Question

Given a pool of 30 year fully-amortizing FRMs making monthly payments to investors with the following characteristics: WAC: 5% Pass-through rate: 4.5% Prepayment assumption: 300 PSA Loans were not seasoned before entering pool This MBS has been active for a few years in collecting payments from borrowers and making payments to investors. It's currently month 32 in the pool. Starting pool balance month in month 32: 54,234,988 What is the dollar amount of prepayment in month 32? CPR is ((300/100)*(0.06*32))/30 = 0.192(not sure about this, that's why I'm asking) Please provide step by step

Answer 1

As per PSA calculations, for 100 PSA, the prepayment rises at the rate of 0.2% of balance amount until it reaches the level of 6% in month 30 and remains stable after that. For 300 PSA, the prepayment after 30^th months would be three time that.

However, since only the principal outstanding after 32 months in given and we do not know the principal amount, the solution becomes complex. The table below helps reach the figure through iterations. The excel calculation with the given figures gives a monthly installment of $905,767. For month 32, prepayment works out to $ 3,213,312. (6%* balance left after principal payment for the month).

168,727,670 0.004166667 360 $905,767 Month No Principal at the beginning of the month Interest Principal prepayment Principal balance at the end of the month Prepayment rate 1                168,727,670              703,032              202,735                      337,050           168,187,885 0.2% 2                168,187,885              700,783              204,984                      671,932           167,310,970 0.4% 3                167,310,970              697,129              208,638                  1,002,614           166,099,719 0.6% 4                166,099,719              692,082              213,684                  1,327,088           164,558,946 0.8% 5                164,558,946              685,662              220,104                  1,643,388           162,695,453 1.0% 6                162,695,453              677,898              227,869                  1,949,611           160,517,973 1.2% 7                160,517,973              668,825              236,942                  2,243,934           158,037,097 1.4% 8                158,037,097              658,488              247,279                  2,524,637           155,265,181 1.6% 9                155,265,181              646,938              258,828                  2,790,114           152,216,238 1.8% 10                152,216,238              634,234              271,532                  3,038,894           148,905,812 2.0% 11                148,905,812              620,441              285,326                  3,269,651           145,350,836 2.2% 12                145,350,836              605,628              300,138                  3,481,217           141,569,481 2.4% 13                141,569,481              589,873              315,894                  3,672,593           137,580,994 2.6% 14                137,580,994              573,254              332,512                  3,842,957           133,405,524 2.8% 15                133,405,524              555,856              349,910                  3,991,668           129,063,945 3.0% 16                129,063,945              537,766              368,000                  4,118,270           124,577,675 3.2% 17                124,577,675              519,074              386,693                  4,222,493           119,968,488 3.4% 18                119,968,488              499,869              405,898                  4,304,253           115,258,337 3.6% 19                115,258,337              480,243              425,524                  4,363,647           110,469,167 3.8% 20                110,469,167              460,288              445,478                  4,400,948           105,622,741 4.0% 21                105,622,741              440,095              465,672                  4,416,597           100,740,472 4.2% 22                100,740,472              419,752              486,015                  4,411,196              95,843,261 4.4% 23                  95,843,261              399,347              506,420                  4,385,495              90,951,347 4.6% 24                  90,951,347              378,964              526,803                  4,340,378              86,084,166 4.8% 25                  86,084,166              358,684              547,083                  4,276,854              81,260,229 5.0% 26                  81,260,229              338,584              567,182                  4,196,038              76,497,008 5.2% 27                  76,497,008              318,738              587,029                  4,099,139              71,810,841 5.4% 28                  71,810,841              299,212              606,555                  3,987,440              67,216,846 5.6% 29                  67,216,846              280,070              625,696                  3,862,287              62,728,863 5.8% 30                  62,728,863              261,370              644,396                  3,725,068              58,359,398 6.0% 31                  58,359,398              243,164              662,602                  3,461,808              54,234,988 6.0% 32                  54,234,988              225,979              679,787                  3,213,312              50,341,889 6.0% 33                  50,341,889              209,758              696,009                  2,978,753              46,667,127 6.0%