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# Chapter 7A Difficulties Solving for the IRR Click here for Streaming Audio To Accompany Presentation (optional)

Chapter 7A Difficulties Solving for the IRR Click here for Streaming Audio To Accompany Presentation (optional). EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz Industrial &amp; Manufacturing Engineering Department Cal Poly Pomona. EGR 403 - The Big Picture.

## Chapter 7A Difficulties Solving for the IRR Click here for Streaming Audio To Accompany Presentation (optional)

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1. Chapter 7ADifficulties Solving for the IRRClick here for Streaming Audio To Accompany Presentation (optional) EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz Industrial & Manufacturing Engineering Department Cal Poly Pomona

2. EGR 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 Analysis EGR 403 - Cal Poly Pomona - SA10

3. Multiple IRR Occurs 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 series Example 7A-1 EGR 403 - Cal Poly Pomona - SA10

4. Example 7A-1 This series of cash flows produces two solutions for IRR: 10.2% and 47.3%. EGR 403 - Cal Poly Pomona - SA10

5. Number of sign changes, m Number of positive values of X 0 0 1 1 2 2 or 0 3 3 or 1 4 4, 2 or 0 Cash Flow Rule of Signs • This happens when we convert the IRR equation to a polynomial. • Then, by Descartes’ rule EGR 403 - Cal Poly Pomona - SA10

6. 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. EGR 403 - Cal Poly Pomona - SA10

7. Zero 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

8. Solving 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

9. Example 7A-2: Solving for a more realistic IRR • 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 47.3% EGR 403 - Cal Poly Pomona - SA10

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