Corporate Finance: From External Financing Needed(EFN) to Sustainable Growth Rate Well in this link I get the EFN definition that I know of, with the spontaneous liabilities term included. I'm trying to derive the Sustainable Growth Rate for a corporation, from this definition of EFN.

How does one calculate the liabilities-that-change-directly-with-sales term, using just previous year's sales (S), total assets(A), total debt(D), total equity(E), projected growth in sales(g), profit margin(PM) and retention ratio(b) as variables?

I found this link(page 11-12) that does the required derivation, but I don't understand the reasoning...

Any help would be appreciated.
We can replace growth rate in the formulation as below
$$\frac{A_0}{S_0}gS_0-\frac{L_0}{S_0}gS_0-PM(1+g)S_0b=0$$
$$(A_0-L_0)g-PMS_0b-PMS_0bg=0$$
$$g=\frac{bPMS_0}{A_0-L_0-bPMS_0}$$

In the paper you linked the author assumed $A_0$ and $L_0$ to be total assets and total debt (pg.11); therefore $A_0-L_0=E_0$
$$g=\frac{bPMS_0}{E_0-bPMS_0}$$
$$g=\frac{b\frac{PMS_0}{E_0}}{1-b\frac{PMS_0}{E_0}}$$
$$g=\frac{b\times ROE}{1-b\times ROE}$$