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{"sheet":"Page 61","index":0,"n_rows":14,"n_cols":8,"rows_kept":14,"cut":false,"hidden":false,"merged":[[0,0,0,7]]}
["NPV EXAMPLE"]
["Discount rate, r",0.06]
[]
["Year",0,1,2,3,4,5]
["Cash flow",-1500,100,200,300,400,500]
["Present value",{"$f":"B5/(1+$B$2)^B4","v":-1500},{"$f":"C5/(1+$B$2)^C4","v":94.339622641509436},177.99928800284798,251.8857849096905,316.83746529520818,373.62908643302842,{"$f":"getformula(G6)","v":"<-- =G5/(1+$B$2)^G4"}]
[]
["Present value of future cash flows"]
[null,{"$f":"SUM(C6:G6)","v":1214.6912472822846},{"$f":"getformula(B9)","v":"<-- =SUM(C6:G6)"}]
[null,{"$f":"NPV(B2,C5:G5)","v":1214.6912472822846},{"$f":"getformula(B10)","v":"<-- =NPV(B2,C5:G5)"}]
[]
["Net present value (NPV)"]
[null,{"$f":"SUM(B6:G6)","v":-285.30875271771549},{"$f":"getformula(B13)","v":"<-- =SUM(B6:G6)"}]
[null,{"$f":"B5+NPV(B2,C5:G5)","v":-285.30875271771538},{"$f":"getformula(B14)","v":"<-- =B5+NPV(B2,C5:G5)"}]

{"sheet":"Page 62","index":1,"n_rows":14,"n_cols":8,"rows_kept":14,"cut":false,"hidden":false,"merged":[[0,0,0,7]]}
["NPV EXAMPLE"]
["Discount rate, r",0.06]
[]
["Year",0,1,2,3,4,5]
["Cash flow",-1000,100,200,300,400,500]
["Present value",{"$f":"B5/(1+$B$2)^B4","v":-1000},{"$f":"C5/(1+$B$2)^C4","v":94.339622641509436},177.99928800284798,251.8857849096905,316.83746529520818,373.62908643302842,{"$f":"getformula(G6)","v":"<-- =G5/(1+$B$2)^G4"}]
[]
["Present value of future cash flows"]
[null,{"$f":"SUM(C6:G6)","v":1214.6912472822846},{"$f":"getformula(B9)","v":"<-- =SUM(C6:G6)"}]
[null,{"$f":"NPV(B2,C5:G5)","v":1214.6912472822846},{"$f":"getformula(B10)","v":"<-- =NPV(B2,C5:G5)"}]
[]
["Net present value (NPV)"]
[null,{"$f":"SUM(B6:G6)","v":214.69124728228451},{"$f":"getformula(B13)","v":"<-- =SUM(B6:G6)"}]
[null,{"$f":"B5+NPV(B2,C5:G5)","v":214.69124728228462},{"$f":"getformula(B14)","v":"<-- =B5+NPV(B2,C5:G5)"}]

{"sheet":"Page 63","index":2,"n_rows":14,"n_cols":4,"rows_kept":14,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["CALCULATING THE NET PRESENT VALUE (NPV) WITH EXCEL"]
["Interest rate, r",0.05]
[]
["Year","Payment","Present value"]
[0,-800,{"$f":"B5/(1+$B$2)^A5","v":-800},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C5)","v":{"$error":"#NAME?"}}]
[1,100,{"$f":"B6/(1+$B$2)^A6","v":95.238095238095241},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C6)","v":{"$error":"#NAME?"}}]
[2,150,136.05442176870747]
[3,200,172.76751970629519]
[4,250,205.67561869797049]
[5,300,235.05784994053769]
[]
["NPV"]
["Summing the present values",null,{"$f":"SUM(C5:C10)","v":44.793505351606001},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C13)","v":{"$error":"#NAME?"}}]
["Using Excel's NPV function",null,{"$f":"B5+NPV(B2,B6:B10)","v":44.793505351606086},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C14)","v":{"$error":"#NAME?"}}]

{"sheet":"Page 64","index":3,"n_rows":33,"n_cols":4,"rows_kept":33,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["CALCULATING THE NET PRESENT VALUE (NPV) WITH EXCEL"]
["Interest rate, r",0.05]
[]
["Year","Payment","Present value"]
[0,-800,{"$f":"B5/(1+$B$2)^A5","v":-800},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C5)","v":{"$error":"#NAME?"}}]
[1,100,{"$f":"B6/(1+$B$2)^A6","v":95.238095238095241},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C6)","v":{"$error":"#NAME?"}}]
[2,150,136.05442176870747]
[3,200,172.76751970629519]
[4,250,205.67561869797049]
[5,300,235.05784994053769]
[]
["NPV"]
["Summing the present values",null,{"$f":"SUM(C5:C10)","v":44.793505351606001},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C13)","v":{"$error":"#NAME?"}}]
["Using Excel's NPV function",null,{"$f":"B5+NPV(B2,B6:B10)","v":44.793505351606086},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C14)","v":{"$error":"#NAME?"}}]
[]
["Discount rate","NPV"]
[0,{"$f":"NPV(A17,$B$6:$B$10)+$B$5","v":200},{"$f":"getformula(B17)","v":"<-- =NPV(A17,$B$6:$B$10)+$B$5"}]
[0.01,{"$f":"NPV(A18,$B$6:$B$10)+$B$5","v":165.85713038939468},{"$f":"getformula(B18)","v":"<-- =NPV(A18,$B$6:$B$10)+$B$5"}]
[0.02,{"$f":"NPV(A19,$B$6:$B$10)+$B$5","v":133.35959923698465},"<-- =NPV(A19,$B$6:$B$10)+$B$5"]
[0.03,102.40949417564309]
[0.04,72.915729625928861]
[0.05,44.793505351606086]
[0.06,17.963812919427937]
[7.0000000000000007E-2,-7.6470145986324951]
[0.08,-32.107713848866752]
[0.09,-55.482467075945578]
[0.1,-77.831246002819171]
[0.11,-99.210126709294059]
[0.12,-119.671578202163]
[0.13,-139.26472709747384]
[0.14000000000000001,-158.03560059294614]
[0.15,-176.02734969220865]
[0.16,-193.28045444943132]

