<p>We can replace growth rate in the formulation as below
$$\frac{A_0}{S_0}gS_0-\frac{L_0}{S_0}gS_0-PM(1+g)S_0b=0$$
$$(A_0-L_0)g-PMS_0b-PMS_0bg=0$$
$$g=\frac{bPMS_0}{A_0-L_0-bPMS_0}$$</p>

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

CC BY-SA 3.0
2015-07-27T21:37:48.973Z
Hi, first thanks for your help. I still have some doubts though. 

In the EFN equation $L_0$ is not supposed to be total debt, but only the debt that changes directly due to sales change, right? And how can we be sure that the same growth applied to Total Assets $A_0$ also applies to $L_0$?
An old man in the sea.
CC BY-SA 3.0
2015-07-28T02:51:36.790Z
In the first link $L_0$ represents the debt that changes directly with sales. In the second link it is assumed to be total debt, though (pg.11). You can never be sure that $A_0$ and $L_0$ will have same groth rate. This an assumption to simplify the formulation.
AnilB
CC BY-SA 3.0
2015-07-26T20:21:10.250Z
2015-07-26T20:21:10.250Z
AnilB
<p>Well in <a href="http://www.zenwealth.com/businessfinanceonline/FF/EFN.html" rel="nofollow">this link</a> 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.</p>

<p>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?</p>

<p>I found <a href="http://homes.chass.utoronto.ca/~krybakov/teaching_files/finance/notes/ch3%20long-term%20planning.pdf" rel="nofollow">this link</a>(page 11-12) that does the required derivation, but I don't understand the reasoning...</p>

<p>Any help would be appreciated.</p>

<corporate-finance>
Corporate Finance: From External Financing Needed(EFN) to Sustainable Growth Rate
An old man in the sea.
# Corporate Finance: From External Financing Needed(EFN) to Sustainable Growth Rate

(Asked by: username_0 on 2015-07-25)

Well in [this link](http://www.zenwealth.com/businessfinanceonline/FF/EFN.html) 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](http://homes.chass.utoronto.ca/~krybakov/teaching_files/finance/notes/ch3%20long-term%20planning.pdf)(page 11-12) that does the required derivation, but I don't understand the reasoning...

Any help would be appreciated.

**Tags:** corporate-finance

---

## 1 answers

### Answer by username_1 on 2015-07-26. Score: 0 | Accepted answer

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 $A\_0-L\_0=E\_0$
$$g=\frac{bPMS\_0}{E\_0-bPMS\_0}$$
$$g=\frac{b\frac{PMS\_0}{E\_0}}{1-b\frac{PMS\_0}{E\_0}}$$
$$g=\frac{b\times ROE}{1-b\times ROE}$$

> **Comments:**
> **username_0**: Hi, first thanks for your help. I still have some doubts though.   In the EFN equation $L_0$ is not supposed to be total debt, but only the debt that changes directly due to sales change, right? And how can we be sure that the same growth applied to Total Assets $A_0$ also applies to $L_0$?  
> **username_1**: In the first link $L_0$ represents the debt that changes directly with sales. In the second link it is assumed to be total debt, though (pg.11). You can never be sure that $A_0$ and $L_0$ will have same groth rate. This an assumption to simplify the formulation.  

---

