Assume I purchase $750,000,000 of 20-year, fixed-rate residential mortgages with an average interest rate of 5.75%. I intend to issue 3 sequential pay tranches backed by these mortgages. Tranche A is $275,000,000 and promises a 4.25% return. Tranche B is $200,000,000 and promises a 5.00% return. Tranche Z is $225,000,000 and promises a 5.75% return. Compute the amortization sheet and the Tranche A cash flows for the first 3 years of the pool. For simplicity, assume these mortgages and the pool have annual payments.
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Mortgages
A mortgage is a formal agreement in which a bank or other financial institution lends cash at interest in return for assuming the title to the debtor's property, on the condition that the obligation is paid in full.
Mortgage
The term "mortgage" is a type of loan that a borrower takes to maintain his house or any form of assets and he agrees to return the amount in a particular period of time to the lender usually in a series of regular equally monthly, quarterly, or half-yearly payments.
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- An investor is considering the purchase of either an IO or PO strip from a CMO offering. The portion of the mortgage pool backing this tranche consists of $1,000,000 in mortgages with a remaining maturity of 10 years and an 8 percent interest rate.a. Assuming annual payments and a zero prepayment rate, prepare a schedule showing the IO and PO cash flows that would be payable to investors in this tranche. If the interest rate demanded by investors on this investment is also 8 percent, what would be the prices of the IO and PO strips?b. If interest rates increased to 10 percent and prepayments remained at a zero rate, how would the price of the IO and PO strips change? Which security, the IO or PO, exhibits the greatest price change from (a)? Why?c. Investor interest rates now decline to 6 percent. What is the price of the IO? PO? Prepayments now increase to a rate of 20 percent per year because mortgage borrowers in the pool begin to refinance at lower interest rates. What would prices…Assume that a lender offers a 30-year, $148,000 adjustable rate mortgage (ARM) with the following terms: Initial interest rate = 7.5 percent Index = one-year Treasuries Payments reset each year Margin = 2 percent Interest rate cap = 1 percent annually; 3 percent lifetime Discount points = 2 percent Based on estimated forward rates, the index to which the ARM is tied is forecasted as follows: Beginning of year (BOY) 2 = 7 percent; (BOY) 3 = 8.5 percent; (BOY) 4 = 9.5 percent; (BOY) 5 = 11 percent. Required: a. Compute the payments and loan balances for the ARM for the five-year period. b. Compute the yield for the ARM for the five-year period.A Financial Institution (FI) originates a pool of 500 30-year mortgages, each averaging $150,000 with an annual mortgage coupon rate of 8 percent. Assume that the entire mortgage portfolio is securitized to be sold as GNMA pass-throughs. The GNMA credit risk insurance fee is 6 basis points, and the FI's servicing fee is 19 basis points. Assume no prepayments. What are the expected monthly cash flows (fees) for the GNMA? $2,947.83 $4,527.72 $13,014.25 $3,123.42 $8,973.62
- Assume that a lender offers a 30-year, $155,000 adjustable rate mortgage (ARM) with the following terms: Initial interest rate = 7.5 percentIndex = one-year TreasuriesPayments reset each yearMargin = 2 percentInterest rate cap = 1 percent annually; 3 percent lifetimeDiscount points = 2 percentFully amortizing; however, negative amortization allowed if interest rate caps reached Based on estimated forward rates, the index to which the ARM is tied is forecasted as follows: Beginning of year (BOY) 2 = 7 percent; (BOY) 3 = 8.5 percent; (BOY) 4 = 9.5 percent; (BOY) 5 = 11 percent. Required: a. Compute the payments and loan balances for the ARM for the five-year period. b. Compute the yield for the ARM for the five-year period.Assume that a lender offers a 30-year, $150,000 adjustable-rate mortgage (ARM) with the following terms:Initial interest rate 7.5 percentIndex 1-year TreasuriesPayments reset each yearMargin 2 percentInterest rate cap 1 percent annually; 3 percent lifetimeDiscount points 2 percentFully amortizing; however, negative amortization allowed if interest rate caps reachedBased on estimated forward rates, the index to which the ARM is tied is forecasted as follows:Beginning of year (BOY) 2 7 percent; (BOY) 3 8.5 percent; (BOY) 4 9.5 percent;(EOY) 5 11 percent.Compute the payments, loan balances, and yield for the ARM for the five-year period.What is the value accumulated at the end of 30 years if $300 deposited at the end of each month in a mutual fund account that earns 12 percent annually during the period. Ans. A mortgage calls for monthly payments of $970.30, including interest at 7.6 percent. The current value of the mortgage is $95,258.72. Approximately how long will it take to fully amortize the mortgage? Ans. An income-producing property is priced at $550,000 and is expected to generate the following after-tax cash flows: Year 1: $50,000; Year 2: $55,000; Year 3: $60,000 and $600,000. Calculate the annual IRR for this investment opportunity. Ans.
