{"text_format":"3","workbook":"xls","n_sheets":6,"sheets":["NPV Rule","IRR Rule","Multiple","Multiple-chart","Exclusive","Incremental"],"not_rendered":{"charts":1},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"NPV Rule","index":0,"n_rows":22,"n_cols":5,"rows_kept":22,"flags":["formulas_cached_only"]}
["NPV RULE FOR CAPITAL BUDGETING"]
[]
[]
["Choose a project if it costs less than the PV of its cash flows.  More generally:  "]
["take a project if its Net Present Value is positive."]
[]
["EXAMPLE"]
[]
["Interest rate",{"v":0.1,"d":"10%"}]
[]
["Year",0,1,2,3]
[]
["Cash flow",{"v":-600,"d":"(600)"},200,200,500]
["PV factor",{"v":1,"d":"100%"},{"v":0.9090909090909091,"d":"91%"},{"v":0.8264462809917354,"d":"83%"},{"v":0.7513148009015777,"d":"75%"}]
["PV of cash flow",{"v":-600,"d":"(600)"},{"v":181.8181818181818,"d":"182"},{"v":165.2892561983471,"d":"165"},{"v":375.6574004507888,"d":"376"}]
["Cumulative PV",{"v":-600,"d":"(600)"},{"v":-418.1818181818182,"d":"(418)"},{"v":-252.8925619834711,"d":"(253)"},{"v":122.76483846731773,"d":"123"}]
["Net Present Value",{"v":122.76483846731773,"d":"123"}]
[]
["Investors would have to invest 123 more (a total of 723) to get the cash flows of 200, 200, "]
["and 500 at an interest rate of 10%.  Therefore the project has a value of 123 for investors."]
["The interest rate is called the cost of capital, because it is the opportunity cost of funds - the"]
["rate investors can earn on alternative investments."]

{"sheet":"IRR Rule","index":1,"n_rows":10,"n_cols":5,"rows_kept":10,"flags":["formulas_cached_only"]}
["IRR RULE"]
[]
[]
["For a standard project,","  NPV > 0 ","      if and only if",null,"  IRR > Cost of Capital"]
[]
["IRR Rule:                    Choose a project ",null,"       if and only if ",null,"   IRR > Cost of Capital"]
[]
["Standard means "]
["      -  cash outflows occur in early years and cash inflows in later years. "]
["      -  the alternative to the project is the status quo."]

{"sheet":"Multiple","index":2,"n_rows":20,"n_cols":4,"rows_kept":20,"flags":["formulas_cached_only"]}
["NONSTANDARD PROJECTS MAY HAVE MORE THAN ONE INTERNAL RATE OF RETURN"]
[]
[]
["Cost of capital ",{"v":0.12,"d":"12%"}]
[]
[]
["Year",0,1,2]
[]
["Net cash flow",{"v":-400000,"d":"(400,000)"},{"v":960000,"d":"960,000"},{"v":-572000,"d":"(572,000)"}]
["PV factor",{"v":1,"d":"100%"},{"v":0.8928571428571428,"d":"89%"},{"v":0.7971938775510202,"d":"80%"}]
["PV of net cash flow",{"v":-400000,"d":"(400,000)"},{"v":857142.857142857,"d":"857,143"},{"v":-455994.89795918355,"d":"(455,995)"}]
["Cumulative PV",{"v":-400000,"d":"(400,000)"},{"v":457142.85714285704,"d":"457,143"},{"v":1147.9591836734908,"d":"1,148"}]
["Net present value",{"v":1147.9591836734908,"d":"1,148"}]
[]
["IRR (Internal Rate of Return)",{"v":0.1,"d":"10%"}]
[]
["For this project, varying the initial guess in the IRR function can cause the IRR to change."]
["This is a good project (positive NPV), but you can't tell it from the IRR function.  The following"]
["chart shows that there are two break-even costs of capital or IRR's.  The NPV is positive at the"]
["actual cost of capital (12%), so it is a good project."]

