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{"sheet":"1. NPV-IRR Plot","index":1,"n_rows":165,"n_cols":9,"rows_kept":165,"cut":false,"hidden":false,"merged":[[71,1,71,2],[78,1,78,2]],"flags":["formulas_cached_only"]}
["Implement Fig. 3 of Osborne, M.J., 2010, A Resolution to the NPV-IRR Debate?, QREF 50(2), pp234-239."]
[]
[null,"CASH FLOWS (ADJUST USING SPINNERS)"]
[null,"I0","c1","c2","c3","c4"]
[null,900,1030,1035,1045,1060]
["A",-100,30,35,45,60]
["B",-100,50,50,40,20]
[null,900,1050,1050,1040,1020]
[]
[null,"WACC","(ADJUST USING SPINNER)"]
[null,0.05]
[null,5]
[]
[null,"DERIVED COEFFICIENTS OF QUARTIC IN RATE R:"]
[null,"a(R^4)+b(R^3)+c(R^2)+dR+e=0"]
[null,"a","b","c","d","e"]
["A",-100,-370,-475,-195,70]
["B",-100,-350,-400,-110,60]
[]
["A","IRR COORDS",null,"Z=(1+IRR)"]
[null,"REAL","COMPLEX","Z(1)","Z(2)"]
[null,-1.7576407157871652,0,-0.7576407157871652,0]
[null,0.21986140108078178,0,1.2198614010807818,0]
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[null,-1.0811103426468085,-0.8016355367103625,-0.0811103426468085,-0.8016355367103625]
[]
["B","IRR COORDS",null,"Z=(1+IRR)"]
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[null,0.25426283437952213,0,1.2542628343795221,0]
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[null,-1.127131417189761,-0.5502272494974721,-0.12713141718976106,-0.5502272494974721]
[]
[null,"DISTANCES BETWEEN IRRs and WACC r"]
["aA",1.8076407157871652,null,"aB",1.55]
[null,0.16986140108078174,null,null,0.20426283437952208]
[null,1.386373016528918,null,null,1.2993800057814993]
[null,1.386373016528918,null,null,1.2993800057814993]
[{"$nulls":6},"Instructions/Observations"]
["Product",0.5901562499999999,null,null,0.5345562499999997,null,"1. Adjust cash flows and WACC by clicking on spinners."]
[{"$nulls":6},"2. Observe that a positive real root (if it exists) is pivotal in determining the sign/size of the NPV. As the positive real root"]
["|NPV|/$",0.48552300738889653,null,null,0.4397807497904677,null,"slides past the WACC, a=|Z-r|=|(1+R)-(1+r)| crosses zero, reduces the NPV to zero, and the sign of the NPV changes"]
["ABS(NPV)",48.552300738889656,null,null,43.978074979046774,null,"3. Push I0(B) up to +25 or higher (keep other values as in Osborne (2010)), and get four complex roots. There is then no way to get NPV<=0 for any  WACC"]
["NPV +/-",48.552300738889656,null,null,43.978074979046795,null,"4. Push c4(A) down (keep other values as in Osborne (2010)) and watch the right real root cross the WACC (so NPV sign changes) and"]
[{"$nulls":6},"watch the two real roots collide and separate vertically (as conjugates) away from each other in the complex plane."]
[{"$nulls":6},"You can see the distances |Z-r| growing as the NPV gets more negative, and no othodox IRR in sight that you could show to a first-year student. "]
["BELOW HERE IS WORKING",{"$nulls":5},"5. Drop I0 and watch the Zs move toward the origin (i.e., the IRRs go to -100%) as I0 gets more and more negative. "]
[{"$nulls":6},"Alternatively, Increase I0 past zero and watch the Zs again move toward the origin as I0 gets larger and positive"]
["ZERO",1,0,null,null,null,"In both cases |a1a2a3a4| goes to (1+r)^4 as |NPV/I0| goes to -1 or +1 (because I0 dominates)."]