- Consider a $100,000 30-year, fixed-rate mortgage with an annual interest rate of 5.50% and monthly payments. How much of the total expenses on mortgage payments go toward interest during the first three years (round to the nearest dollar)?$2, 540 $10, 220 $15,858 S4,274 $16, 167 $19, 172 $3,583The Green Mortgage Company has originated a pool containing 75 ten-year fixed interest rate mortgages with an average balance of $100,400 each. All mortgages in the pool carry a coupon of 12 percent. (For simplicity, assume that all mortgage payments are made annually at 12% interest.) Green would now like to sell the pool to FNMA. Required: a. Assuming a constant annual prepayment rate of 10 percent (for simplicity, assume that prepayments are based on the pool balance at the end of each year), what will be the price that Green should obtain on the date of issuance if market interest rates were (1) 11 percent? (2) 12 percent? (3) 9 percent? b. Assume that five years have passed since the date in (a). What will the pool factor be? If market interest rates are 12 percent, what price can Green obtain then? c. Instead of selling the pool of mortgages in (a), Green decides to securitize the mortgages by issuing 100 pass-through securities. The coupon rate will be 11.5 percent and the…Suppose GHI Bank has a portfolio of 8-year fixed rate mortgages with total principal amount of $50 million and interest rate is 9%. Interest is paid semi-annually and principal is scheduled to be repaid at maturity. GHI Bank finances its loan portfolio with six-month certificate of deposits (CDs) at an interest rate equal to six-month LIBOR plus 50 basis points. Question: Suppose GHI Bank enter into a 8-year fixed-floating interest rate swap is available with a notional amount of $50 million in which GHI Bank pays a fixed 8% every six months and received 6-month LIBOR. Explain how can the bank use this swap to hedge its interest rate exposure.
- An FI purchases a $9.982 million pool of commercial loans at par. The loans have an interest rate of 8 percent, a maturity of five years, and annual payments of principal and interest that will exactly amortize the loan at maturity. What is the duration of this asset? A. 2.122822 years. B. 3.072837 years. C. 3.528992 years. D. 2.846472 years. E. 5.000000 years.assume a $175,000 mortgage loan and 10-year term. The lender is charging an annual interest rate of 6 percent and 4 discount points at origination. a. What is the monthly payment Assuming that it is based on an amortization period of 30 years? b. What will be the required balloon payment at the end of the tenth year? c. What is the effective borrowing cost on the loan if it is held to maturity? Give typing answer with explanation and conclusionThe Green Mortgage Company has originated a pool containing 75 ten-year fixed interest rate mortgages with an average balance of $102,200 each. All mortgages in the pool carry a coupon of 12 percent. (For simplicity, assume that all mortgage payments are made annually at 12% interest.) Green would now like to sell the pool to FNMA. (A) Assuming a constant annual prepayment rate of 10 percent (for simplicity, assume that prepayments are based on the pool balance at the end of each year), what will be the price that Green should obtain on the date of issuance if market interest rates were (1) 11 percent? (2) 12 percent? (3) 9 percent? Market Interest Rate Price of the Pool 11% $7,951,446 12% $7,665,000 9% $8,580,288 (B) Assume that five years have passed since the date in (a). What will the pool factor be? If market interest rates are 12 percent, what price can Green obtain then? What is the Pool Factor? What is the Price of the pool after 5 years?