Horizon Value Calculator (Gordon Growth Model)
Use this calculator to estimate the Horizon Value (also known as Terminal Value) of a company or asset using the Gordon Growth Model. This is typically the value of the cash flows projected to occur *after* an explicit forecast period.
Enter the projected cash flow in the first year *after* your forecast horizon, the appropriate discount rate (e.g., WACC), and the assumed constant perpetual growth rate for cash flows beyond the horizon. Ensure both rates are entered as **decimals** (e.g., 5% as 0.05).
Enter Valuation Inputs
Understanding Horizon Value & Gordon Growth Model
What is Horizon Value (Terminal Value)?
Horizon Value, often called Terminal Value (TV), represents the estimated value of a company or asset at the end of a specific forecast period (the "horizon"). In a Discounted Cash Flow (DCF) analysis, it accounts for the value generated by the asset or company *beyond* the explicit forecast period, into perpetuity.
The Gordon Growth Model Formula
The Gordon Growth Model (GGM) is a common method for calculating Horizon Value. It assumes that cash flows will grow at a constant rate forever. The formula is:
HV = CFT+1 / (r - g)
- HV: Horizon Value (or Terminal Value) at the end of year T.
- CFT+1: The projected cash flow in the first year *after* the explicit forecast period ends (Year T+1).
- r: The discount rate (e.g., WACC) used to value future cash flows. It must be greater than g.
- g: The constant, perpetual growth rate of cash flows.
Key Assumptions and Limitations
The GGM relies on several key assumptions:
- Cash flows grow at a constant rate (g) forever.
- The discount rate (r) remains constant forever.
- The discount rate (r) is strictly greater than the growth rate (g).
These assumptions are simplifications of reality. Choosing appropriate values for CFT+1, r, and g is critical and often involves significant judgment. The GGM is highly sensitive to changes in r and g, particularly when g is close to r.
Horizon Value Calculation Examples
Here are 10 examples demonstrating the calculation:
Example 1: Basic Calculation
Scenario: A simple valuation case.
Inputs: Cash Flow (Year T+1) = $100,000, Discount Rate (r) = 10% (0.10), Growth Rate (g) = 3% (0.03).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $100,000 / (0.10 - 0.03) = $100,000 / 0.07
Result: HV ≈ $1,428,571.43
Example 2: Higher Growth Rate
Scenario: A company with slightly higher perpetual growth.
Inputs: Cash Flow (Year T+1) = $50,000, Discount Rate (r) = 12% (0.12), Growth Rate (g) = 5% (0.05).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $50,000 / (0.12 - 0.05) = $50,000 / 0.07
Result: HV ≈ $714,285.71
Example 3: Lower Discount Rate
Scenario: A less risky asset with a lower discount rate.
Inputs: Cash Flow (Year T+1) = $250,000, Discount Rate (r) = 8% (0.08), Growth Rate (g) = 2% (0.02).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $250,000 / (0.08 - 0.02) = $250,000 / 0.06
Result: HV ≈ $4,166,666.67
Example 4: Growth Rate Close to Discount Rate
Scenario: Demonstrating sensitivity when r is close to g.
Inputs: Cash Flow (Year T+1) = $75,000, Discount Rate (r) = 9% (0.09), Growth Rate (g) = 8% (0.08).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $75,000 / (0.09 - 0.08) = $75,000 / 0.01
Result: HV = $7,500,000
Example 5: Negative Growth Rate (Declining Business)
Scenario: Valuing a business expected to decline slightly in perpetuity.
Inputs: Cash Flow (Year T+1) = $80,000, Discount Rate (r) = 10% (0.10), Growth Rate (g) = -1% (-0.01).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $80,000 / (0.10 - (-0.01)) = $80,000 / (0.10 + 0.01) = $80,000 / 0.11
Result: HV ≈ $727,272.73
Example 6: Zero Growth Rate
Scenario: Valuing a stable cash flow stream with no expected growth.
Inputs: Cash Flow (Year T+1) = $150,000, Discount Rate (r) = 9% (0.09), Growth Rate (g) = 0% (0).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $150,000 / (0.09 - 0) = $150,000 / 0.09
Result: HV ≈ $1,666,666.67
Example 7: Using Smaller Numbers
Scenario: Valuing a smaller project or asset.
