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{"sheet":"Language","index":0,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Exhibit 1 Engl","index":1,"n_rows":37,"n_cols":8,"rows_kept":37,"cut":false,"hidden":true,"merged":[[26,3,26,5],[27,3,27,5],[28,3,28,5]]}
[null,null,"Future Value, Present Value and Return of an Investment"]
["The result is indicated in yellow (or grey). Click inside the cell to see the formula used by Excel."]
[]
["Examples ----->","A","B","C","D","E","F"]
["Rate (per period of payment)",0.05,0.05,2.5000000000000001E-2,0.01,0.05,{"$f":"RATE(G6,G7,G8,G10)","v":5.0003033697862964E-2}]
["Nper (number of payments)",5,5.5,10,60,5,5]
["Pmt (payments received)",0,0,0,0,0,0]
["PV (present value)",-100,-100,-100,-100,{"$f":"PV(F5,F6,F7,F10)","v":-100.00144462636941},-100]
["Type",0,0,0,0,0,0]
["FV (Future Value)",{"$f":"FV(B5,B6,B7,B8)","v":127.62815625000002},{"$f":"FV(C5,C6,C7,C8)","v":130.77994334439492},{"$f":"FV(D5,D6,D7,D8)","v":128.00845441963571},{"$f":"FV(E5,E6,E7,E8)","v":181.66966985640914},127.63,127.63]
[]
[null,null,"Investment with Several and Equal Cash Flows. A bond"]
[]
["Examples ----->","G","H","I",null,null,"Nominal vs effective rate","J"]
["Rate (per period of payment)",0.06,{"$f":"RATE(C16,C17,C18,C20)","v":5.9999999999999991E-2},{"$f":"RATE(D16,D17,D18,D20)","v":2.9933221180265656E-2},null,null,"Nominal annual rate",2.4E-2]
["Nper (number of payments)",3,3,6,null,null,"Periods per year",12]
["Pmt (payments received)",500,500,250,null,null,"Effective rate (IRR)",{"$f":"EFFECT(H15,H16)","v":2.4265767945403027E-2}]
["PV (present value)",{"$f":"PV(B15,B16,B17,B20)","v":-9732.6988050538366},{"$f":"B18","v":-9732.6988050538366},{"$f":"C18","v":-9732.6988050538366}]
["Type",0,0,0]
["FV (Future Value)",10000,10000,10000]
[]
[null,null,"Investments with Cash Flows of Different Sizes. PV, NPV and IRR"]
[]
["Year",0,1,2,3,4,5]
["Cash Flows, CF",-100,-10,20,40,50,60]
["Required return, K",0.1]
["Return  IRR (expected)",{"$f":"IRR(B25:G25)","v":0.12364107640583333},null,"Formula =IRR(B25:G25)"]
["Present Value, PV",{"$f":"NPV(B26,C25:G25)","v":108.89656071679153},null,"Formula =NPV(B26;C25:G25)"]
["Net Present Value, NPV",{"$f":"B28+B25","v":8.8965607167915266},null,"Formula=B28+B25"]
["Sum of  CF 1 to  5",{"$f":"SUM(C25:G25)","v":160},null,"Average CF 1 to  5",null,{"$f":"AVERAGE(C25:G25)","v":32}]
["Accumulated CF (o to 5)",{"$f":"SUM(B25:G25)","v":60}]
["Simple return ",{"$f":"-B31/B25/G24","v":0.12}]
[]
["Year",0,1,2,3,4,5,"IRR"]
["CF Project 1",-100,-10,20,40,50,60,{"$f":"IRR(B35:G35)","v":0.12364107640583333}]
["CF Project 2",-100,{"$f":"-B27*B36","v":12.364107640583333},{"$f":"C36","v":12.364107640583333},{"$f":"D36","v":12.364107640583333},12.364107640583333,{"$f":"F36-B36","v":112.36410764058333},{"$f":"IRR(B36:G36)","v":0.12364107640275757}]
["CF Project 3",-100,{"$f":"PMT(B27,5,-100,0)","v":27.99163198642551},{"$f":"C37","v":27.99163198642551},{"$f":"D37","v":27.99163198642551},27.99163198642551,27.99163198642551,{"$f":"IRR(B37:G37)","v":0.12364107640556377}]

{"sheet":"Anexo 1 Esp","index":2,"n_rows":53,"n_cols":8,"rows_kept":53,"cut":false,"hidden":false,"merged":[[26,3,26,5],[27,3,27,5],[28,3,28,5]]}
[null,null,"Valor Futuro, Valor Actual y Rentabilidad de la Inversión"]
["En amarillo se indica el resultado. Clicar dentro de la celda para ver la fórmula uada por Excel."]
