Understanding Compound Annual Growth Rate (CAGR)
The Compound Annual Growth Rate (CAGR) is a powerful metric used to smooth out volatility and determine a representative annual growth rate of an investment, business, or any metric over a specified period longer than one year. It represents the rate at which an investment would have grown if it had grown at a steady rate each year. CAGR is particularly useful because it accounts for the compounding effect, meaning that growth in one period contributes to growth in subsequent periods.
How CAGR is Calculated:
The formula for CAGR is:
CAGR = ( (Ending Value / Starting Value) ^ (1 / Number of Years) ) – 1
Where:
- Starting Value: The value of the metric at the beginning of the period.
- Ending Value: The value of the metric at the end of the period.
- Number of Years: The total number of years in the period.
The result of this calculation is typically expressed as a percentage.
Why is CAGR Important?
CAGR provides a standardized way to compare growth rates over different periods and across different investments. It helps in:
- Assessing the performance of investments.
- Forecasting future growth trends.
- Comparing the growth of different companies or assets.
- Understanding the overall trajectory of a business metric.
While CAGR offers a valuable smoothed-out view, it's important to remember that it doesn't reflect the actual year-to-year volatility of the growth. The actual growth might have been higher in some years and lower in others.
Example:
Let's say you invested $10,000 in a stock at the beginning of 2019, and by the end of 2023 (5 years later), its value had grown to $20,000. To calculate the CAGR:
- Starting Value = $10,000
- Ending Value = $20,000
- Number of Years = 5
CAGR = ( ($20,000 / $10,000) ^ (1 / 5) ) – 1
CAGR = ( 2 ^ 0.2 ) – 1
CAGR = 1.1487 – 1
CAGR = 0.1487
So, the Compound Annual Growth Rate is approximately 14.87%. This means your investment grew as if it had increased by 14.87% steadily each year for those five years.
function calculateCAGR() {
var startingValue = parseFloat(document.getElementById("startingValue").value);
var endingValue = parseFloat(document.getElementById("endingValue").value);
var numberOfYears = parseFloat(document.getElementById("numberOfYears").value);
var resultDisplay = document.getElementById("result");
if (isNaN(startingValue) || isNaN(endingValue) || isNaN(numberOfYears)) {
resultDisplay.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (startingValue <= 0) {
resultDisplay.innerHTML = "Starting Value must be greater than zero.";
return;
}
if (endingValue < 0) {
resultDisplay.innerHTML = "Ending Value cannot be negative.";
return;
}
if (numberOfYears <= 0) {
resultDisplay.innerHTML = "Number of Years must be greater than zero.";
return;
}
var cagr = Math.pow((endingValue / startingValue), (1 / numberOfYears)) – 1;
var cagrPercentage = (cagr * 100).toFixed(2);
resultDisplay.innerHTML = "The Compound Annual Growth Rate (CAGR) is:
" + cagrPercentage + "%";
}
.calculator-wrapper {
font-family: sans-serif;
display: flex;
flex-wrap: wrap;
gap: 20px;
max-width: 900px;
margin: 20px auto;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 4px rgba(0,0,0,0.1);
}
.calculator-form {
flex: 1;
min-width: 250px;
}
.calculator-form h2 {
margin-top: 0;
color: #333;
}
.form-group {
margin-bottom: 15px;
}
.form-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.form-group input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.calculator-form button {
background-color: #007bff;
color: white;
padding: 10px 15px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
}
.calculator-form button:hover {
background-color: #0056b3;
}
.result-display {
margin-top: 20px;
padding: 15px;
background-color: #e9ecef;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 18px;
text-align: center;
}
.calculator-explanation {
flex: 2;
min-width: 300px;
background-color: #f8f9fa;
padding: 15px;
border-radius: 4px;
}
.calculator-explanation h3,
.calculator-explanation h4 {
color: #333;
}
.calculator-explanation p,
.calculator-explanation ul {
line-height: 1.6;
color: #555;
}
.calculator-explanation ul {
padding-left: 20px;
}
.calculator-explanation li {
margin-bottom: 10px;
}