The federal government proposes to construct a multipurpose water project to pro
ID: 2739674 • Letter: T
Question
The federal government proposes to construct a multipurpose water project to provide water for irrigation and municipal use. In addition, there are flood control and recreation benefits. The annual benefits are per year for each year in the decades indicated are given below. The operation and maintenance cost is $15,000 per year. Assume a 50-year analysis period with no net project salvage value. If an interest rate of 6% is used, and a benefit-cost ratio of unity, what capital expenditure can be justified to build the water project now?
Interest Factor Calculator
Decade Annual Benefit 1 $60,000 2 $64,000 3 $66,000 4 $66,000 5 $70,000Explanation / Answer
PV of operation and maintenance cost (PV of out flow) = Annual maintenance cost * PVAFi=0.06, n 50
= $15,000 * 15.761861
= $2,36,427.92
PV of benefits (PV of inflow) = Annual benefit * PVAFi=0.06, n = 50
Year
Cash flow
PV of annuity factor @ 6%
PV cash flows
1-10
$ 60,000.00
7.360087
$ 441,605.22
11-20
$ 64,000.00
4.109800
$ 263,027.20
21-30
$ 66,000.00
2.294900
$ 151,463.40
31-40
$ 66,000.00
1.281466
$ 84,576.76
41-50
$ 70,000.00
0.715561
$ 50,089.27
PV of benefits
$ 990,761.85
Less: PV of Operation and maintenance exp.
$ 236,427.92
Net present value
$ 754,333.93*
Therefore, the capital expenditure can be justified to build the water project is $ 754,337 (rounded)
Year
Cash flow
PV of annuity factor @ 6%
PV cash flows
1-10
$ 60,000.00
7.360087
$ 441,605.22
11-20
$ 64,000.00
4.109800
$ 263,027.20
21-30
$ 66,000.00
2.294900
$ 151,463.40
31-40
$ 66,000.00
1.281466
$ 84,576.76
41-50
$ 70,000.00
0.715561
$ 50,089.27
PV of benefits
$ 990,761.85
Less: PV of Operation and maintenance exp.
$ 236,427.92
Net present value
$ 754,333.93*
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