Growth in residual income, short and long term, in the OJ model

Abstract

The paper develops the valuation implications of the Ohlson/Juettner-Nauroth (Rev Account Stud 10(2–3):349–365, 2005, OJ) model having two growth parameters in the residual income dynamic—one for the long-term (g) and one for the short-term (g h ). The central result shows that the model can be transformed into \(V_{0} = BV_{0} + (RE_{ 1} /(r - g)) \cdot Scalar,\) where Scalar = 1 + (g h − g)/r. As a benchmark, the scalar equals one if and only if g = g h . The Ohlson (Contemp Account Res 11(2):661–687, 1995) residual income valuation (RIV) model with a single-growth parameter then holds. The OJ model thus generalizes and enriches the set of residual income growth patterns when g ≠ g h . A scalar greater than one admits residual income that (i) grows at a relatively large short-term rate fading downward to a long-term rate or (ii) declines over the long-term. A scalar less than one admits residual income that (iii) grows at a rate fading upward to a long-term rate or (iv) starts out negative and turns positive. Under these scenarios, the RIV model cannot hold in any meaningful sense, even as an approximation. The transformed OJ model also provides a unique angle in explaining market-to-book ratios as a function of profitability and short- and long-term growth, generating empirical implications beyond the constrained RIV model.