Question

A municipal water authority is considering the installation of a new water system. Two options are being considered. The first option is a steel pipeline with an installation cost of $225 million. Annual maintenance and pumping costs begin at $15 million and increase by $1.0 million per year. The second option is a gravity fed concrete canal with an installation cost of $400 million. Annual maintenance costs begin at $0.5 million and increase by $0.4 million per year. The water system is expected to last 100 years and the interest rate is 5% per year compounded yearly. What is the present worth of the first option and second option? Report your answer in millions of dollars.

Please answer full question, and include cashflow diagram if possible.

Answer 1

Option-1:Steel Pipeline			$ Million
Year	Cash Out Flows	DF @ 5%	Present Value
0	225	1.00000	225.00
1	15	0.95238	14.29
2	16	0.90703	14.51
3	17	0.86384	14.69
4	18	0.82270	14.81
5	19	0.78353	14.89
6	20	0.74622	14.92
7	21	0.71068	14.92
8	22	0.67684	14.89
9	23	0.64461	14.83
10	24	0.61391	14.73
11	25	0.58468	14.62
12	26	0.55684	14.48
13	27	0.53032	14.32
14	28	0.50507	14.14
15	29	0.48102	13.95
16	30	0.45811	13.74
17	31	0.43630	13.53
18	32	0.41552	13.30
19	33	0.39573	13.06
20	34	0.37689	12.81
21	35	0.35894	12.56
22	36	0.34185	12.31
23	37	0.32557	12.05
24	38	0.31007	11.78
25	39	0.29530	11.52
26	40	0.28124	11.25
27	41	0.26785	10.98
28	42	0.25509	10.71
29	43	0.24295	10.45
30	44	0.23138	10.18
31	45	0.22036	9.92
32	46	0.20987	9.65
33	47	0.19987	9.39
34	48	0.19035	9.14
35	49	0.18129	8.88
36	50	0.17266	8.63
37	51	0.16444	8.39
38	52	0.15661	8.14
39	53	0.14915	7.90
40	54	0.14205	7.67
41	55	0.13528	7.44
42	56	0.12884	7.22
43	57	0.12270	6.99
44	58	0.11686	6.78
45	59	0.11130	6.57
46	60	0.10600	6.36
47	61	0.10095	6.16
48	62	0.09614	5.96
49	63	0.09156	5.77
50	64	0.08720	5.58
51	65	0.08305	5.40
52	66	0.07910	5.22
53	67	0.07533	5.05
54	68	0.07174	4.88
55	69	0.06833	4.71
56	70	0.06507	4.56
57	71	0.06197	4.40
58	72	0.05902	4.25
59	73	0.05621	4.10
60	74	0.05354	3.96
61	75	0.05099	3.82
62	76	0.04856	3.69
63	77	0.04625	3.56
64	78	0.04404	3.44
65	79	0.04195	3.31
66	80	0.03995	3.20
67	81	0.03805	3.08
68	82	0.03623	2.97
69	83	0.03451	2.86
70	84	0.03287	2.76
71	85	0.03130	2.66
72	86	0.02981	2.56
73	87	0.02839	2.47
74	88	0.02704	2.38
75	89	0.02575	2.29
76	90	0.02453	2.21
77	91	0.02336	2.13
78	92	0.02225	2.05
79	93	0.02119	1.97
80	94	0.02018	1.90
81	95	0.01922	1.83
82	96	0.01830	1.76
83	97	0.01743	1.69
84	98	0.01660	1.63
85	99	0.01581	1.57
86	100	0.01506	1.51
87	101	0.01434	1.45
88	102	0.01366	1.39
89	103	0.01301	1.34
90	104	0.01239	1.29
91	105	0.01180	1.24
92	106	0.01124	1.19
93	107	0.01070	1.14
94	108	0.01019	1.10
95	109	0.00971	1.06
96	110	0.00924	1.02
97	111	0.00880	0.98
98	112	0.00838	0.94
99	113	0.00798	0.90
100	114	0.00760	0.87
		Present Value	904.47

Similarly calculate for Option-2: Not allowing me to post more than 65000 characters,It will come to $562.62