1 Later in the chapter we will revisit this important issue in greater detail to examine the liquidity premium.

Exhibit 21.6 shows the forecasted income statements and balance sheets for three units of a bank: the wholesale bank that lends $1 million, the retail bank that raises $900,000 in one-year CDs, and the treasury. To keep the example as simple as possible, we have assumed no reserve requirements and no taxes. The wholesale bank is match-funded with three-year money that costs 9.5 percent; it earns 9.5 percent on $1 million and pays 9.5 percent on $950,000, for an annual profit of $4,750. Its spread is 0 percent—not a good deal. The retail bank is forecasted to earn the expected one-year spot rate (8 percent, then 10 percent, and finally 10.5 percent), which is assumed to be equal to the one-year forward rate. The retail bank pays the expected one-year spot rate on CDs. It, too, has a 0 percent spread.

In Exhibit 21.6, both the wholesale and retail banks are perfectly match-funded; all of the mismatch profits appear in the treasury. In the first year, the treasury lends at the three-year rate (to the wholesale bank) and borrows at the one-year rate (from the retail bank) for a net profit of $14,250. In the second and third years, it loses money because it still earns the three-year fixed rate, 9.5 percent, but pays the one-year spot rate, 10 percent in year two and 10.5 percent in year three. The mismatch profits of the treasury are reflected in the bank as a whole.

If you were to build a valuation model that forecasted profits to be $23,000 perpetually (that is, a 23 percent return on equity), the bank would appear profitable. The reality is that the bank return on equity is 5 percent or less in the second year and 0.5 percent or less in the third year. Its high

Exhibit 21.6 Financial Statement for Three Units of a Bank

mismatch profits in the first year are an illusion that is discovered only when the forecast of profit takes into account the fact that short-term rates are expected to rise.

The key to handling the problem of mismatch gains or losses is to build a good forecast that takes into account:

• The way spreads are forecasted to change with changing interest rate environments.

• The inflow of funds from loans being paid off and the outflow of funds at new rates as new loans are made.

• The substitution between interest-bearing and non-interest-bearing deposits as interest-rate environments change.

• The portion of mismatch profits that is sustainable because forward rates tend to be higher than their corresponding realized spot rates.

It is not easy to build all of these variables into a forecast. Even if you decide not to do so, it helps to understand the illusion of mismatch profits.

Determining the Quality of Loans

Determining the quality of loans is the most difficult problem for an outsider's valuation, and little information is available to help solve it. Consider loans to emerging market countries or commercial real estate. Although they are sometimes sold in secondary markets for 50 cents on the dollar, this kind of markdown must be viewed with healthy cynicism. The loans that banks keep are probably worth more than those they choose to sell in the secondary market.

The market value of the loan portfolio evolves with changes in interest rates and in the creditworthiness of debt in the bank's loans portfolio. It is possible to find out what percentage of the portfolio is represented by emerging market, leveraged buyout, or commercial real estate lending. These can then be marked to market (at least approximately) as market conditions change.

An Example of Valuing a Bank from the Outside

We valued Citicorp using publicly available 1992 data and Value Line's forecasts of assets, net income, loan loss provisions, and debt balances. We used the income model, and there was no attempt to forecast the effect of the term structure of interest rates on expected cash flows. Our intent is to illustrate how forecasts of the income statement and balance sheet are converted into cash flows to equity—not to provide a detailed (or accurate) forecast. Exhibit 21.7 shows that the total equity value less the market value

Exhibit 21.7 Outside-In Valuation of Citicorp, January 1993

Exhibit 21.7 Outside-In Valuation of Citicorp, January 1993

of preferred stock outstanding results in the discounted cash flow value of Citicorp's common stock outstanding. The difference between the DCF estimate and the market value of common is roughly 12 percent. The cost of equity, 12.8 percent, uses a beta of 1.29, an assumed market-risk premium of 5.4 percent, and a 10-year U.S. Treasury bond rate of 5.8 percent. A perpetuity model was used to estimate the continuing value.

Exhibits 21.8, 21.9, and 21.10 show the income statement, the balance sheet, and free cash flow statement, respectively. Exhibit 21.10 also shows a statement of retained earnings, a part of the model that requires more discussion. The discounted cash flow value of equity is the present value of cash flow to equity holders. Normally, one would say that dividends are the same thing as free cash flow, but caution is required. Free cash flow is the cash that could be paid as dividends in a given year, not the actual dividends that are paid. The difference between the two is primarily a matter of timing. To build a spreadsheet, one must decide what to do with the cash difference between actual and potential dividends.

There are two ways of handling the problem. One way is to carry surplus cash as ''excess marketable securities" and deficits as "unscheduled debt." Under this approach, you must discount actual dividends, not potential dividends, or you will double count earnings on the surplus cash. There is no effect on the value of the company because investments in marketable securities have zero net present value. The other approach is to assume that free cash flow in excess of actual dividends is also disbursed to shareholders. This approach helps keep calculation of key ratios, such as equity as a percent of total assets, as simple as possible You will see that the statement of retained earnings in Exhibit 21.10 starts with the beginning retained earnings, adds net income, subtracts total dividends actually paid, and then subtracts a line called potential dividends to arrive at the end-of-period retained earnings. This process allows us to keep the ratio of equity to total assets at the guideline set by the Bank for International Settlements, and helps to keep the financial statements reasonable to a line manager.

Note that dividend policy has no effect on the company's value in our model. If dividend payout is increased, the potential dividends take up the

Exhibit 21.8 Citicorp—Income Statement

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