{"sheet":"Page 67","index":4,"n_rows":31,"n_cols":3,"rows_kept":31,"cut":false,"hidden":false,"merged":[[0,0,0,6]]}
["CALCULATING THE IRR WITH EXCEL"]
["Year","Payment"]
[0,-800]
[1,100]
[2,150]
[3,200]
[4,250]
[5,300]
[]
["IRR",{"$f":"IRR(B3:B8)","v":6.6965490735638511E-2},{"$f":"getformula(B10)","v":"<-- =IRR(B3:B8)"}]
["Check:  The NPV using IRR as discount rate"]
[null,{"$f":"B3+NPV(B10,B4:B8)","v":0},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(B12)","v":{"$error":"#NAME?"}}]
[]
["Discount rate","NPV"]
[0,{"$f":"$B$3+NPV(A15,$B$4:$B$8)","v":200},{"$f":"getformula(B15)","v":"<-- =$B$3+NPV(A15,$B$4:$B$8)"}]
[0.01,{"$f":"$B$3+NPV(A16,$B$4:$B$8)","v":165.85713038939468},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(B16)","v":{"$error":"#NAME?"}}]
[0.02,133.35959923698465]
[0.03,102.40949417564309]
[0.04,72.915729625928861]
[0.05,44.793505351606086]
[0.06,17.963812919427937]
[7.0000000000000007E-2,-7.6470145986324951]
[0.08,-32.107713848866752]
[0.09,-55.482467075945578]
[0.1,-77.831246002819171]
[0.11,-99.210126709294059]
[0.12,-119.671578202163]
[0.13,-139.26472709747384]
[0.14000000000000001,-158.03560059294614]
[0.15,-176.02734969220865]
[0.16,-193.28045444943132]

{"sheet":"Page 70","index":5,"n_rows":11,"n_cols":3,"rows_kept":11,"cut":false,"hidden":false,"merged":[[0,0,0,6]]}
["CALCULATING THE IRR WITH EXCEL"]
["Year","Payment"]
[0,-1000]
[1,300]
[2,300]
[3,300]
[4,300]
[]
["IRR",{"$f":"IRR(B3:B7)","v":7.713847295204368E-2},{"$f":"getformula(B9)","v":"<-- =IRR(B3:B7)"}]
["Check:  The NPV using IRR as discount rate"]
[null,{"$f":"B3+NPV(B9,B4:B7)","v":8.9130480773746967E-11},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(B11)","v":{"$error":"#NAME?"}}]

{"sheet":"Page 70 bottom","index":6,"n_rows":9,"n_cols":4,"rows_kept":9,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["USING IRR TO CHOOSE BETWEEN INVESTMENTS"]
["Year","Investment A cash flows","Investment B cash flows"]
[0,-1000,-1000]
[1,450,550]
[2,425,300]
[3,350,457]
[4,450,200]
[]
["IRR",{"$f":"IRR(B3:B7)","v":0.24743976038028581},{"$f":"IRR(C3:C7)","v":0.21650722881765838},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C9)","v":{"$error":"#NAME?"}}]

{"sheet":"Page 72","index":7,"n_rows":11,"n_cols":6,"rows_kept":11,"cut":false,"hidden":false,"merged":[[0,0,0,5]]}
["THE IRR AS A RATE OF RETURN ON AN INVESTMENT"]
["IRR",{"$f":"IRR({-200,130.91,130.91})","v":0.20000572916139281},{"$f":"getformula(B2)","v":"<-- =IRR({-200,130.91,130.91})"}]
["Year","Investment\nat beginning\nof year","Payment at\nend of year","Part of payment\nwhich is interest","Part of payment\nwhich is repayment\nof principal"]
[1,200,130.90899999999999,{"$f":"$B$2*B4","v":40.00114583227856},{"$f":"C4-D4","v":90.907854167721439}]
[2,{"$f":"B4-E4","v":109.09214583227856},{"$f":"C4","v":130.90899999999999},{"$f":"$B$2*B5","v":21.819054172965874},{"$f":"C5-D5","v":109.08994582703411}]
[3,{"$f":"B5-E5","v":2.2000052444468565E-3}]
[]
[{"$f":"ggetformula(B5)","v":"=B4-E4"},null,null,{"$f":"ggetformula(D4)","v":"=$B$2*B4"},{"$f":"ggetformula(E4)","v":"=C4-D4"}]
[]
[null,null,{"$f":"ggetformula(B6)","v":"=B5-E5"},null,null,{"$f":"ggetformula(E5)","v":"=C5-D5"}]
[null,null,null,null,{"$f":"ggetformula(D5)","v":"=$B$2*B5"}]

