Constant/Conditional Prepayment Rate (CPR) Calculator
The Constant Prepayment Rate (CPR) is a metric used in the mortgage-backed securities (MBS) world to estimate the annualized percentage of principal expected to be prepaid over a given period.
🧠 How the CPR Calculator Works
The calculator requires:
- Prepaid Principal Amount – The total amount of principal prepaid during a set period.
- Outstanding Principal Amount – The beginning balance of the mortgage pool.
- Periods (Months) – The number of months over which the prepayment occurred.
It first calculates the Single Monthly Mortality (SMM): SMM=Prepaid PrincipalOutstanding PrincipalSMM = \frac{\text{Prepaid Principal}}{\text{Outstanding Principal}}SMM=Outstanding PrincipalPrepaid Principal
Then converts it to CPR using: CPR=1−(1−SMM)12/periodsCPR = 1 – (1 – SMM)^{12 / \text{periods}}CPR=1−(1−SMM)12/periods
This gives a 12-month equivalent of prepayment activity.
📊 Example Calculation
- Prepaid Principal = $2,000
- Outstanding Principal = $100,000
- Period = 6 months
SMM=2,000100,000=0.02SMM = \frac{2,000}{100,000} = 0.02SMM=100,0002,000=0.02 CPR=1−(1−0.02)12/6=1−0.9604=0.0396⇒3.96%CPR = 1 – (1 – 0.02)^{12/6} = 1 – 0.9604 = 0.0396 \Rightarrow 3.96\%CPR=1−(1−0.02)12/6=1−0.9604=0.0396⇒3.96%
So, the CPR is 3.96%.
🧾 Why CPR Matters
CPR is vital for:
- MBS valuation
- Loan portfolio risk management
- Understanding borrower behavior
- Forecasting cash flows
📌 CPR vs. SMM
- SMM: Prepayment rate for a single month
- CPR: Annualized equivalent of the SMM over time
❓FAQs
Q: Can CPR exceed 100%?
No. It ranges from 0% to 100%. A CPR of 100% would imply the entire principal is prepaid within the year.
Q: Is higher CPR good or bad?
It depends. Investors in MBS may face prepayment risk, which can reduce interest income if loans are paid off early.
Q: Is CPR constant in reality?
No, it’s an approximation. Real-world prepayments fluctuate due to market conditions, interest rates, and borrower behavior.
📍 Summary
The Constant Prepayment Rate is an essential metric in mortgage and fixed-income markets. Use this CPR Calculator to estimate it easily and gain insights into prepayment trends.