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