Question

The MZ 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 the 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 will receive interest only payments 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 percent until both A and B classes are repaid. It will receive current interest and principal payments at that time.

a. What will be the weighted average coupon
 (WAC) on the CMO when issued?

b. What will be the maturity of each tranche assuming no prepayment of mortgages in the pool?

c. What will be the WAC at the end of year 3? year 4? year 8?

d. 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 MZ Mortgage Company ask for each security? How much will the company receive as proceeds from the CMO issue?

e. What are the residual cash flows to MZ? What rate of return will be earned on the equity overcollateralization?

f. Optional. Assume that the mortgages in the underlying pool prepay at the rate of 10 percent per year. How will your answers in (b)–(e) change?

g. Optional. Assume that immediately after the securities are issued in case (f), 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

(a)

The Initial WAC is simply the coupon rate of each tranche weighted by the initial tranche balance

 

				Weighted
Tranche	Balance	Weighting	Coupon Rate	Avg Coupon
A	40,500,000	37.50%	8.25%	3.09%
B	22,500,000	20.83%	9.00%	1.87%
Z	45,000,000	41.67%	10.00%	4.17%
Total	$108,000,000			WAC =       9.13%

 

(b)

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 format for this portion of the solution comes directly from Exhibit 18-2.

 

Mortgage Pool

 

Year	Beg. Bal	Payment	Interest	Principal	End Bal
1	$112,500.00	$18,308.86	11,250.00	$7,058.86	$105,441.14
2	105,441.14	$18,308.86	10,544.11	$7,764.74	$97,676.40
3	97,676.40	$18,308.86	9,767.64	$8,541.22	$89,135.18
4	89,135.18	$18,308.86	8,913.52	$9,395.34	$79,739.85
5	79,739.85	$18,308.86	7,973.98	$10,334.87	$69,404.97
6	69,404.97	$18,308.86	6,940.50	$11,368.36	$58,036.61
7	58,036.61	$18,308.86	5,803.66	$12,505.20	$45,531.42
8	45,531.42	$18,308.86	4,553.14	$13,755.72	$31,775.70
9	31,775.70	$18,308.86	3,177.57	$15,131.29	$16,644.42
10	16,644.42	$18,308.86	1,664.44	$16,644.42	$0.00

 

Tranche A

 

	Amount		$40,500
	Rate		8.25%
Year	Beg. Bal	Interest	Principal	End Bal
1	$40,500.00	3,341.25	$11,558.86	$28,941.14
2	28,941.14	2,387.64	12,714.74	16,226.40
3	16,226.40	1,338.68	13,986.22	2,240.18
4	2,240.18	184.82	2,240.18	0.00
5	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00

 

Tranche B

	Amount		$22,500
	Rate		9.00%
Year	Beg. Bal	Interest	Principal	End Bal
1	$22,500.00	$2,025.00	$0.00	$22,500.00
2	22,500.00	2,025.00	0.00	22,500.00
3	22,500.00	2,025.00	0.00	22,500.00
4	22,500.00	2,025.00	13,144.65	9,355.35
5	9,355.35	841.98	9,355.35	0.00
6	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00

 

(c)

The weighted average coupon each year is found by weighting the coupon rate for each class by the outstanding balance of that class.

 

	A	B	Z	Total	WAC
Coupon	8.25%	9.00%	10.00%
End of Year	Balance	Balance	Balance	Balance
0	40500	22500	45000	108000	9.14%
1	28941	22500	49500	100941	9.28%
2	16226	22500	54450	93176	9.45%
3	2240	22500	59895	84635	9.69%
4	0	9355	65885	75240	9.88%
5	0	0	64905	64905	10.00%
6	0	0	53537	53537	10.00%
7	0	0	41031	41031	10.00%
8	0	0	27276	27276	10.00%
9	0	0	12144	12144	10.00%

 

(d)

Tranche A

 

					Cash
Year	Beg. Bal	Interest	Principal	End Bal	Flow
1	$40,500.00	3,341.25	$11,558.86	$28,941.14	14,900.11
2	28,941.14	2,387.64	12,714.74	16,226.40	15,102.39
3	16,226.40	1,338.68	13,986.22	2,240.18	15,324.89
4	2,240.18	184.82	2,240.18	0.00	2,425.00
5	0.00	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00	0.00
			P V at	8.50%	$40,309

