Myth 5.5: The Terminal Value ate my DCF!

When you complete a discounted cash flow valuation of a company with a growth window and a terminal value at the end, it is natural to consider how much of your value today comes from your terminal value but it is easy to interpret this number incorrectly. First, there is a perception that if the terminal value is a high proportion of your value today, the DCF is inherently unreliable, perhaps a reflection of old value investing roots. Second, following up on the realization that a high percentage of your current value comes from your terminal value, you may start believing that the assumptions that you make about high growth therefore don't matter as much as the assumptions you make in your terminal valuation. Neither presumption is correct but they are deeply held!

If the terminal value is a high percent of value, your DCF is flawed!
To understand why the terminal value is such a high proportion of the current value, it is perhaps best to deconstruct a discounted cash flow valuation in the form of the return that you make from investing in the equity of a business. For simplicity, let’s assume that you are discounting cash flows to equity (dividends of free cash flow to equity) to arrive at a value of equity today:

Note that if you were to invest at the current value and hold through the end of your growth period, your returns will take the form of annual cash flows (yield) for the first five years and an expected price appreciation, captured as the difference between the terminal value and the value today. So what? Consider how investors have historically made money on stocks, decomposing US stock returns from 1928 through 2015 in the graph below:

	1-Year Horizon	5-Year Horizon	10-year Horizon
1928-2015	67.09%	67.57%	70.09%
1966-2015	72.43%	73.42%	75.10%
1996-2015	81.51%	84.11%	85.28%

Note that no matter what time period you use in your assessment, the bulk of your return has taken the form of price appreciation and not dividends. Consequently, you should not be surprised to see the bulk of your value in a DCF come from your terminal value. In fact, it is when it does not account for the bulk of the value that you should be wary of a DCF!

Determinants of Terminal Value Proportion
While the terminal value will be a high proportion of the current value for all companies, the proportion of value that is explained by the terminal value will vary across companies. When you buy a mature company, you will get larger and more positive cash flows up front, and not surprisingly, if you put a 5-year or a 10-year growth window, you will get a smaller percentage of your value today from the terminal value than for a growth company, which is likely to have low (or even negative0 cash flows in the early years (because of reinvestment needs) before you can collect your terminal value. This can be seen numerically in the table below, where I estimate the percentage of current equity value that is explained by the terminal equity value for a firm with a high growth period of 5 years, varying the expected growth over the next 5 years and the efficiency with which that growth is delivered (through the return on equity):

Excess Growth Rate (next 5 years)	ROE = COE -2%	ROE = COE	ROE = COE +2%
0%	75.14%	75.14%	75.14%
2%	86.30%	82.53%	80.86%
4%	100.00%	90.76%	86.75%
6%	117.24%	100.00%	93.15%
8%	139.59%	110.44%	100.00%
10%	169.71%	122.33%	107.35%

In fact, if the reinvestment needs are large enough or the company is not quite ready to make profits, you can get more than 100% of your value today  from the terminal value. While that sounds patently absurd, it reflects the reality that when your cash flows are negative in the early years (as a result of high growth and reinvestment), your equity holding may get diluted in those years as the company raises new equity (by issuing shares). Note that to the extent that the cash flows come in as anticipated, with high growth and low/negative cash flows, you will not have to wait until the terminal year to cash out, since the price adjustment will lead the cash flows turning positive. (You can download the spreadsheet and try your own numbers)

If your terminal value accounts for most of your value, your growth assumptions don’t matter
If you accept the premise that the terminal value, in any well-done DCF, will account for a big proportion of the current value of the firm and that proportion will get higher, as growth increases, it seems logical to conclude that you should spend most of your time in a DCF finessing your assumptions about terminal value and very little on the assumptions that you make during the high growth period. Not only is this a dangerous leap of logic, but it is also not true. To see why, let me take the simple example of a firm with after-tax operating income of $100 million in the most recent year, a five-year high growth period , after which earnings will grow at 2% a year forever, with a 8% cost of equity. Holding the terminal growth rate fixed, I varied the growth rate in the high growth period and the return on equity. The resulting terminal values are reported in the table below:

Excess Growth Rate (next 5 years)	ROE = COE -2%	ROE = COE	ROE = COE +2%
0%	$1,227.00	$1,380.00	$1,472.00
2%	$1,326.00	$1,491.00	$1,591.00
4%	$1,431.00	$1,610.00	$1,717.00
6%	$1,542.00	$1,734.00	$1,850.00
8%	$1,659.00	$1,864.00	$1,991.00
10%	$1,783.00	$2,006.00	$2,140.00

Note that assuming a much higher growth rate and return on equity in the first five years has a large impact on my terminal value, even though the terminal growth rate remains unchanged. This effect will get larger for high growth firms and for longer growth periods. The conclusion that I would draw is ironic: as the terminal value accounts for a larger and larger percent of my current value, I should be paying more attention to the assumptions I make about my high growth period, not less!

