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23-Chem-A5 Chemical Plant Design and Economics · December 2014

Question 5 of 6: Project Risk and Profitability Assessment

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — December 2014 — 04-Chem-A5 Chemical Plant Design and Economics. Three-hour, closed-book exam; any non-communicating calculator permitted. Six equally weighted (20-mark) questions are posed and the candidate answers any five; only the first five are marked. All six are answered below for completeness. Question 1 is a conceptual process-design question answered with a flow sheet and organised prose; questions 2, 3 and 4 mix a short essay with numerical work (turnover-ratio pricing, sinking-fund depreciation, and simple/compound loan interest); question 5 combines profitability and risk discussion with a return-and-payout calculation; question 6 is a safety, optimization and environmental essay.

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 Ch. 6, interest and investment Ch. 7, depreciation Ch. 9, profitability and payout Ch. 10, optimum design Ch. 11, plant safety and loss prevention); R. Turton et al., Analysis, Synthesis, and Design of Chemical Processes (4th ed., Prentice Hall) — flowsheet synthesis and process development; T.M. Duncan & J.A. Reimer, Chemical Engineering Design and Analysis (Cambridge, 1998) — the source of the boiling-point data used in Question 1; supporting Canadian tax practice from the Canada Revenue Agency Capital Cost Allowance classes and the half-year rule, and environmental practice from the Canadian Environmental Protection Act (CEPA) and provincial air-quality regulation.

Question 5: Project Risk and Profitability Assessment (20 marks)

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.

(a) Two factors that seriously affect profitability

Product selling price and market demand. Revenue is price times quantity sold, so a swing in the market price of the product (or a shortfall in demand that forces the plant below its design capacity) hits the top line directly and is usually the single largest lever on profitability — a commodity chemical plant can move from profit to loss on a modest price fall alone. Raw-material and energy cost. For most chemical processes the feedstock and utilities dominate the operating cost; a rise in feed or energy price compresses the margin between sales and cost of production and can eliminate profit even when sales hold. (Both are why profitability is always tested with a sensitivity analysis against price and feedstock cost.)

(b) Two feasibility risk factors and their mitigation

Risk factorMitigation
Market / price risk — product price or demand falls below the forecast used in the feasibility study.Run sensitivity and break-even analyses, secure long-term off-take contracts, stage the capacity, and diversify products or markets.
Capital-cost / schedule-overrun risk — construction runs late or over budget, eroding the return.Base the decision on a detailed (Class 1) estimate with a contingency allowance, let firm EPC contracts, and use critical-path scheduling with change control.

(c) Standard return on investment and minimum payout period

Given. Fixed-capital investment $\text{FCI}=\$50\text{M}$; working capital $\text{WC}=20\%$ of the total investment; annual depreciation $d=5\%$ of FCI; annual profit margin (net profit) $=\$5\text{M}$.

Find. (i) the standard percent return on the total investment; (ii) the minimum payout period.

Approach. The working capital is defined as a fraction of the (as-yet-unknown) total investment, so first back out the total investment from the FCI, then form the return as profit over total investment. The payout period uses annual cash flow — net profit plus depreciation — against the fixed-capital investment.

  1. Total capital investment. With $\text{WC}=0.20\,\text{TCI}$ and $\text{FCI}=\text{TCI}-\text{WC}$, $$\text{FCI} = \text{TCI} - 0.20\,\text{TCI} = 0.80\,\text{TCI} \;\Rightarrow\; \text{TCI} = \frac{\text{FCI}}{0.80} = \frac{\$50\text{M}}{0.80} = \boxed{\$62.5\text{ million}}$$ (so the working capital is $0.20\times\$62.5\text{M}=\$12.5\text{M}$).
  2. (i) Standard percent return on total investment. The rate of return is net profit divided by the total capital at risk: $$\text{ROI} = \frac{\text{annual profit}}{\text{TCI}} = \frac{\$5\text{M}}{\$62.5\text{M}} = \boxed{8.0\%}$$
  3. Annual depreciation and cash flow. Depreciation is 5 % of the fixed capital, $d = 0.05\times\$50\text{M} = \$2.5\text{M}$, so the annual cash flow available to recover the plant is $$\text{CF} = \text{profit} + d = \$5\text{M} + \$2.5\text{M} = \$7.5\text{ million/yr}$$
  4. (ii) Minimum payout period. The payout (payback) period is the depreciable fixed-capital investment divided by the annual cash flow: $$n_\text{payout} = \frac{\text{FCI}}{\text{profit}+d} = \frac{\$50\text{M}}{\$7.5\text{M/yr}} = \boxed{6.67\text{ years}}$$
QuantityValue
Total capital investment (FCI/0.8)$\$62.5$ million
Working capital (20 % of TCI)$\$12.5$ million
Annual depreciation (5 % of FCI)$\$2.5$ million/yr
(i) Return on total investment$8.0\%$
(ii) Minimum payout period$6.67$ years
Check: the payout period adds depreciation back to profit because it measures the recovery of capital from cash flow, not from book profit — depreciation is a non-cash charge that stays in the business. Dividing FCI by profit alone would wrongly give $\$50\text{M}/\$5\text{M}=10$ years. Note the return is deliberately taken on the total investment (TCI) while the payout is taken on the fixed investment (FCI), per the P&T definitions.