A collateralized mortgage obligation (CMO) contains FHA and VA mortgages in the amount of $50 million at a fixed rate of 15% with ten-year maturities, subject to annual mortgage payments. The CMO offers tranches A, B, and Z. Due to current market conditions and the existing level of risk aversion, the offerings are over-collateralized by 9% of the mortgages' value (or $4.5 million equity investment).
The assumed prepayment rates are based on the 100% PSA model (adjusted for annual payments): 1.30% in year one, 3.70% in year two, 5.75% in year three, and 6% in year four and thereafter. Prepayments apply to the pool balance at the end of the proceeding year. For example, in year one are $650,000 (1.3%*$50million)
The Tranches are offered as shown below:
Tranche A bonds - $16.5 million with 13% coupon
Tranche B bonds - $9 million with 14% coupon
Tranche Z bonds - $20 million with 15% coupon
The conditions of the issue state that each tranche will receive promised interest as due. Tranche A will receive all scheduled and unscheduled principal paid into the pool until it is fully repaid. Once Tranche A is repaid, Tranche B begins receiving all pool principal payments (including prepayments). Finally, tranche Z receives all pool principal payments (including prepayments) when B is repaid.
Calculate the cash flows to each tranche and find the weighted average coupon at issue, and years 1 through 5. Also, find the residual cash flows occurring to the equity investor and the internal rate of return to the equity investor.