[]
["Ejemplos =====>","A","B","C","D","E","F"]
["Tasa (por periodo de pago)",0.05,0.05,2.5000000000000001E-2,0.01,0.05,{"$f":"RATE(G6,G7,G8,G10)","v":5.0003033697862964E-2},"Rate"]
["Periodos (duración de la inversión)",5,5.5,10,60,5,5,"Nper"]
["Pago (pagos recibidos durante la inversión)",0,0,0,0,0,0,"Pmt"]
["VA, valor actual",-100,-100,-100,-100,{"$f":"PV(F5,F6,F7,F10)","v":-100.00144462636941},-100,"PV"]
["Tipo (dejar en blanco o 0)",0,0,0,0,0,0,"Type"]
["VF, valor futuro",{"$f":"FV(B5,B6,B7,B8)","v":127.62815625000002},{"$f":"FV(C5,C6,C7,C8)","v":130.77994334439492},{"$f":"FV(D5,D6,D7,D8)","v":128.00845441963571},{"$f":"FV(E5,E6,E7,E8)","v":181.66966985640914},127.63,127.63,"FV"]
[]
[null,null,"Inversión con varios CF, todos iguales. Bonos "]
[]
["Ejemplos =====>","G","H","I",null,null,"Tasa nominal vs TAE","J"]
["Tasa (por periodo de pago)",0.06,{"$f":"RATE(C16,C17,C18,C20)","v":5.9999999999999991E-2},{"$f":"RATE(D16,D17,D18,D20)","v":2.9933221180265656E-2},null,null,"Tasa nominal anual",2.4E-2]
["Periodos (duración de la inversión)",3,3,6,null,null,"Periodos por año",12]
["Pago (pagos recibidos durante la inversión)",500,500,250,null,null,"TAE o TIR",{"$f":"EFFECT(H15,H16)","v":2.4265767945403027E-2}]
["VA, valor actual",{"$f":"PV(B15,B16,B17,B20)","v":-9732.6988050538366},{"$f":"B18","v":-9732.6988050538366},{"$f":"C18","v":-9732.6988050538366}]
["Tipo (dejar en blanco o 0)",0,0,0]
["VF, valor futuro",10000,10000,10000]
[]
[null,null,"Inversión con varios CF, de diferente tamaño. VA, VAN y TIR"]
[]
["Año",0,1,2,3,4,5]
["Cash Flows, CF",-100,-10,20,40,50,60]
["Rentabilidad requerida, K",0.1]
["Rentabilidad esperada  TIR",{"$f":"IRR(B25:G25)","v":0.12364107640583333},null,"Fórmula =IRR(B25:G25)"]
["Valor actual, VA o PV",{"$f":"NPV(B26,C25:G25)","v":108.89656071679153},null,"Fórmula =NPV(B26;C25:G25)"]
["Valor actual neto VAN o NPV",{"$f":"B28+B25","v":8.8965607167915266},null,"Fórmula=B28+B25"]
["Suma de  CF 1 a  5",{"$f":"SUM(C25:G25)","v":160},null,"CF promedio anual",null,null,{"$f":"B30/G24","v":32}]
["CF acumaulado (0 a 5)",{"$f":"SUM(B25:G25)","v":60},null,"Beneficio promedio anual ",null,null,{"$f":"B31/G24","v":12}]
["Rentabilidad simple ",{"$f":"-B31/B25/G24","v":0.12}]
[]
["Año",0,1,2,3,4,5,"IRR"]
["CF Proyecto 1",-100,-10,20,40,50,60,{"$f":"IRR(B35:G35)","v":0.12364107640583333}]
["CF Proyecto 2",-100,{"$f":"-B27*B36","v":12.364107640583333},{"$f":"C36","v":12.364107640583333},{"$f":"D36","v":12.364107640583333},12.364107640583333,{"$f":"F36-B36","v":112.36410764058333},{"$f":"IRR(B36:G36)","v":0.12364107640275757}]
["CF Proyecto 3",-100,{"$f":"PMT(B27,5,-100,0)","v":27.99163198642551},{"$f":"C37","v":27.99163198642551},27.99163198642551,27.99163198642551,27.99163198642551,{"$f":"IRR(B37:G37)","v":0.12364107640556377}]
[]
[]
[]
["OTRAS FOMRULAS QUE TE PUEDEN SER UTILES"]
["COMO CALCULAR LA CUOTA MENSUAL DE UNA HIPOTECA (o de cualquier préstamo). "]
["Lo mejor es que lo hagas con cualquier app del movil. Es sencillo, rápido y siempre lo llevas encima, no así el Excel. "]
["Pero just in case, aquí te pongo las fórmulas a usar con Excel. En verde, las hpótesis a usar."]
