Question

Three years ago, your company purchased a 10,000 cubic foot centrifugal blower for $135,000, when the cost index was 584. Now your company wants to purchase a 12,500 cubic foot centrifugal blower. The cost index now is 617. If the power-sizing exponent is 0.59, estimate how much your company will spend on the new centrifugal blower.

Answer 1

The % change in the cost index = (617 - 584)/584 * 100 = 33/584 * 100 = 5.65%

So, the price for the 10,000 cubic foot centrifugal blower would also increase by 5.65% at present. So, the price for a 10,000 cubic foot centrifugal blower at present would be = $135,000 + 5.65% of $135,000 = $135,000 + $7627.5 = $142,627.5

Now, let us calculate the cost of a a 12,500 cubic foot centrifugal blower at present using the following power sizing formula:

C_A/C_B = (S_A/S_B)^x

In which,

C_A = Cost of equiment A

C_B = Cost of equiment B

S_A = Size of equiment A

S_B = Size of equipment B

^x = Power sizing exponent

Putting the values, we get:

C_A/C_B = (S_A/S_B)^x

or, 142,627.5/C_B = (10,000/12,500)^0.59

or, C_B = 142,627.5/(10,000/12,500)^0.59

or, C_B = 142,627.5/(0.8)^0.59

or, C_B = 142,627.5/0.8766 = $162,705.34

So, the cost of a 12,500 cubic foot centrifugal blower at present would be = $162,705.34.