Why is the P/B ratio linked to ROE, and how do I use this relationship?

The P/B ratio and ROE are mathematically linked through the Gordon Growth Model. Understanding this relationship is central to CFA Level I equity valuation.

Derivation of Justified P/B:

Start with the Gordon Growth Model:

> V_0 = D_1 / (r - g)

Express D_1 using ROE:

> D_1 = E_1 x p = (B_0 x ROE) x p

where B_0 is book value per share, ROE is return on equity, and p is payout ratio.

Also, g = ROE x (1 - p) = ROE x b (where b = retention ratio)

Substitute:

> V_0 = (B_0 x ROE x p) / (r - g)

Divide by B_0:

> Justified P/B = (ROE x p) / (r - g) = (ROE - g) / (r - g)

The second form comes from substituting p = 1 - g/ROE.

Key Insight:

> Justified P/B = (ROE - g) / (r - g)

• If ROE = r → P/B = 1.0 (the company earns exactly its cost of equity)
• If ROE > r → P/B > 1.0 (creating shareholder value)
• If ROE < r → P/B < 1.0 (destroying value)

Worked Example:

Pinnacle Logistics has:

• Book value per share (B_0) = $20
• ROE = 18%
• Required return (r) = 12%
• Growth (g) = 6%

Justified P/B = (0.18 - 0.06) / (0.12 - 0.06) = 0.12 / 0.06 = 2.0x

Fair value = 2.0 x $20 = $40 per share

If Pinnacle trades at $55 (P/B = 2.75x), it looks overvalued relative to the justified 2.0x.

Why some stocks have high P/B but low ROE:

• The market expects ROE to improve significantly (growth stocks reinvesting heavily)
• Book value is depressed by write-downs or intangible-heavy business models
• The stock may genuinely be overvalued

Why some stocks have low P/B but high ROE:

• The market perceives high risk (high r)
• Earnings may be cyclically elevated and unsustainable
• Potential governance or regulatory concerns

Exam application: When the CFA exam asks whether a stock is fairly valued, calculate the justified P/B from fundamentals and compare it to the actual P/B. The gap tells you the degree of over- or undervaluation.

Deepen your valuation skills with our CFA Level I course modules.