Valuing a Bank with an Excess Return Model

A standard DCF starts by defining free cash flow as what's left after reinvesting in the business, treating debt purely as a financing choice separate from operations. For a bank, that separation breaks down: deposits and borrowings are the bank's raw material — the thing it buys low and lends out high — not a financing decision layered on top of an otherwise-definable operating business. Capital expenditure is barely meaningful for a bank; regulatory capital requirements are what actually constrains growth. A model built for a manufacturer simply doesn't map onto how a bank works.

Why equity, and why "excess" return

Valuing a bank at the equity level (rather than the enterprise level, as with FCFF) sidesteps the debt-as-raw-material problem: dividends to shareholders, or free cash flow to equity, become the natural cash flow to forecast, discounted at the cost of equity rather than a blended cost of capital that would otherwise need to treat deposits like corporate debt.

The excess return framing goes one step further and separates book equity (money already invested, already reflected on the balance sheet) from the additional value created by earning more than the cost of that equity going forward:

$$\text{Value} = \text{Book equity} + \sum_{t=1}^{n} \frac{(\text{ROE}_t - r_e) \times \text{Equity}_{t-1}}{(1+r_e)^t}$$

In words: a bank's equity is worth its current book value, plus the present value of every future year's excess return — how much more it earns on its equity than shareholders require — applied to the equity base outstanding that year. A bank earning exactly its cost of equity forever is worth precisely its book value; one earning persistently above that cost is worth more than book, and one persistently below is worth less.

Worked example

A regional bank has $2 billion of current book equity, is expected to earn a stable 14% ROE, and has a cost of equity of 10%. Assume this excess return persists for 10 years, after which the bank grows in line with its cost of equity (contributing no further excess value), and equity grows 5% a year from retained earnings.

1. Year 1 excess return: (0.14 - 0.10) \times 2{,}000\text{m} = \80$ million.
2. Excess return grows with the equity base at 5% a year; discounting this growing 10-year annuity-like stream at the 10% cost of equity gives a present value of roughly $620 million (using the growing-annuity formula on the $80 million base).
3. Total bank value: 2{,}000\text{m} + 620\text{m} = \2{,}620$million, implying a price-to-book multiple of$2{,}620/2{,}000 = 1.31$x — directly explained by the bank's ability to sustainably earn 4 percentage points above its cost of equity.

What this means in practice

This is why price-to-book, not price-to-earnings, is the primary multiple quoted for banks: a bank trading below 1.0x book is priced as if its ROE will run below its cost of equity, and one trading well above 1.0x is priced for a durable ROE advantage. Regulatory capital requirements also matter directly here, since a bank forced to hold more equity against the same lending book mechanically dilutes its ROE, which is exactly the number this model is most sensitive to.