Question 3 (the payment structure of securitization)

Three households, A, B, and C, brought their own homes. Each of them borrowed a $100,000 from the bank and will repay the debt in 10 years. For simplicity, weassume the interest rate of the mortgage is zero and every year every household needs to repay $10,000 to the bank. If a household fails to make the annual repayment, the household defaults. Right after the purchase, the bank pooled all three mortgage loans andrestructure them into three tranches.The value of senior tranche and mezzanine tranche is $200,000 and $80,000, respectively. The rest goes to the equity tranche, which is worth $20,000.Each tranche has been securitized and sold to investors.

a) Household A defaults after her 8th annual repayment, while households B and C made all their repayments after 10 years. What is the total amount of payments senior tranche investors have received in the past ten years? How about mezzanine tranche investors and equity tranche investors?

b) Household A defaults after her 8th annual repayment, while households B and C made all their repayments after 10 years. What is the total amount of the annual payment equity tranche investors received at the end of 9th year? How about mezzanine tranche investors?

c) Household A defaults after her 4th annual repayment, households B defaults after her 8th annual repayment, and C made all their repayments after 10 years. What is the total amount of the annul payment equity tranche investors received at the end of 9th year? How about mezzanine tranche investors?

d) Household A defaults after her 4th annual repayment, households B defaults after her 8th annual repayment, and C defaults after her 6th annual repayment. List the total amount of annual payments that investors in each tranche received at the end of each year.