How do you apply P/B and P/TBV in bank valuations?

P/B (price-to-book) = market cap / book value of equity, the standard multiple for banks.

A bank's value comes from equity × a multiple, where the multiple reflects the ROE-to-CoE relationship.

```
P/B = (ROE − g) / (CoE − g)
```

with g = sustainable growth.

P/TBV (price-to-tangible book): equity excluding goodwill and intangibles — more meaningful for banks with large acquisition goodwill.

Inputs:

• ROE: 12%
• CoE: 10%
• g (sustainable growth): 2%

Calculation:
```
P/B = (ROE − g) / (CoE − g)
= (12% − 2%) / (10% − 2%)
= 10% / 8%
= 1.25x
```

If the bank trades at 0.9x, the discount signals a lower ROE expectation or a higher CoE.

some large universal banks have historically traded below 0.5x P/B (low ROE), stressed names at 0.3–0.5x, while high-ROE private banks trade at 1.5–2.5x.