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• The market value of the bank's assets.
• The variability of the market value of the bank's assets.
• The total debt of the bank.
• The proportion of total debt represented by insured deposits.
Although the procedure is somewhat crude, it is possible to obtain cross-sectional estimates of the per-dollar value of the deposit insurance premium by using a put-option-pricing model. Exhibit 21.12 shows some estimates obtained for a cross-section of banks in 1983.2 (As you will see, many have since disappeared through mergers and acquisitions, but the example remains valid.) The highest value was 72.41 basis points per dollar of FDIC-insured deposits for the troubled First Pennsylvania Corp., while the average value was 8.08 basis points. Since normal discounted cash flow
2 E. Ronn and A. Verma, ''Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model," Journal of Finance (September 1986), pp. 871-895.
Exhibit 21.12 Per-Dollar Value of Federal Deposit Insurance
Bank Market value of assets (t million) Face value of Ratio of assets total debt to debt ($ million) Average annual deposit Insurance premium (percent)
First Pennsylvania 3,857 3,866 0.998 0.7241
Crocker National Corp. 15,247 15,195 1.003 0.2666
Continental Illinois 22,287 22,073 1.010 0.1944
Wells Fargo 22,200 21,911 1 013 0.1838
Manufacturers Hanover 34,626 34,313 1.009 0.1269
Bank America 74,642 73,714 1.013 0.1035
First Interstate 37,039 36,405 1.017 0.0856
Chase Manhattan 36,184 35,674 1.014 0.0577
Bankers Trust 20,996 20,266 1.036 0.0568
Citicorp 66,129 63,407 1.143 0.0440
Chemical, New York 32,754 31,718 1.033 0.0270
Security Pacific 29,699 28,682 1.035 0.0162
Mellon 19,864 19,122 1.039 0.0157
NCNB 10,301 9,890 1.042 0.0129
Bank of Boston 10,690 10,231 1.045 0.0106
Morgan, J. P. Average 28,913 26,981 1.072 0.0001 0.0808
Source: Ronn and Verma, 1986
methods cannot capture the value of deposit stability, the retail bank should be credited with a value equal to its insured deposit balance multiplied by an estimate of the average annual deposit insurance premium.
Exhibit 21.13 shows a simplified balance sheet of a hypothetical retail banking unit. Two broad approaches exist for deciding how much equity should be allocated to the retail banking unit. Since most retail banks have required reserves as a buffer against unanticipated account withdrawals, they would carry less equity than the regulatory requirement. We assume, therefore, that the regulators determine the percentage of equity to be carried on the balance sheet. We could compute
Exhibit 21.13 Balance Sheet of a Retail Banking Unit
equity either as a percentage of total assets, or as a percentage of external assets only (reserves, consumer loans, and small business loan). If we adopt the former approach, then equity is a percentage of a major intercompany account, namely loans to the treasury. This philosophy overallocates equity because the total equity of all business units will exceed total equity in the bank. To avoid this aggregation problem, it is better to allocate equity to external assets only. Given the numbers in Exhibit 21.13 and assuming that book equity must be 5 percent of external assets, equity in the retail bank would be $19 million and loans to the treasury would be $1.439 billion.
The Cost of Equity
As always, the cost of equity is the rate of return investors would require for other investments of equivalent risk. Preliminary thinking would indicate that no good market comparable exists for the retail banking unit as we have structured it because no stand-alone banks exist with 80 percent of their assets invested in ''loans to treasury" (or in government securities that return the money rate, the bank's transfer price). We have deliberately chosen the money rate to immunize the value of shareholders' equity against changes in market rates of interest. Even though in our allocation scheme the book equity of the retail banking unit is only about 1 percent of total assets, it has little interest-rate risk. Reserves serve as a buffer to protect against account withdrawals and loan defaults.
The major risk borne by equity in the retail bank is the portion of loan default risk correlated with the economy, a risk that affects only the external assets of the retail bank. Since equity is roughly 5 percent of external assets (that is, the amount required by regulation in our hypothetical example), equity risk will be roughly the same as for comparable retail banks that have a low ratio of loans to deposits.
The Wholesale Bank
The primary business activity of the wholesale bank is making loans. For each dollar of loans, there might be only 20 cents in deposits; therefore, the wholesale bank funds itself by borrowing from the bank's treasury. The critical issue is how to determine the correct transfer price or money rate the wholesale bank must pay for the funds it uses. Once this issue has been resolved, we can turn to capital structure and the cost of equity.