appendix 7a difficulties solving for the irr egr 403 asset allocation in technical decision making...
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Appendix 7ADifficulties Solving for
the IRR
EGR 403 Asset Allocation in Technical Decision Making
Dr. Phillip R. RosenkrantzIndustrial & Manufacturing Engineering Department
Cal Poly Pomona
Based on Newnan © 2009 by Oxford University Press, Inc.
EGR 403 - Cal Poly Pomona - SA10 Revised 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. 11, 12 - Depreciation & Taxes– Ch. 13 - Replacement Analysis
EGR 403 - Cal Poly Pomona - SA10 3
Multiple 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 series
Example 7A-1Cash Flow
-60
-40
-20
0
20
40
60
80
1 2 3 4 5 6
Year Cash Flow0 191 102 -503 -504 205 60
EGR 403 - Cal Poly Pomona - SA10 4
Example 7A-1This series of cash flows produces two solutions for IRR: 10.2% and 47.3%.
EGR 403 - Cal Poly Pomona - SA10 5
Cash Flow Rule of Signs• This happens when we convert the IRR
equation to a polynomial. • Then, by Descartes’ rule
4, 2 or 04
3 or 13
2 or 02
11
00
Number of positive values of X
Number of sign changes, m
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 (a.k.a. IRR)We will use the Modified Internal Rate of Return (MIRR) method
to adjust cash flows so that we have only one sign change.
• Combine cash flows in each period to get a single net Receipt, Ri, or net expense, Ei
• Find the present worth of the expenses with the external financing rate (rate for borrowing money)
• Find the future worth of the receipts with the external investing rate (rate for invested money).
• Find the MIRR which makes the present and future worths equivalent
• If the MIRR is less than the external investing rate, it is not desirable
Engineering Economic Analysis
Newnan Copyright © 2009 by Oxford
University Press, Inc.
Figure revisited ex07A-02.
FIGURE 7A-3 PW versus i for oil well.
FIGURE 7A-5 MIRR for the oil well.
FIGURE 7A-6 MIRR for oil well.