Inputs: Cash Flow (Year T+1) = $5,000, Discount Rate (r) = 15% (0.15), Growth Rate (g) = 4% (0.04).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $5,000 / (0.15 - 0.04) = $5,000 / 0.11
Result: HV ≈ $45,454.55
Example 8: Higher Discount Rate, Lower Growth
Scenario: Valuing a riskier asset with modest growth expectations.
Inputs: Cash Flow (Year T+1) = $200,000, Discount Rate (r) = 18% (0.18), Growth Rate (g) = 3% (0.03).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $200,000 / (0.18 - 0.03) = $200,000 / 0.15
Result: HV ≈ $1,333,333.33
Example 9: Growth Rate Equal to Discount Rate (Will trigger error)
Scenario: An invalid input combination (r=g).
Inputs: Cash Flow (Year T+1) = $100,000, Discount Rate (r) = 7% (0.07), Growth Rate (g) = 7% (0.07).
Expected Outcome: The calculator should show an error message because r must be greater than g (division by zero). This is important to understand the formula's limitation.
Example 10: Cash Flow is Zero
Scenario: If the expected cash flow after the horizon is zero.
Inputs: Cash Flow (Year T+1) = $0, Discount Rate (r) = 10% (0.10), Growth Rate (g) = 3% (0.03).
Formula: HV = CFT+1 / (r - g)
Calculation: HV = $0 / (0.10 - 0.03) = $0 / 0.07
Result: HV = $0
Frequently Asked Questions about Horizon Value & GGM
1. What is Horizon Value?
Horizon Value, or Terminal Value, is the estimated value of an investment, business, or project beyond the explicit forecast period in a financial model, representing the present value of all future cash flows from the end of the forecast period into perpetuity.
2. What is the Gordon Growth Model used for?
The Gordon Growth Model (GGM) is primarily used in finance to value a stock or, more commonly, to calculate the Horizon Value (Terminal Value) in a Discounted Cash Flow (DCF) analysis, by assuming a constant growth rate of dividends or cash flows in perpetuity.
3. What are the required inputs for this calculator?
You need three inputs: the projected cash flow in the first year after your forecast horizon (CFT+1), the discount rate (r), and the perpetual growth rate (g). Both rates (r and g) should be entered as decimals.
4. Why must the Discount Rate (r) be greater than the Growth Rate (g)?
If the growth rate (g) is equal to or greater than the discount rate (r), the denominator (r - g) becomes zero or negative. This results in an infinite or undefined Horizon Value, which is not financially meaningful in this context. It reflects that the model is inappropriate when cash flows are growing faster than they are discounted over an infinite period.
5. What kind of cash flow should I use for CFT+1?
This depends on the valuation method. Common choices include Free Cash Flow to Firm (FCFF) or Free Cash Flow to Equity (FCFE) in the year immediately following your explicit forecast period (Year T+1). Ensure consistency between the cash flow definition and the discount rate (e.g., use WACC for FCFF).
6. What is a typical value for the perpetual growth rate (g)?
The perpetual growth rate (g) should generally be a sustainable rate that the company can maintain indefinitely. It is often assumed to be no more than the long-term growth rate of the economy in which the company operates (e.g., GDP growth), or potentially the inflation rate, as companies cannot typically grow faster than the economy forever.
7. Is the Horizon Value the final value of the company?
No. The Horizon Value calculated by the GGM is the estimated value *at the end of the forecast period (Year T)*. To get the present value of this Horizon Value (which is then added to the present value of the explicit forecast period cash flows), you must discount the Horizon Value back to Year 0 using the discount rate (r) for T years.
8. What are the alternatives to the Gordon Growth Model for Terminal Value?
Another common method is the Exit Multiple method, which estimates Terminal Value based on a multiple (like EV/EBITDA, P/E, etc.) of a financial metric in the terminal year (Year T). Both methods have their pros and cons and are often used together for comparison.
9. How sensitive is the result to the inputs?
The GGM is highly sensitive, particularly to the difference between r and g (the denominator). A small change in either r or g, especially when they are close, can lead to a significant change in the calculated Horizon Value. This is why selecting appropriate rates is critical.
10. Can I use this calculator for dividends?
Yes, the Gordon Growth Model was originally used to value stocks based on expected future dividends: Stock Value = Dividend1 / (r - g), where Dividend1 is the next expected dividend, r is the required rate of return on the stock, and g is the perpetual dividend growth rate. You can use the calculator by entering Dividend1 as the "Projected Cash Flow (Year T+1)".