 

Tranche B

 

					Cash
Year	Beg. Bal	Interest	Principal	End Bal	Flow
1	$22,500.00	$2,025.00	$0.00	$22,500.00	2,025.00
2	22,500.00	2,025.00	0.00	22,500.00	2,025.00
3	22,500.00	2,025.00	0.00	22,500.00	2,025.00
4	22,500.00	2,025.00	13,144.65	9,355.35	15,169.65
5	9,355.35	841.98	9,355.35	0.00	10,197.33
6	0.00	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00	0.00
			P V at	9.50%	$22,110

 

Tranche Z

 

			Total		Cash
Year	Beg. Bal	Interest	Payment	End Bal	Flow
0					($45,000)
1	$45,000.00	4,500.00	0.00	$49,500.00	0.00
2	49,500.00	4,950.00	0.00	54,450.00	0.00
3	54,450.00	5,445.00	0.00	59,895.00	0.00
4	59,895.00	5,989.50	0.00	65,884.50	0.00
5	65,884.50	6,588.45	7,567.98	64,904.97	7,567.98
6	64,904.97	6,490.50	17,858.86	53,536.61	17,858.86
7	53,536.61	5,353.66	17,858.86	41,031.42	17,858.86
8	41,031.42	4,103.14	17,858.86	27,275.70	17,858.86
9	27,275.70	2,727.57	17,858.86	12,144.42	17,858.86
10	12,144.42	1,214.44	13,358.86	0.00	13,358.86
				IRR	10.00%
			P V at	9.75%	$45,768

 

(e)

Residual Class

 

	Total	Other
Year	in pool	Classes	Residual
0			($4,500.00)
1	$18,308.86	$16,925.11	1,383.75
2	$18,308.86	17,127.39	1,181.47
3	$18,308.86	17,349.89	958.96
4	$18,308.86	17,594.65	714.20
5	$18,308.86	17,765.30	543.55
6	$18,308.86	17,858.86	450.00
7	$18,308.86	17,858.86	450.00
8	$18,308.86	17,858.86	450.00
9	$18,308.86	17,858.86	450.00
10	$18,308.86	13,358.86	4,950.00
		IRR	19.10%

 

(f)

Assuming 10% prepayment

 

Mortgage Pool

 

Year	Beg. Bal	Payment	Interest	Principal	End Bal	Prepayment
1	$112,500.00	$18,308.86	11,250.00	$18,308.86	$94,191.14	11250.00
2	94,191.14	$16,355.40	9,419.11	$16,355.40	$77,835.74	9419.11
3	77,835.74	$14,589.84	7,783.57	$14,589.84	$63,245.90	7783.57
4	63,245.90	$12,991.06	6,324.59	$12,991.06	$50,254.84	6324.59
5	50,254.84	$11,538.88	5,025.48	$11,538.88	$38,715.96	5025.48
6	38,715.96	$10,213.17	3,871.60	$10,213.17	$28,502.79	3871.60
7	28,502.79	$8,991.80	2,850.28	$8,991.80	$19,510.99	2850.28
8	19,510.99	$7,845.66	1,951.10	$7,845.66	$11,665.33	1951.10
9	11,665.33	$6,721.45	1,166.53	$6,721.45	$4,943.88	1166.53
10	4,943.88	$5,438.27	494.39	$4,943.88	$0.00	494.39

 

Tranche A

 

					Cash
Year	Beg. Bal	Interest	Principal	End Bal	Flow
1	$40,500.00	3,341.25	$22,808.86	$17,691.14	26,150.11
2	17,691.14	1,459.52	17,691.14	0.00	19,150.66
3	0.00	0.00	0.00	0.00	0.00
4	0.00	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00	0.00
			P V at	8.50%	$40,369

 

Tranche B

 

