Cash Flow calculation in the practice question

[atandon]

Hi David,

Could you pls help me understand why we add the tranche A interest ($1.5 million) to the principal amt since this cash was being paid to the investor. Do we add fund outflow to the principal outstanding when asked to calculate total cash flow? listed the question with answer below for your reference -

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?

107.1. B. $2.40 million
Tranche A receives its interest payment (like all Tranches do) plus all of the principal in the first month (none of the Tranches receive principal until A is amortized).
Tranche A Interest = 6.0%/12*$300 million = $1.5 million.
Tranche A Principal equals the pools scheduled principal plus prepaid principal.
In the first month, the pool's scheduled principal = coupon, C(1) - Interest, I(1) = $5.430 million -7.2%/12*$800 million = 5.430 - 4.800 = $630,300
At 200% PSA, the first month's SMM (p) = 1 - (1 - 0.40%)^(1/12) = 0.03339%; i.e., 100% PSA implies 0.20% in the first month.
Such that the prepaid principal in the first month = 0.03339% * $800 million = $267,157.
Tranche A (receiving all of the principal) receives $630,300 + $267,157 = $897,462 in principal.
Therefore, the total cash flow to Tranche A = $1.5 million + $897,462 = $2,397,462

 

[Basu]

Hi atandon,

The question asks for total cash flow received by Tranche A investors which would be interest received and any principal repayments made by the mortgage pool. $1.5m is the total interest received by Tranche A investors (6% coupon on $300m principal). Also according to the CMO structure, all principal repayments are first made to the Tranche A investors until Tranche A is fully repaid. Hence the total principal repayments made to A is $897,462. So overall cash flow to Tranche A investors is $1.5m + $897.462.

For eg., if you took a $100 loan from both X and Y at 6% coupon and made the condition that any principal prepaid by you will be first made to X until $100 are fully repaid to X and then only you start paying Y. So interest on $100 loan from X is 6% * 100= $6 and suppose you decide to prepay $10 in that year. Because of the condition you made that X should repaid first, X will receive the entire $10 of principal plus $6 interest. So total cash flow to X is $16 for the year. Total cash flow to Y will only be the interest of 6% * 100= $6.

Hope that helps.
Basu

 

[David Harper CFA FRM]

Thanks Basu for a terrific answer (star awarded, enters into weekly drawing)

atandon I added the underlying spreadsheet to the source answer in forum, here it is also.
This utilizes Veronesi's Table 8-3 which takes time to process. The mortgage pool produces for investors both principal and interest (just like an amortizing individual mortgage loan produces a monthly cash flow which consists of an decreasing [over time] interest component plus an increasing principal component). As this mortgage pool aggregates many mortgages, unlike the individual mortgage which won't experience regular unscheduled prepayments, in large numbers we do expect unscheduled monthly prepayments in the big pool, so the cash flow to investors includes three components:

• Scheduled principle (expected amortization), plus
• Unscheduled principle due to prepayments (per the PSA assumption), column 7 in T 8.3 called "Principal Prepaid" (e.g., would be zero under 0% PSA), plus
• Pass-through interest (in this example, the first month's pass through interest on the pool = 7.2% WAC /12 * 800 MM = $4.0 million

The sequential collateralized mortgage obligation (CMO) is a pool of mortgages that produces cash flows as above, but with the feature difference that, instead of all investors sharing principal prepayments (which we can think of as the return of capital versus interest which is the return on capital), the Tranche A receives both types of principal payment (scheduled and unscheduled), in addition to the interest, until its is exhausted. Hope that helps, thanks,

 

[atandon]

Thanks Basu,David. It was very useful.