[]
[null,"Tipo de interés anual",1.4999999999999999E-2]
[null,"Tipo de interés mensual",{"$f":"C46/12","v":1.25E-3}]
[null,"Número de años ",20]
[null,"Número de meses",{"$f":"C48*12","v":240}]
[null,"Principal del préstamo",200000]
[null,"Gastos (comisiones, notario etc)",3000]
[null,"Total del plréstamo",{"$f":"C50+C51","v":203000}]
[null,"Cuota mensual a pagar ",{"$f":"PMT(C47,C49,C52)","v":-979.56718003036372}]

{"sheet":"Anexo 1 Port","index":3,"n_rows":53,"n_cols":8,"rows_kept":53,"cut":false,"hidden":true,"merged":[[26,3,26,5],[27,3,27,5],[28,3,28,5]]}
[null,null,"Valor Futuro, Valor Actual y Rentabilidad de la Inversión"]
["En amarillo se indica el resultado. Clicar dentro de la celda para ver la fórmula uada por Excel."]
[]
["Ejemplos =====>","A","B","C","D","E","F"]
["Tasa (por periodo de pago)",0.05,0.05,2.5000000000000001E-2,0.01,0.05,{"$f":"RATE(G6,G7,G8,G10)","v":5.0003033697862964E-2},"Rate"]
["Periodos (duración de la inversión)",5,5.5,10,60,5,5,"Nper"]
["Pago (pagos recibidos durante la inversión)",0,0,0,0,0,0,"Pmt"]
["VA, valor actual",-100,-100,-100,-100,{"$f":"PV(F5,F6,F7,F10)","v":-100.00144462636941},-100,"PV"]
["Tipo (dejar en blanco o 0)",0,0,0,0,0,0,"Type"]
["VF, valor futuro",{"$f":"FV(B5,B6,B7,B8)","v":127.62815625000002},{"$f":"FV(C5,C6,C7,C8)","v":130.77994334439492},{"$f":"FV(D5,D6,D7,D8)","v":128.00845441963571},{"$f":"FV(E5,E6,E7,E8)","v":181.66966985640914},127.63,127.63,"FV"]
[]
[null,null,"Inversión con varios CF, todos iguales. Bonos "]
[]
["Ejemplos =====>","G","H","I",null,null,"Tasa nominal vs TAE","J"]
["Tasa (por periodo de pago)",0.06,{"$f":"RATE(C16,C17,C18,C20)","v":5.9999999999999991E-2},{"$f":"RATE(D16,D17,D18,D20)","v":2.9933221180265656E-2},null,null,"Tasa nominal anual",2.4E-2]
["Periodos (duración de la inversión)",3,3,6,null,null,"Periodos por año",12]
["Pago (pagos recibidos durante la inversión)",500,500,250,null,null,"TAE o TIR",{"$f":"EFFECT(H15,H16)","v":2.4265767945403027E-2}]
["VA, valor actual",{"$f":"PV(B15,B16,B17,B20)","v":-9732.6988050538366},{"$f":"B18","v":-9732.6988050538366},{"$f":"C18","v":-9732.6988050538366}]
["Tipo (dejar en blanco o 0)",0,0,0]
["VF, valor futuro",10000,10000,10000]
[]
[null,null,"Inversión con varios CF, de diferente tamaño. VA, VAN y TIR"]
[]
["Año",0,1,2,3,4,5]
["Cash Flows, CF",-100,-10,20,40,50,60]
["Rentabilidad requerida, K",0.1]
["Rentabilidad esperada  TIR",{"$f":"IRR(B25:G25)","v":0.12364107640583333},null,"Fórmula =IRR(B25:G25)"]
