Back out the growth rate implied in residual income from the market P/B ratio and an estimated required return on equity

The single-stage residual income model can be inverted to reveal the growth the market expects. Setting price equal to value in the single-stage model, P0 = B0 + (ROE − r) × B0 ÷ (r − g), leaves growth as the only unknown. Solving for it, and dividing through by B0 for the ratio form, gives g = r − (ROE − r) × B0 ÷ (P0 − B0) = r − (ROE − r) ÷ (P/B − 1). A high implied growth rate for a company whose ROE is only slightly above r signals demanding expectations. When ROE is below r, a price above book cannot come from the current spread and implies the market expects ROE to rise above r. The trap is algebraic: the denominator is price minus book, or P/B minus one, not price or P/B alone.