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25 March, 20:39

Suppose you operate a coal power plant and is considering upgrading the flue gas desulphurisation (FGD) facility (or "scrubbers") to reduce sulphur dioxide emissions. A contractor says their new system will cost $5000 per year to operate. Calculate, to the nearest dollar, the present value of the operational costs for the next four years. Assume a discount rate of 2%.

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  1. 25 March, 20:57
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    19039
  2. 25 March, 21:04
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    The present value is $19,039

    Explanation:

    The computation of the Present value is shown below

    = Present value of all yearly cash inflows after applying discount factor

    The discount factor should be computed by

    = 1 : (1 + rate) ^ years

    where,

    rate is 2%

    Year = 0,1,2,3,4 and so on

    Discount Factor:

    For Year 1 = 1 : 1.02^1 = 0.9804

    For Year 2 = 1 : 1.02^2 = 0.9612

    For Year 3 = 1 : 1.02^3 = 0.9423

    For Year 4 = 1 : 1.02^4 = 0.9238

    So, the calculation of a Present value of all yearly cash inflows are shown below

    = (Year 1 cash inflow * Present Factor of Year 1) + (Year 2 cash inflow * Present Factor of Year 2) + (Year 3 cash inflow * Present Factor of Year 3) + (Year 4 cash inflow * Present Factor of Year 4)

    = ($5,000 * 0.9804) + ($5,000 * 0.9612) + ($5,000 * 0.9423) + ($5,000 * 0.9238)

    = $4,901.96 + $4,805.84 + $4,711.61 + $4,619.23

    = $19,039

    We take the first four digits of the discount factor.
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