Construction cost of a sewage treatment plant shows "economies of scale,' where cost increases as the capacity of the plant increases, but at a decreasing rate; that is, the cost curve is concave and can be expressed in the form
C = 1,300,000 Q0.65
where Q is the capacity of the plant in million gallons per day and C is the construction cost (in dollars).
Demand for sewage treatment for a city is projected to increase linearly from zero today to 20 MOD 20 years from now (1 MGD per year increase).
Under the assumption that either one or four plant expansions will occur (20 MGD capacity now or four expansions of 5 MGD each, with the first now), determine the breakeven interest rate at which the cost of one expansion exactly equals the cost of four expansions. Plot the breakeven chart. If the city sets the MARR at 6%, how many expansions (one or four) should occur?
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