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Financial Institutions FNAN 321 Problem Set #18 Securitization Cash Flows Instructions 1. Order: Questions must be submitted in order. Any homework assignment with questions or parts of questions that are submitted out of order will receive no credit or deductions. The term order refers to the question numbers on the assignment. For example, if there are 5 questions, then the submitted solutions must be numbered from 1 to 5 in numerical order and each question must be answered completely under the appropriate number. Questions with subparts must also be answered in order. 2. Work: to receive credit for a given problem, you must show all of your work (for each calculation) in a complete, organized and legible fashion. Listing inputs to your calculator does not constitute showing your work. For calculation problems, your answer must be clearly marked by placing a box or a circle around the final answer. 3. Format: Homework must be hand written. Electronic copies of homework will receive nocredit Each problem set must be submitted individually. Problem sets that are stapled or otherwise bond together (including folding the corners of the pages together) or assignments submitted on the same sheet of paper will receive no credit. 4. Submission: Homework must be submitted in class on the due date. The due date for each assignment is one week after it is assigned unless otherwise stated. Any other form of submission including but not limited to: late assignments, emailed assignments, assignments dropped in my mailbox or the department drop box will receive no-credit. 5. Grading: Each problem on each homework assignment has a point value associated with it. These point values are given directly to the right of the question number. For example, \"Question V (10pts)\" indicates that question five is worth 10 points. On each problem, you will be graded on: accuracy, completeness, exposition and presentation. Total Possible Points = 150 Your Score = __________ Page 1 of 6 Question I (25 pts) Warington Bank originates 100 30-year mortgages with an average principal of $275,000 each and aggregate mortgage coupon of 7%.They plan to securitize the loans and issue GNMA bonds. Warington charges a 84 bp servicing fee and GNMA charges 7 bps for insuring the bond payments. a) Outline the process of securitizing loans and issuing GNMA bonds. (5 pts) b) Find the aggregate monthly payments to GNMA bond holders. (10 pts) c) After 5 years, a similar pool of loans yields an aggregate mortgage coupon of 3%. Find the value of the GNMA bonds. (10 pts) Page 2 of 6 Question II (30 pts - 15 pts each) New England National Bank pools $30,000,000 in mortgage principal that pays an aggregate coupon of 4.1% per annum. a) Assuming the mortgages are interest only, how much principal will remain in the pool at the end of month 8 assuming 100% PSA (all payments are made in arrears). b) Repeat part a assuming 421% PSA Page 3 of 6 Question III (20 pts) Ingenta Bank has securitized a pool of 500 interest only mortgages with and average principal of 450,000 each and 30 years to maturity. The mortgage pool pays an aggregate coupon of 3.42%. Ingenta bank sells the pool to an SPV who collects an annual servicing fee of 21bsp. The SPV then purchase GNMA insurance for 4bps per annum. Find the aggregate expected payment to the bond holders, SPV and GNMA at the end of month 4 assuming 75% PSA (all payments are made in arrears). Recommended: Find the payment to bondholders after one year has passed (at the end of month 12) if loans are fully amortizing. Page 4 of 6 Question IV (35 pts) Bank of England purchases a pool of GNMA bonds with face value of $500M and time to maturity of 30 years. The bonds are securitized in a CMO. The Class A bond has total principal of $200M and pays an 8% coupon. The Class B bond has total principal of $150M and pays a coupon of 5%. The Class C share has total principal of $150M and a coupon of 3%. a) Is it easier or more difficult to value a CMO created from mortgage loans that have not already been securitized in a GNMA bond issue. (5 pts) b) Find the aggregate coupon payments to bond holders of each bond class. For this part, assume the bonds pay an annual coupon. (10 pts) c) Assume the loans are interest only loans. Find the payment bonds holders of each class after 7 years have passed. For this part, assume the bonds pay semiannual coupons and there is no prepayment risk. (10 pts) d) After 12 years $231.5M of principal has been repaid (includes both prepayments and scheduled principal payments). Find the aggregate coupon payments to bond holders of each bond class. For this part, assume bonds are fully amortizing. (10 pts) Page 5 of 6 Question V (10 pts) A GNMA bond with 20 years left to maturity and face value of 500,000 has a market value of $120,000. A 20 year Treasury note with face value of 1,000 has a current market value of $312. a) Find the option adjusted spread. Explain how the option adjusted spread can be used to price a GNMA bond. Question VI (30 pts - 15 pts each) First Financial Bank originates 500 30-year fully amortizing mortgages with an average principal of $320,000 each. The aggregate mortgage coupon rate from the pool is 8%. They collect a 1% servicing fee. The loans are securitized and GNMA bonds are issued on the pool. GNMA charges a 20 bps for insuring the bonds. All payments are made in arrears. a) How much should the bondholders expect to receive at the beginning of month 7 (end of month 6) assuming 100% PSA? (you can calculate the amortization schedule in excel) b) How much should the bond holders expect to receive at the beginning of month 7 assuming 125% PSA? Page 6 of 6