{"sheet":"Multiple-chart","index":3,"n_rows":25,"n_cols":4,"rows_kept":25,"flags":["formulas_cached_only"]}
["Year",0,1,2]
["Net cash flow",{"v":-400000,"d":"(400,000)"},{"v":960000,"d":"960,000"},{"v":-572000,"d":"(572,000)"}]
[]
["Discount Rate","NPV"]
[]
[{"v":0.02,"d":"2%"},{"v":-8612.072279892396,"d":"(8,612)"}]
[{"v":0.04,"d":"4%"},{"v":-5769.2307692308095,"d":"(5,769)"}]
[{"v":0.06,"d":"6%"},{"v":-3417.5863296547323,"d":"(3,418)"}]
[{"v":0.08,"d":"8%"},{"v":-1508.9163237310713,"d":"(1,509)"}]
[{"v":0.1,"d":"10%"},0]
[{"v":0.12,"d":"12%"},{"v":1147.9591836734326,"d":"1,148"}]
[{"v":0.14,"d":"14%"},{"v":1969.836872883956,"d":"1,970"}]
[{"v":0.16,"d":"16%"},{"v":2497.0273483947967,"d":"2,497"}]
[{"v":0.18,"d":"18%"},{"v":2757.8282102844096,"d":"2,758"}]
[{"v":0.2,"d":"20%"},{"v":2777.777777777752,"d":"2,778"}]
[{"v":0.22,"d":"22%"},{"v":2579.9516259069787,"d":"2,580"}]
[{"v":0.24,"d":"24%"},{"v":2185.223725286196,"d":"2,185"}]
[{"v":0.26,"d":"26%"},{"v":1612.4968505920842,"d":"1,612"}]
[{"v":0.28,"d":"28%"},{"v":878.90625,"d":"879"}]
[{"v":0.3,"d":"30%"},0]
[{"v":0.32,"d":"32%"},{"v":-1010.1010101009742,"d":"(1,010)"}]
[{"v":0.34,"d":"34%"},{"v":-2138.5609267097316,"d":"(2,139)"}]
[{"v":0.36,"d":"36%"},{"v":-3373.7024221453466,"d":"(3,374)"}]
[{"v":0.38,"d":"38%"},{"v":-4704.893929846701,"d":"(4,705)"}]
[{"v":0.4,"d":"40%"},{"v":-6122.448979591834,"d":"(6,122)"}]

{"sheet":"Exclusive","index":4,"n_rows":19,"n_cols":5,"rows_kept":19,"flags":["formulas_cached_only"]}
["AN EXAMPLE OF MUTUALLY EXCLUSIVE PROJECTS"]
[]
["Cost of capital",{"v":0.1,"d":"10%"}]
[]
[null,null,"Year",0,1]
[]
["Project A",null,"Cash flow",{"v":-10000,"d":"(10,000)"},{"v":20000,"d":"20,000"}]
[null,null,"PV factor",{"v":1,"d":"100%"},{"v":0.9090909090909091,"d":"91%"}]
[null,null,"PV of cash flow",{"v":-10000,"d":"(10,000)"},{"v":18181.81818181818,"d":"18,182"}]
[null,null,"NPV",{"v":8181.81818181818,"d":"8,182"}]
[null,null,"IRR",{"v":0.9999999999999999,"d":"100%"}]
[]
["Project B",null,"Cash flow",{"v":-20000,"d":"(20,000)"},{"v":35000,"d":"35,000"}]
[null,null,"PV factor",{"v":1,"d":"100%"},{"v":0.9090909090909091,"d":"91%"}]
[null,null,"PV of cash flow",{"v":-20000,"d":"(20,000)"},{"v":31818.181818181816,"d":"31,818"}]
[null,null,"NPV",{"v":11818.181818181816,"d":"11,818"}]
[null,null,"IRR",{"v":0.749999999999996,"d":"75%"}]
[]
["Project B is best, even though its IRR is lower."]

{"sheet":"Incremental","index":5,"n_rows":18,"n_cols":5,"rows_kept":18,"flags":["formulas_cached_only"]}
["PROJECTS CAN BE VALUED ON AN INCREMENTAL BASIS"]
[]
[]
["Cost of capital",{"v":0.1,"d":"10%"}]
[]
[null,null,"Year",0,1]
[]
["Project A",null,"Cash flow",{"v":-10000,"d":"(10,000)"},{"v":20000,"d":"20,000"}]
[null,null,"PV factor",{"v":1,"d":"100%"},{"v":0.9090909090909091,"d":"91%"}]
[null,null,"PV of cash flow",{"v":-10000,"d":"(10,000)"},{"v":18181.81818181818,"d":"18,182"}]
[null,null,"NPV",{"v":8181.81818181818,"d":"8,182"}]
[]
["Project B-A",null,"Cash flow",{"v":-10000,"d":"(10,000)"},{"v":15000,"d":"15,000"}]
[null,null,"PV factor",{"v":1,"d":"100%"},{"v":0.9090909090909091,"d":"91%"}]
[null,null,"PV of cash flow",{"v":-10000,"d":"(10,000)"},{"v":13636.363636363636,"d":"13,636"}]
[null,null,"NPV",{"v":3636.363636363636,"d":"3,636"}]
[]
["Project B has a positive NPV relative to A (on an incremental basis) so should be taken."]