The capital investment cost for a switchgrass-fueled ethanol plant with a capacity of 250,000 gallons per year is $3.1 million. the cost-capacity factor for this particular plant technology is 0.59 for capacities ranging from 200,000 gallons per year to 500,000 gallons per year. what is the estimated capital investment for a similar ethanol plant with a capacity of 500,000 gallons per year?

Cost of a ethanol plant with a capacity of 500,000gallons per year:  $5,322,875.39

Explanation:

Cost-to-Capacity Formula:

q2=   500,000 capaicity for the estimated facility

q1=   200,000 capacity for the actual facility

c1= 3,100,000 cost of the actual facility

x = cost-capacity factor

C2 = 5,322,875.39 = expected cost for the second facility

Notes:

This will be like a cross multiply, but this method introduces a capital factor.

The factor represent if the industry is under economies of scale or diseconomies of scale. This means as the facility grows, the incremental cost decreases for each additional capacity.

When the factor is less than 1 we are assuming an economies of scale

When the factor is greater than one, then we assume a diseconomies of escale ( the cost for an additional capacity increases)

If the factor is 1, it assumes the cost are linear, which is rarely the case.

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