["Valor actual, VA o PV",{"$f":"NPV(B26,C25:G25)","v":108.89656071679153},null,"Fórmula =NPV(B26;C25:G25)"]
["Valor actual neto VAN o NPV",{"$f":"B28+B25","v":8.8965607167915266},null,"Fórmula=B28+B25"]
["Suma de  CF 1 a  5",{"$f":"SUM(C25:G25)","v":160},null,"CF promedio anual",null,null,{"$f":"B30/G24","v":32}]
["CF acumaulado (0 a 5)",{"$f":"SUM(B25:G25)","v":60},null,"Beneficio promedio anual ",null,null,{"$f":"B31/G24","v":12}]
["Rentabilidad simple ",{"$f":"-B31/B25/G24","v":0.12}]
[]
["Año",0,1,2,3,4,5,"IRR"]
["CF Proyecto 1",-100,-10,20,40,50,60,{"$f":"IRR(B35:G35)","v":0.12364107640583333}]
["CF Proyecto 2",-100,{"$f":"-B27*B36","v":12.364107640583333},{"$f":"C36","v":12.364107640583333},{"$f":"D36","v":12.364107640583333},12.364107640583333,{"$f":"F36-B36","v":112.36410764058333},{"$f":"IRR(B36:G36)","v":0.12364107640275757}]
["CF Proyecto 3",-100,{"$f":"PMT(B27,5,-100,0)","v":27.99163198642551},{"$f":"C37","v":27.99163198642551},27.99163198642551,27.99163198642551,27.99163198642551,{"$f":"IRR(B37:G37)","v":0.12364107640556377}]
[]
[]
[]
["OTRAS FOMRULAS QUE TE PUEDEN SER UTILES"]
["COMO CALCULAR LA CUOTA MENSUAL DE UNA HIPOTECA (o de cualquier préstamo). "]
["Lo mejor es que lo hagas con cualquier app del movil. Es sencillo, rápido y siempre lo llevas encima, no así el Excel. "]
["Pero just in case, aquí te pongo las fórmulas a usar con Excel. En verde, las hpótesis a usar."]
[]
[null,"Tipo de interés anual",1.4999999999999999E-2]
[null,"Tipo de interés mensual",{"$f":"C46/12","v":1.25E-3}]
[null,"Número de años ",20]
[null,"Número de meses",{"$f":"C48*12","v":240}]
[null,"Principal del préstamo",200000]
[null,"Gastos (comisiones, notario etc)",3000]
[null,"Total del plréstamo",{"$f":"C50+C51","v":203000}]
[null,"Cuota mensual a pagar ",{"$f":"PMT(C47,C49,C52)","v":-979.56718003036372}]

{"sheet":"Questions","index":4,"n_rows":103,"n_cols":11,"rows_kept":103,"cut":false,"hidden":true,"merged":[[60,1,60,7],[61,1,61,7],[50,1,50,7],[51,1,51,7],[52,1,52,7],[53,1,53,7],[54,1,54,7],[55,1,55,7],[71,1,71,7],[72,1,72,7],[77,1,77,7],[48,8,49,8],[48,10,49,10],[48,9,49,9],[62,1,62,7],[63,1,63,7],[64,1,64,7],[65,1,65,7],[69,1,69,7],[70,1,70,7],[56,1,56,7],[57,1,57,7],[58,1,58,7],[59,1,59,7]]}
[null,"Self-assessment questions (Concepts)"]
[null,"They are the same ones you have in Chapter 5. For these questions you do not need to do any calculations, but you do need to be clear about the concepts."]
