Question

Nippon Steels expenses for heating and cooling a large manufacturing facility are expected to increase according to an arithmetic gradient beginning in year 2. If the cost is $550,000 this year (year 0) and will be $550,000 again in year 1, but then it is estimated to increase by $55,000 each year through year 12, what is the equivalent annual worth in years 1 to 12 of these energy costs at an interest rate of 9% per year? : The equivalent annual worth is determined to be $

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Answer #1
9.00%
NPV@ 0.09
Year Cash flow PV factor PV-Cash flow
0      550,000.00 1.000      550,000.00
1      550,000.00 0.917      504,587.16
2      605,000.00 0.842      509,216.40
3      660,000.00 0.772      509,641.10
4      715,000.00 0.708      506,524.03
5      770,000.00 0.650      500,447.17
6      825,000.00 0.596      491,920.54
7      880,000.00 0.547      481,390.14
8      935,000.00 0.502      469,244.97
9      990,000.00 0.460      455,823.50
10 1,045,000.00 0.422      441,419.29
11 1,100,000.00 0.388      426,286.14
12 1,155,000.00 0.356      410,642.61
Total PV 6,257,143.03
Annual worth = PV*((i*(1+i)^n)/(((1+i)^n)-1))
Annual worth = 6257143.03*((9%*(1+9%)^12)/(((1+9%)^12)-1))
Annual worth =      873,814.14
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