# Price to Book Value Ratio – Interpretation and Derivation (23:02)

In this Price to Book Value Ratio – Interpretation and Derivation lesson, you’ll learn about the relationship between Price to Book Value (P/BV), Return on Equity (ROE), and Cost of Equity (Ke) for commercial banks, including how you can derive a formula for P/BV that links these key variables, plus Net Income Growth, together. You’ll also learn how you can use this information to determine if a bank might be overvalued or undervalued.

Here’s a question that came in the other day:

“I see that in the public comps of your Bank Valuation model, Citi is trading below a 1x P / TBV (Price to Tangible Book Value) multiple.

Is the market saying that Citi’s shares are worth less than the liquidation value of the company? How does that make sense?”

“Also, what does it mean if the bank were trading at a higher P / TBV or P / BV multiple, either over 1x or at a higher number than the comparables?”

The ANSWER is that P / BV (or P / TBV etc.) multiples represent *shorthand* for the valuation of commercial banks.

They’re all about *expected* returns vs. *targeted* returns:

If P / BV is above 1x, it means the ROE of a bank exceeds its Cost of Equity.

If P / BV equals 1x, it means that ROE equals Cost of Equity.

If P / BV is below 1x, it means that ROE is below Cost of Equity.

Multiples: Shorthand for a DCF or Dividend Discount Model Valuation

In a DCF, if you know a company’s Final Year FCF, Terminal FCF

Growth Rate, and the Discount Rate (WACC), you can figure out its *implied* EBIT or EBITDA multiple.

In other words, if you make those assumptions, the multiple tells you how much you’d be willing to pay for the company to earn the return you’re targeting.

For commercial banks, those metrics are meaningless because interest income is a critical component of revenue and you can’t separate operating and non-operating assets and liabilities.

So instead, you rely on Dividends, Net Income Growth, and Cost of Equity for valuation, and they are all linked to the P / BV multiple.

Specifically, the Terminal Equity Value for a commercial bank = Dividends One Year After the Final Year / (Discount Rate – Net Income Growth Rate)

## What Drives Dividends?

The key factors influencing Dividends are the bank’s Book Value, its Return on Equity (ROE), its Payout Ratio, and its Net Income Growth Rate… a bank generates Net Income from its Book Value and ROE, and then it issues a certain amount in the form of Dividends.

And then it grows its Net Income at a certain rate in the next year.

So you can rewrite this formula as:

Implied Equity Value = BV * ROE * Payout Ratio * (1 + NI Growth Rate) / (Cost of Equity – NI Growth Rate)

Since P / BV = Equity Value / Book Value, you can rewrite that as:

P / BV = ROE * Payout Ratio * (1 + NI Growth Rate) / (Cost of Equity – NI Growth Rate)

Then, you can make ROE correspond to the bank’s Net Income in the NEXT period instead, so it becomes:

P / BV = Next Year ROE * Payout Ratio / (Cost of Equity – NI Growth Rate)

Getting Rid of the Payout Ratio Term

A bank has two options for its Net Income: it can pay it out in the form of Dividends, or hold onto it and actually get more Net Income for growth purposes.

You can reflect this relationship as:

Net Income Growth = (1 – Payout Ratio) * ROE

NI Growth = ROE – ROE * Payout Ratio

NI Growth – ROE = – ROE * Payout Ratio

ROE – NI Growth = ROE * Payout Ratio

And then you can plug in this term to the equation:

P / BV = ROE * Payout Ratio / (Cost of Equity – NI Growth Rate)

P / BV = (ROE – NI Growth Rate) / (Cost of Equity – NI Growth Rate)

And this tells you the key relationship between all these terms.

## Real-Life Uses and Interpretation

So are Citi’s shares worth less than its liquidation value?

Technically, yes… but it might be better to think of it as:

“The market believes Citi’s ROE will be less than its Cost of Equity, and therefore its Net Assets are worth less than their current Balance Sheet values.”

If a bank’s ROE and P / BV are both high, that doesn’t tell you much; same if they are both low.

You find the interesting opportunities and (potentially) incorrectly valued banks when the ROE is low but the P / BV multiple is high, or when the ROE is high but the P / BV multiple is low.