Question

Confusing in how to calculate the Cash flow PV

Exam Example NPV & DCFROR calculations Example A process is projected to have a total depreciable capital investment of $90 million, to spent in equal amounts over three years (2007 -2021) The st art-up capital is expected to be $40 million, invested just prior to start-up and recovered at the end of the project life, in year 15. The re annum, are expected to be: venue from production, and associated production costs, in $ million per Costs (MS/a) Revenue (MS/a) Year 4 Year 5 Year 6 Years 7-15 75 113 150 150 78 100 100 Depreciation is calculated on a non-linear basis - shown on the next slide. Taxable income is [Sales revenue less Costs less Depreciation allowance] Tax is 40% of Taxable income Annual cash flow is: [Sales revenue - Costs Tax- Capital invested] The Net Present Value (assuming i = 15%) is to be calculated. The DCFROR over the project life is to be calculated. Seider, Seader & Lewin, Product and Process Design Principles, 2003, Ch 17 (Examples 17.14 &17.29) Seider, Seader, Lewin & Widagdo, 2010, Product and Process Design Principles, Ch. 23.7 (example 23.29) Process Design and Simulation 2019 6-114 Example - NPV & DCFROR Cash flows Example (All cash flows in MS/a) Cash CashCu Taxable Tax Invested Working Depreci- Costs Sales Capita Capital ation Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 30-30.00 30.00 30 -26.09 -56.09 70 52.93 -109.02 19.2 12.62 -96.39 6.22.48 32.52 18.59 77.80 28.8 17.28 10.37 0.37 00 150 32.72 1309 36.91 18.35 -59.45 100 150 39.63 15.85 34.15 14.76 44.68 150 39.63 15.85 34.15 12.84 -31.85 5.18 -100 1501-4482 -17.93 32.07 -10.48 --21.36 12.83 5.42 100 150 20 20 8.53 7.42 6.45 30 30 30 30 4.88 11.51 100 150 50 50 2018 6.64 20 70 9.8921.41 2021 * Depreciation as given by Seider et al., 2010 г-E-D-L, Y: 0 OF # To calculate DCFROR, similar calculations are carried out, iteratively, until the NPV (Cumulative PV) is equal to 0 after 15 years. (in this case i-18.5%) Seider, Seader, Lewin & Widagdo, 2010, Product and Process Design Principles, Ch. 23.7 (example 23.29) Process Design and Simulation 2019 6-115

Answer 1

Cut 30 200 -30 2 30 -26-09 0.8636 1.IS) 2,00.9-70 - S2.93 201o 19-20 12収 2011 3252 sy 2o12 I g.35 36.91 /s)s 0-412 2o13 14-а; 34.1S 04323 2-11 34 IS 12. 84 0.379 2lS3201 0-4-8 IIS 0. 3269 -1s) 2016 8.S3 0 2843 2013 4.42 0 2412 2019 6.45 -1s) 0. 2143 2019 3 0 1 IS 2o2o 3 0 4 88 202 9.89

Discounting factor for 2007 = 1. Since this is 0th year and cash flows are already at present value.

But from the year 2008 onwards cash flows are at different years and by multiplying them with respective year's discounting factor, we bring them also at 0th year or at present value at 2007. And thus the result will be cashflow PV.

Discounting factor from year 2008 onwards....

1÷(1.15). , 1÷(1.15)^2. , 1÷(1.15)^3. , 1÷(1.15)^4 and so on........