fixed income investment...................................

Question 1 (9 points) You have purchased a freehold house (i.e., no condo fee) for $300,000 with 20% down payment and the rest borrowed from your local bank as a 3&year mortgage loan at 6% (APR with monthly compounding). The mortgage can he paid off any time without penalty, i.e., it allows prepayment. (a) (1 point) What is your loan to value (LTV) ratio? (13) (2 points} 1What is your monthly payment? (c) (1 point) If your gross annual income is $72,000. and the property tax on the house is $6,000 per year, what is your payment to income (PTI) ratio? (:1) (1 point) Why does your prepayment option affect the protability of your bank when the interest rate falls? (e) (1 point) Why is your prepayment option equivalent to your right for renancing? (f) (3 points) Assume that the mortgage rate falls to 5.4% (APR with monthly compounding) in three years. Will you renance your loan despite that your bank charges you $2,000 refinancing fee? Why or why not? Be numerically specic. Please clearly indicate which answer is for which part. Question 2 ( 10 points ) A mortgage pass through security of 30 - year confirming mortgages is issued with initial balance of $250 million and initial WAM of 354 months . The WAC is 8% , and coupon rate ( to the investors ) is 7% . The rates are quoted as monthly simple interest rates ( i. . , APR with monthly compounding ) To ensure sufficient accuracy , you are required to keep at least 6 decimals , e .g . X yyyy y , on the monthly mortgage rate . The accuracy on the dollar amount can be rounded to dollar ( 2 ) ( 2 points ) What mortgage payment is to be received by the pass through in the first month ( b ) ( 1 point ) For simplicity , the single monthly mortality ( SMM ) for the first month is give as 0 001767 . What is the total amount of principal to be received by the pass- through in this month ? ( 0 ) ( 1 point ) What is the cash flow to the investors of the pass through in the first month ( 1 ) ( 1 point ) What mortgage payment is to be received by the pass through in the second month ? ( e ) ( 2 points ) If the prepayment speed on the second month is calculated based on the PSA 150 what is the cash flow to the investors of the pass through in the second month ? (1 ( 2 points ) The pass through is divided into I million shares and sold to the investors at 95% of par ( Le . the original balance ) . An investor who bought one share of the pass through wants to know his cash flow yield . Write an explicit mathematical Alien sion to expression to explain to the investor on the cash flow yield and indicate how it can be found and how it will be reported on the basis of Bond Equivalent Yield BEY lie APR based on semiannual compounding assumption ) . You are required to show specific values i f they are already known , and to indicate the unknowns with appropriate variables ( 8 ) ( 1 point ) Explain to the investor on why the cash flow yield in part (f depends on the assumption of the prepayment speed I = 250