Residual Income

Section: Residual Income Valuation Estimated study time: 60 minutes Content: Residual income (RI) is the earnings of a business after deducting a charge for the opportunity cost of equity capital employed. The residual income in a period is: RI_t = Net Income_t - (r_e * Book Value_{t-1}), where r_e is the required return on equity and Book Value_{t-1} is the equity book value at the beginning of the period. This is equivalent to: RI_t = (ROE_t - r_e) * Book Value_{t-1}. Residual income is positive when the firm earns more than its cost of equity (ROE > r_e) and negative when it earns less. The concept is closely related to economic value added (EVA), which applies the same framework to total capital (using NOPAT and WACC instead of net income and cost of equity). The residual income valuation model expresses intrinsic stock value as book value per share plus the present value of all future per-share residual incomes: V0 = B0 + Sum[RI_t / (1 + r_e)^t]. Under the simplest single-stage assumptions with constant ROE and growth g, this simplifies to: V0 = B0 + [RI1 / (r_e - g)] = B0 + [(ROE - r_e)*B0 / (r_e - g)]. Dividing by B0 gives the justified P/B: V0/B0 = 1 + (ROE - r_e)/(r_e - g). This confirms the earlier result: when ROE = r_e, the stock is worth exactly book value (no value added or destroyed); when ROE > r_e, the stock is worth more than book value; and when ROE < r_e, the stock is worth less than book value — it is a value destroyer. The strength of the residual income model relative to dividend discount…