Terminal Value Formula: Perpetuity Growth vs Exit Multiple, With a Worked Example

What the terminal value is

A discounted cash flow forecasts a company's free cash flow for a number of years, usually five to ten, and discounts each one to today. But a going concern does not stop at year ten. The terminal value stands in for every cash flow after the forecast period, compressed into one number at the end of the final year, which is then discounted back like any other. In the illustrative company used throughout these guides, Harbor Foods, the ten forecast years are worth about $911 million today and the terminal value about $1,249 million, so 58% of the $2.16 billion enterprise value comes from the part of the future nobody forecast in detail. That proportion is normal, and it is why the terminal assumptions deserve more scrutiny than next year's margin. The DCF model example builds the full model; this article isolates its largest piece.

Method 1: the perpetuity growth formula (Gordon growth)

Terminal value = FCF in the final year × (1 + g) ÷ (r − g)
Present value = terminal value ÷ (1 + r)^n

where g is the growth rate assumed forever, r the discount rate and n the number of forecast years. Harbor's free cash flow starts at $100 million, grows 8% a year for five years and 5% for five more, so year-ten free cash flow is 100 × 1.08⁵ × 1.05⁵ = $187.5 million. With g = 2.5% and r = 9%:

• Terminal value = 187.5 × 1.025 ÷ (0.09 − 0.025) = 192.2 ÷ 0.065 = $2,957 million.
• Present value = 2,957 ÷ 1.09¹⁰ = 2,957 ÷ 2.367 = $1,249 million.

The formula is a geometric series: a cash flow growing at g forever, discounted at r, sums to the next year's cash flow divided by (r − g). It needs r to be greater than g, and it is extremely sensitive to the gap between them, because that gap is the denominator. The growth rate is meant to be the rate the business can sustain indefinitely, which cannot exceed the long-run growth of the economy it operates in; something near or below nominal GDP growth, often 2% to 3%, is the usual range. The WACC formula article covers the discount rate.

Method 2: the exit multiple

Terminal value = final-year metric × exit multiple

The exit multiple method assumes the business is sold at the end of the forecast at a multiple of some final-year figure, usually EBITDA for acquirers and free cash flow or earnings for investors. Using Harbor's year-ten free cash flow:

The appeal is that multiples are observable: you can see what similar businesses trade for today. The danger is the same thing. Today's multiple reflects today's interest rates, sentiment and cycle position, none of which has any business in year ten. A multiple taken from a boom and applied to a forecast that ends in a normal year overstates the value, and vice versa. Use a multiple that is normal for the business over a full cycle, not the one on the screen.

Cross-checking one method with the other

The two methods are the same assumption in different clothes, which makes each a check on the other. A perpetuity growth rate implies an exit multiple, and an exit multiple implies a growth rate:

Implied multiple = (1 + g) ÷ (r − g)
Implied growth = (multiple × r − 1) ÷ (multiple + 1)

At r = 9%, Harbor's 2.5% terminal growth implies a multiple of 1.025 ÷ 0.065 = 15.8× free cash flow. Is that a reasonable price for a mature packaged-food business in year ten? If comparable companies trade between 12× and 18× through a cycle, yes. Going the other way, a 15× exit multiple implies growth of (15 × 0.09 − 1) ÷ 16 = 2.2%, and 18× implies 3.3%. A model that uses 4% terminal growth with a 9% discount rate is quietly assuming a 20.8× exit multiple; a model that uses a 25× multiple is quietly assuming 5.5% growth forever. Writing the implied figure next to the chosen one is the fastest way to notice when an assumption has drifted out of the plausible range.

How much the inputs move the answer

Holding everything else in Harbor's model fixed:

Half a point of terminal growth is worth about $2 a share, roughly 5%, on a $39 stock. A point on the discount rate is worth more, because it changes both the terminal value and the discounting of every year before it: $47.57 at 8% and $33.18 at 10%. These are the figures the stock valuation calculator prints in its sensitivity grid, and the intrinsic value article shows how to turn them into a range rather than a point.

Common mistakes

• Growth at or above the discount rate. The denominator goes to zero or negative and the formula returns nonsense. Growth must be well below the rate.
• Growth above the economy. A company growing faster than nominal GDP forever would eventually be the economy. Terminal growth is for the mature phase, not the growth phase; extend the forecast period instead if the business is still growing fast.
• Forgetting to discount. The terminal value sits at the end of year n and must be divided by (1 + r)^n. Adding it undiscounted roughly doubles the value in a ten-year model.
• Growing the wrong year. The formula multiplies the final year's cash flow by (1 + g) to get the first terminal-period cash flow. Skipping that step understates the value by one year's growth; applying it twice overstates it.
• A multiple on the wrong metric. An EBITDA multiple applied to free cash flow, or an equity multiple (P/E) applied to a firm-level cash flow, mixes two definitions. Match the multiple to the metric it was observed on.
• Final-year distortions. If year ten happens to carry unusually high capital spending or a working-capital release, the terminal value inherits the distortion forever. Normalise the final year first.

The stock valuation guide places the terminal value within the whole method, and the reverse DCF guide shows the same arithmetic run backwards from the price.