Chapter 7A Difficulties Solving for the IRR Click here for Streaming Audio To Accompany Presentation (optional)EGR 403 - The Big PictureMultiple IRRExample 7A-1Cash Flow Rule of SignsCash Flow Rule of Signs Expands on This NotionZero Sign ChangesSolving for RORExample 7A-2: Solving for a more realistic IRRChapter 7ADifficulties Solving for the IRR Click here for Streaming Audio To Accompany Presentation (optional)EGR 403 Capital Allocation TheoryDr. Phillip R. RosenkrantzIndustrial & Manufacturing Engineering DepartmentCal Poly PomonaEGR 403 - Cal Poly Pomona - SA10 2EGR 403 - The Big Picture•Framework: Accounting & Breakeven Analysis•“Time-value of money” concepts - Ch. 3, 4•Analysis methods–Ch. 5 - Present Worth–Ch. 6 - Annual Worth–Ch. 7, 7a, 8 - Rate of Return (incremental analysis)–Ch. 9 - Benefit Cost Ratio & other techniques•Refining the analysis–Ch. 10, 11 - Depreciation & Taxes–Ch. 12 - Replacement AnalysisEGR 403 - Cal Poly Pomona - SA10 3Multiple IRROccurs when a cash flow produces more than one point at which NPW = 0. This happens when there is more than one sign change in the cash flow seriesExample 7A-1Cash Flow-60-40-200204060801 2 3 4 5 6Year Cash Flow0 191 102 -503 -504 205 60EGR 403 - Cal Poly Pomona - SA10 4Example 7A-1This series of cash flows produces two solutions for IRR: 10.2% and 47.3%.EGR 403 - Cal Poly Pomona - SA10 5Cash Flow Rule of Signs•This happens when we convert the IRR equation to a polynomial. •Then, by Descartes’ rule4, 2 or 043 or 132 or 021100Number of positive values of XNumber of sign changes, mEGR 403 - Cal Poly Pomona - SA10 6Cash 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.EGR 403 - Cal Poly Pomona - SA10 7Zero Sign Changes•Receiving a gift. •Giving your friend a loan and not being paid back.In either case no “i” can be computed.EGR 403 - Cal Poly Pomona - SA10 8Solving for ROR•We use an “external rate of return” to adjust cash flows so that we have only one sign change. •External interest rate is almost like a money market rate and is different than the MARR.•Move the least amount of positive cash flow forward that you can to eliminate all but one sign change. (Note: Cannot move negatives cash flows forward)EGR 403 - Cal Poly Pomona - SA10 9Example 7A-2: Solving for a more realistic IRRYear Cash Flow External Interest Rate = 6% Revised0 19 Move two years: 19 (F/P, 6%, 2) = 21.40 01 10 Move one year: 10 (F/P, 6%, 1) = 10.60 02 -50 21.4 + 10.6 = 32 -183 -50 -504 20 205 60 60IRR = 8.4%• We have two sign changes. • The easiest way to reduce that to one is by moving the cash flow in years 0 and 1 to year 2.• Use the “external interest rate” to move the two cash flows ahead• 8.4% is a more realistic IRR for this project than 10.2% or
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