Paying for Growth
To make this relationship explicit, let us start by defining the two fundamental drivers of growth, a measure of how much the company reinvests (reinvestment rate) and how well it reinvests (Return on invested capital)
Changing the growth rate will have two effects: it will change the cash flow (by altering reinvestment) and change the denominator, and it is the net effect that determines whether and how much value will change.
The Excess Return Effect
Tying growth to reinvestment leads us to a simple conclusion. It is not the growth rate per se, but the excess returns (the difference between return on invested capital and the cost of capital) that drives value. In the table below, I take much of the hypothetical example from above (a company with expected operating income of $100 million next year and a cost of capital of 10%) and examine the effects of changing growth rate on value, for a range of returns on capital.
There are a few valuation purists who argue that the only assumption that is consistent with a mature, stable growth company is that it earns zero excess returns, since no company can have competitive advantages that last forever. If you make that assumption, you might as well dispense with estimating a stable growth rate and estimate a terminal value with a zero growth rate. While I see a basis for the argument, it runs into a reality check, i.e., that excess returns seem to last far longer than high growth rates do. Thus, your high growth period has to be extended to cover the entire excess return period, which may be twenty, thirty or forty years long, defeating the point of computing terminal value. It is for this reason that I adopt the practice of assuming that excess returns will move towards zero in stable growth and giving myself discretion on how much, with zero excess return being my choice for firms with few or no sustainable competitive advantages, a positive excess return for firms with strong and sustainable competitive advantages and even negative excess return for badly managed firms with entrenched management.
Two Dangerous Practices
If you follow the practice of tying growth to reinvestment, you will be well-armed against some of the more dangerous practices in terminal value estimation.
1. Grow the nth year's cash flow: If you consider the perpetual growth equation in its simplest form, it looks as follows:
The sheer simplicity of the equation can lull you into a false sense of complacency. After all, if you have projected the free cash flows for the your high growth period of 5 years, i.e, the cash flows after taxes and reinvestment, and you want to estimate your terminal value at the end of year 5, it seems to follow that you can grow your free cash flow in year 5 one more year at the stable growth rate to get your numerator for the terminal value calculation. The danger with doing is that you have effectively locked in whatever your reinvestment rate was in year 5 now into perpetuity and to the extent that this reinvestment rate is no longer compatible with your stable growth rate, you will misvalue your firm. For example, assume that you have a firm with $100 million in after-tax operating earnings that you expect to grow 10% a year for the next five years, with a reinvestment rate of 66.67%% and a return on investment of 15% backing up the growth; after year 5, assume that the expected growth rate will drop to 3%, with a cost of capital of 10%. In the table below, I illustrate the effect on value today of using the “just grow the year 5 free cash flow” and contrast it with the value that you would obtain if you recomputed your terminal year's cash flow, with a reinvestment rate of 80%, compatible with your stable growth rate and return on capital
It is conventional wisdom that it is the growth rate in the perpetual growth equation that is the most significant driver of the resulting value. That may be true if you hold all else constant and change only the growth rate, but it is not, if you recognize that growth is never free and that changing the growth rate has consequences for your cash flows. Specifically, it is not the growth rate per se that determines value but how efficiently you generate that growth, and that efficiency is captured in the excess returns earned by your firm.