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Pascal edited section_textit_DDM_textit_RIM__.tex
almost 8 years ago
Commit id: b1d0d68f4c0a60354daa7a35eb03b96568d2da89
deletions | additions
diff --git a/section_textit_DDM_textit_RIM__.tex b/section_textit_DDM_textit_RIM__.tex
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--- a/section_textit_DDM_textit_RIM__.tex
+++ b/section_textit_DDM_textit_RIM__.tex
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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 $R$
\begin{equation}
$V_{t}=\displaystyle\sum_{i=1}^{K}\frac{C_{t+i}}{(1+R)^i}+V_{t+K}$ V_{t}=\displaystyle\sum_{i=1}^{K}\frac{C_{t+i}}{(1+R)^i}+V_{t+K}
\end{equation}
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
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Applying equation 1 to equities leads to
\begin{equation}
$P_{t}=\displaystyle\sum_{i=1}^{K}\frac{D_{t+i}}{(1+R)^i}+P_{t+K}$ P_{t}=\displaystyle\sum_{i=1}^{K}\frac{D_{t+i}}{(1+R)^i}+P_{t+K}
\end{equation}
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 total return of the shareholder 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.