Conclusion
If you are valuing equity in a going concern with a long life, you should not be surprised to see the terminal value in your DCF account for a high percentage of value. Contrary to what some may tell you, this is not a flaw in your valuation but a reflection of how investors make money from equity investments, i.e., predominantly from capital gains or price appreciation. You should also be aware of the fact that even though the terminal value will be a high proportion of current value, you should still pay attention to your assumptions about cash flows and growth during your high growth period, since your terminal value will be determined largely by these assumptions.

YouTube Video

Attachments

1. Returns on US Stocks: Dividends and Capital Gains
2. Spreadsheet to compute effect of growth assumptions on terminal value

DCF Myth Posts

Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. It's all about D in the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant in the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.

Myth 5.4: Negative Growth Rates forever? Impossible!

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.

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:

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:

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:

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 you can get more for divesting assets than as continuing investments (present value of cash flows), liquidating them will increase your terminal value. 

Negative Growth: Managerial Implications

Our unwillingness to consider using negative growth in valuation has turned the game over to growth advocates. Not surprisingly, there are many in academia and practice who argue that the essence of good management is to grow businesses and that the end game for companies is corporate sustainability. That's nonsense! If you are a firm in a declining business where new investments consistently generate less than the cost of capital, your attempts to sustain and grow yourself can only destroy value rather than increase it. It is with this, in mind, that I argued in an earlier post that the qualities that we look for in a CEO or top manager will be different for companies at different stages of the life cycle: 

A visionary at the helm is a huge plus early in corporate life, but it is skill as a business builder that allows young companies to scale up and become successful growth companies. As growth companies get larger, the skill set shifts again towards opportunism, the capacity to find growth in new places, and then again at mature companies, where it management’s ability to defend moats and competitive advantages that allow companies to harvest cash flows for longer periods. In decline, it is not vision that you value but pragmatism and mercantilism, one reason that I chose Larry the Liquidator as the role model. It is worth noting, though, that the way we honor and reward managers follows the growth advocate rule book, with those CEOs who grow their companies being put on a much higher pedestal (with books written by and about them and movies on their lives) than those less ambitious souls who presided over the gradual liquidation of the companies under their command. 

Conclusion
I believe that the primary reason that we continue to stay with positive growth rates in valuation is behavioral. It seems unnatural and even unfair to assume that the firm that you are valuing will see shrinking revenues and declining margins, even if that is the truth. There are two things worth remembering here. The first is that your valuation should be your attempt to try to reflect reality and refusing to deal with that reality (if it is pessimistic) will bias your valuation. The second is that assuming a company will shrink may be good for that company's value, if the business it is in has deteriorated. I must confess that I don't use negative growth rates often enough in my own valuations and I should draw on them more often not only when I value companies like brick and mortar retail companies, facing daunting competition, but also when I value technology companies like GoPro, where the product life cycle is short and it is difficult to keep revitalizing your business model.

YouTube Video


Attachments

1. Percent of negative revenue growth companies, by sector
2. Percent of negative revenue growth companies, by country and region

DCF Myth Posts

Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. It's all about D in the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant in the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.

Myth 5.3: Growth is good, more growth is better!

The perils of holding all else constant in perpetual growth equations and playing with individual inputs, not only leads to the use of impossibly high growth rates but also inflates the importance of growth in the terminal value estimation. Growth is not free and it has to be paid for with reinvestment and in the terminal value equation, this effectively means that you cannot leave cash flows fixed and change the growth rate. As the growth rate increases, even within reasonable bounds, the company will have to reinvest more to deliver that growth, leading to lower cash flows, thus making the effect on value unpredictable.

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)

In stable growth, the expected growth rate has to be a product of these two numbers

Growth rate = Reinvestment Rate (RR) * Return on Invested Capital (ROIC)

Over finite time periods, the growth rate for a company can be higher or lower than this "sustainable" growth rate, as profit margins and operating efficiency change, but once you get to the terminal value, where you are looking at forever, there is no evading its reach. Isolating the reinvestment rate in the equation and plugging back into the terminal value equation, here is what we get:

Thus, as g changes, both the numerator and denominator change. For a firm that expects to generate $100 million in after-tax operating income next year, with a cost of capital of 10%, the terminal value can be estimated as a function of the ROIC it earns on its marginal investments in perpetuity. With a growth rate of 3% and a return on capital is 12%, for instance, the terminal value is:

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.