{"sheet":"Page 75","index":8,"n_rows":12,"n_cols":4,"rows_kept":12,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["TWO PROJECTS"]
["Discount rate, r",0.12]
[]
["Year","Project A","Project B"]
[0,-1000,-800]
[1,500,420]
[2,500,420]
[3,500,420]
[4,500,420]
[5,500,420]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B10)","v":802.38810117250205},{"$f":"C5+NPV($B$2,C6:C10)","v":714.00600498490167},{"$f":"getformula(C12)","v":"<-- =C5+NPV($B$2,C6:C10)"}]

{"sheet":"Page 76","index":9,"n_rows":12,"n_cols":4,"rows_kept":12,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["TWO PROJECTS"]
["Discount rate, r",0.12]
[]
["Year","Project A","Project B"]
[0,-1000,-800]
[1,500,420]
[2,500,420]
[3,500,420]
[4,500,420]
[5,500,420]
[]
["IRR",{"$f":"IRR(B5:B10)","v":0.41041496500867924},{"$f":"IRR(C5:C10)","v":0.44029693630616085},{"$f":"getformula(C12)","v":"<-- =IRR(C5:C10)"}]

{"sheet":"Page 77","index":10,"n_rows":29,"n_cols":3,"rows_kept":29,"cut":false,"hidden":false,"merged":[[0,0,0,2]]}
["SIMPLE CAPITAL BUDGETING EXAMPLE"]
["Discount rate",0.15]
[]
["Year","Cash flow"]
[0,-1000]
[1,100]
[2,200]
[3,300]
[4,400]
[5,500]
[6,600]
[]
["PV of future cash flows",{"$f":"NPV(B2,B6:B11)","v":1172.1263483613764},{"$f":"getformula(B13)","v":"<-- =NPV(B2,B6:B11)"}]
["NPV",{"$f":"B5+NPV(B2,B6:B11)","v":172.12634836137636},{"$f":"getformula(B14)","v":"<-- =B5+NPV(B2,B6:B11)"}]
["IRR",{"$f":"IRR(B5:B11)","v":0.19710389330225198},{"$f":"getformula(B15)","v":"<-- =IRR(B5:B11)"}]
[]
[]
["Discount\nrate","NPV"]
[0,{"$f":"$B$5+NPV(A19,$B$6:$B$11)","v":1100},{"$f":"getformula(B19)","v":"<-- =$B$5+NPV(A19,$B$6:$B$11)"}]
[0.03,{"$f":"$B$5+NPV(A20,$B$6:$B$11)","v":849.33882364202555},{"$f":"getformula(B20)","v":"<-- =$B$5+NPV(A20,$B$6:$B$11)"}]
[0.06,637.66757154609036]
[0.09,457.83033564046696]
[0.12,304.15789606756607]
[0.15,172.12634836137636]
[0.18,58.10099215098262]
[0.21,-40.857414386805544]
[0.24,-127.14037802396456]
[0.27,-202.70514763244239]
[0.3,-269.16250466923407]

{"sheet":"Page 79","index":11,"n_rows":13,"n_cols":4,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["RANKING PROJECTS WITH NPV AND IRR"]
["Discount rate, r",0.15]
[]
["Year","Project A","Project B"]
[0,-500,-500]
[1,100,250]
[2,100,250]
[3,150,200]
[4,200,100]
[5,400,50]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B10)","v":74.419666571529888},{"$f":"C5+NPV($B$2,C6:C10)","v":119.96462898263826},{"$f":"getformula(C12)","v":"<-- =C5+NPV($B$2,C6:C10)"}]
["IRR",{"$f":"IRR(B5:B10)","v":0.19770388847350806},{"$f":"IRR(C5:C10)","v":0.27379980888879141},{"$f":"getformula(C13)","v":"<-- =IRR(C5:C10)"}]

{"sheet":"Page 79 bottom","index":12,"n_rows":13,"n_cols":4,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["RANKING PROJECTS WITH NPV AND IRR"]
["Discount rate, r",0.08]
[]
["Year","Project A","Project B"]
[0,-500,-500]
[1,100,250]
[2,100,250]
[3,150,200]
[4,200,100]
[5,400,50]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B10)","v":216.64056014858818},{"$f":"C5+NPV($B$2,C6:C10)","v":212.11477989229411},{"$f":"getformula(C12)","v":"<-- =C5+NPV($B$2,C6:C10)"}]
["IRR",{"$f":"IRR(B5:B10)","v":0.19770388847350806},{"$f":"IRR(C5:C10)","v":0.27379980888879141},{"$f":"getformula(C13)","v":"<-- =IRR(C5:C10)"}]

