Appendix 7A Difficulties Solving for the IRR EGR 403 Asset Allocation in Technical Decision Making...
-
date post
22-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of Appendix 7A Difficulties Solving for the IRR EGR 403 Asset Allocation in Technical Decision Making...
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.