Note that as you increase the growth rate in perpetuity from 0% to 3%, the effect on the terminal value is unpredictable, decreasing when the return on invested capital < cost of capital, unchanged when the ROIC = Cost of capital and increasing when the ROIC> Cost of capital. In fact, you an just as easily construct an equity version of the terminal value and show that the growth rate in equity earnings can affect equity value only if the ROE that you assume in perpetuity is different from your cost of equity.

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 20%, compatible with your stable growth rate and return on capital

Note that just growing out the FCFF yields a value today of only $605 million, about half of the (right) value that you get with a recomputed FCFF.

2. Stable Growth firms don't need to reinvest: I am not sure what the roots of this absurd practice are but they are deep. Analysts seems to be willing to assume that when you get to stable growth, you can set capital expenditures = depreciation, ignore working capital changes and effectively make the reinvestment rate zero, while allowing the firm to continue growing at a stable growth rate. That argument fails at two levels. The first is that if you reinvest nothing, your invested capital stays constant during your stable growth period, and as operating income rises, your return on invested capital will approach infinity. The second is that even if you assume a growth rate = inflation rate, you will have to replace your existing productive assets as they age and the same inflation that aids you on your revenues will cause the capital expenditures to exceed depreciation.

Conclusion
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.

YouTube Video


Attachments

1. Terminal Value Diagnostic Spreadsheet

DCF Myth Posts

Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. It's all about D in the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant in the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.

Myth 5.2: As g-> r...To Infinity and Beyond!

In my last post, I started off by providing a rationale for a terminal value and presented alternatives to the perpetual growth model. That said, most DCFs are built with the the perpetual growth equation, setting up for a potential valuation disaster. Mathematically, the denominator is a powder keg waiting to blow, since as you increase g, holding the cash flow and r constant, your value will approach infinity before turning negative, leading to what I call “Buzz Lightyear” valuations.

The Growth Cap
If you want to draw on the perpetual growth equation, either because you believe your business will last forever or for convenience, the growth rate that you can use in it is constrained to be less than or equal to the growth rate of the economy in which you operate. This is not a debatable assumption, since it is mathematical, not one that owes its presence to economic theory. Within this statement, though, there are estimation choices that you will have to face about how to define the growth cap.

1. Domestic versus Global: As a cap, you can use the growth in the domestic economy (if your company will remain a purely domestic operator) or growth in the global economy, and the economy’s growth rate has to be computed in the same terms that you are using for the rest of your valuation. That may seem to give you license to use high growth rates for emerging market companies but I would suggest caution, since emerging market economies as they get bigger will tend to see their growth rates move towards a global growth rate. Thus, while it is true that the Indian and Chinese economies have higher real growth rates than the global economy in the near term (5-10 years), they will see their growth rates converge on the global average (closer to 2%) sooner rather than later. 
2. Real versus Nominal: In an earlier post, I argued that one of the hallmarks of a well-done DCF is consistency in how cash flows are defined and discount rates are computed. Specifically, you can choose to estimate your cash flows in real terms or nominal terms, with the former reflecting growth without the helping hand of inflation and the latter inclusive of it. If your valuation is in real terms, the cap on your growth rate will be the real growth rate in the economy, and if in nominal terms, it will be the nominal growth rate. 
3. Currency: If you choose to do your valuation in nominal terms, you have to pick a currency to denominate your cash flows in, and that currency will have an expected inflation component attached to it. The nominal growth rate cap will have to be defined consistently, with the same expected inflation built into it as well. Thus, if you are valuing your company in a high-inflation currency, your nominal growth rate forever can be much higher than if you value it in a low-inflation currency.

What if your company is in a high growth sector or a high growth market? The answer lies in the "forever", since no sector or market, no matter how high its growth is right now, can continue to grow at a rate faster than the overall economy forever. One of the greatest perils in valuation is ignoring the growth cap, either because you forget the mathematical basis for why it exists in the first place or because you have mismatched your cash flows and your discount rate, perhaps estimating the former in a high inflation currency and the latter in a low-inflation one or vice versa.

A Risk Free Rate Proxy?

