In financial management, the perpetuity growth model is commonly used to estimate the terminal value (TV) of an investment, project, or company beyond an explicit forecast period in a discounted cash flow (DCF) valuation. Because forecasting cash flows accurately far into the future is difficult, analysts typically project cash flows for a limited number of years (e.g., five years) and then use a single terminal value to capture all subsequent cash flows.

In a DCF valuation, the value of a company equals the present value of all its future free cash flows. Since these cash flows theoretically continue indefinitely, they are divided into:

• (a) Explicit forecast period (year 1 to year n): cash flows estimated year by year.
• (b) Terminal period (year n+1 onward): summarized by a terminal value.

When the company is assumed to grow at a stable, constant rate forever after the forecast period, the perpetuity growth model is used.

Perpetuity Growth Formula for Terminal Value

Where:

• \(\text{TV}_{n}\) = terminal value at the end of year \(n\)
• \(\text{FCF}_{n + 1}\) = free cash flow in the first year after the explicit forecast period
• \(r\) = discount rate (often WACC, the weighted average cost of capital)
• \(g\) = long-term growth rate (often near long-term GDP growth or inflation plus real growth)

This method is appropriate for mature, stable firms whose long-term growth is expected to remain steady.

There are two equivalent approaches to apply this formula in a DCF valuation:

1. Compute TV at year n using \(\text{FCF}_{n + 1}\).
2. Compute TV at year n−1 using \(\text{FCF}_{n}\).

Example

Answers

1. Typical Approach – Terminal Value at Year 5

Forecast to year 5 and compute a terminal value at the end of year 5 using \(\text{FCF}_{6}\).

\(\text{TV}_{5}\) is the value at the end of year 5 instead of year 6.

Total firm value:

This is the typical approach: forecast to year \(n\), compute \(\text{TV}_{n}\) using \(\text{FCF}_{n + 1}\).

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2. Alternative Approach – Terminal Value at Year 4

Forecast to year 5 as before, but compute the terminal value one year earlier, at the end of year 4, using \(\text{FCF}_{5}\).

\(\text{TV}_{4}\) is the value at the end of year 4 instead of year 5.

Total firm value:

The total value is the same as in the first approach. The alternative method simply shifts the point at which the terminal value is placed and can involve fewer steps.

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Conclusions

When you calculate the terminal value at year \(n\) using \(\text{FCF}_{n + 1}\) with the typical approach, you are following the standard textbook approach. It clearly separates the valuation into two parts:

• Years 1 to \(n\): cash flows are forecast year by year.
• Year \(n + 1\) onward: all future cash flows are captured in a single terminal value at the end of year \(n\).

This makes it easy to identify which part of the value comes from detailed forecasts and which arises from long-term steady-state assumptions.

However, with a sound understanding of the perpetuity growth model, one will note that the growth rate from year \(n\) to year \(n + 1\) does not necessarily need to be \(g\) in Equation (1). Instead, as shown in the example, the terminal value can be calculated at year \(n - 1\) using \(\text{FCF}_{n}\). This alternative approach is particularly useful in examinations because it reduces the number of separate computation and discounting steps. With fewer steps, the risk of calculation errors is lower, while still producing the same firm value.