, including credit card loans, mortgage loans, and corporate loans, all involving loans of varying maturities. On the liability side, banks could carry a variety of customer deposits as well as different forms of straight and hybrid debt. Banks need to invest in working capital and in property, plant, and equipment, although the amounts are typically small fractions of total assets. Obviously, this variety makes the analysis of real- world banks more complex, but the principles laid out in the ABC example remain generally applicable. This section discusses some practical challenges in the analysis and valuation of banks. Convergence of Forward Interest Rates For ABC Bank, we assumed a perpetual difference in short-term and long- term interest rates. As a result, ABC generates a permanent, positive net inter- est income from a maturity mismatch: using short-term customer deposits as funding for investments in long-term loans. However, following the expecta- tions theory of interest rates, long-term rates move higher when short-term rates are expected to increase, and vice versa. Following this theory, it is nec- essary to ensure that our expectations for interest rates in future years are consistent with the current yield curve. Exhibit 38.11 shows an example of a set of future one-, three-, five-, and ten-year interest rates that are consistent with a hypothetical yield curve as of 2019. The forecasts for a bank’s interest income and expenses should be based on these forward rates, which constitute the matched-opportunity rates for the different product lines. For example, if the bank’s deposits have a three-year maturity on average, you should use the interest rates from the forward three-year interest rate curve minus an expected spread for the bank to forecast the expected interest rates on deposits in your DCF 14 Note that the taxes on the matched capital and the maturity mismatch are included as charges in the economic spread.