[null,"Answer True or False in column \"I\". Find the correct answers in column K. Correct answer = +1. Wrong = -1. Blank = 0.",null,null,null,null,null,null,null,-1]
[null,"Questions about PV, VF, IRR and K",null,null,null,null,null,null,"Your","Your","Correct"]
[null,"Bond A. Maturity 3 years. € 5 coupon per year. Upon maturity you receive € 100. Price paid € 100.",null,null,null,null,null,null,"Answer","Grade","Answer"]
[1,"Bond A. Your expected return is 5%. T or F?",null,null,null,null,null,null,null,{"$f":"IF(I6=K6,1,IF(I6=\"\",0,$J$3))","v":0},"V"]
[2,"Now you buy it for € 95, your expected return will be less than 5%. T or F?",null,null,null,null,null,null,null,{"$f":"IF(I7=K7,1,IF(I7=\"\",0,$J$3))","v":0},"F"]
[3,"Same bond A, but it pays € 2.5 coupon each semester. The IRR will be the same, that is, 5%. T or F?",null,null,null,null,null,null,null,0,"F"]
[4,"Same as in question 3. The simple annual return or APR will be 5%. T or F?",null,null,null,null,null,null,null,0,"V"]
[5,"Same bond A. You want to obtain a return higher than 5%, therefore you should pay more than € 100. T or F?",null,null,null,null,null,null,null,0,"F"]
[6,"Bond A. Market interest rates have dropped and Bond A is trading at 4%; as a consequence, the market price of the bond will be greater than € 100 T or F?",null,null,null,null,null,null,null,0,"V"]
[7,"If the interest rates (or required return K of the bond) fall, it rises in price. T or F?",null,null,null,null,null,null,null,0,"V"]
[8,"Zero coupon bond (does not pay coupons). At maturity they pay you € 100. To get a 5% return you should pay more than its par value (€ 100). T or F?",null,null,null,null,null,null,null,0,"F"]
[9,"When interest rates rise, the price of bonds and almost all assets falls. T or F?",null,null,null,null,null,null,null,0,"V"]
[null,"Questions about NPV, PV and IRR."]
[10,"If a project has a positive NPV, its IRR is greater than the required return K. T or F?",null,null,null,null,null,null,null,0,"V"]
[{"$f":"A16+1","v":11},"The NPV tells us the profitability that a project promises, but expressed in euros and not in percentage. T or F?",null,null,null,null,null,null,null,0,"F"]
[{"$f":"A17+1","v":12},"The NPV indicates the value that a project can add to the value of the company. T or F?",null,null,null,null,null,null,null,0,"V"]
[13,"The NPV of a project tells me the euros that project generates for the company. T or F?",null,null,null,null,null,null,null,0,"F"]
[14,"The initial amount to invest in an investment project is indicated by the NPV of that project. T or F?",null,null,null,null,null,null,null,0,"F"]
[15,"The IRR is the return on the initial amount invested in year 0. T or F?",null,null,null,null,null,null,null,0,"V"]
[16,"In buying a company, the PV indicates to me what I should pay for it. T or F?",null,null,null,null,null,null,null,0,"V"]
[17,"The PV depends exclusively on the cash flows that the project promises. T or F?",null,null,null,null,null,null,null,0,"F"]
[18,"To decide whether invest or not in a project, I may use the NPV.T or F?",null,null,null,null,null,null,null,0,"V"]
[19,"NPV is the same as PV present value. T or F?",null,null,null,null,null,null,null,0,"F"]
[null,"Questions about the Perpetuity"]
[20,"Formula of perpetuity. The K indicates the return that you demand from the investment. T or F?",null,null,null,null,null,null,null,0,"V"]
[{"$f":"A27+1","v":21},"As CF of perpetuity you should use the one that is sustainable for many future years. T or F?",null,null,null,null,null,null,null,0,"V"]
[22,"I can use perpetuity to calculate the expected return on an investment that lasts 5 years. T or F?",null,null,null,null,null,null,null,0,"F"]
[23,"In formula of a perpetuity, a hypothesis of (K-g) = (3% - 2.5%) is perfectly reasonable. T or F?",null,null,null,null,null,null,null,0,"F"]
[24,"To use the perpetuity formula it is necessary that the future CF are almost equal. T or F?",null,null,null,null,null,null,null,0,"V"]
[25,"In a startup Company, it makes sense to use a perpetuity to calculate the value of the company. T or F?",null,null,null,null,null,null,null,0,"F"]
[]
[null,null,null,null,null,null,null,"Points Earned",null,{"$f":"SUM(J6:J32)","v":0}]
[null,null,null,null,null,null,null,"If you are under 15, you should review"]
[]
[null,"FINANCIAL CALCULATION WITH EXCEL. CAP 5 QUESTIONS AND ANSWERS."]
