.mdrc-container {
max-width: 700px;
margin: 20px auto;
padding: 25px;
background: #f9fbfd;
border: 1px solid #e1e4e8;
border-radius: 8px;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
color: #333;
}
.mdrc-header {
text-align: center;
margin-bottom: 25px;
}
.mdrc-header h2 {
margin: 0;
color: #2c3e50;
}
.mdrc-row {
margin-bottom: 20px;
}
.mdrc-label {
display: block;
font-weight: 600;
margin-bottom: 8px;
color: #4a5568;
}
.mdrc-input-group {
display: flex;
align-items: center;
}
.mdrc-input {
width: 100%;
padding: 12px;
border: 1px solid #cbd5e0;
border-radius: 6px;
font-size: 16px;
transition: border-color 0.2s;
}
.mdrc-input:focus {
border-color: #3182ce;
outline: none;
}
.mdrc-select {
width: 100%;
padding: 12px;
border: 1px solid #cbd5e0;
border-radius: 6px;
font-size: 16px;
background-color: white;
}
.mdrc-btn {
width: 100%;
background-color: #2b6cb0;
color: white;
padding: 15px;
border: none;
border-radius: 6px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
}
.mdrc-btn:hover {
background-color: #2c5282;
}
.mdrc-result-box {
margin-top: 25px;
padding: 20px;
background-color: #ffffff;
border: 1px solid #e2e8f0;
border-left: 5px solid #3182ce;
border-radius: 4px;
display: none;
}
.mdrc-result-item {
display: flex;
justify-content: space-between;
align-items: center;
margin-bottom: 10px;
padding-bottom: 10px;
border-bottom: 1px solid #edf2f7;
}
.mdrc-result-item:last-child {
border-bottom: none;
margin-bottom: 0;
padding-bottom: 0;
}
.mdrc-result-label {
color: #718096;
font-size: 14px;
}
.mdrc-result-value {
font-size: 20px;
font-weight: 700;
color: #2d3748;
}
.mdrc-info-text {
font-size: 13px;
color: #718096;
margin-top: 5px;
}
/* Content styling */
.mdrc-article {
max-width: 700px;
margin: 40px auto;
font-family: inherit;
line-height: 1.6;
color: #333;
}
.mdrc-article h2 {
color: #2c3e50;
margin-top: 30px;
}
.mdrc-article p {
margin-bottom: 15px;
}
.mdrc-article ul {
margin-bottom: 15px;
padding-left: 20px;
}
.mdrc-article code {
background: #f1f5f9;
padding: 2px 5px;
border-radius: 4px;
font-family: monospace;
color: #d53f8c;
}
function calculateMonthlyDiscountRate() {
// 1. Get input values using var
var annualRateInput = document.getElementById('mdrc_annual_rate').value;
var method = document.getElementById('mdrc_method').value;
var resultBox = document.getElementById('mdrc_result');
var monthlyRateDisplay = document.getElementById('mdrc_monthly_rate_display');
var factorDisplay = document.getElementById('mdrc_factor_display');
var annualVerifyDisplay = document.getElementById('mdrc_annual_verify');
// 2. Validate inputs
if (annualRateInput === "" || isNaN(annualRateInput)) {
alert("Please enter a valid Annual Discount Rate.");
resultBox.style.display = "none";
return;
}
// 3. Convert input to decimal for calculation
var r_annual = parseFloat(annualRateInput) / 100;
var r_monthly = 0;
// 4. Perform Calculation based on Method
if (method === "effective") {
// Formula: (1 + r)^(1/12) – 1
// This is the geometric mean, preserving the effective annual rate
r_monthly = Math.pow((1 + r_annual), (1.0 / 12.0)) – 1;
} else {
// Formula: r / 12
// This is the arithmetic mean, often used for APR or simple approximations
r_monthly = r_annual / 12.0;
}
// 5. Calculate Discount Factor for Month 1: 1 / (1 + r)^1
var discountFactor = 1 / (1 + r_monthly);
// 6. Format results for display
// Convert monthly rate back to percentage
var monthlyRatePercent = r_monthly * 100;
// Display with high precision (4-6 decimals are common for monthly rates)
monthlyRateDisplay.innerHTML = monthlyRatePercent.toFixed(4) + "%";
// Display Factor (usually 4 decimals)
factorDisplay.innerHTML = discountFactor.toFixed(4);
// Display Verification (showing the user what Annual rate this maps back to)
annualVerifyDisplay.innerHTML = parseFloat(annualRateInput).toFixed(2) + "%";
// 7. Show Result
resultBox.style.display = "block";
}
How to Calculate Monthly Discount Rate
In financial modeling, particularly when performing a Discounted Cash Flow (DCF) analysis on a monthly basis, converting an annual discount rate to a monthly discount rate is a critical step. The discount rate represents the time value of money, reflecting the opportunity cost of capital or the required rate of return.
Using the correct monthly rate ensures that the Net Present Value (NPV) of your monthly cash flows is accurate. There are two primary methods for this conversion: the Effective (Geometric) method and the Nominal (Arithmetic) method.
1. The Effective Monthly Rate Formula
This is the most precise method for valuation purposes. It assumes that interest compounds monthly. If you have an annual effective rate (like a WACC derived from annual market data) and want to apply it to monthly periods such that the compounding equals the annual rate exactly, use this formula:
r_monthly = (1 + r_annual)^(1/12) - 1
Example: If your Annual Discount Rate is 12%:
Calculation: (1 + 0.12)^(1/12) – 1 = 1.00948 – 1 = 0.00948
Result: 0.948% per month.
2. The Nominal Monthly Rate Formula
This method is simpler and is simply the annual rate divided by 12. This is often used when the "Annual Rate" quoted is an APR (Annual Percentage Rate) which is defined as the periodic rate multiplied by the number of periods.
r_monthly = r_annual / 12
Example: If your Annual Discount Rate is 12%:
Calculation: 0.12 / 12 = 0.01
Result: 1.00% per month.
Which Method Should You Use?
- Use the Effective Method if your annual rate represents an effective yield or CAGR (Compound Annual Growth Rate). This is standard for most sophisticated DCF models.
- Use the Nominal Method if your annual rate is quoted as a nominal APR, or for quick approximations where the compounding effect is negligible.
Applying the Rate: Discount Factors
Once you have your monthly discount rate (r), you calculate the discount factor for any given month (n) using the formula:
Discount Factor = 1 / (1 + r)^n
This factor is then multiplied by the cash flow of that month to determine its Present Value (PV).