# Equity and increase in sales

I am reading this book shoe dog by phil knight. There is mention of equity in one of the pages where the banker says *Your rate of growth is too fast for your equity * It is very confusing. From what i have read from google i understand that Equity= Assets - liabilities. Moreover , Assets increase when the sales of a product increase.I want to know how the sales increase is dangerous for equity. There is this excerpt from the book.]1

• Presumably this is looking at the ratio of sales to equity. If this ratio grows, then the company becomes higher risk (e.g. if a fraction of customers fail to pay on time then you could run out of cash faster). It is not a problem in a high margin company if profits grow fast enough and are left in the company to add to equity so equity grows even faster than sales, but otherwise could be. – Henry Apr 13 at 19:23

Here is a reason why growth of a firm's sales could be too fast. Suppose the volume of sales of the firm's product is $$N$$ in period 0 and $$N+\Delta$$ in period 1. Suppose also that each unit of product sells for $$P$$, and the cost of the inputs for one unit is $$cP$$ where $$0 < c < 1$$. Thus the profit per unit is $$(1-c)P$$, and total profit is $$N(1-c)P$$ in period 0 and $$(N+\Delta)(1-c)P$$ in period 1. So far that looks satisfactory.

But suppose further that (as is quite possible) there is a lag of one period between purchase of the inputs to produce a unit and sale of that unit. To keep things simple, assume there is no credit allowed on either purchases or sales, so that the cash outflow for the purchases occurs one period before the cash inflow from the associated sale. Then in period 0 the cash inflow for period 0 sales is $$NP$$ while the cash outflow for the inputs for the period 1 sales is $$(N+\Delta)cP$$. Thus net cash inflow in period 0 ($$NCI_0$$) is given by:

$$NCI_0 = NP - (N+\Delta)cP = [N - (N+\Delta)c]P$$

The condition for this to be positive is:

$$N > (N+\Delta)c$$

which is equivalent to:

$$\Delta < \frac{N(1-c)}{c}\qquad(A)$$

If sales growth is sufficiently fast that relation $$A$$ does not hold, then, despite the firm being profitable, there will be a net cash outflow in period 0, and if such sales growth continues over many periods, there will be a continuing net cash outflow. The question then is whether the firm can finance the cash outflow for long enough to see it through until a time when sales become more stable so that its profits begin to be realised in cashflow terms.

Finance could in principle be via either equity or debt. However, a growing firm is unlikely in practice to be able to obtain debt finance unless the lender is satisfied that the firm's owners are risking their own equity to a sufficient degree. It is possible therefore for a firm's sales to be growing at a faster rate than it is likely to be able to finance given its level of equity.