Answer-first summary for fast verification
Answer: $2.40 million
### Correct answer: **B. $2.40 million** Break the cash flow into its components: 1. **Tranche A interest** - Tranche A principal = $300 million - Coupon = 6.0% per year = 0.5% per month - Monthly interest = $300 million × 0.5% = **$1.50 million** 2. **Pool scheduled monthly payment** - Total mortgage pool payment = **$5.430 million** - Pool interest in month 1 = $800 million × 7.2% / 12 = **$4.80 million** - Scheduled principal = $5.430 million − $4.800 million = **$0.630 million** 3. **Prepayment principal at 200% PSA** - 100% PSA in month 1 implies CPR = 0.20% - Therefore 200% PSA implies CPR = 0.40% - SMM ≈ 1 − (1 − 0.004)^(1/12) ≈ **0.0334%** - Prepayment on $800 million ≈ $800 million × 0.0334% ≈ **$0.268 million** 4. **Total principal to Tranche A** - Since this is a sequential CMO, **all principal goes first to Tranche A** - Total principal to A = $0.630 million + $0.268 million = **$0.898 million** 5. **Total cash flow to Tranche A** - Interest + principal = $1.50 million + $0.898 million = **$2.398 million ≈ $2.40 million** So the total cash flow received by Tranche A in the first month is **$2.40 million**.
Author: Manit Arora
Ultimate access to all questions.
Question 107.1. A mortgage pool has a principal balance of $800 million and the weighted average coupon (WAC) of the mortgages in the pool is 7.2%. A sequential structure collateralized mortgage obligation (CMO) divides the pool into four bonds: Tranche A has $300 million principal, Tranche B has $200 million principal, Tranche C has $175 million principal, and Tranche D has $125 million principal. All principal payments are directed first to Tranche A, until this bond bond is fully amortized, then principal is directed to Tranche B, and so on. (Sequential structuring is also known as time tranching.) All four bonds pay a coupon of 6.0% per annum. In the first month, the coupon paid by the mortgage pool (i.e., principal plus interest) is $5.430 million. The realized prepayment rate is 200% PSA. In the first month, what is the total cash flow received by Tranche A?
A
$1.96 million
B
$2.40 million
C
$3.10 million
D
$4.90 million
No comments yet.