The Perpetual Growth Rate (often denoted as g) is a critical assumption used in the Discounted Cash Flow (DCF) valuation model, specifically within the Gordon Growth Model, to determine the terminal value of a business. It represents the constant rate at which a company's free cash flows are expected to grow indefinitely.
While this rate is typically estimated based on macroeconomic factors like GDP growth or inflation (usually between 2% and 4%), financial analysts often need to calculate the Implied Perpetual Growth Rate. This calculation reveals what growth rate is currently "baked into" the current market price or a target Enterprise Value.
Implied Perpetual Growth Rate Calculator
The required rate of return or discount rate.
The expected FCF for the first year of the terminal period.
The current valuation or estimated terminal value.
Please enter valid positive numbers for all fields.
Implied Perpetual Growth Rate
0.00%
function calculateGrowthRate() {
// Get inputs by ID
var waccInput = document.getElementById('waccInput').value;
var fcfInput = document.getElementById('fcfInput').value;
var tvInput = document.getElementById('terminalValueInput').value;
var errorMsg = document.getElementById('errorMsg');
var resultBox = document.getElementById('resultBox');
var resultValue = document.getElementById('resultValue');
var resultExplanation = document.getElementById('resultExplanation');
// Reset display
errorMsg.style.display = 'none';
resultBox.style.display = 'none';
// Validation: Ensure inputs are numbers and TV is not zero
var r = parseFloat(waccInput);
var fcf = parseFloat(fcfInput);
var tv = parseFloat(tvInput);
if (isNaN(r) || isNaN(fcf) || isNaN(tv) || tv === 0) {
errorMsg.style.display = 'block';
return;
}
// Logic: Solving Gordon Growth Model for g
// Standard Formula: TV = FCF / (r – g)
// Rearranging for g:
// TV * (r – g) = FCF
// (TV * r) – (TV * g) = FCF
// (TV * r) – FCF = TV * g
// g = ((TV * r) – FCF) / TV
// Note: r is a percentage input (e.g., 8 for 8%), need to handle decimals carefully.
// Convert WACC to decimal for calculation (e.g., 8.5 becomes 0.085)
var rDecimal = r / 100;
// Calculate g in decimal form
// Formula: g = r – (FCF / TV)
var gDecimal = rDecimal – (fcf / tv);
// Convert back to percentage for display
var gPercent = gDecimal * 100;
// Display Results
resultBox.style.display = 'block';
resultValue.innerText = gPercent.toFixed(2) + "%";
// Add context to the result
var explanation = "";
if (gPercent > r) {
explanation = "Warning: The implied growth rate is higher than the discount rate. This is mathematically impossible in the stable growth model (denominator becomes negative). Check your Free Cash Flow or Valuation inputs.";
resultValue.style.color = "#dc3545";
} else if (gPercent > 5) {
explanation = "This rate is significantly higher than historical global GDP growth (typically 2-4%). Ensure your projections are realistic for a 'perpetual' timeframe.";
resultValue.style.color = "#ffc107"; // Warning color
} else if (gPercent < 0) {
explanation = "This implies a perpetuity where the business shrinks every year.";
resultValue.style.color = "#2c3e50";
} else {
explanation = "This rate falls within a typical range for stable, mature companies (0% – 4%).";
resultValue.style.color = "#28a745"; // Success color
}
resultExplanation.innerText = explanation;
}
The Formula for Perpetual Growth
While the calculator above solves for the implied rate based on value, the underlying logic comes from the Gordon Growth Model (GGM). The standard formula for Terminal Value is:
TV = FCFn+1 / (WACC – g)
Where:
TV: Terminal Value (value of the business beyond the projection period).
FCFn+1: Free Cash Flow expected in the first year of the terminal period.
WACC: Weighted Average Cost of Capital (Discount Rate).
g: Perpetual Growth Rate.
To find the Implied Growth Rate (g), we rearrange the formula:
g = WACC – (FCFn+1 / TV)
How to Estimate a Realistic Perpetual Growth Rate
If you are not back-solving from an existing price but instead trying to choose a rate for your own valuation model, follow these guidelines:
GDP Ceiling: The growth rate should not exceed the long-term GDP growth rate of the economy in which the company operates (typically 2% to 3% for developed economies). If a company grows faster than the economy forever, it would eventually become larger than the entire economy, which is impossible.
Inflation Floor: In nominal terms, the rate should typically be at least equal to the expected long-term inflation rate (typically 1% to 2%).
Company Maturity: Only apply this rate to companies that have reached a "steady state" of operations. High-growth startups should not use the perpetual growth model until their growth stabilizes.
Interpreting the Calculator Results
When using the calculator above:
If the result is Between 1% and 3%: The market expects the company to grow in line with the broader economy.
If the result is > 4%: The current valuation implies aggressive growth assumptions that may be difficult to sustain indefinitely.
If the result is Negative: The market expects the company's cash flows to decline over time.