1. 1 Chapter 3 Appendix B Development of Objective Function

2. 2 Chapter 3 Optimize L/D for a Pressure Vessel

3. 3 Chapter 3 erroneous assumptions (1)dished ends (not flat) A e = 2(1.16 D 2 ) = 2.32 D 2 (2)thickness is a function of D (not constant) (3)fabrication costs $ ends > $ sides (1.5x)

4. 4 Chapter 3

5. 5 capacitypressure psi gal100250400 25001.72.42.9 250002.22.94.3

6. 6 Chapter 3

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10. 10 Chapter 3

11. 11 Chapter 3

12. 12 Chapter 3

13. 13 Chapter 3

14. 14 Chapter 3

15. 15 Chapter 3

16. 16 Chapter 3

17. 17 Chapter 3

18. 18 Chapter 3

19. 19 Chapter 3

20. 20 Chapter 3

21. 21 Chapter 3

22. 22 Chapter 3 Insulation example -- fixed vs. operating costs (F i ) annualization factor (repayment multiplier) for F i = constant = F (cash flow)

23. 23 Chapter 3 There are several disadvantages to using IRR in optimization (requires iterative solution). NPV can be shown to be equivalent to using an annualization factor (series present worth factor). - Steam Generator Example

24. 24 Chapter 3

25. 25 Chapter 3 Steam Generator Flow Diagram

26. 26 Chapter 3

27. 27 Chapter 3 In the previous section we only briefly mentioned the financial assumptions used in profitability analysis. Any detailed analysis of a project requires specifying the following parameters: (1)initial investment (2)future cash flows (3)salvage value (4)economic life (5)depreciation (6)depletion (7)investment tax credit (8)taxes (9)inflation (10)debt/equity ratio

28. 28 REVENUE OPERATIONS SALES INCOME MANUFACTURING (CASH OPERATING) EXPENSES OPERATING INCOME (PROFIT) NET INCOME BEFORE TAXES FEDERAL INCOME TAXES NET INCOME AFTER TAXES CASH FLOW SALVAGE VALUE DEPRECIATION Figure 3.3 Computation of Cash Flow Chapter 3

29. 29 Chapter 3

30. 30 Chapter 3

31. 31 Chapter 3

32. 32 Chapter 3

33. 33 Chapter 3

34. 34 Chapter 3

35. 35 Chapter 3

36. 36 Chapter 3

37. 37 Insulation Thickness x (cm) Insulation Cost ($) Value of fuel saved ($/year) Payback period (years) Return on investment (% per year) Net Present value ($) Internal rate of return (%) 12,1355,2811.277916,013247 24,2708,1821.646123,847191 36,40510,0202.015028,028155 48,54011,2882.384230,250130 510,67512,2152.75 3631,301112 612,81012,9843.10 3231,80998 714,94513,4803.482931,37886 A summary of the calculations is Chapter 3