Question

1.(Level-Payment Mortgages) Compute the monthly payment on a 30-year level payment mortgage assuming an annual mortgage rate of 5% and an initial mortgage principal of $400,000. (2147.29)

2.(Mortgage Pass-Throughs) Consider a $400 million pass-through MBS that has just been created (so the 'seasoning' of the pass-through is equal to 0). The underlying pool of mortgages each has a maturity of 20 years and an annual mortgage coupon rate of 6%. The pass-through rate of the mortgage pool is 5%. Assuming a prepayment multiplier of 100 PSA what is the total amount of interest paid to the pass-through investors? (171.18)

3.(Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments? (181.09)

4.(Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments if the rate of prepayments increases to 200 PSA? (268.15)

5.(Principal-Only MBS and Interest-Only MBS) Suppose we construct principal-only (PO) and interest-only (IO) mortgage-backed securities (MBS) using the mortgage pass-through of the previous questions. Assume a prepayment multiplier of 100 PSA. What is the present value of the PO MBS if we use an annual risk-free rate of 4.5% to value the cash-flows?

Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

ALL I NEED IS THE ANSWER OF QUESTION 5.

Answer 1

5. The Calculation sheet is given below :

	Total	PO MBS PV
	Principal	0.00375
Month	Payment
1	0.932	0.93
2	1.003	1.00
3	1.073	1.06
4	1.143	1.13
5	1.212	1.19
6	1.281	1.25
7	1.350	1.31
8	1.418	1.38
9	1.485	1.44
10	1.552	1.49
11	1.618	1.55
12	1.683	1.61
13	1.748	1.66
14	1.812	1.72
15	1.875	1.77
16	1.937	1.82
17	1.999	1.88
18	2.059	1.92
19	2.119	1.97
20	2.178	2.02
21	2.235	2.07
22	2.292	2.11
23	2.348	2.15
24	2.402	2.20
25	2.456	2.24
26	2.508	2.28
27	2.559	2.31
28	2.610	2.35
29	2.658	2.39
30	2.706	2.42
31	2.692	2.40
32	2.678	2.38
33	2.664	2.35
34	2.650	2.33
35	2.637	2.31
36	2.623	2.29
37	2.609	2.27
38	2.596	2.25
39	2.582	2.23
40	2.569	2.21
41	2.555	2.19
42	2.542	2.17
43	2.529	2.15
44	2.516	2.13
45	2.502	2.11
46	2.489	2.10
47	2.477	2.08
48	2.464	2.06
49	2.451	2.04
50	2.438	2.02
51	2.425	2.00
52	2.413	1.99
53	2.400	1.97
54	2.388	1.95
55	2.375	1.93
56	2.363	1.92
57	2.351	1.90
58	2.338	1.88
59	2.326	1.87
60	2.314	1.85
61	2.302	1.83
62	2.290	1.82
63	2.278	1.80
64	2.266	1.78
65	2.254	1.77
66	2.243	1.75
67	2.231	1.74
68	2.219	1.72
69	2.208	1.71
70	2.196	1.69
71	2.185	1.67
72	2.173	1.66
73	2.162	1.65
74	2.151	1.63
75	2.140	1.62
76	2.128	1.60
77	2.117	1.59
78	2.106	1.57
79	2.095	1.56
80	2.084	1.54
81	2.073	1.53
82	2.063	1.52
83	2.052	1.50
84	2.041	1.49
85	2.030	1.48
86	2.020	1.46
87	2.009	1.45
88	1.999	1.44
89	1.988	1.43
90	1.978	1.41
91	1.968	1.40
92	1.957	1.39
93	1.947	1.37
94	1.937	1.36
95	1.927	1.35
96	1.917	1.34
97	1.907	1.33
98	1.897	1.31
99	1.887	1.30
100	1.877	1.29
101	1.867	1.28
102	1.858	1.27
103	1.848	1.26
104	1.838	1.25
105	1.829	1.23
106	1.819	1.22
107	1.810	1.21
108	1.800	1.20
109	1.791	1.19
110	1.781	1.18
111	1.772	1.17
112	1.763	1.16
113	1.753	1.15
114	1.744	1.14
115	1.735	1.13
116	1.726	1.12
117	1.717	1.11
118	1.708	1.10
119	1.699	1.09
120	1.690	1.08
121	1.681	1.07
122	1.673	1.06
123	1.664	1.05
124	1.655	1.04
125	1.646	1.03
126	1.638	1.02
127	1.629	1.01
128	1.621	1.00
129	1.612	0.99
130	1.604	0.99
131	1.595	0.98
132	1.587	0.97
133	1.579	0.96
134	1.570	0.95
135	1.562	0.94
136	1.554	0.93
137	1.546	0.93
138	1.538	0.92
139	1.530	0.91
140	1.522	0.90
141	1.514	0.89
142	1.506	0.88
143	1.498	0.88
144	1.490	0.87
145	1.482	0.86
146	1.474	0.85
147	1.467	0.85
148	1.459	0.84
149	1.451	0.83
150	1.444	0.82
151	1.436	0.82
152	1.429	0.81
153	1.421	0.80
154	1.414	0.79
155	1.406	0.79
156	1.399	0.78
157	1.392	0.77
158	1.384	0.77
159	1.377	0.76
160	1.370	0.75
161	1.362	0.75
162	1.355	0.74
163	1.348	0.73
164	1.341	0.73
165	1.334	0.72
166	1.327	0.71
167	1.320	0.71
168	1.313	0.70
169	1.306	0.69
170	1.299	0.69
171	1.293	0.68
172	1.286	0.68
173	1.279	0.67
174	1.272	0.66
175	1.266	0.66
176	1.259	0.65
177	1.252	0.65
178	1.246	0.64
179	1.239	0.63
180	1.233	0.63
181	1.226	0.62
182	1.220	0.62
183	1.213	0.61
184	1.207	0.61
185	1.200	0.60
186	1.194	0.60
187	1.188	0.59
188	1.182	0.58
189	1.175	0.58
190	1.169	0.57
191	1.163	0.57
192	1.157	0.56
193	1.151	0.56
194	1.145	0.55
195	1.139	0.55
196	1.133	0.54
197	1.127	0.54
198	1.121	0.53
199	1.115	0.53
200	1.109	0.52
201	1.103	0.52
202	1.097	0.52
203	1.091	0.51
204	1.086	0.51
205	1.080	0.50
206	1.074	0.50
207	1.069	0.49
208	1.063	0.49
209	1.057	0.48
210	1.052	0.48
211	1.046	0.47
212	1.041	0.47
213	1.035	0.47
214	1.030	0.46
215	1.024	0.46
216	1.019	0.45
217	1.013	0.45
218	1.008	0.45
219	1.003	0.44
220	0.997	0.44
221	0.992	0.43
222	0.987	0.43
223	0.982	0.43
224	0.976	0.42
225	0.971	0.42
226	0.966	0.41
227	0.961	0.41
228	0.956	0.41
229	0.951	0.40
230	0.946	0.40
231	0.941	0.40
232	0.936	0.39
233	0.931	0.39
234	0.926	0.39
235	0.921	0.38
236	0.916	0.38
237	0.911	0.38
238	0.906	0.37
239	0.902	0.37
240	0.897	0.37
	0.000	280.10

The discount rate to calculated PV of PO secuiy = 4.5%/12 = 0.00375

The PV of the PO securty is $280.10 million (see last column)