As you peruse discounted cash flow valuations, it is striking how infrequently you see projections of negative growth into the future, even for companies where the trend lines in revenues and earnings have been anything but positive. Furthermore, you almost never see a terminal value calculation, where the analyst assumes a negative growth rate in perpetuity. In fact, when you bring up the possibility, the first reaction that you get is that it is impossible to estimate terminal value with a negative growth rate. In this post, I will present evidence that negative growth is neither uncommon nor unnatural and that the best course, from a value perspective, for some firms is to shrink rather than grow.

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Negative Growth Rates: More common than you think!

The belief that most firms have positive growth over time is perhaps nurtured by the belief that it is unnatural for firms to have negative growth and that while companies may have a year or two of negative growth, they bounce back to positive growth sooner rather than later. To evaluate whether this belief has a basis in fact, I looked at compounded annual growth rate (CAGR) in revenues in the most recent calendar year (2015), the last five calendar years  (2011-2015)and the last ten calendar years (2006-2015) for both US and global companies and computed the percent of all companies (my sample size is 46,814 companies) that have had negative growth over each of those time periods:

Region Number of firms % with negative revenue growth in 2015 % with negative CAGR in revenues: 2011-2015 % with negative CAGR in revenues: 2006-2015
Australia, NZ and Canada 5014 41.44% 36.73% 28.20%
Developed Europe 7082 33.42% 30.03% 24.25%
Emerging Markets 21196 43.06% 29.35% 21.50%
Japan 3698 33.41% 20.76% 31.80%
United States 9823 39.69% 26.76% 28.10%
Grand Total 46814 39.86% 28.64% 24.69%

Note that almost 40% of all companies, in both the US and globally, saw revenues decline in 2015 and that 25% of all companies (and 27% of US companies) saw revenues decline (on a CAGR basis) between 2006 and 2015. (If you are interested in a break down by country, you can download the spreadsheet by clicking here.) Digging a little deeper, while there are company-specific reasons for revenue declines, there are also clearly sector effects, with companies in some sectors more likely to see revenues shrink than others. In the table below, I list the ten non-financial sectors with the highest percentage of companies (I excluded financial service companies because revenues are difficult to define, not because of any built-in bias):

Industry Grouping Number of firms % Negative in 2015 % with Negative CAGR from 2011-2015 % with Negative CAGR  from 20106-2015
Publshing & Newspapers 346 53.77% 48.44% 45.69%
Computers/Peripherals 327 43.30% 42.12% 45.65%
Electronics (Consumer & Office) 152 43.70% 47.11% 44.44%
Homebuilding 164 31.51% 22.69% 35.87%
Oil/Gas (Production and Exploration) 959 79.22% 43.75% 35.40%
Food Wholesalers 126 37.00% 30.59% 33.33%
Office Equipment & Services 160 40.58% 32.54% 33.33%
Real Estate (General/Diversified) 418 41.33% 32.72% 32.52%
Telecom. Equipment 473 43.00% 37.36% 32.43%
Steel 757 73.23% 50.65% 32.08%

So what? For some of these sectors (like real estate and homebuilding), the negative revenue growth may just be a reflection of long cycles playing out but for others, it may be an indication that the business is shrinking. If you are valuing a company in one of these sectors, you should be more open to the possibility that growth in the long term could be negative. (If you interested in downloading the full list, click on this link.)

Negative Growth Rates: A Corporate Life Cycle Perspective

One framework that I find useful for understanding both corporate finance and valuation issues is the corporate life cycle, where I trace a company’s life from birth (as a start-up) to decline and connect it to expectations about revenue growth and profit margins:

Negative Growth Rates

If you buy into this notion of a life cycle, you can already see that valuation, at least as taught in classes/books and practiced, is not in keeping with the concept. After all, if you apply a positive growth rate in perpetuity to every firm that you value, the life cycle that is more in keeping with this view of the world is the following:

Negative Growth Rates

The problem with this life cycle perspective is that the global market place is not big enough to accommodate these ever-expanding behemoths. It follows, therefore, that there have to be companies (and a significant number at that) where the future holds shrinkage rather than growth. Fitting this perspective back into the corporate life cycle, you should be using a negative growth rate in revenues and perhaps declining margins to go with those shrinking revenues in your valuation, if your company is already in decline. If you are valuing a company that is mature right now (with positive but very low growth) but the overall market is stagnant or starting to decline, you should be open to the possibility that growth could become negative at the end of your forecast horizon.

There is an extension of the corporate life cycle that may also have implications for valuation. In an earlier post, I noted that tech companies age in dog years and often have compressed life cycles, growing faster, reaping benefits for shorter time periods and declining more precipitously than non-tech companies. When valuing tech companies, it may behoove us to reflect these characteristics in shorter (and more exuberant) growth periods, fewer years of stable growth and terminal growth periods with negative growth rates.

Negative Growth Rates: The Mechanics

As I noted in my last post, the growth rate in perpetuity cannot exceed the growth rate of the economy but it can be lower and that lower number can be negative. It is entirely possible that once you get to your terminal year, that your cash flows have peaked and will drop 2% a year in perpetuity thereafter. Mathematically, the perpetual growth model still holds:

Negative Growth Rates

If you do assume negative growth, though, you have to examine whether as the firm shrinks, it will be able to divest assets and collect cash. If the answer is no, the effect of negative growth is unambiguously negative and the terminal value will decline as growth gets more negative. If the answer is yes, the effect of negative growth in value will depend upon how much you will get from divesting assets.

To illustrate, consider the example of the firm with $100 million in expected after-tax operating income next year, that is in perpetual growth and let’s assume a perpetual growth rate of -5% a year forever. If you assume that as the firm shrinks, there will be no cash flows from selling or liquidating assets, the terminal value with a 10% cost of capital is:

Terminal value = $100/ (.10-(-.05)) = $666.67

If you assume that there are assets that are being liquidated as the firm shrinks, you have to estimate the return on capital on these assets and compute a reinvestment rate. If the assets that you are liquidating, for instance, have a 7.5% return on invested capital, the reinvestment rate will be -66.67%.

Reinvestment rate = -5%/7.5% = 66.67%

If you are puzzled by a negative reinvestment rate, it as the cash inflow that you are generating from asset sales, and your terminal value will then be:

Terminal value = $100 (1-(-0.6667))/ (.10 – (-.05)) = $1,111.33

Put simply, the same rule that governs whether the terminal value will increase if you increase the growth rate, i.e., whether the return on capital is greater than the cost of capital, works in reverse when you have negative growth. As long as

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