[null,"To respond (Col. I) copy & paste the number that appears in results (G43:G47) in yellow."]
[null,"Correct answer 1; error 0. Correct solution and comments on Col. K"]
[null,"Formulas are already entered in cells G43:G47. View comments in each cell."]
[]
[null,"DATA for questions 1 to 16",null,"Data","Unit","RESULTS"]
[null,"Required return (K)",null,0.03,null,"PV =",{"$f":"PV(D43,D44,D45,D47)","v":-266711.30631627346}]
[null,"Maturity",null,10,"year or semester","FV =",{"$f":"FV(D43,D44,D45,D46)","v":154144.48275411705}]
[null,"Payment PMT",null,10000,"€","Rate =",{"$f":"RATE(D44,D45,D46,D47)","v":6.6141475800501448E-2}]
[null,"Present Value PV",null,-200000,null,"APR =",{"$f":"G45*D48","v":6.6141475800501448E-2}]
[null,"Future Value FV",null,243798.9,"€","Effect = ",{"$f":"EFFECT(G46,D48)","v":6.6141475800501448E-2}]
[null,"Payment periods per year",null,1]
[null,null,null,null,null,null,null,null,"Your Answer","Grade","Correct Answer"]
[null,"CAP 5 SELF-ASSESSMENT QUESTIONS (Calculations)"]
[1,"18 month corporate promissory note. Nominal value, which we will get at maturity, 10,000 euros. It doesn't pay coupons. How much do you have to pay for the promissory note to get a 4% return?",null,null,null,null,null,null,null,{"$f":"IF(I51=K51,1,0)","v":0},-9428.660343181924]
[{"$f":"A51+1","v":2},"How much should you pay if you want the return to be 5%?",null,null,null,null,null,null,null,0,-9294.2864090336498]
[{"$f":"A52+1","v":3},"How much should you pay if you want the return to be 4% and the promissory note has a 12-month maturity?",null,null,null,null,null,null,null,0,-9615.3846153846152]
[4,"Treasury bill, maturity 12 months. It doesn't pay coupons. Face value 100,000 euros. You pay 97,327 euros. What profitability do you get at maturity?",null,null,null,null,null,null,null,0,2.7464115815755138E-2]
[5,"With the same data, what profitability do you get if the maturity is 18 months?",null,null,null,null,null,null,null,0,1.8226608811543976E-2]
[6,"You invest 10,000 euros in a three-year term deposit at 4%. Interest is paid in the end. How many euros will you receive?",null,null,null,null,null,null,null,0,11248.640000000001]
[7,"With the same data, how many euros will you receive if the period is five years?",null,null,null,null,null,null,null,0,12166.529024000003]
[8,"Government bond with a maturity of ten years. Nominal value 1,000 euros. Annual coupon of 4% or 40 euros per year. How much do you have to pay to get a 4% return?",null,null,null,null,null,null,null,0,-999.99999999999989]
[9,"Same data. How much do you have to pay to get a 5% return?",null,null,null,null,null,null,null,0,-922.78265070815178]
[10,"Same data as in question 8. How much do you have to pay to get a 3% return?",null,null,null,null,null,null,null,0,-1085.3020283677583]
[11,"Same bond 8. You buy it at 950 euros. What annual return will you have earned at maturity?",null,null,null,null,null,null,null,0,4.6361305427803895E-2]
[12,"Same bond 8. You pay 900 euros. What annual return will you have earned at maturity?",null,null,null,null,null,null,null,0,5.3149258123545221E-2]
