How do I calculate a growth rate for free cash flows in the terminal period?

Tie it to the inflation rate ~2% or use the long-term growth rate of the economy, 3% (Assuming you are working on a US company)

I've calculated an implied growth rate of 9.5% for the company I'm valuing. I understand that the growth rate shouldn't exceed GDP growth rate (this is a U.S. company)...however their revenues have been growing at around 20% and management is very optimistic about accelerated earnings in the future. Can this 9.5% growth be justified or do I have to revise my model?

Can this 9.5% growth be justified or do I have to revise my model?

No. If a company grows significantly faster than the region in which it operates, you're assuming that it eventually dominates the whole economy. A 9.5% terminal growth rate for a developed market company is way too high. You either need to use a longer DCF (i.e. pick a terminal year farther out) or assume the company grows faster in the interim but reaches its terminal state sooner.

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I'm currently using a 5-year forecast period. I'll try forecasting to 10 years and be very conservative with the numbers and see how that goes.

Aside from your initial suggestions, is there anything else I should look at?

I'm not sure how you're deriving your FCF figures, but keep in mind that terminal growth is driven by ROIC and reinvestment rate, i.e. terminal growth = ROIC * RR . If you're assuming a high terminal growth rate, you are also assuming a high ROIC, high reinvestment rate (low free cash flow), or both. You need to look at each of these assumptions carefully to determine how realistic they are. Most companies don't sustain a high ROIC indefinitely.

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I've calculated a terminal growth rate of about 5% using an average of historical ROIC x RR. This results in an implied share price 57% below share price. I do not believe the company (Harmon International Industries Inc) is overvalued seeing as they have been around for a long time and have been generating high growth revenues in recent years.

I calculated my FCF as EBIAT + DA +Stock Based Compensation + Change NWC - CapEx