.err-calculator-widget {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 800px;
margin: 0 auto;
padding: 20px;
background: #f9f9f9;
border: 1px solid #e0e0e0;
border-radius: 8px;
}
.err-calc-header {
text-align: center;
margin-bottom: 30px;
}
.err-calc-header h2 {
color: #2c3e50;
margin: 0;
}
.err-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
@media (max-width: 600px) {
.err-grid {
grid-template-columns: 1fr;
}
}
.err-input-group {
margin-bottom: 15px;
}
.err-input-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
color: #34495e;
}
.err-input-group input {
width: 100%;
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.err-input-group input:focus {
border-color: #3498db;
outline: none;
}
.err-btn-container {
grid-column: 1 / -1;
text-align: center;
margin-top: 10px;
}
button.err-calculate-btn {
background-color: #27ae60;
color: white;
border: none;
padding: 12px 30px;
font-size: 18px;
border-radius: 5px;
cursor: pointer;
transition: background 0.3s;
}
button.err-calculate-btn:hover {
background-color: #219150;
}
.err-result-box {
grid-column: 1 / -1;
margin-top: 25px;
padding: 20px;
background-color: #fff;
border-left: 5px solid #27ae60;
box-shadow: 0 2px 5px rgba(0,0,0,0.05);
display: none;
}
.err-result-value {
font-size: 32px;
font-weight: bold;
color: #2c3e50;
margin-bottom: 10px;
}
.err-result-sub {
font-size: 14px;
color: #7f8c8d;
line-height: 1.5;
}
.err-article {
margin-top: 50px;
padding-top: 20px;
border-top: 1px solid #eee;
}
.err-article h3 {
color: #2c3e50;
}
.err-article p {
line-height: 1.6;
color: #444;
}
.err-article ul {
padding-left: 20px;
color: #444;
}
.err-article li {
margin-bottom: 10px;
}
What is Economic Rate of Return (ERR)?
The Economic Rate of Return (ERR) is a metric used primarily in cost-benefit analysis to determine the efficiency of an investment project. Unlike the financial Internal Rate of Return (IRR), which focuses on private cash flows and profitability for the investor, the ERR considers the broader economic impact, including societal benefits and the opportunity cost of capital.
The ERR represents the discount rate at which the Net Present Value (NPV) of all economic costs and benefits equals zero. If the calculated ERR exceeds the "Social Discount Rate" (often set by government policy or central banks, typically between 3% and 10%), the project is generally considered economically viable.
Formula and Methodology
This calculator solves for the rate (r) in the following equation:
0 = -C0 + Σ [ Bt / (1+r)t ] + [ TV / (1+r)N ]
- C0: Initial Capital Outlay (The immediate cost to start).
- Bt: Annual Economic Benefit (Value generated per year).
- TV: Terminal Value (Residual value of assets at the end).
- N: Project Lifespan in years.
- r: The Economic Rate of Return (the variable we solve for).
How to Interpret the Results
Positive ERR: If the calculator returns a positive percentage (e.g., 15%), it means the economic benefits outweigh the costs over time, compounding at that rate.
Negative ERR: If the result is negative, the project destroys economic value; the total benefits (even when not discounted) may be less than the initial cost, or the payback period is too long relative to the lifespan.
Example Calculation
Consider a municipal solar panel project:
- Initial Capital Outlay: 100,000
- Annual Benefit (Energy Savings): 25,000
- Project Lifespan: 5 Years
- Residual Value: 10,000
Using the calculator, the ERR for this project would be approximately 10.42%. If the municipality's hurdle rate (Social Discount Rate) is 5%, this project is approved.
function calculateERR() {
var initialCapital = parseFloat(document.getElementById('initialCapital').value);
var annualBenefit = parseFloat(document.getElementById('annualBenefit').value);
var lifespan = parseInt(document.getElementById('projectLifespan').value);
var terminalValue = parseFloat(document.getElementById('terminalValue').value);
// Validation
if (isNaN(initialCapital) || initialCapital <= 0) {
alert("Please enter a valid Initial Capital Outlay.");
return;
}
if (isNaN(annualBenefit)) annualBenefit = 0;
if (isNaN(lifespan) || lifespan <= 0) {
alert("Please enter a valid Project Lifespan in years.");
return;
}
if (isNaN(terminalValue)) terminalValue = 0;
// Simple check: Do total returns exceed cost?
var totalReturn = (annualBenefit * lifespan) + terminalValue;
var roi = totalReturn – initialCapital;
var resultBox = document.getElementById('resultBox');
var resultText = document.getElementById('errResult');
var explanationText = document.getElementById('errExplanation');
var grossInfo = document.getElementById('grossReturnInfo');
resultBox.style.display = "block";
// Edge Case: Total return is less than initial cost
// This mathematically results in a negative ERR.
if (totalReturn < initialCapital) {
// Approximate negative return
var totalLossPercent = ((totalReturn / initialCapital) – 1) * 100;
// This is a rough approximation for display purposes when calculation fails to converge on negatives
// Ideally, we still run the iteration, but let's prep text.
}
// Numerical Solution: Binary Search for ERR (Rate)
// Function: NPV(rate) = -Initial + Sum(Benefit/(1+r)^t) + Terminal/(1+r)^N
// We want to find rate where NPV = 0.
var low = -0.9999; // Lower bound (-99.99%)
var high = 100.0; // Upper bound (10,000%) – unlikely to be higher
var guess = 0;
var npv = 0;
var iterations = 100;
var solved = false;
for (var i = 0; i < iterations; i++) {
guess = (low + high) / 2;
npv = -initialCapital;
// Add PV of Annuity
// Formula: PV = Pmt * (1 – (1+r)^-n) / r
if (Math.abs(guess) < 0.0000001) {
npv += annualBenefit * lifespan; // Simple sum if rate is 0
} else {
npv += annualBenefit * ((1 – Math.pow(1 + guess, -lifespan)) / guess);
}
// Add PV of Terminal Value
npv += terminalValue / Math.pow(1 + guess, lifespan);
if (Math.abs(npv) 0) {
// Rate is too low (positive NPV means we discounted too little)
low = guess;
} else {
// Rate is too high
high = guess;
}
}
var finalRate = guess * 100;
// Formatting Output
if (finalRate 99%";
resultText.style.color = "#c0392b";
explanationText.innerHTML = "The project does not recover its initial costs even without discounting.";
} else if (finalRate > 10000) {
resultText.innerHTML = "> 10,000%";
explanationText.innerHTML = "The return is exceptionally high due to low costs or immediate high returns.";
} else {
resultText.innerHTML = finalRate.toFixed(2) + "%";
if (finalRate < 0) {
resultText.style.color = "#c0392b"; // Red for negative
explanationText.innerHTML = "The Economic Rate of Return is negative. The project costs exceed the economic benefits over the specified timeframe.";
} else {
resultText.style.color = "#27ae60"; // Green for positive
explanationText.innerHTML = "This is the discount rate at which the project breaks even (NPV = 0). Compare this to your Social Discount Rate (SDR).";
}
}
grossInfo.innerHTML = "Total Undiscounted Net Benefit: " + roi.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
}