69:
Firstly, IRR is sometimes misapplied, under an assumption that interim positive cash flows are reinvested elsewhere in a different project at the same rate of return offered by the project that generated them. This is usually an unrealistic scenario and a more likely situation is that the funds will
686:
Like the internal rate of return, the modified internal rate of return is not valid for ranking projects of different sizes, because a larger project with a smaller modified internal rate of return may have a higher net present value. However, there exist variants of the modified internal rate of
198:
The formula adds up the negative cash flows after discounting them to time zero using the external cost of capital, adds up the positive cash flows including the proceeds of reinvestment at the external reinvestment rate to the final period, and then works out what rate of return would cause the
169:
417:
521:
608:
91:
672:
70:
be reinvested at a rate closer to the firm's cost of capital. The IRR therefore often gives an unduly optimistic picture of the projects under study. Generally for comparing projects more fairly, the
426:
To calculate the MIRR, we will assume a finance rate of 10% and a reinvestment rate of 12%. First, we calculate the present value of the negative cash flows (discounted at the finance rate):
278:
432:
77:
Secondly, more than one IRR can be found for projects with alternating positive and negative cash flows, which leads to confusion and ambiguity. MIRR finds only one value.
533:
199:
magnitude of the discounted negative cash flows at time zero to be equivalent to the future value of the positive cash flows at the final time period.
164:{\displaystyle {\text{MIRR}}={\sqrt{\frac {FV({\text{positive cash flows, reinvestment rate}})}{-PV({\text{negative cash flows, finance rate}})}}}-1}
620:
71:
795:
Hajdasiński, Mirosław M. (January 1995). "Remarks in the
Context of 'The Case for a Generalized Net Present Value Formula'".
835:
730:
Beaves, Robert G. (January 1988). "Net
Present Value and Rate of Return: Implicit and Explicit Reinvestment Assumptions".
768:
Shull, David M. (January 1992). "Efficient
Capital Project Selection Through a Yield-Based Capital Budgeting Technique".
845:
412:{\displaystyle {\text{NPV}}=-1000+{\frac {-4000}{(1+r)^{1}}}+{\frac {5000}{(1+r)^{2}}}+{\frac {2000}{(1+r)^{3}}}=0}
423:
In this case, the answer is 25.48% (with this conventional pattern of cash flows, the project has a unique IRR).
63:
51:
516:{\displaystyle PV({\text{negative cash flows, finance rate}})=-1000+{\frac {-4000}{(1+10\%)^{1}}}=-4636.36}
812:
527:
Second, we calculate the future value of the positive cash flows (reinvested at the reinvestment rate):
179:
is the number of equal periods at the end of which the cash flows occur (not the number of cash flows),
603:{\displaystyle FV({\text{positive cash flows, reinvestment rate}})=5000\cdot (1+12\%)^{1}+2000=7600}
840:
703:
Lin, Steven A. Y. (January 1976). "The
Modified Internal Rate of Return and Investment Criterion".
50:
to rank alternative investments of equal size. As the name implies, MIRR is a modification of the
47:
804:
777:
739:
712:
206:
829:
184:
209:, have inbuilt functions to calculate the MIRR. In Microsoft Excel this function is
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816:
202:
678:
The calculated MIRR (17.91%) is significantly different from the IRR (25.48%).
808:
781:
743:
716:
43:
756:
39:
667:{\displaystyle {\text{MIRR}}={\sqrt{\frac {7600}{4636.36}}}-1=17.91\%}
221:
If an investment project is described by the sequence of cash flows:
17:
54:(IRR) and as such aims to resolve some problems with the IRR.
74:
should be used for reinvesting the interim cash flows.
623:
536:
435:
281:
94:
666:
602:
515:
411:
163:
687:return which can be used for such comparisons.
8:
757:Internal Rate of Return: A Cautionary Tale
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27:Measure of an investment's attractiveness
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187:(at the beginning of the first period),
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548:positive cash flows, reinvestment rate
118:positive cash flows, reinvestment rate
682:Comparing projects of different sizes
7:
661:
575:
488:
25:
447:negative cash flows, finance rate
195:(at the end of the last period).
140:negative cash flows, finance rate
46:'s attractiveness. It is used in
72:weighted average cost of capital
58:Problems associated with the IRR
32:modified internal rate of return
85:MIRR is calculated as follows:
579:
563:
551:
543:
492:
476:
450:
442:
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378:
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310:
143:
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1:
66:, MIRR resolves two of them.
862:
809:10.1080/00137919508903144
797:The Engineering Economist
782:10.1080/00137919208903083
770:The Engineering Economist
744:10.1080/00137918808966958
732:The Engineering Economist
717:10.1080/00137917608902796
705:The Engineering Economist
614:Third, we find the MIRR:
203:Spreadsheet applications
62:While there are several
52:internal rate of return
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604:
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413:
165:
669:
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64:problems with the IRR
836:Mathematical finance
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92:
664:
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846:Capital budgeting
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48:capital budgeting
16:(Redirected from
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207:Microsoft Excel
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5:
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803:(2): 201–210.
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738:(4): 275–302.
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711:(4): 237–247.
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42:measure of an
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268:then the IRR
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185:present value
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37:
33:
19:
800:
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685:
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613:
526:
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422:
272:is given by
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197:
193:future value
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174:
84:
76:
68:
61:
35:
31:
29:
776:(1): 1–18.
81:Calculation
841:Investment
830:Categories
691:References
230:Cash flow
211:=MIRR(...)
205:, such as
44:investment
817:206731554
662:%
650:−
576:%
561:⋅
508:−
489:%
469:−
457:−
303:−
291:−
156:−
127:−
40:financial
813:ProQuest
639:4636.36
511:4636.36
217:Example
38:) is a
815:
246:−4000
238:−1000
175:where
659:17.91
262:2000
254:5000
227:Year
636:7600
626:MIRR
598:7600
592:2000
558:5000
472:4000
460:1000
375:2000
341:5000
306:4000
294:1000
97:MIRR
36:MIRR
30:The
18:MIRR
805:doi
778:doi
740:doi
713:doi
284:NPV
191:is
183:is
832::
811:.
801:40
799:.
774:38
772:.
736:33
734:.
709:21
707:.
573:12
486:10
259:3
251:2
243:1
235:0
213:.
189:FV
181:PV
819:.
807::
784:.
780::
746:.
742::
719:.
715::
674:.
656:=
653:1
644:3
630:=
610:.
595:=
589:+
584:1
580:)
570:+
567:1
564:(
555:=
552:)
544:(
541:V
538:F
523:.
505:=
497:1
493:)
483:+
480:1
477:(
463:+
454:=
451:)
443:(
440:V
437:P
419:.
407:0
404:=
396:3
392:)
388:r
385:+
382:1
379:(
370:+
362:2
358:)
354:r
351:+
348:1
345:(
336:+
328:1
324:)
320:r
317:+
314:1
311:(
297:+
288:=
270:r
177:n
171:,
159:1
150:n
144:)
136:(
133:V
130:P
122:)
114:(
111:V
108:F
101:=
34:(
20:)
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