Constant/Conditional Prepayment Rate (CPR) Calculator
Use this tool to calculate the estimated principal prepayment amount for the first month, given the current outstanding loan balance and the Annual Constant Prepayment Rate (CPR).
The CPR is converted to a monthly rate (Single Monthly Mortality or SMM) for the calculation.
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Understanding CPR and SMM
What is CPR?
Constant/Conditional Prepayment Rate (CPR) is an annual rate used in mortgage-backed securities (MBS) and other loan analysis to estimate the percentage of the outstanding principal balance that is likely to be prepaid over a year, beyond scheduled principal payments.
It assumes that the rate of prepayment is constant over the life of the loan or pool of loans, conditional on the outstanding balance.
Why Convert CPR to SMM?
Since loan payments and prepayments typically occur monthly, the annual CPR needs to be converted to a monthly rate. This monthly rate is called the Single Monthly Mortality (SMM).
The relationship between CPR and SMM is given by the formula:
SMM = 1 - (1 - CPR)1/12
Where CPR is expressed as a decimal (e.g., 5% = 0.05).
Calculating First Month Prepayment
The estimated prepayment amount for a given month is calculated by applying the SMM to the outstanding principal balance at the beginning of that month.
Prepayment Amount = Principal Balance * SMM
This calculator performs this calculation specifically for the *first month*, using the initial principal balance provided.
Example Calculation Walkthrough
Suppose you have a principal balance of $200,000 and an Annual CPR of 8%.
1. Convert CPR to Decimal: 8% = 0.08
2. Calculate SMM: SMM = 1 - (1 - 0.08)1/12 = 1 - (0.92)1/12 ≈ 1 - 0.993065 ≈ 0.006935
So, the SMM is approximately 0.6935%.
3. Calculate First Month Prepayment: Prepayment Amount = $200,000 * 0.006935 ≈ $1387
Based on an 8% annual CPR, the estimated prepayment in the first month on a $200,000 balance is about $1387.
CPR Calculation Examples
Below are examples demonstrating how the first month's estimated prepayment is calculated using different inputs. Click to see the steps.
Example 1: Basic CPR Calculation (5% CPR)
Scenario: Calculate the first month's prepayment for a loan with a $100,000 balance and a 5% Annual CPR.
1. Known Values: Principal Balance = $100,000, Annual CPR = 5%.
2. Convert CPR to Decimal: 5% = 0.05
3. Calculate SMM: SMM = 1 - (1 - 0.05)1/12 = 1 - (0.95)1/12 ≈ 1 - 0.995765 ≈ 0.004235
4. Calculate Prepayment: Prepayment = $100,000 * 0.004235 ≈ $423.50
Result: Estimated First Month Prepayment ≈ $423.50
Example 2: Higher CPR (15% CPR)
Scenario: A loan pool with a $5,000,000 balance is expected to prepay at a 15% Annual CPR.
1. Known Values: Principal Balance = $5,000,000, Annual CPR = 15%.
2. Convert CPR to Decimal: 15% = 0.15
3. Calculate SMM: SMM = 1 - (1 - 0.15)1/12 = 1 - (0.85)1/12 ≈ 1 - 0.986671 ≈ 0.013329
4. Calculate Prepayment: Prepayment = $5,000,000 * 0.013329 ≈ $66,645
Result: Estimated First Month Prepayment ≈ $66,645
Example 3: Lower CPR (2% CPR)
Scenario: Analyze a stable portfolio with a $10,000,000 balance and a low 2% Annual CPR.
1. Known Values: Principal Balance = $10,000,000, Annual CPR = 2%.
2. Convert CPR to Decimal: 2% = 0.02
3. Calculate SMM: SMM = 1 - (1 - 0.02)1/12 = 1 - (0.98)1/12 ≈ 1 - 0.998315 ≈ 0.001685
4. Calculate Prepayment: Prepayment = $10,000,000 * 0.001685 ≈ $16,850
Result: Estimated First Month Prepayment ≈ $16,850
Example 4: Small Balance CPR ($5,000 Balance)
Scenario: Estimate prepayment for a small personal loan ($5,000 balance) at a 10% Annual CPR.
1. Known Values: Principal Balance = $5,000, Annual CPR = 10%.
2. Convert CPR to Decimal: 10% = 0.10
3. Calculate SMM: SMM = 1 - (1 - 0.10)1/12 = 1 - (0.90)1/12 ≈ 1 - 0.991554 ≈ 0.008446
4. Calculate Prepayment: Prepayment = $5,000 * 0.008446 ≈ $42.23
Result: Estimated First Month Prepayment ≈ $42.23
Example 5: High Balance CPR ($100,000,000 Balance)
Scenario: Calculate prepayment for a large institutional portfolio ($100,000,000 balance) at a 7% Annual CPR.
1. Known Values: Principal Balance = $100,000,000, Annual CPR = 7%.
2. Convert CPR to Decimal: 7% = 0.07
3. Calculate SMM: SMM = 1 - (1 - 0.07)1/12 = 1 - (0.93)1/12 ≈ 1 - 0.994271 ≈ 0.005729
4. Calculate Prepayment: Prepayment = $100,000,000 * 0.005729 ≈ $572,900
Result: Estimated First Month Prepayment ≈ $572,900
Example 6: CPR of 0% (No Prepayment)
Scenario: What happens if the Annual CPR is 0%?