["WACC+1",1.05,0,null,null,null,"6. Push c2 up to a very large number, and it appears that two Zs go to the origin (IRRs going to -100%), and the other"]
[{"$nulls":6},"two Zs go to plus and minus a large (and growing number). This gives a saddle plot in the second tab. Simultaneously pushing c4 down to "]
["+i",0,1,null,null,null,"a negative number gives four distinct real roots and accentuates the saddle plot."]
["-i",0,-1]
[]
["Modified Pascal's Triangle"]
["r^4","r^3","r^2","r",1]
[1,4,6,4,1]
[0,1,3,3,1]
[0,0,1,2,1]
[0,0,0,1,1]
[0,0,0,0,1]
[]
["Coefficients",{"$nulls":4},"UNIT CIRCLE"]
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["Equation Solution",{"$nulls":4},6,0.37699111843077515,0.9297764858882515,0.3681245526846779]
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["Real Roots",2,2,null,null,12,0.7539822368615503,0.7289686274214116,0.6845471059286886]
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["Real Roots",2,2,null,null,19,1.1938052083641213,0.3681245526846781,0.9297764858882513]
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["Plots of the quartics in R."]
["We should see the plot cross the x-axis four times if there are four real roots, twice if there are two real roots, and not at all if there are no real roots."]
[]
[null,"a","b","c","d","e"]
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{"sheet":"3. About(Quartic Soln Software)","index":3,"n_rows":44,"n_cols":4,"rows_kept":44,"cut":false,"hidden":false,"merged":[[33,3,33,11],[34,3,34,11]],"flags":["formulas_cached_only"]}
["About Quartic"]
[]
["August  25, 2013: Timothy Falcon Crack"]
["TFC Downloaded the spreadsheet Polynomial.xls from http://newtonexcelbach.wordpress.com/2010/09/19/complex-numbers-and-solving-quartic-polynomial-equations/"]
["TFC deleted all but the call up of the QUARTIC software, and implemented the Osborne solution using it. Authorship of the QUARTIC software is described below"]
[]
[]
["Disclaimer"]
[]
["This program is free software; you can redistribute it and/or"]
["modify it under the terms of the GNU General Public License"]
["as published by the Free Software Foundation; either version 2"]
["of the License, or (at your option) any later version."]
[]
["This program is distributed in the hope that it will be useful,"]
["but WITHOUT ANY WARRANTY; without even the implied warranty of"]
["MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  "]
[]
[]
[" "]
["dougjenkins@interactiveds.com.au"]
["www.interactiveds.com.au"]
[]
["ã"," Copyright  2011 Interactive Design Services Pty Ltd.  all rights reserved"]
[]
[]
["Revision History"]
[]
["Current Version",null,1.03,"2012-10-22"]
[]
["Rev","Date","By","Description"]
[]
[1,"2006-11-27T20:58:59.450","DAJ","First release"]
[1.01,"2006-12-12T22:21:16.400","DAJ","Complex solutions added"]
["1.01.1","2007-03-11T10:31:15.790","DAJ","Quartic fixed for four equal roots"]
[1.02,"2010-04-12","DAJ","Correction to Cubicc for case of two equal roots"]
[1.03,"2010-08-04","DAJ","Input changed to array format"]
[1.04,"2010-09-19","DAJ","Corrected for case of Q = 0 and one real negative root. EvalPoly1C function added. Error value check added to Quartic and CubicC"]
[1.05,"2010-09-22","DAJ","More corrections to Quartic.  CubicC amended to always return real roots first."]
["Renamed Polynomial"]
[1,"2011-01-12","DAJ","Jenkins-Traub function (RPolyJT) added."]
[1.01,"2011-01-16","DAJ","Quadratic solution modified; evaluation by synthetic division added"]
[1.02,"2012-10-21","DAJ","Correction to CubicC to set sgnR = 1 if R = 0; Cubic and Cubicc fixed for case where R2 = Q3 and R > 0"]
[1.03,"2012-10-22","DAJ","Quartic corrected for A=0, Quadratic corrected to output number of roots for linear equation."]