{"sheet":"Page 80","index":13,"n_rows":34,"n_cols":4,"rows_kept":34,"cut":false,"hidden":false,"merged":[[0,0,0,7]]}
["RANKING PROJECTS WITH NPV AND IRR"]
["Discount rate, r",0.15]
[]
["Year","Project A","Project B"]
[0,-500,-500]
[1,100,250]
[2,100,250]
[3,150,200]
[4,200,100]
[5,400,50]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B10)","v":74.419666571529888},{"$f":"C5+NPV($B$2,C6:C10)","v":119.96462898263826},{"$f":"getformula(C12)","v":"<-- =C5+NPV($B$2,C6:C10)"}]
["IRR",{"$f":"IRR(B5:B10)","v":0.19770388847350806},{"$f":"IRR(C5:C10)","v":0.27379980888879141},{"$f":"getformula(C13)","v":"<-- =IRR(C5:C10)"}]
[]
["Data table:  NPV and discount rates"]
[]
[null,"Project A NPV","Project B NPV"]
[null,{"$f":"B12","v":74.419666571529888},{"$f":"C12","v":119.96462898263826},{"$f":"getformula(C18)&\", data table header\"","v":"<-- =C12, data table header"}]
[0,450,350]
[0.02,382.56585312939899,311.52578452873877]
[0.04,321.69060216594437,275.89971481417626]
[0.06,266.60416089180558,242.8442981808987]
[0.08,216.64056014858818,212.11477989229411]
[0.1,171.22215944017705,183.49466939044146]
[0.12,129.84649718123376,156.79195529113611]
[0.14000000000000001,92.075299740910282,131.83589192702266]
[0.16,57.525263455499271,108.47426197332982]
[0.18,25.860298112485907,86.571037082626958]
[0.2,-3.2150205761316215,66.004372427983526]
[0.22,-29.960994939285172,46.664882327018404]
[0.24,-54.607513509569287,28.454153250999298]
[0.26,-77.358060866970732,11.283457949008664]
[0.28000000000000003,-98.393142223358154,-4.9273595213890076]
[0.3,-117.8732160315439,-20.250853099843141]

{"sheet":"Page 81","index":14,"n_rows":10,"n_cols":5,"rows_kept":10,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["CALCULATING THE CROSSOVER POINT FOR A AND B"]
["Year","Project A","Project B","Differential cash flows:\ncash flow(A) - cash flow (B)"]
[0,-500,-500,{"$f":"B3-C3","v":0},{"$f":"getformula(D3)","v":"<-- =B3-C3"}]
[1,100,250,{"$f":"B4-C4","v":-150},{"$f":"getformula(D4)","v":"<-- =B4-C4"}]
[2,100,250,-150]
[3,150,200,-50]
[4,200,100,100]
[5,400,50,350]
[]
[null,null,"IRR",{"$f":"IRR(D3:D8)","v":8.5127661320580916E-2},{"$f":"getformula(D10)","v":"<-- =IRR(D3:D8)"}]

{"sheet":"Page 82","index":15,"n_rows":13,"n_cols":4,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["RANKING PROJECTS WITH NPV AND IRR"]
["Discount rate",0.08]
[]
["Year","Project A","Project B"]
[0,-500,-500]
[1,100,250]
[2,100,250]
[3,150,200]
[4,200,100]
[5,400,50]
[]
["NPV",{"$f":"B5+NPV(B2,B6:B10)","v":216.64056014858818},{"$f":"C5+NPV(B2,C6:C10)","v":212.11477989229411},{"$f":"getformula(C12)","v":"<-- =C5+NPV(B2,C6:C10)"}]
["IRR",{"$f":"IRR(B5:B10)","v":0.19770388847350806},{"$f":"IRR(C5:C10)","v":0.27379980888879141},{"$f":"getformula(C13)","v":"<-- =IRR(C5:C10)"}]

{"sheet":"Page 83+84","index":16,"n_rows":23,"n_cols":5,"rows_kept":23,"cut":false,"hidden":false,"merged":[[0,0,0,4],[17,0,17,4]]}
["BUYING A CAR"]
["List price of car",11000]
["Downpayment",5000]
["Cash cost of car",10000]
["Bank rate of interest",0.09]
[]
["Year","Payment in cash","Payment with credit","Cash spent or saved with credit plan"]
[0,{"$f":"-B4","v":-10000},{"$f":"-B3","v":-5000},{"$f":"C8-B8","v":5000},{"$f":"getformula(D8)","v":"<-- =C8-B8"}]
[1,null,-2000,{"$f":"C9-B9","v":-2000},{"$f":"getformula(D9)","v":"<-- =C9-B9"}]
[2,null,-2000,-2000]
[3,null,-2000,-2000]
[]
["Internal rate of return",null,null,{"$f":"IRR(D8:D11)","v":9.7010257403278732E-2},{"$f":"getformula(D13)","v":"<-- =IRR(D8:D11)"}]
[]
["NPV of cash saved",null,null,{"$f":"D8+NPV(B5,D9:D11)","v":-62.589331976349058},{"$f":"getformula(D15)","v":"<-- =D8+NPV(B5,D9:D11)"}]
[]
[]
["Borrowing the money from the bank"]
["Year","Payment in cash","Bank loan cash flows","Total cash flows to car owner"]
[0,-10000,5000,{"$f":"B20+C20","v":-5000},{"$f":"getformula(D20)","v":"<-- =B20+C20"}]
[1,null,{"$f":"PMT($B$5,3,C20)","v":-1975.2737866447023},{"$f":"B21+C21","v":-1975.2737866447023},{"$f":"getformula(D21)","v":"<-- =B21+C21"}]
[2,null,{"$f":"C21","v":-1975.2737866447023},-1975.2737866447023]
[3,null,{"$f":"C22","v":-1975.2737866447023},-1975.2737866447023]

