Question

The Nittany Mortgage Company is issuing a CMO with three tranches. The A tranche will consist of $40.5 million with a coupon of 8.25 percent. The B tranche will be issued with a coupon of 9.0 percent and a principal of $22.5 million. The Z tranche will carry a coupon of 10.0 percent with a principal of $45 million. The mortgages backing the security issue were originated at a fixed rate of 10 percent with a maturity of 10 years (annual payments). The issue will be overcollateralized by $4.5 million, and issuer will receive all net cash flows after priority payments are made to each class of securities. Priority payments will be made to the class A tranche and will include the promised coupon, all amortization from the mortgage pool, and interest that will be accrued to the Z class until the principal of $40.5 million due to the A tranche is repaid. The B class securities receive interest-only payments until the A class is repaid, and then receive priority payments of amortization and accrued interest. The Z class will accrue interest at 10 percent until both A and B classes are repaid. It will receive current interest and principal payments a that time. 1. What will be the weighted average coupon (WAC) on the CMO when issued? 2. What will be the maturity of each tranche assuming no prepayment of the mortgages in the pool? 3. What will be the WAC at the end of year 3? year 4? year 8? 4. If class A, B, and Z investors demand an 8.5 percent, 9.5 percent, and 9.75 percent yield to maturity, respectively, at the time of issue, what price should Nittany Mortgage Company ask for each security? How much will the company receive as proceeds from the CMO issue? 5. What are the residual cash flows to Nittany? What rate of return will be earned on the equity overcollateralization? 6. Assume that the mortgages in the underlying pool prepay at the rate of 10 percent per year. How will your answers in (1)-(5) change? 7. Assume that immediately after the securities are issued in case (6), the price of all securities suddenly trades up by 10 percent over the issue price. What will the yield to maturity be for each security?

Answer 1

Solution)
1) MBS is composed of three different pools of mortgages with a principal balance of $108 million. The tranche A consists of $40.5 million worth of mortgages that yield 8.25%. The tranche B has a $22.5 million mortgage balance at a 9% rate. The last tranche Z has $45 million worth of mortgages with a rate of 10%
WAC = [($40.5 million x 0.0825) + ($22.5 million x 0.09) + ($45 million x 0.10)] / $108 million
WAC = ($3.34125 + $2.025 + $4.5) / $108 million
WAC = $9.86625/$108 million = 9.135416667%

2) Payment Rule: Priority payments will be made to the A tranche and will include the promised coupon, all amortization from the pool, and interest will be accrued to the Z tranche until A is completely repaid. The B class will receive interest payments only until the A class is repaid, and then will receive priority payments of amortization and accrued interest. The Z class will accrue interest at 10% until both A and B are repaid. It will receive current interest and principal payments at that time.
To calculate the maturity of each tranche, the yearly interest and principal paid on each tranche must be calculated. Remember that the interest that would have been paid on the Z tranche is applied first to pay down the principal on the A tranche. The Z tranche accrues interest which is added to its principal until all preceding tranches are paid off.
The annually mortgage payments are $108 m = PVA_(10,10%) x PMT
PMT = $17576502.6473113.

Year	Beg. Bal	Payment	Interest	Principal	End Bal
1	112,500,000.00	17,576,502.65	11,250,000.00	6,326,502.65	106,173,497.35
2	106,173,497.35	17,576,502.65	10,617,349.74	6,959,152.91	99,214,344.44
3	99,214,344.44	17,576,502.65	9,921,434.44	7,655,068.20	91,559,276.24
4	91,559,276.24	17,576,502.65	9,155,927.62	8,420,575.02	83,138,701.21
5	83,138,701.21	17,576,502.65	8,313,870.12	9,262,632.53	73,876,068.69
6	73,876,068.69	17,576,502.65	7,387,606.87	10,188,895.78	63,687,172.91
7	63,687,172.91	17,576,502.65	6,368,717.29	11,207,785.36	52,479,387.55
8	52,479,387.55	17,576,502.65	5,247,938.76	12,328,563.89	40,150,823.66
9	40,150,823.66	17,576,502.65	4,015,082.37	13,561,420.28	26,589,403.38
10	26,589,403.38	17,576,502.65	2,658,940.34	14,917,562.31	11,671,841.07
11	11,671,841.07	12,839,025.18	1,167,184.11	11,671,841.07	0.00

3) WAC at the end of year 3
Total principal left in A = 40.5 millions - Principal paid = 40.5 - 20.9472 = 19.55928
Total Amt = Tranche A's Balance + Tranche B's Fund + Tranche C's Fund
= 19.559 + 22.5 + 45 = 87.05928
WAC = [($19.559 million x 0.0825) + ($22.5 million x 0.09) + ($45 million x 0.10)] / $108 million
WAC = ($1.613 + $2.025 + $4.5) / $108 million
WAC = $8.138/$108 million = 9.3483896%

WAC at the end of year 4
Total principal left in A = 40.5 millions - Principal paid = 40.5 - 29.362 = 11.138 millions
Total Amt = Tranche A's Balance + Tranche B's Fund + Tranche C's Fund
= 11.138 + 22.5 + 45 = 78.638 millions
WAC = [($11.138 million x 0.0825) + ($22.5 million x 0.09) + ($45 million x 0.10)] / $ 78.638 millions
WAC = ($ 0.91894 + $2.025+ $4.5) / $ 78.638 million
WAC = $7.44394/$ 78.638 million = 9.466%

WAC at the end of year 8
Total principal of fund left = 40.150 millions
This amount is solely left in Z's Tranche which interest rate is 10%
WAC = [($40.150 million x 0.10)] / $ 40.150 millions
WAC = ($4.015) / $ 40.150 million = 10.0%