I have posted two other examples (and Excel workbooks) of CMO structures in the past. Floater & Inverse-Floater CMO and Sequential Pay CMO. Now, we are going to look at a CMO PAC (Planned Amortization Class). It is a simple example, with only two tranches, the PAC and Companion (or sometimes called Support) bonds. The PAC structure differs from the sequential, in that PAC bonds are designed to produce more stable cash flows. In my example, I assume a $100 million pool of mortgages backed by a government agency. The WAC (weighted average coupon) is 4.5% and the servicing fee (including the guarantee fee) is 50 basis points. That makes the net interest rate 4.00%. The WAM (weighted average maturity) is 360 months. As always with my spreadsheets, only the yellow cells are input cells. Other colored cells are formulas or cells that are not used for this example.
The reason the PAC bond is more stable than other structures is that the cash flows are determined by a high and low collar of prepayment rates. In this case the prepayment rates are PSA ( Public Securities Association) rates. If you are not familiar with PSA, do a search on my blog for examples and Excel spreadsheets. It is assumed that the mortgage pool’s expected PSA will be 100. The mortgage pool of loans is referred to now on as the “collateral”.
The initial collar I chose for my example is a low PSA of 50 and a high of 200. My assumption for the initial PSA on the collateral is 100 PSA. As long as the collateral PSA remains within the initial collar, the PAC will get the fixed principle payments, set out in my example.
The chart above shows the principal payment amounts over the life of the structure. The PAC (orange) line equals the lowest principal payment , 50 PSA (blue) line, until the black 200 PSA line becomes the lowest principal payment at month 131. The PAC principal payment then follows the 200 PSA line until the 360th month, and therefore the PAC receives the lowest principal amount.
Download the workbook called PAC_CMO. There are five sheets in the workbook. The first “Inputs” sheet contains the yellow input cells and the collateral’s amortization schedule. The “Low PSA Collar” and “High PSA Collar” sheets that contain amortization schedules for the collars are hidden. The forth sheet is the “Tranches” sheet. The cash flows are for the Collateral, PAC, and Companion structures. The collateral structure represents its the cash flow, given the 4.00% net yield and PSA of 100, as I set out in my example. The PAC Bond structure has the principal cash flows taken from the Low PSA and High PSA collars sheets. To the right of those two columns, is a “Minimum” column. That column provides the PAC with the lowest principal of the other two columns, provided the collateral PSA stays between the low and high PSA. The $64,680,507.37, above the “Minimum” cell, is the sum of the minimum principal cash flows and the amount allocated to the PAC.
The Companion bond gets the difference in principal between the collateral and the PAC bond. The $35,319,492.62 is the sum of all principal flowing to the Companion bond.
What happens if the collateral PSA lands outside the collar? As long as the Companion bond has not paid off, the PAC is ensured of prepayment protection.
This table shows the consistent average life of the PAC given an instant change in collateral PSA levels. It uses VBA to calculate your the new numbers, if you changed the assumptions.
Click the button to calculate new numbers.