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Pascal PIERRE edited section_Building_a_Profitability_Valuation__.tex
about 6 years ago
Commit id: b3a7f33f02f529611671cbff75dbd4c7b25679e5
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\subsection{Some remarks on the Cash-Flow based valuation model}
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Our equation linking $\frac{EV}{IC}$ with the $ROIC$ and the $WACC$ is completely in line with valuation models and concepts such as EVA. The idea is the same : value is created when a business is able to earn more than its cost of capital ($ROIC > WACC$); in this situation, the market value of a business warrants a premium relative to its book
value. value ($\frac{EV}{IC}$ >1). \\
Just as we did for the $DDM$, the $DC$F can be transformed and simplified in order to take into account growth dynamics in a very simplified manner. For example, a
$FCF$ $DCF$ version of the Gordon Growth Model ($GMM$) would look like :
\begin{equation}
P_{t}=\frac{D_{t+1}}{R-g} EV_{t}=\frac{FCF_{t+1}}{R-g}
\end{equation}
Or, Using the clean surplus accounting rule and replacing $\rho ROIC_{t+1}$ (where $\rho$ is the proportion of NOPAT converted into Free Cash Flows) by $ROIC_{t+1}-g$ where $g$ is the perpetual growth rate in Free Cash Flows, we get :
\begin{equation}
P_{t}=\frac{\rho E_{t+1}}{R-g}
\end{equation}
By dividing both terms of the equation by the book value $B_{t}$ we get :
\begin{equation}
\frac{P_{t}}{B_{t}}=\frac{\rho ROE_{t+1}}{R-g}
\end{equation}
Where $\rho$ is the payout ratio. We can use the clean surplus accounting rule and replace $\rho ROE_{t+1}$ by $ROE_{t+1}-g$ where $g$ is the perpetual growth rate in dividends. We therefore have another version of the GGM based on the price-to-book :
\begin{equation}
\frac{P_{t}}{B_{t}}=\frac{ROE_{t+1}-g}{R-g} \frac{EV_{t}}{IC_{t}}=\frac{ROIC_{t+1}-g}{R-g}
\end{equation}