On (r, g) and the Identity ROE = EP*MTB
42 Pages Posted: 3 Feb 2021
Date Written: December 2, 2020
The paper concerns concepts of equity valuation. Three primary financial ratios -- (forward) return on equity (ROE), (forward) earnings to price ratio (EP), and the (current) market-to-book ratio (MTB) – are connected to the standard valuation parameters, r = cost of equity (discount factor), and g = growth. The framework relies on a Gordon-Williams type of PVD model and combines it with an add-on steady-state growth requirement: Subject to clean surplus accounting, (the expected) earnings, dividends, and book values all grow at the same rate. This condition is adapted from “The Second Fundamental Law of Capitalism”, articulated by Piketty (2014). Applying these ideas result in a benchmark model: (i) a weighted average representation, EP = BTM*r + (1- BTM) *Div.Yield , and (ii) the inequalities 0 < BTM < 1 and Div.Yield < EP < r < ROE. Additional analysis relaxes the steady-state growth condition: the g-parameter is now replaced by forecasts of near future earnings growth which get updated as time passes. An empirical part of the paper evaluates whether the steady-state growth concept holds as an average for S&P 500 firms. Results are generally supportive.
JEL Classification: G12, M41
Suggested Citation: Suggested Citation