{"sheet":"Page 84 bottom","index":17,"n_rows":15,"n_cols":5,"rows_kept":15,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["IRR VERSUS NPV--THE DEALER'S PROBLEM"]
["List price of car",11000]
["Downpayment",5000]
["Cash cost of car",10000]
["Bank rate of interest",0.09]
[]
["Year","Payment in cash","Payment with credit","Differential dealer cash flow"]
[0,10000,5000,{"$f":"C8-B8","v":-5000},{"$f":"getformula(D8)","v":"<-- =C8-B8"}]
[1,null,2000,{"$f":"C9-B9","v":2000},{"$f":"getformula(D9)","v":"<-- =C9-B9"}]
[2,null,2000,2000]
[3,null,2000,2000]
[]
["Internal rate of return",null,null,{"$f":"IRR(D8:D11)","v":9.7010257403349121E-2},{"$f":"getformula(D13)","v":"<-- =IRR(D8:D11)"}]
[]
["NPV of cash saved",null,null,{"$f":"D8+NPV(B5,D9:D11)","v":62.589331976349058},{"$f":"getformula(D15)","v":"<-- =D8+NPV(B5,D9:D11)"}]

{"sheet":"Page 85","index":18,"n_rows":63,"n_cols":7,"rows_kept":63,"cut":false,"hidden":false,"merged":[[0,0,0,6]]}
["CONVENTIONAL AND NON-CONVENTIONAL CASH FLOW PATTERNS"]
["Year","Cash flow\nproject A","Cash flow\nproject B","Cash flow\nproject C","Cash flow\nproject D","Cash flow\nproject E","Cash flow\nproject F"]
[0,-100,-100,100,25,-25,-250]
[1,200,-50,55,35,80,35]
[2,500,60,35,{"$f":"-200","v":-200},-100,145]
[3,50,80,50,33,200,330]
[4,60,99,-100,55,55,55]
[5,35,100,-35,155,-250,-250]
[null,"­\nConventional cash flow pattern"," ­\nConventional cash flow pattern"," ­\nConventional cash flow pattern"," ­\nNon-conventional cash flow pattern"," ­\nNon-conventional cash flow pattern"," ­\nNon-conventional cash flow pattern"]
[null,"Initial negative cash flow followed by positive cash flows","Two initial negative cash flows followed by positive cash flows","Initial positive cash flows followed by negative cash flows","Two positive cash flows, then negative, then three positive cash flows","Initial negative cash flow, then positive, then negative, positive, negative cash flows","Negative cash flows at beginning and end, other cash flows positive"]
[]
["IRR",{"$f":"IRR(B3:B8)","v":2.4901306822561367},{"$f":"IRR(C3:C8)","v":0.28494462575658863},-0.17470987610592836,0.5629148168641176,0.10993087007623914,0.19086842037647478]
[null,null,null,null,{"$f":"IRR(E3:E8,60%)","v":0.6087541131566272},{"$f":"IRR(F3:F8,160%)","v":1.7357065507165199},{"$f":"IRR(G3:G8,-20%)","v":-0.22738746870194726}]
[]
[]
[]
["Datat table, project D"]
[null,{"$f":"NPV(A18,E4:E8)+E3","v":103},{"$f":"getformula(B18)","v":"<-- =NPV(A18,E4:E8)+E3"}]
[0,103]
[0.1,50.130859168834661]
[0.25,15.214400000000001]
[0.4,3.1222109835187872]
[0.5,0.49794238683126935]
[0.52,0.26520831002718737]
[0.54,0.10503263596574186]
[0.56000000000000005,9.0771102329156861E-3]
[0.57999999999999996,-3.0085010801265355E-2]
[0.6,-1.9073486328128553E-2]
[0.62,3.6207221462792205E-2]
[0.64,0.1304874048131488]
[0.66,0.25906125818057291]
[0.68,0.41772446524951334]
[0.7,0.60271914706904184]
[0.72,0.81068524071097059]
[0.74,1.0386175038017456]
[0.76,1.2838274480502285]
[0.78,1.5439095972633154]
[]
["Data table, project E",null,null,null,"Data table, project F"]
[0,{"$f":"F3+NPV(A40,F4:F8)","v":-40},null,null,0,{"$f":"G3+NPV(E40,G4:G8)","v":65}]
[0,-40,null,null,-0.3,-200.38674361873063]
[0.01,-34.716157518216328,null,null,-0.2,36.181640625000114]
[0.02,-29.842242691390727,null,null,0.02,59.028365144207953]
[0.03,-25.346764590800252,null,null,0.03,55.868328474530756]
[0.04,-21.200818827718248,null,null,0.04,52.615749219618976]
[0.05,-17.377857452594814,null,null,0.05,49.286109721576508]
[0.06,-13.853481020179219,null,null,0.06,45.893323388829458]
[7.0000000000000007E-2,-10.605250517267049,null,null,7.0000000000000007E-2,42.449887139125394]
[0.08,-7.6125171067036277,null,null,0.08,38.967018533188593]
[0.09,-4.8562678675996622,null,null,0.09,35.454779220921068]
[0.1,-2.3189859112951403,null,null,0.1,31.922186139794235]
[0.11,1.5476571191989308E-2,null,null,0.11,28.377311744568317]
[0.3,20.324851263018694,null,null,0.3,-35.14852151804638]
[0.6,19.31610107421875,null,null,0.6,-106.36749267578131]
[0.9,12.687023014830991,null,null,0.9,-149.17695132545185]
[1.2,6.9822602778002008,null,null,1.2,-175.64358495135082]
[1.5,2.6479999999999961,null,null,1.5,-192.83199999999999]
[1.8,-0.63068959362169963,null,null,1.8,-204.53010650324268]
[2.1,-3.1636276954213542,null,null,2.1,-212.82174591904595]
[2.4,-5.1712249895588052,null,null,2.4,-218.90519608664815]
[2.7,-6.8016038513637191,null,null,2.7,-223.50100961212814]
[3,-8.154296875,null,null,3,-227.060546875]
[3.3,-9.2973590299163948,null,null,3.3,-229.87699352750781]

