The Conditional Prepayment Rate (CPR) calculator helps financial professionals estimate the annualized rate at which borrowers prepay their loans or mortgages. It is a critical tool in mortgage-backed securities, loan portfolio management, and risk assessment, enabling institutions to predict cash flows and manage prepayment risks effectively.
Formula of Conditional Prepayment Rate (CPR) Calculator
Step 1: Define the Formula
The CPR is calculated using the monthly prepayment rate (MPR):
CPR = 1 - (1 - MPR)^12
Where:
- CPR is the annualized Conditional Prepayment Rate (expressed as a percentage).
- MPR is the Monthly Prepayment Rate (expressed as a percentage).
Step 2: Calculate the Monthly Prepayment Rate
The Monthly Prepayment Rate (MPR) is determined using:
MPR = Prepayments during the month / Beginning Outstanding Balance
Where:
- Prepayments during the month is the total amount prepay by borrowers.
- Beginning Outstanding Balance is the total principal balance at the start of the month.
Step 3: Substitute MPR into the CPR Formula
Once the MPR is calculate, substitute it into the CPR formula:
CPR = 1 - (1 - MPR)^12
Step 4: Adjust for Percentage Conversion
If the MPR is express as a decimal (e.g., 0.01 for 1%), the CPR will also be a decimal. Multiply by 100 to convert it into a percentage.
Table of Common Calculations
| Monthly Prepayment Rate (MPR) | CPR (as a Percentage) |
|---|---|
| 0.01 (1%) | 11.39% |
| 0.02 (2%) | 22.22% |
| 0.03 (3%) | 32.97% |
| 0.05 (5%) | 47.13% |
Example of Conditional Prepayment Rate (CPR) Calculator
Problem
A loan portfolio starts the month with a total outstanding balance of $1,000,000. Borrowers prepay $20,000 during the month. Calculate the Conditional Prepayment Rate (CPR).
Solution
- Calculate the Monthly Prepayment Rate (MPR):
MPR = Prepayments during the month / Beginning Outstanding Balance
MPR = 20,000 / 1,000,000 = 0.02 (or 2%). - Substitute MPR into the CPR formula:
CPR = 1 - (1 - MPR)^12
CPR = 1 - (1 - 0.02)^12
CPR = 1 - (0.98)^12
CPR = 1 - 0.7847 = 0.2153 - Convert to a percentage:
CPR = 0.2153 × 100 = 21.53%
Result
The Conditional Prepayment Rate is 21.53%.
Most Common FAQs
The CPR represents the annualized rate at which borrowers prepay their loans, allowing institutions to model early repayments.
The CPR helps predict the cash flow of mortgage-backed securities, allowing investors to assess the timing and amount of payments they will receive.
The CPR is an annualized rate, while the SMM rate reflects prepayments as a monthly percentage of the remaining balance.