In: Finance
Consider an MPT with the following characteristics:
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)?
Number of mortgages in the pool = 100
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