**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.

**A Risk Free Rate Proxy?**

__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:

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 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, what 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

*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.

**YouTube Video**

**DCF Myth Posts**

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.