Question

10 years ago a piece of 80KW machine set cost $240000. The cost index for this class of eqiupment 10 years ago was 150 and is now 200.The cost capacity factor is 0.7 changing the capacity to 120KW machine requires to add another machine which currently costs $270000. The total cost of the 120120kW unit is

Answer 1

The question involves calculating the current cost of upgrading an 80KW machine to 120KW by applying a cost index change and using a capacity factor to scale the cost non-linearly, and then adding the cost of an additional machine.

Step-by-step explanation:

The student is asking about the cost of upgrading a piece of equipment from 80KW to 120KW capacity, taking into account the cost index changes over time and the addition of another machine. To solve this problem, we apply the concept of cost index and capacity-based scaling to find the updated cost.

Step-by-Step Explanation

Calculate the equivalent cost of the old machine at the current cost index.

Estimate the cost of the new machine based on the capacity factor.

Add the cost of the additional machine necessary to reach 120KW.

The cost of the old machine in today's dollars can be found using the formula Current Cost = (Cost Index Now / Cost Index Then) × Past Cost. This calculation considers inflation or deflation in the cost of equipment over time.

Then, to account for the change in capacity, we use the capacity factor formula: New Capacity Cost = (New Capacity / Old Capacity)^Capacity Factor × Old Capacity Cost. The capacity factor accounts for the non-linear relationship between cost and capacity.

Finally, we add the cost of the additional machine needed to achieve the new capacity requirement. The total cost for the 120KW is the sum of the scaled cost of the old machine and the cost of the additional machine.