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Consider an MPT that is backed by 100 mortgages with average balance of $350,000 and monthly...

Consider an MPT that is backed by 100 mortgages with average balance of $350,000 and monthly payment. The MPT has a WAC = 5% and WAM = 60 months. There is no servicing fee on this security. Assuming the prepayment model of CPR=5% and market rate is 3%, how much should this security sell for?

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Expert Solution

As PSA rate is not given , i assume PSA =100% , effective CPR = PSA * CPR = 100 *0.05 = 5%

Similarly , WAC = 5% , WAM = 60 Months.

effective Monthly CPR = 5/60 = 0.083%

Value of MPT = 100 * 350,000 = 35,000,000

Using the concept of discounted cash flow at rate of 3% = 0.25% monthly ,

Selling price of the , MPT = $35,319,826 for 100 mortgage => $ 353,198.26 each mortgage

Remaining Mortgage Balance $35,000,000 Pass-Through Cash-Flows (Using PSA Prepayment Benchmark) PSA Parameters
Mortgage Rate 5.000% Time CPR Rate
Pass-Through Rate 5.000% Prepayment Multiplier (in PSA units) 100% 1 0.1%
Initial Monthly Payment $660,493.178 30 2.5%
Seasoning (Months) 0 Average Life (Years) 2.59 60 5.0%
Term of Loan (Months) 60
Market Value $35,319,826
`
Conditional Single-Monthly Beginning Monthly Interest Monthly Interest Scheduled Total Ending Market
Prepayment Mortality Monthly Monthly Paid In By Paid Out To Pass- Principal Principal Mortgage Mortgage
Month Rate (CPR) (SMM) Rate Balance Payment Mortgage Holders Through Investors Repayment Prepayment Payment Balance Value
1 0.08% 0.01% 35,000,000 660,493.178 145,833.33 145,833.33 514,659.844 2,386.144 517,045.988 34,482,954.01 658846.1
2 0.17% 0.01% 34,482,954 660,447.476 143,678.98 143,678.98 516,768.501 4,712.010 521,480.511 33,961,473.50 657157.6
3 0.25% 0.02% 33,961,474 660,355.854 141,506.14 141,506.14 518,849.715 6,966.541 525,816.255 33,435,657.25 655427.8
4 0.33% 0.03% 33,435,657 660,218.294 139,315.24 139,315.24 520,903.055 9,148.763 530,051.818 32,905,605.43 653657.2
5 0.42% 0.03% 32,905,605 660,034.784 137,106.69 137,106.69 522,928.095 11,257.731 534,185.826 32,371,419.60 651845.9
6 0.50% 0.04% 32,371,420 659,805.325 134,880.92 134,880.92 524,924.410 13,292.525 538,216.935 31,833,202.67 649994.3
7 0.58% 0.05% 31,833,203 659,529.926 132,638.34 132,638.34 526,891.582 15,252.252 542,143.834 31,291,058.83 648102.7
8 0.67% 0.06% 31,291,059 659,208.607 130,379.41 130,379.41 528,829.195 17,136.049 545,965.244 30,745,093.59 646171.5
9 0.75% 0.06% 30,745,094 658,841.396 128,104.56 128,104.56 530,736.840 18,943.080 549,679.919 30,195,413.67 644201.1
10 0.83% 0.07% 30,195,414 658,428.331 125,814.22 125,814.22 532,614.108 20,672.539 553,286.647 29,642,127.02 642191.7
11 0.92% 0.08% 29,642,127 657,969.461 123,508.86 123,508.86 534,460.598 22,323.649 556,784.248 29,085,342.78 640143.8
