Question

Consider a sequential pay CMO that is backed by 100 mortgages with average balance of $150,000 each. The mortgages have monthly payments with WAM = 30 years and WAC = 6%. There is a servicing fee of 0.4% and prepayment is according to 150% PSA. Tranche A holds $6,000,000 of the mortgage pool principal at origination, tranche B holds $3,000,000 and tranche Z holds $5,000,000. The rest of the pool principal is held by the SPV as a residual. The SPV has set a pass-through rate (coupon rate net of the servicer/guarantee fee) of 4% for Tranche A, 4.5% for Tranche B and 5% for Tranche Z. What is tranche A's outstanding principal balance at the end of the first month (beginning of the second month)?

Answer 1

1). Obtain principal prepayments. CPR according to 100% PSA.

CPR = 150%*0.06*1/30 =.003.

Convert CPR to SMM = 1 - (1 - CPR)^1/12 = 0.000250.

Principal Payments = $15,000,000.00 * 0.000250344 = 3,755.17

2). Obtain scheduled payment to solve for scheduled principal since Tranche A will get all this principal.

PMT(i/y=6%/12,N=360,PV=15,000,000) = $89,932.58

Scheduled Principal = PMT - Scheduled Interest

= 89,932.58 - 15,000,000*(6%/12) =89,932.58 - 75,000 = 14,932.58

3). Z-tranche’s interest rate payment pays down A tranche’s principal too. Interest payment is net of the servicer / guarantee fee.

Tranche Z interest rate payment = 5M *5%/12 = 20,833.33 .

This is principal paydown for Tranche A

4). Tranche A principal balance at the end of the first month

= 6,000,000.00 - 3,755.17 -14,932.58 - 20,833.33 = $5,960,478.92