{"sheet":"Page 87","index":19,"n_rows":34,"n_cols":3,"rows_kept":34,"cut":false,"hidden":false,"merged":[[13,0,13,2],[0,0,0,6]]}
["SANITARY LANDFILL, INC."]
["Year","Cash flow"]
[0,-800]
[1,450]
[2,450]
[3,450]
[4,450]
[5,450]
[6,-1500]
[]
["First IRR",{"$f":"IRR(B3:B9,0)","v":2.6843898878733619E-2},{"$f":"getformula(B11)","v":"<-- =IRR(B3:B9,0)"}]
["Second IRR",{"$f":"IRR(B3:B9,25%)","v":0.27741685573861674},{"$f":"getformula(B12)","v":"<-- =IRR(B3:B9,25%)"}]
[]
["Data Table: NPV of cash flows"]
["Discount rate","NPV"]
[0,{"$f":"$B$3+NPV(A16,$B$4:$B$9)","v":-50},{"$f":"getformula(B16)","v":"<-- =$B$3+NPV(A16,$B$4:$B$9)"}]
[0.02,{"$f":"$B$3+NPV(A17,$B$4:$B$9)","v":-10.900294452395769},{"$f":"getformula(B17)","v":"<-- =$B$3+NPV(A17,$B$4:$B$9)"}]
[0.04,17.848260362074143,"<-- =$B$3+NPV(A18,$B$4:$B$9)"]
[0.06,38.122892845056299,"<-- =$B$3+NPV(A19,$B$4:$B$9)"]
[0.08,51.465076360481135]
[0.1,59.143151153135591]
[0.12,62.20260928927064]
[0.14000000000000001,61.506614460234118]
[0.16,57.768762146432323]
[0.18,51.579650656321746]
[0.2,43.428497942386912]
[0.22,33.720779016992424]
[0.24,22.792656394627556]
[0.26,10.922817839236245]
[0.28000000000000003,-1.6577883623540401]
[0.3,-14.757928063861527]
[0.32,-28.219450520495343]
[0.34,-41.911798130735065]
[0.36,-55.727451260729595]

{"sheet":"Page 89","index":20,"n_rows":11,"n_cols":5,"rows_kept":11,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["IRR ASSUMES REINVESTMENT OF INTERMEDIATE CASH FLOW AT IRR"]
["Year","Cash flow",null,"Cash flow reinvested at IRR"]
[0,-1000,null,{"$f":"B3","v":-1000},{"$f":"getformula(D3)","v":"<-- =B3"}]
[1,200,null,{"$f":"B4*(1+$B$11)^(5-A4)","v":275.70709835526446},{"$f":"getformula(D4)","v":"<-- =B4*(1+$B$11)^(5-A4)"}]
[2,300,null,{"$f":"B5*(1+$B$11)^(5-A5)","v":381.66709439947095},{"$f":"getformula(D5)","v":"<-- =B5*(1+$B$11)^(5-A5)"}]
[3,400,null,{"$f":"B6*(1+$B$11)^(5-A6)","v":469.64420435496868}]
[4,200,null,{"$f":"B7*(1+$B$11)^(5-A7)","v":216.71276020460093}]
[5,150,null,{"$f":"B8*(1+$B$11)^(5-A8)","v":150},{"$f":"getformula(D8)","v":"<-- =B8*(1+$B$11)^(5-A8)"}]
[]
[null,null,null,{"$f":"SUM(D4:D8)","v":1493.7311573143049},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(D10)","v":{"$error":"#NAME?"}}]
["IRR",{"$f":"IRR(B3:B8)","v":8.3563801023004647E-2},{"$f":"getformula(B11)","v":"<-- =IRR(B3:B8)"},{"$f":"(D10/-D3)^(1/5)-1","v":8.3563801023009976E-2},{"$f":"getformula(D11)","v":"<-- =(D10/-D3)^(1/5)-1"}]

{"sheet":"Page 90","index":21,"n_rows":13,"n_cols":5,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["REINVESTING INTERMEDIATE CASH FLOWS AT A RATE DIFFERENT FROM THE IRR"]
["Reinvestment rate",0.05]
["Year","Cash flow",null,"Cash flow reinvested at IRR"]
[0,-1000,null,{"$f":"B4","v":-1000},{"$f":"getformula(D4)","v":"<-- =B4"}]
[1,200,null,{"$f":"B5*(1+$B$2)^(5-A5)","v":243.10124999999999},{"$f":"getformula(D5)","v":"<-- =B5*(1+$B$2)^(5-A5)"}]
[2,300,null,{"$f":"B6*(1+$B$2)^(5-A6)","v":347.28750000000002},{"$f":"getformula(D6)","v":"<-- =B6*(1+$B$2)^(5-A6)"}]
[3,400,null,{"$f":"B7*(1+$B$2)^(5-A7)","v":441}]
[4,200,null,{"$f":"B8*(1+$B$2)^(5-A8)","v":210}]
[5,150,null,{"$f":"B9*(1+$B$2)^(5-A9)","v":150},{"$f":"getformula(D9)","v":"<-- =B9*(1+$B$2)^(5-A9)"}]
[]
[null,null,null,{"$f":"SUM(D5:D9)","v":1391.3887500000001},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(D11)","v":{"$error":"#NAME?"}}]
["IRR",{"$f":"IRR(B4:B9)","v":8.3563801023004647E-2},{"$f":"getformula(B12)","v":"<-- =IRR(B4:B9)"},{"$f":"(D11/-D4)^(1/5)-1","v":6.8291314594900454E-2},{"$f":"getformula(D12)","v":"<-- =(D11/-D4)^(1/5)-1"}]
[null,null,null,{"$f":"MIRR(B4:B9,0,B2)","v":6.8291314594900454E-2},{"$f":"getformula(D13)","v":"<-- =MIRR(B4:B9,0,B2)"}]

