Explain how residual income valuation links to the justified P/B ratio derived from forecasted fundamentals

The residual income model explains the price-to-book ratio directly. Dividing value, which is book value plus the present value of future residual income, by B0 gives the justified ratio P/B = 1 + PV of future residual income ÷ B0. If the company is expected to earn more than its cost of equity, that present value is positive and P/B exceeds one. If ROE equals r, P/B equals one; if ROE is below r, P/B is below one. With constant ROE and growth, the justified ratio becomes P/B = (ROE − g) ÷ (r − g). An analyst compares the market P/B with the justified figure to judge valuation. The trap is reading a P/B below one as automatically cheap, when it may simply reflect returns below the cost of equity.