Question

The Cebu City plans to increase the capacity of her existing water transmission lines. Two plans are under consideration. Plan A requires the construction of a parallel pipeline, the flow being maintained by gravity. The initial cost is P151,582,222 and the life is 40 years, with an annual operating cost of P6,350,911 for the 1st 20 years and P14,898,843 for the next 20 years. Plan B requires the construction of a booster pumping station costing P100M with the life of 40 years. The pumping equipment cost an additional amount of P25M, it has a life of 20 years and a salvage value of P2M. The annual operating cost is P5M. Using the Present Value (PV) Method and an interest of 22% cpd. annually, what is the PV of Plan A?

Answer 1

initial cost is P151,582,222--------------------------------(I)

annual operating cost of P6,350,911 for the 1st 20 years and P14,898,843 for the next 20 years.

Interest rate (r) = 22%.

Formula-

Peset value of the Annuity =

A= Annuity payment

r= interest rate

n= number of year

Present value of the First 20 payments=

=>Present value of the First 20 payments= P28,326,753--------------------------(II)

value of the LAST 20 payments at the end of 20th year =

=> value of the LAST 20 payments at the end of 20th year=P 66,452,804

as we konw PV =

Hence Present value of the LAST 20 payments now =

=>Present value of the LAST 20 payments now=P 1,245,422------------------------(III)

Hence total pv of plan A (I+II+III)= P151,582,222+P28,326,753+P1,245,422=P 181,154,397

Alternative Way-

	A	B	A*B
Year	Cash flow	Present value factor@22%	present value(PV) Of the cash flow
0	151,582,222	1	151582222
1	6,350,911	0.8196721311	5205664.75
2	6,350,911	0.6718624026	4266938.32
3	6,350,911	0.5507068874	3497490.43
4	6,350,911	0.4513990880	2866795.43
5	6,350,911	0.3699992525	2349832.32
6	6,350,911	0.3032780758	1926092.07
7	6,350,911	0.2485885867	1578763.99
8	6,350,911	0.2037611366	1294068.84
9	6,350,911	0.1670173251	1060712.17
10	6,350,911	0.1368994468	869436.20
11	6,350,911	0.1122126613	712652.63
12	6,350,911	0.0919775913	584141.50
13	6,350,911	0.0753914682	478804.50
14	6,350,911	0.0617962854	392462.71
15	6,350,911	0.0506526930	321690.75
16	6,350,911	0.0415186008	263680.94
17	6,350,911	0.0340316400	216131.92
18	6,350,911	0.0278947869	177157.31
19	6,350,911	0.0228645794	145210.91
20	6,350,911	0.0187414585	119025.34
21	14,898,843	0.0153618513	228873.81
22	14,898,843	0.0125916814	187601.48
23	14,898,843	0.0103210503	153771.71
24	14,898,843	0.0084598773	126042.38
25	14,898,843	0.0069343256	103313.43
26	14,898,843	0.0056838735	84683.14
27	14,898,843	0.0046589127	69412.41
28	14,898,843	0.0038187809	56895.42
29	14,898,843	0.0031301483	46635.59
30	14,898,843	0.0025656953	38225.89
31	14,898,843	0.0021030289	31332.70
32	14,898,843	0.0017237942	25682.54
33	14,898,843	0.0014129461	21051.26
34	14,898,843	0.0011581525	17255.13
35	14,898,843	0.0009493053	14143.55
36	14,898,843	0.0007781191	11593.07
37	14,898,843	0.0006378026	9502.52
38	14,898,843	0.0005227890	7788.95
39	14,898,843	0.0004285156	6384.39
40	14,898,843	0.0003512423	5233.10
		Total PV	181154397

Note-Present value factor at year t = 1/(1.22)^t