question archive A bank issues two mortgages M1 and M2 for $1 million each
A bank issues two mortgages M1 and M2 for $1 million each
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A bank issues two mortgages M1 and M2 for $1 million each. Both mortgages mature at the end of the year with principle repayment equal to $1 million. M1 has an interest rate of 15% while M2 has an interest rate of 5% and both only pay a single interest payment at maturity. Both borrowers repay full principle plus interest at the end of the year in normal times (probability .95) but default in a recession (probability .05). M1's liquidation value in a recession is $500,000 while M2's liquidation value in a recession is $700,000.
The bank creates a mortgage backed security from M1 and M2 which has only two tranches: a senior tranche which has an expected return of 4% and a junior tranche which has an expected return of 13.7%. The MBS pays out all proceeds from the mortgage repayments to the two tranches in each state of the world (i.e. the senior and junior tranche holders are the only stakeholders in the MBS). The senior tranche has priority to be repaid over the junior tranche. What is the market value of the senior and junior tranches at the time that they are issued?
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Senior Tranche = $1,000,000
Junior Tranche= $976,253
Step-by-step explanation
Step 1: Calculate the total cash flow from the mortgages (normal vs recession)
| Cash Flow (Normal) | Cash Flow (Recession) | |
| M1 | 1,150,000.00 | 500,000.00 |
| M2 | 1,050,000.00 | 700,000.00 |
| Total | 2,200,000.00 | 1,200,000.00 |
Step 2: Calculate the cash to-be-received by each tranche under each outcome
| Cash Flow (Normal) | Cash Flow (Recession) | |
| Senior Tranche | 1,040,000.00 | 1,040,000.00 |
| Junior Tranche | 1,160,000.00 | 160,000.00 |
| Total | 2,200,000.00 | 1,200,000.00 |
The senior tranche is the top priority. It will always receive 1,040,000 (1,000,000 x 4% expected return) unless there is not enough cash coming from the mortgages.
The junior tranche will get the residual amount.
The totals in Step #2 will always equal the totals in Step #1.
Step 3: Calculate the expected value of each tranche.
Probability of Normal Economy x Cash Flow if Normal Economy + Probability of Recession x Cash Flow if Recession
Senior Tranche: 95% x 1,040,000 + 5% x 1,040,000 = 1,040,000
Junior Tranche: 95% x 1,160,000 + 5% x 160,000 = 1,110,000
Step 4: Calculate the present value of the expected values
Expected Value / (1 + Expected Return)
Senior Tranche: 1,040,000 / (1 + 4%) = 1,000,0000
Junior Tranche: 1,110,000 / (1 + 13.7%) = 976,253.30
