How do I derive and apply the justified P/B ratio from ROE and growth in a Level II context?

At CFA Level II, the justified P/B moves beyond the single-stage formula to incorporate residual income thinking and multi-period ROE forecasts.

Single-Stage Justified P/B (Review):

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

This holds when ROE and growth are constant forever. At Level II, you need to handle changing ROE.

Residual Income Interpretation:

The justified P/B can be decomposed as:

> P/B = 1 + PV(future residual income) / B_0

If ROE = r_e permanently, all future RI = 0, and P/B = 1.0 (stock trades at book value). The premium (P/B > 1) comes entirely from expected residual income.

Multi-Period ROE Example — Wavecrest Electronics (fictional):

*BV grows by retained earnings: BV_1 = $30 + ($30 x 22% x 0.60 retention) = $33.96. (Simplified for illustration.)

With r_e = 11%, assume ROE fades to cost of equity by Year 4:

V_0 = B_0 + PV(RI_1) + PV(RI_2) + PV(RI_3)

= $30 + $3.30/1.11 + $2.35/1.11^2 + $1.10/1.11^3

= $30 + $2.97 + $1.91 + $0.80

= $35.68

Justified P/B = $35.68 / $30.00 = 1.19x

Applying Justified P/B in Comparable Analysis:

When comparing peers, calculate each company's justified P/B and compare to its actual P/B:

Nexford's actual P/B is below its justified level — potentially undervalued. Granite trades above justified P/B despite having ROE below its cost of equity — potentially overvalued.

Key Level II Insights:

1. ROE persistence matters. Companies with sustainable competitive advantages maintain ROE > r_e longer, justifying higher P/B.
2. Mean reversion of ROE — most companies' ROE reverts toward cost of equity. The speed of reversion determines how much premium P/B is justified.
3. Tobin's Q connection — justified P/B > 1 implies the market values the company above replacement cost of its assets.
4. Intangible-heavy firms — low book value inflates P/B mechanically. Use P/B cautiously for software, pharma, and brand-driven companies.

Exam tip: At Level II, expect vignettes that give you multi-year ROE forecasts and ask you to compute justified P/B using residual income. The key skill is knowing when ROE > r_e (value creating) vs. ROE < r_e (value destroying).

Master justified multiples with our CFA Level II equity course.