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%.

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.

19039