# External Financing and Corporate Growth

In a book on Corporate Finance, the author writes that 'all other things constant' the higher the rate of growth in sales or assets, the greater will be the need for external financing(bank loans, debt securities, or equity). His reasoning is based on the $\text{Assets}=\text{Liabilities} + \text{Equity}$ equation. My question is why can't a company manager use his cash, in the current-assets, to drive the growth in sales or assets? And why should this equality be maintained in this situation? To answer just that by def. of equity, i.e. assets minus liabilities, in this last question seems to be not answering at all...

Any help would be appreciated

The assertion of the book is based on the phenomenon of commercial credit - the fact that business-to-business sales almost always are on credit, and the differences between terms-of-credit that a company gives to its customers, compared to the terms of credit that enjoys from its suppliers. It describes the (short-term) phenomenon, peculiar to some, that "the higher the sales and the profits, the lower the cash available".

A simplified bottom-up unfolding of how this can happen is as follows: Assume that a company has steady monthly sales $S$ for the years 2013 and 2014. Assume that the terms-of-credit that extends to its customers is "60 days/two months". Roughly, this means that the Accounts Receivables at the end of, say, year 2013 equal the amount of two months of sales (assume away any seasonality), denote it $AR_{2014} =2S$. On the other side, the company has only a "1 month" period to pay its suppliers. Assume the monthly Costs of Sales is $cS$.

So during year 2014 the Cash flow from the Customers-Suppliers loop has been

$$CF_{2014}=12\cdot S - 12\cdot cS = 12(1-c)S$$.

Now assume that starting from January 2015, Sales go up 20%.

During the year 2015 the Collections will be $2S + 10\cdot 1.2\cdot S$: November-December 2014 Sales collected in January-February 2015, and 10 months of collecting the increased sales amount.

As for Accounts Payable, during 2015 the company will have to pay $CSpay = cS + 111\cdot 1.2\cdot cS$ (we keep Inventories constant in value for simplicity).

So for 2015 we will have

$$CF_{2015}=2S + 1.2\cdot 10\cdot S - cS - 1.2\cdot11\cdot cS$$

$$=[14 - 14.2c]S$$

Depending on the value of $c$ we may have $CF_{2015} < CF_{2014}$ (in the specific example, we will need to have $c >0.91$ , i.e. a very small mixed profit margin $1-c$).

Namely, the combination of sales growth with the gap in the terms of credit, may result in the company having less cash available to cover its other, operational expenses like salaries etc. But even if this is not the case, the increase in Cash Flow may not be enough to cover the increase in other Assets that accompany an increase in Sales: an increase of the value of Inventories, but also possibly investments. Both will require increased cash. Also, operational expenses, like marketing or labor cost may have to increase. If the terms-of-credit gap is large and the sales growth aggressive, the company will require a Cash injection from shareholders or a bank loan to be able to pay all its obligations, even though its Sales has gone up.

The above are compacted nicely into a Balance-Sheet-point of view (where the equality $\text{Assets}=\text{Liabilities} + \text{Equity}$ holds always by construction, given how the terms involved are defined and measured). In fact, the Balance Sheet approach is the way many Finance Directors use to get a quick taste of what kind of financing will the company need next year. Essentially, the increased funds "automatically" injected by increased suppliers credit (due to increased purchases), plus any projected increased retained profits, may not be enough to cover the increase in the Current Assets due to the increase in Accounts Receivable (and possibly the increase in Inventories and in Fixed Assets that accompany the growth of Sales growth). It may be the case that such an expansion may be profitable in terms of "Profit & Loss" while at the same time having a negative effect on the Cash Flow, in the short-term.

Indeed, the difference could be covered by running down the cash reserves of the company, but in many cases, companies do not hold so much cash to do that. Then, one has to close the gap by for example, increasing Liabilities, say, taking a loan.

• Alecos many thanks for your help. Much appreciated ;) Later on the author talks about the internal growth rate that is the maximum growth rate a company can grow without resorting to external financing(equity or debt). – An old man in the sea. Jul 25 '15 at 10:15
• @Anoldmaninthesea This would be the increase in sales that can be financed solely by increased credit from the suppliers and by running down any cash reserves. Also, it could be indirectly financed by retaining profits. But this would be essentially equity-financing: instead of asking the shareholders to inject cash, you do not disburse dividends (or you disburse less). From a transactional point of view this is not the same as asking for new cash, and it is accomplished easier -but from the Balance Sheet point of view it is equity-financing (although it is not exactly "external"). – Alecos Papadopoulos Jul 25 '15 at 11:20

So I don't quite agree with Alecos' answer. Let me give a perspective from corporate finance. The equality you see is based on the budget constraint of the firm. The firm has assets in place. It must've paid for those assets somehow. Either the owners of the firm paid for them (which counts as equity) or lenders to the firm of some form or other paid for them (which counts as debt). How does cash fit in to that framework? Well, in this equation, cash is counted as an asset. The cash had to ultimately come from somewhere too, either directly from external finance or the profits accrued to the firm using assets purchased through external finance. And, cash will eventually go to equity holders or debt holders in some form or another, either through dividends or payment of principle and interest.

Importantly, the firm does not, itself, really 'own' anything. The firm is built of money from other places, and so everything it has is either owed to debt holders or owned by equity holders. That includes the cash it holds.

Why does growth require external finance? It doesn't always. If the firm has enough cash from operations to cover any investments it makes it can plug profits from assets in place back into its production and operate for an extended period without injection of additional external finance (it still must've used external finance at some point to buy the productive assets it's currently using). However, it is almost certainly not optimal for the firm to never rely on this internal financing. One reason why is precisely because internal financing is cheap. Imagine that we have a one period firm with some internal funds and a scalable project with decreasing returns. Further, imagine the project always has returns higher than the risk free rate, $r_f$. Since the firm is only operating for one period, using a dollar of internal funds for the investment project only costs them $(1+r_f)$. But the benefit of investing is always higher than the $(1+r_f)$. So the firm will use up all its internal funds in investing. Then the firm will have to rely on external funds. External funds tend to be more costly, and greater reliance on external funds costs more, so the firm will begin to use external funds until the costs of funding is the equal to the marginal return on investment. That would be the static equilibrium.

Now, what would happen if more investment opportunities were to appear? The firm would then be forced to rely on external funds to pay for that investment. And we're back to the relationship above.

But you'll notice in this example the firm will always exhaust the cash it has, either through investing or paying out to equity holders. In a full dynamic model, the firm actually has a benefit to holding cash, as they want to avoid having to rely on costly external finance as much as possible. But it is still the case that for relatively large investment opportunities, they will end up relying on cash. For a model where this holds true, check out DeAngelo, DeAngelo and Whited (2011). Even in these dynamic models, the market value of assets (including cash) is equal to the value of debt plus the value of equity, modulo some accounting of taxes on corporations, because the value of those assets is the expected discounted value of future cash flows, and those cash flows will all go to either debt holders or equity holders. So the equality still holds.