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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 & Manufacturing Engineering Department Cal Poly Pomona. EGR 403 - The Big Picture.

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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


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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


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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


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Example 7A-1

This series of cash flows produces two solutions for IRR: 10.2% and 47.3%.

EGR 403 - Cal Poly Pomona - SA10


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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


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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


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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


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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


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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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