12 1.00% 0.08% 29,085,343 657,464.842 121,188.93 121,188.93 536,275.914 23,895.665 560,171.578 28,525,171.20 638057.7
13 1.08% 0.09% 28,525,171 656,914.542 118,854.88 118,854.88 538,059.662 25,387.868 563,447.530 27,961,723.67 635933.8
14 1.17% 0.10% 27,961,724 656,318.637 116,507.18 116,507.18 539,811.455 26,799.574 566,611.029 27,395,112.64 633772.5
15 1.25% 0.10% 27,395,113 655,677.213 114,146.30 114,146.30 541,530.910 28,130.129 569,661.039 26,825,451.60 631574.2
16 1.33% 0.11% 26,825,452 654,990.367 111,772.72 111,772.72 543,217.652 29,378.909 572,596.561 26,252,855.04 629339.2
17 1.42% 0.12% 26,252,855 654,258.203 109,386.90 109,386.90 544,871.307 30,545.324 575,416.631 25,677,438.41 627068.1
18 1.50% 0.13% 25,677,438 653,480.836 106,989.33 106,989.33 546,491.510 31,628.816 578,120.326 25,099,318.08 624761.1
19 1.58% 0.13% 25,099,318 652,658.391 104,580.49 104,580.49 548,077.899 32,628.860 580,706.759 24,518,611.32 622418.8
20 1.67% 0.14% 24,518,611 651,791.001 102,160.88 102,160.88 549,630.121 33,544.962 583,175.083 23,935,436.24 620041.5
21 1.75% 0.15% 23,935,436 650,878.810 99,730.98 99,730.98 551,147.825 34,376.663 585,524.489 23,349,911.75 617629.6
22 1.83% 0.15% 23,349,912 649,921.969 97,291.30 97,291.30 552,630.670 35,123.539 587,754.209 22,762,157.54 615183.7
23 1.92% 0.16% 22,762,158 648,920.641 94,842.32 94,842.32 554,078.317 35,785.197 589,863.514 22,172,294.03 612704.1
24 2.00% 0.17% 22,172,294 647,874.996 92,384.56 92,384.56 555,490.438 36,361.280 591,851.717 21,580,442.31 610191.4
25 2.08% 0.18% 21,580,442 646,785.216 89,918.51 89,918.51 556,866.706 36,851.464 593,718.171 20,986,724.14 607645.9
26 2.17% 0.18% 20,986,724 645,651.490 87,444.68 87,444.68 558,206.806 37,255.463 595,462.269 20,391,261.87 605068.1
27 2.25% 0.19% 20,391,262 644,474.016 84,963.59 84,963.59 559,510.425 37,573.022 597,083.447 19,794,178.43 602458.5
28 2.33% 0.20% 19,794,178 643,253.002 82,475.74 82,475.74 560,777.259 37,803.923 598,581.182 19,195,597.24 599817.5
29 2.42% 0.20% 19,195,597 641,988.666 79,981.66 79,981.66 562,007.011 37,947.983 599,954.994 18,595,642.25 597145.7
30 2.50% 0.21% 18,595,642 640,681.233 77,481.84 77,481.84 563,199.390 38,005.055 601,204.445 17,994,437.81 594443.5
31 2.58% 0.22% 17,994,438 639,330.937 74,976.82 74,976.82 564,354.113 37,974.854 602,328.968 17,392,108.84 591711.4
32 2.67% 0.22% 17,392,109 637,938.030 72,467.12 72,467.12 565,470.909 37,857.489 603,328.399 16,788,780.44 588949.8
33 2.75% 0.23% 16,788,780 636,502.762 69,953.25 69,953.25 566,549.510 37,652.919 604,202.429 16,184,578.01 586159.4
34 2.83% 0.24% 16,184,578 635,025.395 67,435.74 67,435.74 567,589.653 37,361.138 604,950.792 15,579,627.22 583340.5
35 2.92% 0.25% 15,579,627 633,506.198 64,915.11 64,915.11 568,591.085 36,982.179 605,573.264 14,974,053.95 580493.7
36 3.00% 0.25% 14,974,054 631,945.451 62,391.89 62,391.89 569,553.559 36,516.109 606,069.668 14,367,984.29 577619.5
