NivaarExam PrepOfficial exam papers ↗

23-Chem-A5 Chemical Plant Design and Economics · December 2019

Question 3 of 6: Choosing Between Two Projects by the Internal-Rate-of-Return Method

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

Notes on this paper

National Exams / EGBC — December 2019 — 16-Chem-A5 Chemical Plant Design and Economics. Three-hour closed-book examination; one aid sheet (both sides) and an approved Sharp/Casio calculator are permitted. Six questions are printed and any five constitute a complete paper (each worth 20 marks); all six are solved below for completeness. The two calculation questions (Q3, Q4) are worked with explicit engineering-economy factors; the four discussion questions (Q1, Q2, Q5, Q6) are answered as structured lists with supporting description, as the paper directs.

Reference texts: M. S. Peters, K. D. Timmerhaus & R. E. West, Plant Design and Economics for Chemical Engineers (5th ed., McGraw-Hill) — profitability measures (rate of return, incremental analysis), straight-line depreciation, after-tax cash flow, and the anatomy of a process/economic study; R. Turton, R. C. Bailie, W. B. Whiting & J. A. Shaeiwitz, Analysis, Synthesis, and Design of Chemical Processes (4th ed., Prentice Hall) — the process flow diagram and its information content, equipment/economics; G. Towler & R. Sinnott, Chemical Engineering Design (Coulson & Richardson Vol. 6, 2nd ed.) — utilities, offsites and storage; O. Levenspiel, Chemical Reaction Engineering (3rd ed.) and H. S. Fogler, Elements of Chemical Reaction Engineering — reactor scale-up. Engineering-economy factors follow the standard notation $(A/P,i,n)$ and $(P/A,i,n)$; as the question specifies straight-line depreciation, that method is used throughout (rather than the Canadian CCA declining-balance system).

Question 3: Choosing Between Two Projects by the Internal-Rate-of-Return Method (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.

Given. Two mutually exclusive projects, 20-year life, straight-line depreciation to zero salvage (100% depreciable), income-tax rate $t=0.52$, before-tax MARR $=12.5\%$. Financial data:

QuantityInorganic Chemicals PlantTextile Fibers Expansion
Projected revenue $R$$\$33{,}700{,}000$$\$30{,}900{,}000$
Total capital investment $P$$\$52{,}500{,}000$$\$57{,}300{,}000$
Total annual cost $C$$\$25{,}100{,}000$$\$21{,}500{,}000$
Straight-line depreciation $D=P/20$$\$2{,}625{,}000$/yr$\$2{,}865{,}000$/yr

Find. The after-tax internal rate of return of each project and of the incremental investment, and hence which project the firm should fund.

02468101214161820-$4.80M (extra capital)+$0.509M/yr+$0.509M/yrIncremental after-tax cash flow: Textile expansion over Inorganic plantperiod (year)
Figure 2 — Incremental after-tax cash flow (Textile expansion minus Inorganic plant): an extra capital outlay of $\$4{,}800{,}000$ at year 0 buys an extra $\$508{,}800$ of after-tax income each year for 20 years. The rate that makes this stream break even is the incremental IRR.

Approach. Convert each project to a level after-tax annual cash flow, find each project’s IRR, then — because the projects are mutually exclusive and unequal in size — test the incremental investment against the (after-tax) MARR to decide which to fund.

  1. Convert the before-tax MARR to an after-tax basis. Because the projects are compared on after-tax cash flows, the hurdle rate must also be after tax. Using the standard approximation $i_{at}=i_{bt}(1-t)$, $i_{at}=0.125(1-0.52)=\boxed{6.0\%}$. (This is exactly the 6% after-tax hurdle rate that reappears in Q4, confirming the intended basis.)
  2. After-tax annual cash flow. With straight-line depreciation acting as a tax shield, the level after-tax cash flow is $\text{ATCF}=(R-C)(1-t)+tD$. For the inorganic plant, $\text{ATCF}_1=(33{,}700{,}000-25{,}100{,}000)(0.48)+0.52(2{,}625{,}000)$, i.e. $4{,}128{,}000+1{,}365{,}000=\boxed{\$5{,}493{,}000/\text{yr}}$.
  3. Same for the textile expansion. $\text{ATCF}_2=(30{,}900{,}000-21{,}500{,}000)(0.48)+0.52(2{,}865{,}000)=4{,}512{,}000+1{,}489{,}800=\boxed{\$6{,}001{,}800/\text{yr}}$.
  4. IRR of each project. Each project is a single outlay $P$ returning a 20-year annuity ATCF, so the IRR solves $(P/A,i,20)=P/\text{ATCF}$. For project 1, $(P/A,i,20)=52{,}500{,}000/5{,}493{,}000=9.558\Rightarrow i_1=8.36\%$; for project 2, $(P/A,i,20)=57{,}300{,}000/6{,}001{,}800=9.547\Rightarrow i_2=8.38\%$. Both exceed the 6% after-tax MARR, so each is acceptable on its own.
  5. Incremental analysis (the deciding test). Because the two projects are mutually exclusive and differ in size, the higher IRR alone does not decide the choice; we test whether the extra capital of the larger project earns at least the MARR. The increment (Textile − Inorganic) is $\Delta P=57{,}300{,}000-52{,}500{,}000=4{,}800{,}000$ and $\Delta\text{ATCF}=6{,}001{,}800-5{,}493{,}000=508{,}800$. Then $(P/A,i,20)=4{,}800{,}000/508{,}800=9.434\Rightarrow \boxed{i_{\Delta}=8.54\%}$.
  6. Decision. The incremental return of 8.54% exceeds the 6% after-tax MARR, so the extra $\$4{,}800{,}000$ invested in the larger project is justified. The firm should fund the Textile Fibers Plant Expansion. (A before-tax check gives the same ranking: both before-tax IRRs are about 15.5% and the incremental before-tax IRR is about 15.8%, well above the 12.5% before-tax MARR.)
QuantityInorganicTextileIncrement
After-tax annual cash flow$\$5{,}493{,}000$$\$6{,}001{,}800$$\$508{,}800$
After-tax IRR8.36%8.38%8.54%
vs. 6% after-tax MARRacceptacceptincrement justified

Recommendation: fund the Textile Fibers Plant Expansion — its additional investment earns a return above the firm’s hurdle rate.

Check: the before-tax MARR is converted to an after-tax basis with the common textbook approximation $i_{at}=i_{bt}(1-t)=6\%$, which is consistent with the 6% after-tax hurdle rate used in Q4 of the same paper. If an examiner instead intends the 12.5% to be applied directly to the after-tax cash flows, neither project clears the hurdle; the ranking (Textile > Inorganic by incremental IRR) is unchanged regardless of the basis chosen.