Implied Perpetuity Growth: What Your DCF Really Assumes

Key Takeaways

• Implied perpetuity growth solves the Gordon formula in reverse to extract the embedded growth rate.
• A rate above the long run economy growth rate is mathematically and economically suspect.
• The most common mistake is forgetting that g must always sit below the discount rate r.
• The number tells you when an apparently reasonable DCF is doing the heavy lifting in year ten plus.

How It Works

The classic Gordon growth formula for terminal value is.

Terminal Value = FCFF(n+1) / (r - g)

Solve for g.

g = r - (FCFF(n+1) / Terminal Value)

You can also back into g from an exit multiple terminal value. Compute terminal value using an EV to EBITDA exit multiple, then plug it back into the Gordon equation and solve for the implied perpetuity growth.

This calculation is essential because, as Damodaran notes in his work on terminal value, the closing value typically represents 60 to 80 percent of the total enterprise value in most DCF analyses of going concern businesses. The growth rate assumption is doing most of the work.

What It Is

In every DCF model you eventually stop forecasting cash flows year by year. Beyond the explicit horizon, often year 10, the rest of the firm's value is captured in a single number called terminal value. The two standard methods to compute terminal value are the perpetuity growth method and the exit multiple method.

The implied perpetuity growth rate is what you get when you reverse engineer either method to ask, given the terminal value already in the model, what constant growth rate after the explicit forecast period would the Gordon formula need to produce that same value.

The Intuition

A DCF is only as honest as its assumptions. Most analysts will state explicit revenue and margin forecasts for the first decade but bury the terminal assumption inside an exit multiple. The implied perpetuity growth rate forces that hidden assumption into the open.

If a model returns an implied growth of 5 percent in a world where long run GDP growth runs at roughly 2 to 3 percent, the model is assuming the company outgrows the entire economy forever. That cannot happen. Damodaran calls this the growth cap. A stable growth rate cannot exceed the riskless rate or the nominal growth rate of the economy where the firm operates.

Worked Example

A model has a year 10 free cash flow to the firm of 1,200 million. The exit multiple chosen is 10 times EBITDA, and year 10 EBITDA is 2,000 million. Terminal value is therefore 20,000 million.

The cost of capital, r, is 8.0 percent. Assume the year 11 free cash flow grows from year 10 by an unknown rate g.

20,000 = 1,200 x (1 + g) / (0.08 - g)

Solve for g. Cross multiply.

20,000 x (0.08 - g) = 1,200 + 1,200g
1,600 - 20,000g = 1,200 + 1,200g
400 = 21,200g
g = 1.89 percent

That is the implied perpetuity growth rate. At under 2 percent, well below long run nominal GDP, the exit multiple is defensible. If the math had produced 4.5 percent, you would need to either lower the exit multiple or raise expected year 10 free cash flow.

Common Mistakes

1. Letting g approach r. As g moves close to r the denominator collapses and terminal value explodes. Most analysts cap g at the risk free rate to keep the math stable.
2. Forgetting reinvestment. Damodaran reminds analysts that growth is earned. In stable growth, reinvestment rate equals g divided by ROIC. If you imply g of 4 percent at an ROIC of 8 percent, half of all cash flow must be reinvested. Many models forget this and double count.
3. Comparing nominal g to real GDP. The discount rate is nominal, so the growth rate must be nominal as well. Compare to nominal GDP, roughly 4 percent in developed markets, not real GDP.
4. Ignoring currency. A US dollar DCF cannot use Brazilian inflation as a growth proxy. Match the currency of cash flows with the currency of g.
5. Skipping the check entirely. The most damaging error is not computing implied perpetuity growth at all. Analysts pick an exit multiple, accept the answer, and never ask what long run growth rate it embeds.

Frequently Asked Questions

What is implied perpetuity growth in simple terms? It is the constant growth rate that, if a company grew at it forever, would justify the terminal value you already plugged into your DCF. It exposes the long run assumption.

How does implied perpetuity growth affect investment decisions? If the implied rate is unreasonably high, the DCF target price is fragile. Lowering the rate by even one percentage point can cut terminal value sharply, as the worked example shows.

What is a real-world example of implied perpetuity growth? Sell side analysts often use exit multiples of 12 to 15 times EBITDA for software firms. Backing out the implied growth frequently reveals rates above 5 percent, which signals an aggressive base case rather than a conservative one.

How can investors use implied perpetuity growth effectively? Cap it at the long run nominal risk free rate. If your implied growth exceeds the 10 year Treasury yield, treat the model as optimistic and stress test by setting g equal to the risk free rate.

How is implied perpetuity growth different from a forecast growth rate? A forecast growth rate is what you project explicitly during the first 5 to 10 years. Implied perpetuity growth is the steady rate the model assumes forever after that, and it is usually far lower than the forecast rate.

Sources

1. Damodaran, A. Closure in Valuation: Estimating Terminal Value. NYU Stern. https://pages.stern.nyu.edu/~adamodar/pdfiles/papers/termvalue.pdf
2. Damodaran, A. Session 9: Terminal Value. NYU Stern. https://pages.stern.nyu.edu/~adamodar/pdfiles/valonlineslides/session9.pdf
3. Damodaran, A. The Big Enchilada: Stable Growth and Terminal Value. NYU Stern. https://pages.stern.nyu.edu/~adamodar/pdfiles/eqnotes/dcfstabl.pdf
4. McKinsey & Company. The right role for multiples in valuation. https://www.mckinsey.com/capabilities/strategy-and-corporate-finance/our-insights/the-right-role-for-multiples-in-valuation

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.