The MZ Mortgage Company is issuing a CMO with three tranches. The A tranche consists of $40.5 million with a coupon of 8.25 percent. The B tranche is issued with a coupon of 9.0 percent and a principal of $22.5 million. The Z tranche carries a coupon of 10.0 percent with a principal of $45 million. The mortgages backing the security issuance are originated at a fixed rate of 10 percent with a maturity of 10 years (annual payments). The issuance will be over-collateralized by $4.5 million, and the CMO issuer will receive all net cash flows after payments are made to each class of securities.priority payments will be made to the class A tranche, which includes the promised coupon, all amortization from the mortgage pool, and interest that will be accrued to the Z class until the principal of $40.5 million due to the A tranche is repaid. The B class securities will receive interest only payments until the A class is paid off completely. The Z class will accrue interest at 10 percent until both A and B classes are paid off, and then starts to collect payments.Firstly, assuming 0% prepayment, but 5%/year of the underlying mortgages are in default for the first 9 years. We assume the default activity always occurs at the end of a year. Hence, if the beginning balance in a given year is $100, we assume at the end of that year, $5 worth of loan principal will be in default and needs to be written off from the beginning loan pool balance for the next year. Secondly, assume that it takes 1 year to complete the foreclosure process. The recovery rate from foreclosure is given to you in this homework. (For example, a 65% recovery rate means that if somebody defaults a loan with $1 balance in Year 1, we will get $0.65 back in year 2 through foreclosure.) You may notice that the path of the recovery rate given in this exercise in not constant. Instead, it depends on timing of the default (e.g., default in year 1 implies a different recovery rate than if default in year 9). This is a reasonable assumption (I encourage you to think about why, although you are not required to answer it in this homework). Finally, assume CMO issuer offers its timely payment guarantee. The timely payment guarantee means that if the cash flows collected from the mortgage pool is not enough to cover the fanatical obligations to the tranche holders, the CMO issuer will have to inject its own capital to pay off those CMO investors.

8.5.2

C3 B H Begin Balance Principal & Interest payments into pool D E Assumed Default (5% peryear for first 9 years) Recovery rate 5% Recovery From Foreclosure Total Amount Amortizatior Interest A 1 Period 2 Rate 3 Total Available for Distributi 10% 112,500,000.00 1 $ 2 3 4 5 6 4 5 6 7 8 9 10 11 12 13 7 8 9 10 14 8.25% Amount Invested $ 40,500,000.00 Total Payments Tranche A Coupon Rate Amound Owed to Security Holder at End of Period All Principal from Pool and Interest from Z Class Coupon Interest 0 $ 40,500,000.00 1 2 15 Period 16 17 18 19 20 21 22 3 4 5 6 7 23 24 25 26 8 9 10 9% Amount Invested $ 22,500,000.00 Tranche B Coupon Rate All Principal from Pool and Interest from Z Class Coupon Interest Amount Owed to Security Holder at End of Period 0 $ 22,500,000.00 Total Payments 1 2 27 28 29 30 31 32 33 34 35 36 37 38 3 4 5 6 7 8 C3 X D F H 37 7 8 38 39 9 40 10 41 $ 45,000,000.00 Tranchez Interest Coupon Rate Accrued Interest 10% Amount Invested Total Payments 42 Amount Owed to Security Holder at End of Period 0 $ 45,000,000.00 Principal Allocation 43 44 1 45 2 46 3 47 4 48 5 49 6 50 7 8 51 9 10 52 53 54 55 56 57 Total Cash Flows into Pool 58 Period 59 Total Payments to A, B, and Z Classes Residual Cash Flows to Equity Class $ (4,500,000.00)