APV Approach Using Gordon Growth Model to Calculate Terminal Value

An expert calculator for financial analysts and students to determine the terminal value of a firm using the perpetuity growth method within an Adjusted Present Value (APV) framework.

Terminal Value Calculator

Calculation Results

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Intermediate Values:

• FCFF₁:
• Discount Rate:
• Growth Rate:
• Forecast Period:

Formula Used: Terminal Value = [FCFF₁ / (Discount Rate – Growth Rate)]. The Present Value is then calculated by discounting this Terminal Value back ‘N’ years.

What is the APV Approach Using Gordon Growth Model to Calculate Terminal Value?

The APV approach using Gordon Growth Model to calculate terminal value is a valuation method used to determine a company’s worth beyond the explicit forecast period. The Adjusted Present Value (APV) method first values a company as if it had no debt, and then adds the value of any financing benefits, like tax shields. The Terminal Value represents all future cash flows after a specific forecast period (typically 5-10 years).

The Gordon Growth Model (also known as the perpetuity growth model) is employed to calculate this terminal value. It assumes the company’s free cash flow to the firm (FCFF) will grow at a steady, constant rate forever. This technique is fundamental in discounted cash flow (DCF) analysis, where the terminal value can often account for a significant portion of the total enterprise value.

The Formula and Explanation

The core of this calculation lies in the Gordon Growth Model formula applied to free cash flows. The formula is:

Terminal Value (TV) = [Free Cash Flow in Year N+1] / (Discount Rate - Perpetual Growth Rate)

Once the Terminal Value at the end of the forecast period (Year N) is calculated, it must be discounted back to its present value (Year 0) to be useful in today’s terms:

Present Value of TV = TV / (1 + Discount Rate)^N

Variables Table

Description of variables used in the terminal value calculation.

Variable	Meaning	Unit	Typical Range
FCFF₁	Free Cash Flow to Firm in the first year of the terminal period.	Currency ($)	Varies by company
Discount Rate	The rate used to discount future cash flows. In a pure APV context, this is the Unlevered Cost of Equity.	Percentage (%)	8% – 15%
g	The perpetual growth rate at which FCFF is assumed to grow forever.	Percentage (%)	1% – 3% (should not exceed long-term GDP growth)
N	The number of years in the explicit forecast period.	Years	5 – 10

Practical Examples

Example 1: Stable Tech Company

Imagine a mature software company with stable cash flows. An analyst projects its FCFF for the next year (Year 6) to be $50 million. They estimate the unlevered cost of equity at 10% and a perpetual growth rate of 2.5%.

• Inputs: FCFF₁ = $50,000,000, Discount Rate = 10%, g = 2.5%, N = 5 years
• Terminal Value Calculation: $50,000,000 / (0.10 – 0.025) = $666,666,667
• Results: The terminal value at Year 5 is approximately $667 million. The present value of this is $666,666,667 / (1 + 0.10)^5 = $413,927,533.

Example 2: Industrial Manufacturer

Consider an industrial firm. Its projected FCFF for Year 11 is $20 million. Due to its cyclical nature, the analyst uses a higher discount rate of 12%, but a conservative growth rate of 2%.

• Inputs: FCFF₁ = $20,000,000, Discount Rate = 12%, g = 2%, N = 10 years
• Terminal Value Calculation: $20,000,000 / (0.12 – 0.02) = $200,000,000
• Results: The terminal value at Year 10 is $200 million. The present value is $200,000,000 / (1 + 0.12)^10 = $64,392,785. For more on valuation, see our guide on the business valuation methods.

How to Use This APV Approach Calculator

1. Enter Free Cash Flow to Firm (FCFF₁): Input the projected unlevered cash flow for the first year after your forecast horizon.
2. Enter Discount Rate: Input the appropriate discount rate. For an adjusted present value method, this should be the unlevered cost of equity.
3. Enter Perpetual Growth Rate (g): Input the sustainable, long-term growth rate. This rate should be realistic, typically not exceeding the long-term economic growth rate.
4. Enter Forecast Period (N): Provide the number of years in your explicit forecast to ensure the terminal value is discounted correctly.
5. Interpret the Results: The calculator provides both the terminal value at year N and its crucial present value today, which can be added to the present value of explicit period cash flows in your valuation model.

Key Factors That Affect the Terminal Value

• Perpetual Growth Rate (g): This is one of the most sensitive assumptions. A small change in ‘g’ can lead to a massive change in the terminal value. It is critical to choose a conservative and defensible rate.
• Discount Rate: The discount rate (WACC or unlevered cost of equity) reflects the riskiness of the cash flows. A higher rate implies more risk and results in a lower terminal value. See our WACC calculator for more.
• FCFF Forecast Accuracy: The calculation hinges on the FCFF in the first year of perpetuity (FCFF₁). An overly optimistic or pessimistic forecast will directly skew the entire terminal value. Understanding its components is key; learn more about unlevered free cash flow.
• Length of the Explicit Forecast Period (N): A longer forecast period pushes the terminal value further into the future, making its present value smaller, assuming a positive discount rate.
• Economic and Industry Stability: The Gordon Growth Model assumes a state of stable, perpetual growth, which is only suitable for companies that have reached maturity in stable industries.
• Relationship between Discount Rate and Growth Rate: The model is undefined if g ≥ Discount Rate. The spread between the two is a key driver of value. A smaller spread results in a much higher terminal value.

Frequently Asked Questions (FAQ)

1. Why is the perpetual growth rate (g) so important?

The perpetual growth rate is a highly sensitive input because it’s used in a perpetuity formula. A tiny adjustment (e.g., from 2.0% to 2.5%) can drastically alter the terminal value, which often makes up over 75% of a company’s total DCF valuation.

2. What is a reasonable perpetual growth rate?

A reasonable rate is typically between the long-term inflation rate (around 2-3%) and the long-term nominal GDP growth rate (around 4-5%). Choosing a rate higher than GDP growth implies you believe the company will eventually grow larger than the economy itself, which is unsustainable.

3. What happens if the growth rate is higher than the discount rate?

Mathematically, the formula breaks down and yields a negative (and nonsensical) value. Conceptually, it implies infinite value, which is impossible. This scenario signals an error in your assumptions; no company can grow faster than its risk-adjusted discount rate forever.

4. What’s the difference between using this for APV vs. a standard DCF?

In a standard DCF, you typically use Weighted Average Cost of Capital (WACC) as the discount rate and Free Cash Flow to the Firm (FCFF). In an APV valuation, you use the Unlevered Cost of Equity to discount the FCFF, as the effects of debt (like the tax shield) are calculated and added separately. This calculator is designed for that APV framework. For a different approach, you might use a DCF valuation model.

5. Why do we calculate the Present Value of the Terminal Value?

The Gordon Growth formula gives you the value of the company at the *end* of the forecast period (Year N). To make it useful for today’s valuation, you must discount that future value back to Year 0. Money in the future is worth less than money today due to the time value of money.

6. Can the terminal value be negative?

Yes, if the company is projected to have negative free cash flow into perpetuity. This would imply the business is value-destructive and will continue to burn cash forever, a rare but possible scenario for certain declining industries.

7. Is the Gordon Growth Model the only way to calculate terminal value?

No. The other common method is the Exit Multiple Method, where you assume the company is sold at the end of the forecast period for a multiple of its EBITDA or EBIT. The two methods are often used together as a cross-check.

8. When is it inappropriate to use the Gordon Growth Model?

It is inappropriate for high-growth, early-stage companies, or companies in unstable industries where assuming a constant perpetual growth rate is unrealistic. The model is best suited for mature, stable companies.