37 3.08% 0.26% 14,367,984 630,343.438 59,866.60 59,866.60 570,476.837 35,963.030 606,439.867 13,761,544.42 574718.4
38 3.17% 0.27% 13,761,544 628,700.456 57,339.77 57,339.77 571,360.688 35,323.083 606,683.771 13,154,860.65 571791
39 3.25% 0.27% 13,154,861 627,016.807 54,811.92 54,811.92 572,204.888 34,596.443 606,801.331 12,548,059.32 568837.6
40 3.33% 0.28% 12,548,059 625,292.803 52,283.58 52,283.58 573,009.222 33,783.321 606,792.544 11,941,266.77 565858.9
41 3.42% 0.29% 11,941,267 623,528.763 49,755.28 49,755.28 573,773.485 32,883.965 606,657.450 11,334,609.32 562855.4
42 3.50% 0.30% 11,334,609 621,725.014 47,227.54 47,227.54 574,497.476 31,898.659 606,396.134 10,728,213.19 559827.6
43 3.58% 0.30% 10,728,213 619,881.893 44,700.89 44,700.89 575,181.005 30,827.720 606,008.725 10,122,204.46 556776.1
44 3.67% 0.31% 10,122,204 617,999.741 42,175.85 42,175.85 575,823.889 29,671.506 605,495.395 9,516,709.07 553701.3
45 3.75% 0.32% 9,516,709 616,078.910 39,652.95 39,652.95 576,425.956 28,430.404 604,856.360 8,911,852.71 550603.8
46 3.83% 0.33% 8,911,853 614,119.759 37,132.72 37,132.72 576,987.039 27,104.843 604,091.882 8,307,760.83 547484.1
47 3.92% 0.33% 8,307,761 612,122.651 34,615.67 34,615.67 577,506.981 25,695.283 603,202.264 7,704,558.56 544342.9
48 4.00% 0.34% 7,704,559 610,087.962 32,102.33 32,102.33 577,985.635 24,202.221 602,187.856 7,102,370.71 541180.5
49 4.08% 0.35% 7,102,371 608,016.071 29,593.21 29,593.21 578,422.860 22,626.188 601,049.047 6,501,321.66 537997.6
50 4.17% 0.35% 6,501,322 605,907.365 27,088.84 27,088.84 578,818.525 20,967.750 599,786.275 5,901,535.38 534794.8
51 4.25% 0.36% 5,901,535 603,762.240 24,589.73 24,589.73 579,172.509 19,227.508 598,400.017 5,303,135.37 531572.5
52 4.33% 0.37% 5,303,135 601,581.095 22,096.40 22,096.40 579,484.698 17,406.097 596,890.794 4,706,244.57 528331.3
53 4.42% 0.38% 4,706,245 599,364.339 19,609.35 19,609.35 579,754.987 15,504.186 595,259.173 4,110,985.40 525071.8
54 4.50% 0.38% 4,110,985 597,112.387 17,129.11 17,129.11 579,983.282 13,522.478 593,505.759 3,517,479.64 521794.5
55 4.58% 0.39% 3,517,480 594,825.660 14,656.17 14,656.17 580,169.495 11,461.708 591,631.203 2,925,848.44 518500
56 4.67% 0.40% 2,925,848 592,504.585 12,191.04 12,191.04 580,313.550 9,322.646 589,636.196 2,336,212.24 515188.7
57 4.75% 0.40% 2,336,212 590,149.595 9,734.22 9,734.22 580,415.377 7,106.094 587,521.472 1,748,690.77 511861.4
58 4.83% 0.41% 1,748,691 587,761.131 7,286.21 7,286.21 580,474.919 4,812.886 585,287.805 1,163,402.97 508518.5
59 4.92% 0.42% 1,163,403 585,339.637 4,847.51 4,847.51 580,492.124 2,443.889 582,936.013 580,466.95 505160.6
60 5.00% 0.43% 580,467 582,885.565 2,418.61 2,418.61 580,466.953 0.000 580,466.953 0.00 501788.2
0.00% 0.00% 0 0.000 0.00 Total value 35319826

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