Question

Consider the mortgage pool data below for a Mortgage Backed Security (MBS). Beginning balance $800,000,000 WAC 5.750% WAM 354 Passthrough rate 5.250% PSA schedule 150% Please answer the questions below about the first scheduled payment to the investors of this MBS. SHOW YOUR WORK Dollar amounts may be rounded to the nearest dollar. (a) What is the CPR for this payment? (b) What is the SMM for this payment? (c) For this payment, what is the amount of the total scheduled mortgage payment, the gross interest paid with that payment, and the scheduled principal repaid with that payment? (You can use your BA II Plus to calculate this data. Show what you would enter into your calculator to obtain this data.) (d) What is the net interest payment available to the MBS investors after servicing fees have been paid? (e) What is the forecasted prepayment amount based on the SMM calculated in (b) above? (f) What will be the total principal repayment to the MBS investors in the first payment? (g) What will be the total payment made to the MBS investors?

Answer 1

100 PSA assumes following graduated CPR for a 30 years Mortgage:

- CPR= 0.2%, for the first month of origination. It gradually increases each month 0.2% till 30 month. Hence, on 20th month, CPR would be (0.2%)* 20 = 4%

- CPR : 6% from 30th month till 360th month

(a). WAM : 354. Hence, 6 months have elapsed. The CPR would be 6*(0.2%) = 1.2% (Answer)

(b) SMM would be = 1- (1-CPR)^(1/12) = 1- (1-0.012)^(1/12) = 1- 0.9989 = 0.001 (Answer)

(c) Following values are entered into the financial calculator (Assuming yearly coupon payment)

PV= -800,000,000 ; FV= 0; I/Y= (5.75/12)%= 0.4791%, N=30*12= 360, monthly PMT=4,668,582 (approx)

So, in the 6 months, total scheduled mortgage payments are = 6*4,668,582 = 28,011,497 (approx) (Answer)

Net interest payment in 6 months = (5.75/2)% * 800,000,000 = 23,000,000 (Answer)

Net Principal payment in 6 months = 28,011,497- 23,000,000 = 5,011,497. This excludes the principal prepayment, which will be done based on CPR.

Prepayment for 6 months = 800000000 * (1+2+3+4+5+6) * (1.2%)/12 = 16,800,000

Hence, total principal payment = 5,011,497 + 16,800,000 =21,811,497 (Answer)

(d) Net interest payment available to MBS investors after paying the servicing fee = (5.25% / 2) * 800,000,000 = 21,000,000 (Answer)

(e) Forecasted prepayment in first 6 months = 16,800,000 (as calculated in answer C) (Answer)

(f) First interest payment= (5.75/12)% * 800000000 = 3833333

total payment (monthly) = 4,668,582 (as calculated before)

hence, principal paid = 835248 (Answer)