NivaarExam PrepOfficial exam papers ↗

23-Chem-A5 Chemical Plant Design and Economics · Undated paper

Question 4 of 6: Depreciation, Tax and After-Tax Cash Flow — Straight-Line vs MACRS

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

Notes on this paper

National Exams / EGBC — May 2019 — 16-Chem-A5 Chemical Plant Design and Economics. Three-hour closed-book examination; one aid sheet (both sides) and an approved 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. Three questions carry numbers (Q1 route economics, Q3 production cost, Q4 depreciation); the other three (Q2 supercritical extraction, Q5 the design hierarchy intrinsic to a chemical process, Q6 VOC-abatement P&ID) are answered as structured description with a supporting diagram where the paper asks for one.

Reference texts: M. S. Peters, K. D. Timmerhaus & R. E. West, Plant Design and Economics for Chemical Engineers (5th ed., McGraw-Hill) — total-product-cost anatomy, straight-line depreciation, after-tax cash flow, profitability; R. Turton, R. C. Bailie, W. B. Whiting & J. A. Shaeiwitz, Analysis, Synthesis, and Design of Chemical Processes (4th ed., Prentice Hall) — the economic-potential screen, reaction-path selection and the process flow diagram; J. M. Douglas, Conceptual Design of Chemical Processes (McGraw-Hill) — the level-2 economic-potential hierarchy and the balanced vinyl-chloride process; G. Towler & R. Sinnott, Chemical Engineering Design (Coulson & Richardson Vol. 6, 2nd ed.) — utilities, VOC control and product recovery; R. H. Perry & D. W. Green, Perry’s Chemical Engineers’ Handbook (9th ed.) — supercritical-fluid extraction. Depreciation is worked in the U.S. MACRS/straight-line framework the question specifies; the Canadian CCA declining-balance analogue is noted where relevant.

Question 4: Depreciation, Tax and After-Tax Cash Flow — Straight-Line vs MACRS (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. $\text{FCI}=\$100\text{M}$; gross profit $G=\$50\text{M/yr}$; tax rate $t=0.35$; full-rate operation years 1–10; zero salvage.

Find. Annual depreciation $D$, income tax and after-tax cash flow (ATCF) for 10 years under (a) straight-line and (b) 7-year MACRS.

Approach. Depreciation is a non-cash charge that shields income from tax; taxable income $=G-D$, tax $=t(G-D)$, and after-tax cash flow $\text{ATCF}=G-\text{tax}=(G-D)(1-t)+D$. Only the depreciation schedule differs between the two methods.

  1. (a) Straight-line depreciation. $D=\dfrac{\$100\text{M}}{10}=\$10\text{M/yr}$ every year. Then taxable income $=50-10=\$40\text{M}$, tax $=0.35(40)=\boxed{\$14\text{M/yr}}$ and $\text{ATCF}=50-14=\boxed{\$36\text{M/yr}}$ — identical for all ten years (10-yr totals: $D=\$100\text{M}$, tax $=\$140\text{M}$, ATCF $=\$360\text{M}$).
  2. (b) MACRS depreciation factors. The 7-year property class (200% declining balance with the half-year convention) writes off the asset over eight tax years at 14.29 / 24.49 / 17.49 / 12.49 / 8.93 / 8.92 / 8.93 / 4.46% (summing to 100%). $D_y=(\text{rate}_y)\times\$100\text{M}$.
  3. Year-by-year MACRS income statement. Applying tax $=0.35(G-D_y)$ and $\text{ATCF}_y=50-\text{tax}_y$ gives the schedule in the table below; year 1 shields the most income ($D_1=\$14.29\text{M}$, tax $=\boxed{\$12.50\text{M}}$, ATCF $=\$37.50\text{M}$), while years 9–10 are fully depreciated ($D=0$, tax $=\$17.5\text{M}$, ATCF $=\$32.5\text{M}$).
  4. Compare the two methods. Over the full 10 years the totals are identical — depreciation $\$100\text{M}$, tax $\$140\text{M}$, ATCF $\$360\text{M}$ — because the same $100M is written off either way. MACRS merely front-loads the depreciation, deferring tax into later years and thereby raising the present value of the after-tax cash flow.
  5. Timing note. Because tax is paid on the previous year’s income, the first payment falls in year 2 (year 1 pays nothing) and the last in year 11; this shifts every tax outflow one year later without changing the undiscounted totals, again favouring the taxpayer on a present-value basis.

MACRS 7-year schedule (all figures in $millions):

YearMACRS rateDepreciation $D$ ($M)Taxable $G-D$ ($M)Tax @35% ($M)ATCF ($M)
114.29%14.2935.7112.5037.50
224.49%24.4925.518.9341.07
317.49%17.4932.5111.3838.62
412.49%12.4937.5113.1336.87
58.93%8.9341.0714.3735.63
68.92%8.9241.0814.3835.62
78.93%8.9341.0714.3735.63
84.46%4.4645.5415.9434.06
90%0.0050.0017.5032.50
100%0.0050.0017.5032.50
Total100%100400140360
Quantity (10-yr)Straight-lineMACRS 7-yr
Total depreciation$100M$100M
Total income tax$140M$140M
Total after-tax cash flow$360M$360M
Year-1 depreciation$10M$14.29M
Year-1 tax / ATCF$14M / $36M$12.50M / $37.50M
Present value of ATCFlowerhigher (tax deferred)
Check

The MACRS rates are the standard IRS 7-year table (200% DB, half-year convention); depreciation therefore spans eight tax years even though the class life is seven. Under Canadian rules the analogue is the Capital Cost Allowance: a Class 43 processing asset at a 30% declining-balance rate with the half-year rule in year 1, which — unlike MACRS — never fully depreciates the asset (an asymptotic tail).