2
$\begingroup$

http://image-src.bcg.com/Images/BCG-Value-Creators-2017-Appendix-July-2017_tcm9-166061.pdf

The paper here decomposes total shareholder return into different components. Here is my derivation of the decomposition, price $P$ and dividend $D$ are in per share basis, other variables ($S$ for shares outstanding) are on firm level:

$$ \begin{eqnarray} TSR_t &=& \frac{P_t + D_t}{P_{t-1}} \\ &=& (\frac{P_t}{P_{t-1}} + \frac{D_t}{P_{t-1}})\\ &=& (\frac{P_t/(EBIT_t/S_t)}{P_{t-1}/(EBIT_{t-1}/S_{t-1})}\frac{EBIT_t/S_t}{EBIT_{t-1}/S_{t-1}} + \frac{D_t}{P_{t-1}})\\ &=& (\frac{P_t/EPS_t}{P_{t-1}/EPS_{t-1}}\frac{EBIT_t}{EBIT_{t-1}} \frac{S_{t-1}}{S_t} + \frac{D_t}{P_{t-1}})\\ &=& (\frac{P_t/EPS_t}{P_{t-1}/EPS_{t-1}}\frac{Sales_t}{Sales_{t-1}} \frac{S_{t-1}}{S_t}\frac{EBITMargin_t}{EBITMargin_{t-1}} + \frac{D_t}{P_{t-1}})\\ &\approx& g_{multiple} + g_{sales} + g_{EBITMargin} + g_{shares} + DivYield \\ \end{eqnarray} $$ The last step comes from taking log on both sides of the equation.

However, where does that net debt growth part come from?

Update

I have done a similar simple decomposition with Amazon, and quickly find that the definition just doesn't work when Earning is negative. One simply cannot take log of a negative number, One can only multiply those terms instead of adding. BCG paper always use sum which doesn' seem like possible. The decomposition that I do as listed above works well when Earning is not negative. As @DavidAddison mentioned, the TRS doesn't match up with my calculation based on my data (Also CaptalIQ).

I think there is still some merits to this decomposition, because you can see what factors drive the return more clearly, at least historically.

Improve this question
$\endgroup$
10
  • $\begingroup$ What are $S_t$ and $\mathit{TSR}_t$? $\endgroup$
    – Matthew Gunn
    Jan 26, 2018 at 16:08
  • $\begingroup$ @MatthewGunn $S_t$ represents the number of shares outstanding and $TSR_t$ is the total shareholder return. $\endgroup$
    – zsljulius
    Jan 26, 2018 at 16:09
  • $\begingroup$ So why is $\frac{S_t}{S_{t-1}}$ there? Issuing new shares at the current price doesn't generate positive returns. Retiring shares at the current price doesn't generate negative returns. $\endgroup$
    – Matthew Gunn
    Jan 26, 2018 at 16:16
  • $\begingroup$ @MatthewGunn at time t-1, we pay total P(t-1)S(t-1) for the whole equity, if the firm issues new shares between t-1 and t at t price of P(t-1), then S(t) is greater than S(t-1), and P(t) and D(t) should be adjusted automatically downwards since people who buys new shares know that each share value is diluted. The numerator just represents Total Firm Equity Value at time t and denomintor represents the total firm equity value at time t-1. $\endgroup$
    – zsljulius
    Jan 26, 2018 at 16:21
  • 2
    $\begingroup$ Can you find any references where they precisely define terms? $\endgroup$
    – Matthew Gunn
    Jan 26, 2018 at 17:46

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.