In a ten year discounted cash flow at a 9% cost of capital, the terminal value at 2.5% perpetual growth is 70% of enterprise value. How much does enterprise value move if the perpetual growth assumption is 3.5% instead?

In a ten year discounted cash flow at a 9% cost of capital, the terminal value at 2.5% perpetual growth is 70% of enterprise value. How much does enterprise value move if the perpetual growth assumption is 3.5% instead?

Approach: Compare the two terminal multiples implied by the perpetuity formula, then apply the percentage change only to the share of value the terminal piece carries.

12.7%. The terminal multiple is 1/(r - g), which is 1/0.065, or 15.38, at 2.5% growth and 1/0.055, or 18.18, at 3.5%, a rise of 18.2%. That applies to the 70% of enterprise value the terminal piece carries, so enterprise value rises by 0.70 * 18.2%, which is 12.7%. A one point change in an assumption about growth in year eleven moves the answer by more than a full year of the company's own growth. The sensitivity worsens as r - g narrows: at 9% with 4.5% growth the multiple is 22.2, so the same one point step adds another 22%. That is why terminal values are cross-checked against an exit multiple and why a perpetual growth rate above nominal economic growth cannot be defended.

Follow-up: The exit multiple cross-check implies 11 times EBITDA. What perpetual growth rate corresponds to that, and what do you do when the two disagree?

Key concepts: terminal value, perpetual growth, sensitivity, enterprise value.