Question

Nippon Steel's 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 $57,000 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 14% per year? The equivalent annual worth is determined to be $

Answer 1

The calculation involves determining the equivalent annual worth of increasing heating and cooling expenses at a rate of $57,000 per year, using an interest rate of 14% over the period from year 1 to year 12.

Step-by-step explanation:

The question pertains to calculating the equivalent annual worth of the escalating heating and cooling expenses at a facility, using an arithmetic gradient and interest rate to find the annual equivalent over the given period.

To find the equivalent annual worth, we use the arithmetic gradient series (G) formula in conjunction with present worth (P) and annual worth (A) formulas adjusted for an interest rate (i) of 14% and calculate over the years the expenses increase. Since the expenses are constant at $550,000 for the first two years, we need to calculate the present worth of this value for those years separately and then add to the present worth of the gradient series.

The gradient begins in year 2 and continues each year up to year 12, so the first step is to determine the present worth of the $57,000 gradient, and then find its equivalent annual worth, finally combining with the equivalent annual worth of the initial expenses to get the total annual worth across the period from year 1 to year 12.