{"sheet":"Page 91","index":22,"n_rows":15,"n_cols":6,"rows_kept":15,"cut":false,"hidden":false,"merged":[[0,0,0,5]]}
["MIRR WITH DIFFERENT FINANCING AND REINVESTMENT RATES"]
["Financing rate",0.08]
["Reinvestment rate",0.05]
["Year","Cash flow",null,"FV of cash flow reinvested ","PV of cash flow borrowed"]
[0,-1000,null,{"$f":"B5","v":-1000},{"$f":"IF(B5<=0,B5/(1+$B$2)^A5,0)","v":-1000},{"$f":"getformula(E5)","v":"<-- =IF(B5<=0,B5/(1+$B$2)^A5,0)"}]
[1,800,null,{"$f":"IF(B6>0,B6*(1+$B$3)^(5-A6),0)","v":972.40499999999997},{"$f":"IF(B6<=0,B6/(1+$B$2)^A6,0)","v":0},{"$f":"getformula(E6)","v":"<-- =IF(B6<=0,B6/(1+$B$2)^A6,0)"}]
[2,-300,null,{"$f":"IF(B7>0,B7*(1+$B$3)^(5-A7),0)","v":0},{"$f":"IF(B7<=0,B7/(1+$B$2)^A7,0)","v":-257.20164609053495},{"$f":"getformula(E7)","v":"<-- =IF(B7<=0,B7/(1+$B$2)^A7,0)"}]
[3,-200,null,0,-158.76644820403391,{"$f":"getformula(E8)","v":"<-- =IF(B8<=0,B8/(1+$B$2)^A8,0)"}]
[4,900,null,945,0]
[5,150,null,150,0]
[]
["Modified investment",null,null,{"$f":"SUM(E5:E10)","v":-1415.9680942945688},{"$f":"getformula(D12)","v":"<-- =SUM(E5:E10)"}]
["Modified future value",null,null,{"$f":"SUM(D6:D10)","v":2067.4049999999997},{"$f":"getformula(D13)","v":"<-- =SUM(D6:D10)"}]
["IRR",{"$f":"IRR(B5:B10)","v":0.11553750268500496},{"$f":"getformula(B14)","v":"<-- =IRR(B5:B10)"},{"$f":"(D13/-D12)^(1/5)-1","v":7.8634777925447708E-2},{"$f":"getformula(D14)","v":"<-- =(D13/-D12)^(1/5)-1"}]
[null,null,null,{"$f":"MIRR(B5:B10,B2,B3)","v":7.863477792544793E-2},{"$f":"getformula(D15)","v":"<-- =MIRR(B5:B10,B2,B3)"}]

{"sheet":"Page 92","index":23,"n_rows":13,"n_cols":4,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["DIFFERENT LIFE SPANS"]
["Discount rate, r",0.12]
[]
["Year","Truck A","Truck B"]
[0,-100,-250]
[1,150,300]
[2,{"$f":"B6","v":150},{"$f":"C6","v":300}]
[3,{"$f":"B7","v":150},{"$f":"C7","v":300}]
[4,{"$f":"B8","v":150}]
[5,{"$f":"B9","v":150}]
[6,{"$f":"B10","v":150}]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B11)","v":516.71109852834866},{"$f":"C5+NPV($B$2,C6:C11)","v":470.54938046647214},{"$f":"getformula(C13)","v":"<-- =C5+NPV($B$2,C6:C11)"}]

{"sheet":"Page 92 bottom","index":24,"n_rows":13,"n_cols":4,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["DIFFERENT LIFE SPANS\nat end of year 3, truck B is replaced"]
["Discount rate, r",0.12]
[]
["Year","Cash flow (A)","Cash flow (B)"]
[0,-100,-250]
[1,150,300]
[2,{"$f":"B6","v":150},{"$f":"C6","v":300}]
[3,{"$f":"B7","v":150},{"$f":"300-250","v":50},{"$f":"getformula(C8)","v":"<-- =300-250"}]
[4,{"$f":"B8","v":150},300]
[5,{"$f":"B9","v":150},300]
[6,{"$f":"B10","v":150},300]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B11)","v":516.71109852834866},{"$f":"C5+NPV($B$2,C6:C11)","v":805.47713510334461},{"$f":"getformula(C13)","v":"<-- =C5+NPV($B$2,C6:C11)"}]