1. Known Values: Principal Balance = $50,000, Annual CPR = 0%.
2. Convert CPR to Decimal: 0% = 0.00
3. Calculate SMM: SMM = 1 - (1 - 0.00)1/12 = 1 - (1)1/12 = 1 - 1 = 0
4. Calculate Prepayment: Prepayment = $50,000 * 0 = $0
Result: Estimated First Month Prepayment = $0 (As expected, 0% CPR means no estimated prepayments.)
Example 7: CPR of 100% (Full Prepayment)
Scenario: A theoretical case where Annual CPR is 100%. This would imply the entire balance is expected to prepay within a year.
1. Known Values: Principal Balance = $25,000, Annual CPR = 100%.
2. Convert CPR to Decimal: 100% = 1.00
3. Calculate SMM: SMM = 1 - (1 - 1.00)1/12 = 1 - (0)1/12 = 1 - 0 = 1
4. Calculate Prepayment: Prepayment = $25,000 * 1 = $25,000
Result: Estimated First Month Prepayment = $25,000. (An SMM of 1 means 100% of the balance prepays in the first month).
Example 8: Non-Integer CPR (6.5% CPR)
Scenario: Using a non-integer CPR rate of 6.5% on a $300,000 balance.
1. Known Values: Principal Balance = $300,000, Annual CPR = 6.5%.
2. Convert CPR to Decimal: 6.5% = 0.065
3. Calculate SMM: SMM = 1 - (1 - 0.065)1/12 = 1 - (0.935)1/12 ≈ 1 - 0.994444 ≈ 0.005556
4. Calculate Prepayment: Prepayment = $300,000 * 0.005556 ≈ $1666.80
Result: Estimated First Month Prepayment ≈ $1666.80
Example 9: Loan Servicing Analysis ($75,000 Balance, 4% CPR)
Scenario: A loan servicer is estimating prepayments on a $75,000 loan with a 4% CPR assumption.
1. Known Values: Principal Balance = $75,000, Annual CPR = 4%.
2. Convert CPR to Decimal: 4% = 0.04
3. Calculate SMM: SMM = 1 - (1 - 0.04)1/12 = 1 - (0.96)1/12 ≈ 1 - 0.996614 ≈ 0.003386
4. Calculate Prepayment: Prepayment = $75,000 * 0.003386 ≈ $253.95
Result: Estimated First Month Prepayment ≈ $253.95
Example 10: Bond Portfolio Analysis ($20,000,000 Balance, 9% CPR)
Scenario: An analyst estimates prepayments for a $20,000,000 bond portfolio assuming a 9% CPR.
1. Known Values: Principal Balance = $20,000,000, Annual CPR = 9%.
2. Convert CPR to Decimal: 9% = 0.09
3. Calculate SMM: SMM = 1 - (1 - 0.09)1/12 = 1 - (0.91)1/12 ≈ 1 - 0.992178 ≈ 0.007822
4. Calculate Prepayment: Prepayment = $20,000,000 * 0.007822 ≈ $156,440
Result: Estimated First Month Prepayment ≈ $156,440
Limitations of CPR
CPR is a simplifying assumption. Actual prepayment behavior is complex and influenced by many factors, including interest rates, economic conditions, seasonality, and borrower characteristics. The actual prepayment rate in any given month can deviate significantly from the calculated SMM.
Frequently Asked Questions about CPR Calculation
1. What does CPR stand for?
CPR stands for Constant/Conditional Prepayment Rate.
2. What is SMM?
SMM stands for Single Monthly Mortality. It is the monthly equivalent rate derived from the annual CPR and represents the estimated percentage of the outstanding principal that prepays each month.
3. How is SMM calculated from CPR?
The formula is SMM = 1 - (1 - CPR)1/12, where CPR is in decimal form.
4. Why do you convert CPR to SMM?
CPR is an annual rate, but prepayments typically occur throughout the year. SMM converts the annual rate to a consistent monthly rate, which is then applied to the monthly principal balance for calculations.
5. What is the basic formula for calculating the prepayment amount for a month?
The estimated prepayment amount for a month is calculated as: Principal Balance * SMM.
6. Does this calculator account for scheduled principal payments?
No, this calculator provides the *estimated prepayment amount only*, based on the CPR/SMM. It does not calculate or include the scheduled principal portion of a regular loan payment.
7. What are the valid ranges for the inputs?
Current Principal Balance must be a non-negative number ($0 or greater). Annual CPR must be a percentage between 0% and 100% (inclusive).
8. Are the calculated prepayments guaranteed to happen?
No, CPR is an *assumption* or *estimate* of prepayment behavior based on historical data or market conditions. Actual prepayments can vary significantly from month to month.
9. How is CPR used in finance?
CPR is widely used in the analysis and valuation of mortgage-backed securities (MBS) and other amortizing assets. It helps investors and analysts project future cash flows and estimate the average life of the securities.
10. What does a higher CPR mean?
A higher CPR indicates an expectation of faster prepayments. This can happen when interest rates fall, making refinancing attractive, or due to factors like increased housing turnover.
