23-Chem-A5 Chemical Plant Design and Economics · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2013 — 04-Chem-A5 Chemical Plant Design and Economics. Three-hour, open-book exam; any non-communicating calculator permitted. The paper poses seven equally weighted essay questions and the candidate answers any five; only five are marked. All seven are answered below for completeness. These are conceptual design-and-economics questions — the solutions are written as organised prose (clarity and organisation are explicitly marked). The one numerical illustration (a Canadian Capital Cost Allowance schedule in Q2) is worked from stated assumptions.
Reference texts: M.S. Peters, K.D. Timmerhaus & R.E. West, Plant Design and Economics for Chemical Engineers (5th ed., McGraw-Hill) — the exam's named primary text (cost estimation, profitability, depreciation, optimisation); R. Turton et al., Analysis, Synthesis, and Design of Chemical Processes (4th ed., Prentice Hall) — process synthesis, safety, and economics; W.D. Seider et al., Product and Process Design Principles (3rd ed., Wiley) — separation-train synthesis and heuristics; supporting Canadian tax practice from the Canada Revenue Agency Capital Cost Allowance classes and the half-year rule.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
The two broad categories. Following Peters, Timmerhaus & West, the total product cost (TPC) of an operating plant is split into (A) manufacturing costs (also called operating or production costs) and (B) general expenses. Manufacturing cost is everything spent inside the plant fence to make the product; general expenses are the corporate-level costs of running the business that owns the plant.
(A) Manufacturing costs subdivide into three groups:
(B) General expenses comprise administrative costs (executive salaries, office maintenance, legal and accounting), distribution and marketing (selling) costs (sales offices, shipping containers, advertising, technical sales service), research and development, and financing (interest on borrowed capital). The sum of manufacturing cost and general expenses is the total product cost, and dividing by annual production gives the unit cost against which selling price is judged.
Total product cost versus marginal cost. Total product cost includes all costs — both the fixed charges that do not change with output and the variable costs that do. Marginal cost is a different quantity: it is the incremental cost of producing one additional unit of product, i.e. the change in total cost divided by the change in output, $MC = \dfrac{\Delta(\text{total cost})}{\Delta(\text{units})}$. Because the fixed charges (depreciation, taxes, insurance) are already committed and do not rise when one more unit is made, marginal cost contains essentially only the variable direct costs — extra raw material, extra utilities, and any output-dependent labour or supplies. Marginal cost is therefore normally well below the fully-loaded average total product cost.
When to use marginal cost. Marginal cost is the correct basis for short-run incremental decisions made when a plant already exists and has spare capacity: whether to accept an additional order at a reduced price, whether to increase output to satisfy incremental demand, the floor price below which incremental sales lose money, and make-or-buy or run-versus-shutdown choices. In such decisions the fixed charges are sunk and irrelevant to the increment, so comparing incremental revenue against marginal cost — not against average total cost — gives the profit-maximising answer. For long-run pricing, capacity, and investment decisions the full total product cost (which must recover the fixed charges) is the proper measure.