If you accept the rationale that growth is capped at the growth rate of the economy, you are now confronted with a daunting and perhaps impossible task, i.e., to value an individual company, you will now have to estimate expected growth rate in the economy (domestic or global) and expected inflation in the currency of your choice. I, for one, want no part of this estimation challenge, for two reasons. The first is that I find long term macroeconomic forecasting to be a futile exercise and have absolutely no faith in either myself or the institutional entities that claim to be good at this task. The second is that any time I spend on these macroeconomic forecasts is time that I am not spending on understanding my company and its business, key to valuing that company. Consequently, I use a simpler and more easily observable number as a cap on stable growth: the risk free rate that I have used in the valuation. Not only does this take into account the currency automatically (since higher inflation currencies have higher risk free rates) but it is reasonable to argue that it is a good proxy for the nominal growth rate in the economy.  Since it is the component of my valuations that I am taken to task most frequently about, I have three arguments to offer and while none standing alone may be persuasive, you may perhaps accept a combination of them.

1. An Empirical Argument:
To understand the link between the risk free rate (a nominal interest rate) and nominal economic growth rates, consider the following decompositions of both:

Risk free rate = Expected Inflation + Expected real interest rate

Nominal economic growth = Expected Inflation + Expected real growth rate

The table below the risk free rate in US dollars (measured with a ten-year treasury bond rate) and nominal economic growth (the sum of expected inflation and real GDP growth) from 1954 to 2015 in the United States, broken into two sub-periods.

Period	10-Year T.Bond Rate	Inflation Rate	Real GDP Growth	Nominal GDP growth rate	Nominal GDP - T.Bond Rate
1954-2015	5.93%	3.61%	3.06%	6.67%	0.74%
1954-1980	5.83%	4.49%	3.50%	7.98%	2.15%
1981-2008	6.88%	3.26%	3.04%	6.30%	-0.58%

The nominal GDP growth rate was about 0.74% higher than the risk free rate over the entire period (1954-2015), but it has lagged the risk free rate by 0.58% since 1981. I know this table, by itself,  proves nothing, but there is reason to heed to the link. In the last sixty years in the United States,  nominal interest rates and nominal growth have been closely tied to each other, with an increase in one tied to an increase in the other. It is true that there is evidence in the data, especially in the 1954-1980 time period, that real growth can exceed real interest rates for extended periods, and economic intuition provides a rationale for why. If those who take no risk earn the riskfree rate, the economy, at least on average and over long time periods, has to deliver a little bit more to reward the risk takers. However, not only can that differential not be a large number but it is also worth remembering that the nominal growth rate is the growth rate in the entire economy, composed of both mature and growth companies. If you allow every mature company to grow at the rate at which the economy is growing, where does the growth come to sustain the growth companies in the economies? Put differently, setting the growth rate for mature companies below the growth rate of the economy cannot hurt you but setting it above that of the economy can cause valuations to implode. I'll take my chances on the former!

2. A Consistency Rationale 
If you are not convinced by this reasoning, I will offer another reason for tying the two numbers together. When you use a riskfree rate in a valuation, you are implicitly making assumptions about economic growth and inflation in the future and if you want your valuation to be consistent, you should make similar assumptions in estimating your cash flows. Thus, if you believe, the risk free rate today is too low or even negative (because the central banks have kept it so), and you use that risk free rate to come up with your discount rates, you have to keep your growth rate in perpetuity very low or negative to keep your valuation from imploding. That is the point that I was making in my post on negative interest rates. In the last decade, as interest rates have hit historic lows, the danger of this mismatch has become greater. Analysts have been quick to shift to using lower risk free rates (to 2% or lower) in their discount rate calculations while continuing to use nominal growth in the US economy (5-6%) as the cap on their growth rates. That is a recipe for disaster!

3. A Self-Control Basis
There is a third and final reason and this may reflect my personal weaknesses. When I value companies, I know that I fight my preconceptions and the urges I feel to tweak the numbers to deliver the result that I want to see. There is no number that can have more consequence for value than the growth rate in the terminal value and having a cap on that number removes the most potent vehicle for bias in valuation.

In sum, you may or may not be convinced by my arguments for capping the perpetual growth rate at the risk free rate, but I would strongly recommend that you create your own cap on growth and tie that cap to the risk free rate in your valuation. Thus, you may decide a looser version of my cap, allowing your perpetual growth rate to be as much as (but not more than) one percent higher than the risk free rate.

Conclusion
The perpetual growth model is a powerful device for applying closure in a discounted cash flow valuation but it is a mathematical honey trap, with the growth rate in the denominator acting as the lure for analysts who are inclined by bias or ignorance to play with it. If you are tempted, it is worth also remembering that it is the first place that that people who are well versed in valuation look to check for valuation ineptitude, since there are far more subtle ways to bias your valuations than playing with the growth rate.

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DCF Myth Posts

Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. It's all about D in the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant in the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.