Use the tabs below to convert between CPR, SMM, and PSA; compute CPR from an observed month’s prepayments; or run a simple projection.

Conditional Prepayment Rate (CPR) Calculator

Convert between CPR and SMM, or compute CPR from observed prepayments.

Convert CPR ↔ SMM
CPR from $ Prepayment
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Related Calculators

CPR Formula

In mortgage and MBS analytics, CPR (Conditional/Constant Prepayment Rate) is usually computed by annualizing a monthly prepayment rate (SMM). First compute SMM from observed unscheduled prepayment, then convert SMM to CPR.

\begin{aligned}
SMM &= \frac{UP}{BOP - SP} \\
CPR &= 1 - (1 - SMM)^{12}
\end{aligned}
  • Where UP is the unscheduled principal prepayment during the month
  • BOP is the beginning-of-month outstanding principal balance
  • SP is the scheduled principal for the month
  • SMM is the single-month (single-period) prepayment rate
  • CPR is the annualized conditional (constant) prepayment rate

To calculate CPR from observed monthly prepayments: (1) compute SMM = UP / (BOP − SP), then (2) convert to CPR = 1 − (1 − SMM)12. Conversely, SMM = 1 − (1 − CPR)1/12.

What is a constant prepayment rate?

Definition:

A constant prepayment rate (CPR), also called the conditional prepayment rate, is an annualized measure of how quickly outstanding principal is expected to be prepaid (in addition to scheduled principal), conditional on the loan remaining outstanding at the start of each month.

CPR is most commonly used for mortgage loans and mortgage-backed securities, but similar prepayment-rate concepts can be applied to other amortizing loans that allow prepayment (for example, home equity, auto, and some student loans).

How to calculate a constant prepayment rate?

Example Problem:

The following example outlines how to calculate a constant prepayment rate from an observed month’s prepayment.

First, determine the beginning-of-month balance (BOP). In this example, the beginning-of-month balance is $100,000.

Next, determine the scheduled principal (SP) due for the month. In this example, the scheduled principal is $500.

Then, determine the unscheduled principal prepayment (UP) made during the month. In this example, the unscheduled prepayment is $995.

Compute SMM and then CPR:

SMM = UP / (BOP − SP)

SMM = 995 / (100000 − 500) = 995 / 99500 = 0.01 = 1.00%

CPR = 1 − (1 − SMM)12 = 1 − (0.99)12 ≈ 0.1136 = 11.36%

FAQ

What factors can affect the Constant Prepayment Rate (CPR)?
Several factors can influence the CPR, including prevailing interest rates, the borrower's financial health, changes in property values, and the overall economic environment. For instance, lower interest rates might encourage refinancing, leading to higher prepayment rates.

How does CPR impact investors in mortgage-backed securities?
CPR directly affects the cash flow and yield of mortgage-backed securities. Higher CPR rates can lead to shorter cash flow durations and potentially lower yields, as the principal is repaid faster than expected. Conversely, lower CPR rates can extend the duration of cash flows, affecting yield predictions and investment value.

Can CPR be used for all types of loans?
While CPR is primarily used to analyze prepayment risks in mortgage loans and mortgage-backed securities, it can be applied to other loan types with prepayment features, such as auto loans and some student loans. However, the specific factors influencing prepayment may vary by loan type.