Principles of Bank Valuation  745 discount to their fair market value. As a result, if you accounted properly for the impact of the change in its asset mix on the cost of equity and the result- ing reduction in the beta of its business, ABC’s equity value would remain unchanged. Tax Penalty on Holding Equity Risk Capital  Holding equity risk capital rep- resents a cost for banks, and it is important to understand what drives this cost. Consider again the example of ABC Bank issuing new equity and invest- ing in risk-free assets, thereby increasing its equity risk capital. In the absence of taxation, this extra layer of risk capital would have no impact on value, and there would be no cost to holding it. But interest income is taxed, and that is what makes holding equity risk capital costly; equity, unlike debt or deposits, provides no tax shield. In this example, ABC will pay taxes on the risk-free interest income from the $50 million of risk-free bonds that cannot be offset by tax shields on interest charges on deposits or debt, because the investment was funded with equity, for which there are no tax-deductible interest charges. The true cost of holding equity capital is this so-called tax penalty, whose present value equals the equity capital times the tax rate. If ABC Bank were to increase its equity capital by $50 million to invest in risk-free bonds, holding everything else constant, this would entail destroying $15 million of present value (30 percent times $50 million) because of the tax penalty. As long as the cost of equity reflects the bank’s leverage and business risk, the tax penalty is implicitly included in the equity DCF. However, in the economic-spread analysis discussed next, we explicitly include the tax penalty as a cost of the bank’s lending business. Economic-Spread Analysis The equity DCF approach does not reveal the sources of value creation in a bank. To understand how much value ABC Bank is creating in its different product lines, we can analyze them by their economic spread.9 We define the pretax economic spread on ABC’s loan business in 2019 as the interest rate on loans minus the matched-opportunity rate (MOR) for loans, multiplied by the amount of loans outstanding at the beginning of the year: S L r k BT L L = − = − = ( ) , . ( . % . %) . 1 133 7 6 5 5 1 15 9 where SBT is the pretax spread in millions of dollars, L is the amount of the loans (also in millions of dollars), rL is the interest rate on the loans, and kL is the MOR for the loans. 9 The approach is similar to those described by J. Dermine, Bank Valuation and Value-Based Management (New York: McGraw-Hill, 2009). 746  Banks The matched-opportunity rate is the cost of capital for the loans—that is, the return the bank could have captured for investments in the financial mar- ket with similar duration and risk as the loans. Note that the actual interest rate a bank is paying for deposit or debt funding is not necessarily relevant, because the maturity and risk of its loans and mortgages often do not match those of its deposits and debt. For example, the MOR for high-quality four- year loans should be close to the yield on investment-grade corporate bonds with four years to maturity that are traded in the market. Banks create value on their loan business if the loan interest rate is above the matched-opportu- nity rate. To obtain the economic spread after taxes (SAT), it is necessary to deduct the taxes on the spread itself, a tax penalty on the equity required for the loan business (TPE), and the tax on any maturity mismatch in the funding of the loans (TMM): S L r k T AT L L = − − − − ( )( ) 1 TPE TMM The tax penalty on equity occurs because, in contrast to deposit and debt funding, equity provides no tax shield, as dividend payments are not tax de- ductible.10 Thus, the more a bank relies on equity funding instead of deposits or debt, the less value it creates, everything else being equal. Of course, banks have to fund their operations at least partly with equity. One reason is that regulators in most countries have established solvency restrictions that require banks to hold on to certain minimum equity levels relative to their asset bases. In addition, banks with little or no equity funding would not be able to attract deposits from customers or debt, because their default risk would be too high. For ABC’s loan business, this tax penalty in 2019 is calculated as follows:11 TPE 3 = × × × = ( )( ) = T L e k L D 30 1 133 7 8 0 4 6 1 %( , . ) . % . % . where eL is the required equity capital divided by the amount of loans out- standing and kD is the MOR for deposits. In addition, the tax on a maturity mismatch (TMM) needs to be included if the maturity of the loans does not correspond to that of the bank’s deposits. Typically, the maturity of a bank’s loans is longer than that of the deposits by which it funds its operations, and a difference arises in the matched-oppor- tunity rates. For example, in the case of ABC Bank, the loans have a longer maturity than the deposits. As a result, the MOR for loans (5.1 percent) is above the MOR for deposits (4.6 percent). The maturity difference in itself does not create or destroy any value, as it does not affect the economic spread 10 Debt funding provides a tax shield, whereas equity funding generates a tax penalty. See also Der- mine, Bank Valuation, 77. 11 In case of multiple loan products, you can allocate the tax penalty to the individual product lines ac- cording to their equity capital requirements.