Question

Harris County is planning to construct a Dam some tens of miles away from the Houston Metropolis Recreation center to facilitate Power Generation and fishing in the El Santos River Basin. The first cost for the Dam will amount to $7,500,000. Annual maintenance and repairs will amount to $25,000 for the first six years, to $30,000 for each year in the next eight years, and to $35,000 per year for the next six years. At the end of the 20th year, $24,000 is estimated to be deposited into Harris county account as tax credits earned for its environmental compliance in the construction and operation of the Dam. In addition a major overhaul costing $550,000 will be required at the end of the seventh year. Use an interest rate of 10% and :

Determine the engineering economy symbols and their corresponding values.

Construct the cash flow diagram

Calculate the Capital Recovery for the project

Determine the total Annual Worth for the Project

What is the Present worth of this project

Answer 1

Cost is indicated as positive value and tax credit as negative value.

Cash flow diagram is as follows: All values are in '000

Cash Inflow	7500          25             25               25               25             25               25                580               30               30               30              30              30               30              30               35                35             35               35                35              24
Period		0               1                2                 3                 4                 5                6                 7                 8                9                 10               11              12              13               14               15               16              17               18               19             20
Cash Outflow	7500          25             25               25               25             25               25                580               30               30               30              30              30               30              30               35                35             35               35                35            35

Capital Recovery Factor for the initial capital investment of 7.5 Million $ @ 10% Interest Rate

= 7,500,000 *{(0.1*(1+0.1)^20)/((1+0.1)^20)-1}

= 7,500,000 *0.11746

= 880,947.2 $

Year	Description	Amount	PV Factor	PV Amount
0	Initial Investment	7,500,000	1.0000	7,500,000
1	Annual Maintenance & Repairs-1	25,000	0.9091	22,727
2	Annual Maintenance & Repairs-1	25,000	0.8264	20,661
3	Annual Maintenance & Repairs-1	25,000	0.7513	18,783
4	Annual Maintenance & Repairs-1	25,000	0.6830	17,075
5	Annual Maintenance & Repairs-1	25,000	0.6209	15,523
6	Annual Maintenance & Repairs-1	25,000	0.5645	14,112
7	Annual Maintenance & Repairs-2	30,000	0.5132	15,395
7	Major Overhaul Costing	550,000	0.5132	282,237
8	Annual Maintenance & Repairs-2	30,000	0.4665	13,995
9	Annual Maintenance & Repairs-2	30,000	0.4241	12,723
10	Annual Maintenance & Repairs-2	30,000	0.3855	11,566
11	Annual Maintenance & Repairs-2	30,000	0.3505	10,515
12	Annual Maintenance & Repairs-2	30,000	0.3186	9,559
13	Annual Maintenance & Repairs-2	30,000	0.2897	8,690
14	Annual Maintenance & Repairs-2	30,000	0.2633	7,900
15	Annual Maintenance & Repairs-3	35,000	0.2394	8,379
16	Annual Maintenance & Repairs-3	35,000	0.2176	7,617
17	Annual Maintenance & Repairs-3	35,000	0.1978	6,925
18	Annual Maintenance & Repairs-3	35,000	0.1799	6,295
19	Annual Maintenance & Repairs-3	35,000	0.1635	5,723
20	Annual Maintenance & Repairs-3	35,000	0.1486	5,203
20	Tax Credit Earned	(24,000)	0.1486	(3,567)
	Present Value Worth of Project			8,018,035

Present Value Worth of Project = 8,018,035 $

Average Annual Worth of Project = 8,018,035 *{(0.1*(1+0.1)^20)/((1+0.1)^20)-1}

= 941,795.3 $