Growth Rates: Definition, Formulas, and Applications

Key takeaways
* Growth rates express the percentage change of a variable over a specific period.
* They can be positive (increase) or negative (decrease).
* Common measures include simple growth rate and compound annual growth rate (CAGR).
* Growth rates are used in economics, corporate performance, investing, and population studies.
* Interpret growth rates alongside scale, volatility, industry context, and inflation.

What are growth rates?

A growth rate quantifies how much a variable changes, as a percentage, between two points in time. Originally used in biology for population studies, growth rates are now applied to GDP, company revenues and earnings, dividends, portfolio returns, retail sales, and more. They help compare performance over time and set expectations for future change.

How to calculate growth rates

Simple growth rate
* Formula: Growth rate = (Ending value − Starting value) / Starting value
* Use when you want the percentage change between two points (e.g., year-over-year revenue change).

Compound Annual Growth Rate (CAGR)
* Formula: CAGR = (EV / BV)^(1/n) − 1
* EV = ending value, BV = beginning value, n = number of years
* CAGR describes the constant annual growth rate that would produce the observed change over a multi-year period. It smooths year-to-year volatility but does not reflect actual interim swings.

GDP and real growth
* GDP growth rate uses the same basic formula but is often reported in real terms to remove inflation’s effect.
* Real GDP growth = (Real GDP_end − Real GDP_start) / Real GDP_start, where real GDP adjusts nominal GDP for inflation.

Population growth
* Annual population growth = (Population_end − Population_start) / Population_start ÷ number_of_years
* Multiply by 100 for a percentage.

Applications of growth rates

Corporate and investment analysis
* Analysts and managers use growth rates for revenue, earnings, cash flows, dividends, and valuation inputs.
* Dividend growth is central to dividend-discount models; the Gordon Growth Model (for a stock paying growing dividends) estimates intrinsic value from a steady dividend growth rate.
* Internal growth rate (IGR) indicates the maximum growth a firm can support from retained earnings without outside financing.
* Investors often adjust reported growth rates to account for taxes, inflation, and fees when calculating real returns.

Industry and macro comparisons
* Industries have benchmark growth norms (e.g., high-tech firms typically show faster growth than mature consumer staples).
* Historical industry growth can guide projections but may not predict future changes because of economic cycles and structural shifts.
* Retail sales growth is commonly used to gauge consumer confidence and spending trends.

Example: comparing two countries
* Country A (mature economy): GDPs — Year 1: $1.20T, Year 2: $1.26T (5.0%), Year 3: $1.29T (2.4%).
* Country B (emerging economy): GDPs — Year 1: $20B, Year 2: $25B (25.0%), Year 3: $35B (40.0%).
* Two-year CAGRs:
* Country A: CAGR = (1.29 / 1.20)^(1/2) − 1 ≈ 3.68%
* Country B: CAGR = (35 / 20)^(1/2) − 1 ≈ 32.29%
Interpretation: mature economies often grow at modest, slowing rates; emerging economies can produce higher percentage growth though on a much smaller base.

Common benchmarks and practical guidance
* What’s “normal” for a company depends on industry, size, maturity, and economic conditions. Generally, outperforming nominal GDP growth and inflation is desirable.
* Startups: very rapid growth is expected early. For example, some tech accelerators view 5–7% weekly revenue growth as good and ~10% weekly as exceptional, but growth typically slows as the company matures.
* Excel: compute CAGR with =(EV/BV)^(1/n)-1 or use the RRI function: =RRI(n, BV, EV).

Limitations of growth rates
* Path blindness: a growth rate between two points ignores volatility and interim fluctuations.
* Scale insensitivity: identical percentage growths can represent vastly different absolute changes (e.g., $50k vs. $5M).
* Poor cross-context comparability: the same rate may be excellent in one industry and weak in another.
* Projection risk: past growth does not guarantee future growth—structural, competitive, and macro changes can alter trajectories.

Bottom line

Growth rates are a concise way to express how variables change over time and are widely used across economics, finance, and business. Simple growth rates and CAGR are the most common tools, but interpretation requires attention to scale, volatility, inflation adjustments, and industry context. Use growth rates as a starting point for analysis, not as a standalone verdict.