{"sheet":"Page 94","index":25,"n_rows":16,"n_cols":4,"rows_kept":16,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["DIFFERENT LIFE SPANS\nComputing the equivalent annuity cash flow (EAC)"]
["Discount rate, r",0.12]
[]
["Year","Cash flow (A)","Cash flow (B)"]
[0,-100,-250]
[1,150,{"$f":"300","v":300}]
[2,{"$f":"B6","v":150},{"$f":"C6","v":300}]
[3,{"$f":"B7","v":150},{"$f":"C7","v":300}]
[4,{"$f":"B8","v":150}]
[5,{"$f":"B9","v":150}]
[6,{"$f":"B10","v":150}]
[]
["NPV",{"$f":"B5+NPV($B$2,B6:B11)","v":516.71109852834866},{"$f":"C5+NPV($B$2,C6:C11)","v":470.54938046647214},{"$f":"getformula(C13)","v":"<-- =C5+NPV($B$2,C6:C11)"}]
["EAC--Equivalent\nannuity cash flow",{"$f":"-PMT(B2,6,B13)","v":125.67742815753701},{"$f":"-PMT(B2,3,C13)","v":195.91275486012321},{"$f":"getformula(C14)","v":"<-- =-PMT(B2,3,C13)"}]
[]
[{"$f":"ggetformula(B14)","v":"=-PMT(B2,6,B13)"}]

{"sheet":"Page 95","index":26,"n_rows":24,"n_cols":3,"rows_kept":24,"cut":false,"hidden":false,"merged":[[0,0,0,2]]}
["LIGHT BULBS\nChoosing between cheap incandescents and\nexpensive fluorescents"]
["Annual discount rate",0.08]
["Monthly discount rate",{"$f":"(1+B2)^(1/12)-1","v":6.4340301100034303E-3},{"$f":"getformula(B3)","v":"<-- =(1+B2)^(1/12)-1"}]
["Electric cost per kilowatt\n(a kilowatt = 1000 watts)",0.1]
[]
["Incandescent bulb"]
["     Watts",100]
["     Cost",1]
["     Hours per month used",250]
["     Lifetime of bulb (hours)",1000]
["     Lifetime in months",{"$f":"B10/B9","v":4}]
["     Monthly cost",{"$f":"B9*$B$4*B7/1000","v":2.5},{"$f":"getformula(B12)","v":"<-- =B9*$B$4*B7/1000"}]
["NPV of lifetime use",{"$f":"B8+PV(B3,B11,-B12)","v":10.841196016604345},{"$f":"getformula(B13)","v":"<-- =B8+PV(B3,B11,-B12)"}]
["Monthly equivalent annuity cash flow (EAC) for cheap incandescent",{"$f":"-PMT(B3,B11,B13)","v":2.7540341637116041},{"$f":"getformula(B14)","v":"<-- =-PMT(B3,B11,B13)"}]
[]
["Equivalent fluorescent bulb"]
["     Watts",15]
["     Cost",5]
["     Hours per month used",{"$f":"B9","v":250}]
["     Lifetime of bulb (hours)",10000]
["     Lifetime in months",{"$f":"B20/B19","v":40}]
["     Monthly cost",{"$f":"B19*$B$4*B17/1000","v":0.375},{"$f":"getformula(B22)","v":"<-- =B19*$B$4*B17/1000"}]
["NPV of lifetime use",{"$f":"B18+PV(B3,B21,-B22)","v":18.188088073996234},{"$f":"getformula(B23)","v":"<-- =B18+PV(B3,B21,-B22)"}]
["Monthly equivalent annuity cash flow (EAC) for expensive fluorescent",{"$f":"-PMT(B3,B21,B23)","v":0.51717375479142147},{"$f":"getformula(B24)","v":"<-- =-PMT(B3,B21,B23)"}]

{"sheet":"Page 97+98","index":27,"n_rows":13,"n_cols":6,"rows_kept":13,"cut":false,"hidden":false,"merged":[[0,0,0,5]]}
["PROFITABILITY INDEX EXAMPLE"]
["Discount rate, r",0.1]
[]
["Project","Investment (t=0)","t=1","t=2","NPV"]
["A",-100,150,170,{"$f":"B5+NPV($B$2,C5:D5)","v":176.85950413223134},{"$f":"getformula(E5)","v":"<-- =B5+NPV($B$2,C5:D5)"}]
["B",-120,200,140,{"$f":"B6+NPV($B$2,C6:D6)","v":177.52066115702473}]
["C",-150,300,300,370.6611570247934]
[]
[]
[{"$f":"A4","v":"Project"},"NPV","Resource requirement \n(hours/week)","PI","Rank"]
[{"$f":"A5","v":"A"},{"$f":"E5","v":176.85950413223134},30,{"$f":"B11/C11","v":5.8953168044077113},{"$f":"RANK(D11,$D$11:$D$13)","v":3},{"$f":"getformula(E11)","v":"<-- =RANK(D11,$D$11:$D$13)"}]
[{"$f":"A6","v":"B"},{"$f":"E6","v":177.52066115702473},20,{"$f":"B12/C12","v":8.8760330578512363},{"$f":"RANK(D12,$D$11:$D$13)","v":1},"<-- =RANK(D12,$D$11:$D$13)"]
[{"$f":"A7","v":"C"},370.6611570247934,50,{"$f":"B13/C13","v":7.4132231404958677},2,{"$f":"getformula(E13)","v":"<-- =RANK(D13,$D$11:$D$13)"}]