					Cash
Year	Beg. Bal	Interest	Principal	End Bal	Flow
1	$22,500.00	$2,025.00	$0.00	$22,500.00	2,025.00
2	22,500.00	2,025.00	3,614.26	18,885.74	5,639.26
3	18,885.74	1,699.72	18,885.74	0.00	20,585.46
4	0.00	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00	0.00
			P V at	9.50%	$22,232

 

Tranche Z

 

			Total		Cash
Year	Beg. Bal	Interest	Payment	End Bal	Flow
0					($45,000)
1	$45,000.00	4,500.00	0.00	$49,500.00	0.00
2	49,500.00	4,950.00	0.00	54,450.00	0.00
3	54,450.00	5,445.00	1,149.10	58,745.90	1,149.10
4	58,745.90	5,874.59	18,865.65	45,754.84	18,865.65
5	45,754.84	4,575.48	16,114.37	34,215.96	16,114.37
6	34,215.96	3,421.60	13,634.77	24,002.79	13,634.77
7	24,002.79	2,400.28	11,392.08	15,010.99	11,392.08
8	15,010.99	1,501.10	9,346.76	7,165.33	9,346.76
9	7,165.33	716.53	7,437.99	443.88	7,437.99
10	443.88	44.39	488.27	0.00	488.27
				IRR	10.00%
			P V at	9.75%	$45,588

 

Residual

 

	Total	Other
Year	in pool	Classes	Residual
0			($4,500.00)
1	$29,558.86	$28,175.11	1,383.75
2	$25,774.52	24,789.92	984.60
3	$22,373.42	21,734.56	638.86
4	$19,315.65	18,865.65	450.00
5	$16,564.37	16,114.37	450.00
6	$14,084.77	13,634.77	450.00
7	$11,842.08	11,392.08	450.00
8	$9,796.76	9,346.76	450.00
9	$7,887.99	7,437.99	450.00
10	$5,438.27	488.27	4,950.00
		IRR	16.10%

 

(g)

10 percent price increase after issue

 

Tranche A

 

					Cash
Year	Beg. Bal	Interest	Principal	End Bal	Flow	10% Price Increase
0						($44,550)
1	$40,500.00	3,341.25	$22,808.86	$17,691.14	26,150.11	26,150.11
2	17,691.14	1,459.52	17,691.14	0.00	19,150.66	19,150.66
3	0.00	0.00	0.00	0.00	0.00	0.00
4	0.00	0.00	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00	0.00	0.00
			P V at	8.50%	$40,369
					YTM	1.18%

 

Tranche B

 

					Cash
Year	Beg. Bal	Interest	Principal	End Bal	Flow	10% Price Increase
0						($24,750)
1	$22,500.00	$2,025.00	$0.00	$22,500.00	2,025.00	2,025.00
2	22,500.00	2,025.00	3,614.26	18,885.74	5,639.26	5,639.26
3	18,885.74	1,699.72	18,885.74	0.00	20,585.46	20,585.46
4	0.00	0.00	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00	0.00	0.00
9	0.00	0.00	0.00	0.00	0.00	0.00
10	0.00	0.00	0.00	0.00	0.00	0.00
			P V at	9.50%	$22,232
					YTM	5.12%

 

Class Z

 

			Total		Cash
Year	Beg. Bal	Interest	Payment	End Bal	Flow	10% Price Increase
0					($45,000)	($49,500)
1	$45,000.00	4,500.00	0.00	$49,500.00	0.00	0.00
2	49,500.00	4,950.00	0.00	54,450.00	0.00	0.00
3	54,450.00	5,445.00	1,149.10	58,745.90	1,149.10	1,149.10
4	58,745.90	5,874.59	18,865.65	45,754.84	18,865.65	18,865.65
5	45,754.84	4,575.48	16,114.37	34,215.96	16,114.37	16,114.37
6	34,215.96	3,421.60	13,634.77	24,002.79	13,634.77	13,634.77
7	24,002.79	2,400.28	11,392.08	15,010.99	11,392.08	11,392.08
8	15,010.99	1,501.10	9,346.76	7,165.33	9,346.76	9,346.76
9	7,165.33	716.53	7,437.99	443.88	7,437.99	7,437.99
10	443.88	44.39	488.27	0.00	488.27	488.27
				YTM		8.18%
			PV at	9.75%	$45,588