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## Assume that a pool of mortgages with an aggregate par

Assume that a pool of mortgages with an aggregate par value of \$500 million is used as collateral for asset-backed security. The weighted average coupon on the mortgages is 8.1% and the pass-through coupon rate is 7.2%.

1. Calculate the interest payments during the first month.

Assume the MBS is packaged into the following sequential-pay tranches.

 Tranche Par, \$ millions Payment Rule A 150 The monthly coupon payment is made in proportion to the beginning principal balance. Principal payments should be made first to A, then B, then C and finally D tranches. B 140 C 110 D 100
1. Assume in addition to the interest payment you calculated in (a) above, scheduled principal payment of \$20 million and additional principal prepayment of \$15 million is made during the month. Prepare a schedule to show all the disbursements to the four tranches.
2. Assume immediately after the disbursements above, there are defaults in the mortgages and the pool repossessed and sold the underlying properties to realize a net cash flow of \$250 million. How should that be distributed to the tranches?
3. Assume instead of the tranches above, the pool is organized as a planned amortization class (PAC) tranches and support tranche as follows.
 Tranche Par, \$ million Payment Rule P-A 150 The monthly coupon payment is distributed in proportion to the beginning principal balance. All scheduled principal payments are made first to the PAC tranches in proportion to their par. Support tranche gets distribution from scheduled principal payment only after the PAC tranches are paid off. Any principal payment in excess of schedule is paid to the Support tranche until it is completely paid off. Then excess will be paid to the PAC tranches. P-B 100 P-C 100 Support 150
1. Prepare payment schedule assuming payment of the coupon determined in (a), and scheduled principal payment of \$20 million and excess principal prepayment of \$15 million.
2. Prepare payment schedule assuming that after the first month’s payment in (i) the borrower’s default and repossession of the underlying properties resulted in realization of a net \$250 million.

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