Question

Consider an MPT with the following characteristics:

• Number of mortgages in the pool: 100
• All 100 mortgages are fully amortizing 15 year FRM with monthly payments
• All mortgages have a 4% interest rate
• Average mortgage balance: $180,000
• Prepayment is according to 200% PSA
• There is no servicing fee
• The beginning pool balance in month 15 is $16,356,436.86

a) What is the regularly scheduled payment in month 15?

b) How much of the scheduled payment received is attributable to interest in month 15?

c) How much of the scheduled payment received is attributable to principal in month 15?

d) What is the dollar amount of the prepayment in month 15?

e) How much cash do investors get in month 15?

f) Ariel has a 5% share in this MPT. How much will he receive in month 15?

g) What is the pool balance at the end of month 15 (beginning of month 16)?

Answer 1

Interest rate = 4%

Term of MPT = 15 years = 180 months

Initial Average mortgage balance = $180,000

Initial pool balance = $180,000*100 = $18,000,000

Beginning pool balance in month 15 = $16,356,436.86

a)

Scheduled monthly payment (as a fraction of initial pool balance) = (C/1200)/(1-(1+C/1200)^-M₀)

Where C% is the interest rate. implies, C = 4

M0 is the initial term of MPT = 180

Scheduled monthly payment (as a fraction of initial pool balance) = (4/1200)/(1-(1+4/1200)^-180)

= 0.003333/(1-0.549360) = 0.007397

Scheduled monthly payment = 0.007397 * initial pool balance = 0.007397 * $18,000,000

= $133,143.83

b)

scheduled payment attributed to interest = Beginning pool balance in month 15*(C/1200)

= $16,356,436.86 * (4/1200) = $54,521.46

c)

scheduled payment attributed to principal = Scheduled monthly payment - scheduled payment attributed to interest

= $133,143.83 - $54,521.46 = $78,622.37

d)

Constant prepayment rate, CPR = min{(PSA/100)*0.2*max{1,min{MONTH,30}},100}

Where MONTH = 15

PSA = 200

CPR = min{(200/100)*0.2*max{1,min{15,30}},100}

CPR = min{(200/100)*0.2*max{1,15},100}

CPR = min{2*0.2*15,100}

CPR = min{6,100} = 6

Single monthly mortality SMM is given by the formula

(1-SMM/100)¹² = 1-CPR/100

(1-SMM/100)¹² = 1-6/100 = 1-0.06 = 0.94

1-SMM/100 = 0.94^(1/12)

1-SMM/100 = 0.994857

SMM/100 = 1-0.994857 = 0.005143

SMM = 0.005143 * 100 = 0.514301

Prepayment (as a fraction of initial pool balance) = Pool factor * SMM/100

Pool factor= Beginning pool balance in month 15/Initial pool balance = $16,356,436.86/$18,000,000

Pool factor = 0.908691

Prepayment (as a fraction of initial pool balance) = 0.908691* 0.514301/100 = 0.004673

Prepayment = 0.004673*initial pool balance = 0.004673*$18,000,000 = $84,121.36

e)

cash received by investors = scheduled monthly payment + prepayment - servicing fee

here servicing fee = 0

cash received by investors = scheduled monthly payment + prepayment

= $133,143.83 + $84,121.36 = $217,265.19

f)

Share of Ariel in the MPT = 5%

cash received by ariel = 5% * cash received by investors = 5% * $217,265.19 = $10,863.26

g)

Pool balance at end of month 15 = Pool balance at beginning of month 15 - scheduled payment attributed to principal - Prepayment =  $16,356,436.86 - $78,622.37 - $84,121.36 = $16,193,693.12