[13,"Same bond. But now, the coupon is paid on a six-monthly basis (20 euros per semester). If you pay 1,000 euros, what six-monthly profit profit will you have earned at maturity?",null,null,null,null,null,null,null,0,2.0000000000004917E-2]
[14,"Same data as in question 13. What is the simple annual return you have earned?",null,null,null,null,null,null,null,0,4.0000000000009833E-2]
[15,"Same data as in question 13. What is the effective annual return or IRR you have earned?",null,null,null,null,null,null,null,0,4.0400000000009983E-2]
[16,"You bought a flat for 200,000 euros. You expect to get a rent of 10,000 euros each year. You also expect the floor to be revalued by an average of 2% per year over the next ten years. What profitability will you have achieved if after ten years your forecasts are met and you sell the apartment?",null,null,null,null,null,null,null,0,6.6141475800501448E-2]
[]
[null,"Calculation with Perpetuity",null,"K =","g =","CF =","PV ="]
[null,null,null,0.1,0.03,1,{"$f":"F69/(D69-E69)","v":14.285714285714285}]
[17,"The ABC stock promises a dividend of 1 euro per year. You don't expect the share price to rise or fall in the future. You want to get your stock investment a K return of 10%. What price should you pay for the stock?",null,null,null,null,null,null,null,{"$f":"IF(I70=K70,1,0)","v":0},10]
[{"$f":"A70+1","v":18},"Same data. You expect the 1 euro dividend to grow by 3% each year. What price should you pay for the stock?",null,null,null,null,null,null,null,{"$f":"IF(I71=K71,1,0)","v":0},14.285714285714285]
[19,"You bought a flat for 200,000 euros. You expect to get a rent of 10,000 euros in the first year, with an annual increase of 2%. What profitability do you get?",null,null,null,null,null,null,null,{"$f":"IF(I72=K72,1,0)","v":0},7.0000000000000007E-2]
[20,"You bought a flat for 200,000 euros. You expect to get a rent of 10,000 euros the first year. What growth rate g is desired in order to accomplish your expected return to reach 8%?",null,null,null,null,null,null,null,{"$f":"IF(I73=K73,1,0)","v":0},0.03]
[]
[null,null,null,null,null,null,null,"Total Correct Answers",null,{"$f":"SUM(J51:J73)","v":0}]
[null,null,null,null,null,null,null,"Highest score possible",null,20]
[null,"LAST QUESTION"]
[21,"Calculate the IRR, PV and NPV of investments A, B, C and D, whose expected cash flows and required rate of return K are shown in the table below. "]
[]
[null,"Project","A","B","C","D"]
[null,"Required Return K",0.1,0.1,0.1,0.1]
[null,0,-100,-100,-40,-100]
[null,1,10,-20,-20,-20]
[null,2,10,0,-10,0]
[null,3,10,10,0,10]
[null,4,10,20,10,20]
[null,5,10,30,15,30]
[null,6,10,30,20,40]
[null,7,10,30,20,40]
[null,8,10,20,20,40]
[null,9,10,20,15,50]
[null,10,110,100,20,50]
[]
[null,"Sum of cash flows",{"$f":"SUM(C76:C86)","v":-59.900000000000006},{"$f":"SUM(D76:D86)","v":-89.9},{"$f":"SUM(E76:E86)","v":-59.900000000000006},{"$f":"SUM(F76:F86)","v":-89.9}]
[null,"IRR = "]
[null,"PV = "]
[null,"NPV = "]
[]
[null,"CORRECT ANSWERS"]
[null,"Sum of cash flows",{"$f":"SUM(C82:C92)","v":100},{"$f":"SUM(D82:D92)","v":140},{"$f":"SUM(E82:E92)","v":50},{"$f":"SUM(F82:F92)","v":160}]
[null,"IRR = ",{"$f":"IRR(C82:C92,0.1)","v":0.10000000000000009},{"$f":"IRR(D82:D92,0.1)","v":0.11333692491236147},{"$f":"IRR(E82:E92,0.1)","v":8.5700450414291307E-2},{"$f":"IRR(F82:F92,0.1)","v":0.13059962361886357}]
