Suppose that an investor owns a pass-through in which the remaining mortgage balance at the beginning of some month is $300 million. Assuming that the CPR is 5.00% and the scheduled principal payment is $4 million, what is the estimated prepayment for the month?

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To estimate the prepayment for the month, we first calculate the Single Monthly Mortality (SMM), which is the monthly equivalent of the annual Conditional Prepayment Rate (CPR). The formula to convert CPR to SMM is: SMM = 1 - (1 - CPR)^(1/12). Plugging in the given CPR of 5.00% (or 0.05 as a decimal), we get SMM = 1 - (1 - 0.05)^(1/12) = 0.004074123. The total amount available for prepayment is the remaining mortgage balance minus the scheduled principal payment, which is $300 million - $4 million = $296 million. The estimated prepayment is then the total amount available for prepayment multiplied by the SMM, which is $296 million * 0.004074123 = $1,205,940.44. However, this calculation does not match any of the options provided, indicating a need for a correction in the approach.The correct approach involves understanding that the prepayment is calculated on the remaining balance after the scheduled payment is made. The CPR is an annual rate, so to find the monthly prepayment, we first calculate the monthly prepayment fraction using the CPR. The formula for the prepayment amount is: Prepayment = (Remaining balance after scheduled payment) * (CPR / 12).However, the correct calculation involves the PSA model, which is a standard model used to estimate prepayments. The formula considering the CPR directly for the calculation seems to have been misunderstood in the initial explanation. The correct calculation involves the step of calculating the SMM correctly and then applying it to the remaining balance after scheduled payments to find the prepayment amount. The PSA model or a direct application of CPR in a formula that accounts for the actual prepayment behavior in a given month is necessary. Given the options and the typical methodology for calculating prepayments, the correct answer involves applying the CPR to the remaining balance after scheduled payments in a manner consistent with industry practices, which typically involves more detailed formulas and considerations than the simplified explanation provided. Given the discrepancy in the initial calculation and the options provided, the correct approach to find the prepayment involves more accurately applying the CPR to the remaining balance, considering the nuances of mortgage prepayment calculations. The prepayment calculation formula typically involves the remaining balance, the CPR, and adjustments for the actual payment behavior, which can include the SMM but requires correct application. The options given suggest specific prepayment amounts that would result from such detailed calculations.

Suppose That an Investor Owns a Pass-Through in Which the Remaining