# A Profitability-Valuation Framework Based on a Firm's Cash-Flows

Abstract

The traditional Profitability-Valuation framework is based on the Residual Income Model (hereafter RIM) which is in fact a derivation of the Dividend Discount Model (hereafter DDM). Drawbacks of the dividend or earnings approach to valuation are well known, and practitioners in the equity investment community tend to prefer cash-flow based valuation metrics. We show that it is perfectly feasable to build a Profitability-Valuation framework based on a firm’s cash-flows.

# Introduction

In a prior working paper, Pierre and al. have shown how to build a stock selection framework based on the profitability of a firm and its stock price valuation. This Profitability-Valuation framework is derived from the Residual Income Model (hereafter RIM) which is in fact a derivation of the Dividend Discount Model (hereafter DDM). In this context, Pierre and al. show that profitability is necessarely measured using Return On Equity (hereafter ROE) while the valuation metric is necessarely the Price To Book (hereafter PB). As such, screening for stocks using ROE and PB consists in buying stocks that appear cheap from a dividend perspective or, more generally from an earnings perspective. Dividends can, indeed, be replaced by earnings as long as the clean surplus accounting rule that underpins the RIM is observed.

Drawbacks of the dividend or earnings approach to valuation are well known. For example, earnings are a pure accounting measure that can be manipulated because it incorporates non-cash items of the income statement. Another drawback often mentioned by practitioners is that profitability measures based on earnings depend on a firm’s gearing, defined as the amount of debt relative to equity. A company can have an attractive ROE despite having an unattractive Return on Invested Capital (hereafter ROIC). More importantly, a company using financial leverage to enhance its ROE actually makes it more volatile often at the expense of its financial strength (measured by the health of the balance sheet). For these reasons, practitioners in the equity investment community tend to prefer cash-flow based valuation metrics.

The purpose of this working paper is to show that it is perfectly feasable to adapt the Profitatbiliy-Valuation framework so as to hinge it on a firm’s cash-flows instead of earnings. Using cash-flows has several advantages: first of all, it allows us to avoid the debt caveat. Secondly, by using cash-flows when valuing a firm, practitioners adopt a more entrepreneurial attitude towards stock valuation; typically, a private equity firm or any type of firm that wishes to value a potential target will do so by discounting cash-flows instead of earnings or dividends.

The paper is organised as follow. First section recapitulates theoretical and empirical findings in Pierre and al. regarding the link between DDM, RIM, PB-ROE, and how to combine financial screens and fundamental analysis when using the Profitablity-Valuation framework. In the second section, we show how to adapt this approach to cash-flow based valuations measures; links between Profitablity-Valuation screens, fundamental analysis and Discounted Cash-Flow models (hereafter DCF) are also explicitly described. In this section we also show how a cash-flow based Profitablity-Valuation framework is in fact identical to the Economic Value Added (hereafter EVA) which is also known as Residual Cash-Flow and thus comparable to Residual Income.

# DDM, RIM and the PB-ROE approach

## Valuing assets

We start off firslty by reminding the general model for valuing assets. A well know accounting identity expresses the relation between the value of an asset, the income stream it generates and to which the holder of the asset is entitled ($$C_{1}$$,$$C_{2}$$, . . . $$C_{n}$$) and an endogeneous return $$R$$ $V_{t}=\displaystyle\sum_{i=1}^{K}\frac{C_{t+i}}{(1+R)^i}+\frac{V_{t+K}}{(1+R)^K}$

In other words, $$R$$ is what you earn if you pay $$V_{0}$$, receive $$C_{1}$$,$$C_{2}$$, . . . $$C_{K}$$ and sell the asset at $$V_{t+K}$$. The value of the asset when you sell it is the terminal value of the asset. This basic principle is at the root of many equity valuation models; the DDM is the exact translation of this accounting principle where dividends are the revenues a shareholder is entitled to.

## The DDM

Applying equation (1) to equities leads to $P_{t}=\displaystyle\sum_{i=1}^{K}\frac{D_{t+i}}{(1+R)^i}+\frac{P_{t+K}}{(1+R)^K}$ where $$P_{t}$$ is the stocks price at $$t$$, $$D_{t+i}$$ the future dividend at $$t+i$$, $$R$$ the discount rate and $$P_{t+K}$$ the terminal value. Again, $$R$$ is necessarely the average total return of the shareholder over one period if he pays $$P_{t}$$, receive $$D_{t+1}$$,$$D_{t+2}$$, . . . $$D_{t+K}$$ and sells the stock at $$P_{t+K}$$. It is worth mentioning that the dividends are always reinvested and that the total shareholder return is going to be $$(1+R)^K-1$$ over $$K$$ periods.

The Gordon Growth Model is a simple version of the DDM where it is assumed that dividends will grow at a constant rate, duration of equity is infinite so that terminal value is negligeable: $P_{t}=\displaystyle\sum_{i=1}^{\infty}\frac{D_{t+i}}{(1+R)^i}\approx\frac{D_{1}}{R-g}$ where $$g$$ is the expected constant dividend growth rate to perpetuity.This equation highlights the fact that future returns are driven by the current valuation and future growth.

Although the DDM is theoretically correct, it carries some well known caveats. One in particular is its expression of equity valuation purely from a dividend distribution standpoint. Value creation is not apparent in this formula. By injecting the book value of equity in the DDM one can explain how dividends are generated through time and why investment and economic returns are at the basis of dividend growth and value creation. The Residual Income Model (RIM hereafter) makes this possible.

## Linking the RIM with the DDM

The RIM developed by Ohlson and Felthman (1995) assumes an accounting identity, the clean surplus rule , which states that the c