Engineering Economic Analysis 9 th Edition Chapter 7

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

Three Major Methods of Economic Analysis • PW - Present Worth • AW - Annual Worth • IRR - Internal Rate of Return 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 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 2

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. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 3

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. Reset the cash flow to determine the IRR. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 4

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 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 5

Calculating IRR • PWB/PWC = 1 • 1252. 28(P/A, i, 5)/5000 = 1 • (P/A, i, 5) = 5000/1252. 28 = 3. 9927 Example 7 -1 From Compound Interest Tables Interest rate (P/A, i, 5) 7% 4. 100 8% 3. 993 9% 3. 890 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 6

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

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

Calculating IRR - Bond Example 7 -4 a 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% An easier way > 7 -4 a & 7 b Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 9

Rate of Return (ROR) Analysis • Most frequently used measure of merit in industry • More accurately called Internal Rate of Return (IRR) Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 0

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. Two-alternative situation Decision DROR ³ MARR Choose higher-cost alternative DROR < MARR Choose lower-cost alternative Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 1

ROR on Alternatives with Equivalent Benefits Example 7 -5 MARR = 10% Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 2

Criterion Is to Maximize Return Not ROR Examples 7 - 6, 7 & 8 What happens to NPW when MARR is varied? Try 6, 30 & 35%. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 3

Fixed Input and Differing Outputs Example 7 -9 Choose the ranking so that the difference represents an increment of investment; goes from to + over time. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 4

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 = ¥ Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 5

Engineering Economic Analysis 9 th Edition Chapter Appendix 7 A Difficulties Solving for an Interest Rate Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 6

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

Cash Flow Rule of Signs • May be converted to a polynomial • Then, by Descartes’ rule Number of sign changes, m 0 1 Number of positive values of X 0 1 2 3 2 or 0 3 or 1 4 4, 2 or 0 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 8

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 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 9

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

Zero Sign Changes • Receiving a gift • Giving your friend a loan and not being paid back In either case, no “i” can be computed. Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 2 1

One Sign Change The Normal Situation Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 2 2

Two or More Sign Changes • More than one IRR may exist • Use an NPW plot to determine how many exist Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 2 3