Based on past experience, a chemicals firm estimates that the cost of new capacity additions obeys the lawf(y) =.0205y58where y is measured in tons per year and f(y) in millions of dollars. Demand isgrowing at the rate of 3,000 tons per year, and the accounting department recommends a rate of 12 percent per year for discounting future costs.a. Determine the optimal timing of plant additions and the optimal size of eachaddition.b. What is the cost of each addition?c. What is the present value of the cost of the next four additions? Assume anaddition has just been made for the purposes of your calculation. (Refer toAppendix 1–A for a discussion of cost discounting.)
Based on past experience, a chemicals firm estimates that the cost of new capacity additions obeys the law
f(y) =.0205y58
where y is measured in tons per year and f(y) in millions of dollars. Demand is
growing at the rate of 3,000 tons per year, and the accounting department recommends a rate of 12 percent per year for discounting future costs.
a. Determine the optimal timing of plant additions and the optimal size of each
addition.
b. What is the cost of each addition?
c. What is the present value of the cost of the next four additions? Assume an
addition has just been made for the purposes of your calculation. (Refer to
Appendix 1–A for a discussion of cost discounting.)
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