1. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.1 Engineering Economic Analysis 9th Edition Chapter 7 RATE OF RETURN ANALYSIS

2. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.2 If PW = A(P/A,i,n) Then (P/A,i,n) = PW/A Solve for (P/A,i,n) and look up interest in Compound Interest Tables Three Major Methods of Economic Analysis PW - Present Worth AW - Annual Worth IRR - Internal Rate of Return

3. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.3 Internal Rate of Return Lender’s Viewpoint The interest rate on the balance of a loan such that the unpaid loan balance equals zero when the final payment is made.

4. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.4 Reset the cash flow to determine the IRR. Internal Rate of Return Investor’s Viewpoint The interest rate earned on the unrecovered investment such that the unrecovered investment equals zero at the end of the life of the investment.

5. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.5 Calculating Rate of Return The IRR is the interest rate at which the benefits equal the costs. IRR = i* PW Benefit - PW Cost = 0 PW Benefit/PW Cost = 1 NPW = 0 EUAB - EUAC = 0 PW Benefit = PW Cost

6. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.6 3.8909% 3.9938% 4.1007% (P/A,i,5)Interest rate From Compound Interest Tables Example 7-1 Calculating IRR PWB/PWC = 1 1252.28(P/A,i,5)/5000 = 1 (P/A,i,5) = 5000/1252.28 = 3.9927

7. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.7 Example 7-2 EUAB - EUAC = 0 100 + 75(A/G,i,4) - 700(A/P, i, 4) = 0 Look up and iterate, book answer is 7% Calculating IRR

8. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.8 Example 7-3 The iterations may be graphed and the true IRR will be indicated at the point where the NPW curve = 0. Calculating IRR

9. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.9 Example 7-4a Period rate 1000 = 40(P/A,i,2) + 950(P/F,i,2) By lookup and interpolation i*  1.5% Nominal rate = 2 x 1.5% = 3% Effective rate = (1 + 1.5%) 2 - 1 = 3.02% 7-4a & 7bAn easier way > Calculating IRR - Bond

10. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.10 Rate of Return (ROR) Analysis Most frequently used measure of merit in industry More accurately called Internal Rate of Return (IRR)

11. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.11 Two-alternative situationDecision  ROR  MARR Choose higher-cost alternative  ROR  MARR Choose lower-cost alternative Calculating ROR Where two mutually exclusive alternatives will provide the same benefit, ROR is performed using an incremental rate of return-DROR-on the difference between the alternatives.

12. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.12 Example 7-5 MARR = 10% ROR on Alternatives with Equivalent Benefits

13. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.13 Examples 7- 6, 7 & 8 What happens to NPW when MARR is varied? Try 6, 30 & 35%. Criterion Is to Maximize Return Not ROR

14. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.14 Example 7-9 Choose the ranking so that the difference represents an increment of investment; goes from - to + over time. Fixed Input and Differing Outputs

15. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.15 Analysis Period Just as in PW and AW analysis, the analysis period must be considered: Useful life of the alternative equals the analysis period Alternatives have useful lives different from the analysis period The analysis period is infinite, n = ¥

16. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.16 Engineering Economic Analysis 9th Edition Chapter Appendix 7A Difficulties Solving for an Interest Rate

17. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.17 Multiple IRR Occurs when a cash flow produces more than one point at which NPW = 0 Example 7A-1

18. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.18 4, 2 or 04 3 or 13 2 or 02 11 00 Number of positive values of X Number of sign changes, m Cash Flow Rule of Signs May be converted to a polynomial Then, by Descartes’ rule

19. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.19 Cash Flow Rule of Signs Expands on This Notion There may be as many positive values of “i” as there are sign changes in the cash flow. Sign changes are counted when: + to - - to + A zero cash flow is ignored

20. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.20 Cash Flow Rule of Signs - Possibilities - 4, 3, 2, 1 or 0 4 3, 2, 1 or 0 3 2, 1 or 0 2 1 or 0 1 0 0 Number of positive values of “i” Number of sign changes, m

21. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.21 Zero Sign Changes Receiving a gift Giving your friend a loan and not being paid back In either case, no “i” can be computed.

22. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.22 One Sign Change The Normal Situation

23. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc.23 Two or More Sign Changes More than one IRR may exist Use an NPW plot to determine how many exist