Cash Flows & DCFintermediate

Terminal Value: Perpetuity and Growing Perpetuity

A DCF forecasts cash flows for an explicit horizon, then captures everything beyond it in a single terminal value. The two standard formulas are the level perpetuity, $\text{TV} = \frac{\text{CF}}{r}$ , and the growing perpetuity (the Gordon form), $\text{TV} = \frac{\text{CF}_{n+1}}{r - g}$ , valid only when $r > g$ . A crucial timing nuance sits in the numerator. The growing perpetuity uses the cash flow of the first year after the horizon, $\text{CF}_{n+1} = \text{CF}_n (1 + g)$ , not the final forecast year $\text{CF}_n$ . The terminal value is computed as at year $n$ and must then itself be discounted back to today. It rests on the same cash flows, so a cash measure, not an accounting balance.

Why it matters

You cannot forecast forever, so at some point you draw a line and say the business settles into a steady state. The terminal value packs all the cash beyond that line into one number standing at the end of the explicit period. The growing-perpetuity formula is a present value as of year n, which is why you still discount it back n years. The detail students miss is the numerator. A perpetuity formula values a stream that starts one period later, so you must grow the final year by one more step to get $\text{CF}_{n+1}$ . Use $\text{CF}_n$ by mistake and you understate the terminal value by a factor of $(1 + g)$ .

Formulas

Terminal value, level perpetuity

\text{TV}_n = \frac{\text{CF}}{r}

A constant cash flow forever, valued as at year n. With no growth the numerator is simply the steady annual cash flow. This value still has to be discounted back to today.

Terminal value, growing perpetuity (the n versus n+1 nuance)

\text{TV}_n = \frac{\text{CF}_{n+1}}{r - g} = \frac{\text{CF}_n\,(1 + g)}{r - g}

Valid only when r is greater than g. The numerator is the cash flow of the first year beyond the horizon, CF at n+1, which is the final forecast year CF at n grown by one more period. Using CF at n instead understates the terminal value.

Discount the terminal value back to today

\text{PV of TV} = \frac{\text{TV}_n}{(1 + r)^n}

The perpetuity formula gives a value as at year n, so it must be discounted over n periods to reach present value, exactly like any other year-n cash flow.

Worked examples

Scenario

The final explicit forecast year (year 5) has free cash flow of US$100. Beyond year 5, cash flow grows at 2 percent forever and the discount rate is 9 percent. Compute the terminal value as at year 5, and flag the timing trap.

Solution

The terminal value uses the first post-horizon cash flow, not the year-5 figure. So the numerator is US$100 times 1.02, which is US$102, the year-6 cash flow. The terminal value as at year 5 is 102 divided by (0.09 minus 0.02), that is 102 divided by 0.07, which is about US$1,457. To use it in the DCF you then discount this back five years. A common error is to put US$100 in the numerator instead of US$102, which would understate the terminal value by 2 percent, the full one-year growth step.

Common mistakes

✗The growing-perpetuity numerator is the final forecast year’s cash flow. It is the first year beyond the horizon, CF at n+1, which is the final year grown by one more period. Using CF at n understates the terminal value.
✗The terminal value is already a present value. The perpetuity formula gives a value as at the end of the explicit horizon, year n, so it must still be discounted back to today.
✗A higher terminal growth rate is always better. As g approaches r the denominator collapses and the value explodes, which is a modelling artefact. Terminal growth above the long-run economy-wide rate is not credible.
✗The terminal value is a minor part of a DCF. It often makes up the majority of the total value, so its growth and discount-rate assumptions deserve the most scrutiny.

Revision bullets

•Terminal value captures all cash beyond the explicit forecast horizon
•Level perpetuity: TV equals CF divided by r
•Growing perpetuity: TV equals CF at n+1 divided by (r minus g), valid only when r exceeds g
•Numerator is the first post-horizon year, the final year grown by one more period
•Using the final forecast year instead understates TV by a factor of (1 plus g)
•TV is valued as at year n and must be discounted back to today

Quick check

In the growing-perpetuity terminal value, the numerator should be

After computing a growing-perpetuity terminal value as at year n, the analyst must

Connected topics

Free Cash Flow NPV & Additivity Discounting Enterprise DCF TV Cross-Check

Sources

Titman & Martin, Ch. 2
Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
Develops the perpetuity and growing-perpetuity terminal value and the timing of the post-horizon cash flow.

How to cite this page

Dr. Phil's Quant Lab. (2026). Terminal Value: Perpetuity and Growing Perpetuity. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-terminal-value-basics

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