[null,"PV = ",{"$f":"NPV(C81,C83:C92)","v":99.999999999999943},{"$f":"NPV(D81,D83:D92)","v":110.31462898940565},{"$f":"NPV(E81,E83:E92)","v":34.652792041864721},{"$f":"NPV(F81,F83:F92)","v":123.86686115614312}]
[null,"NPV = ",{"$f":"C102+C82","v":0},{"$f":"D102+D82","v":10.314628989405648},{"$f":"E102+E82","v":-5.3472079581352787},{"$f":"F102+F82","v":23.866861156143116}]

{"sheet":"Preguntas","index":5,"n_rows":103,"n_cols":11,"rows_kept":103,"cut":false,"hidden":false,"merged":[[77,1,77,7],[60,1,60,7],[61,1,61,7],[62,1,62,7],[63,1,63,7],[64,1,64,7],[50,1,50,7],[72,1,72,7],[69,1,69,7],[70,1,70,7],[71,1,71,7],[65,1,65,7],[51,1,51,7],[52,1,52,7],[53,1,53,7],[55,1,55,7],[54,1,54,7],[56,1,56,7],[57,1,57,7],[58,1,58,7],[59,1,59,7]]}
[null,"CAP. 5 PREGUNTAS DE AUTOEVALUACION (Conceptos)"]
[null,"Son las mismas que tienes en el Cap 5. Para estas preguntas no necesitas hacer ningún cálculo, pero sí tener claros los conceptos. "]
[null,"Responder V o F en columna \"I\". Respuesta correcta en columna K. Repuesta correcta = +1. Incorrecta = -1. En blanco = 0. ",null,null,null,null,null,null,null,-1]
[null,"Preguntas sobre VA, VF, TIR y K",null,null,null,null,null,null,"Tu Res-","Califi-","Respuesta"]
[null,"Bono A. Vencimiento 3 años. Cupón de 5€ año. Al vencimiento recibes 100€. Precio 100€.",null,null,null,null,null,null,"puesta","cación","Correcta"]
[1,"Bono A. Tu rentabilidad esperada es de 5%. V o F?",null,null,null,null,null,null,null,{"$f":"IF(I6=K6,1,IF(I6=\"\",0,$J$3))","v":0},"V"]
[2,"Ahora lo compras por 95€, tu rentabilidad esperada será menor que 5%. V o F?",null,null,null,null,null,null,null,{"$f":"IF(I7=K7,1,IF(I7=\"\",0,$J$3))","v":0},"F"]
[3,"Mismo bono A, pero paga 2,5€ de cupón cada semestre. La TAE del bono o TIR será la misma, es decir 5%. V o F?",null,null,null,null,null,null,null,0,"F"]
[4,"Igual que pregunta 3. La rentabilidad simple anual será del 5%. V o F?",null,null,null,null,null,null,null,0,"V"]
[5,"Mismo bono A. Quieres obtener una rentabilidad superior al 5%, por tanto deberías pagar más de 100€. V o F?",null,null,null,null,null,null,null,0,"F"]
[6,"Bono A. Han bajado los tipos de interés en el mercado y el bono A cotiza al 4%. Su precio de mercado seguro que es mayor que 100€ V o F?",null,null,null,null,null,null,null,0,"V"]
[7,"Si bajan los tipos de interés o rentabilidad exigida K del bono, este sube de precio. V o F?",null,null,null,null,null,null,null,0,"V"]
[8,"Bono cupón cero (no paga cupones). A vencimiento te pagan 100€. Para obtener una rentabilidad del 5% deberías pagar más que su valor par (100€). V o F?",null,null,null,null,null,null,null,0,"F"]
[9,"Cuando suben los tipos de interés baja el precio de los bonos y de casi todos los activos. V o F?",null,null,null,null,null,null,null,0,"V"]
[null,"Preguntas sobre VAN, VA y TIR"]
[10,"Si un proyecto tiene un VAN positivo, su TIR es mayor que la rentabilidad exigida K. V o F?",null,null,null,null,null,null,null,0,"V"]
[{"$f":"A16+1","v":11},"El VAN nos dice la rentabilidad que un proyecto promete, pero expresada en euros y no en porcentaje. V o F?",null,null,null,null,null,null,null,0,"F"]
[{"$f":"A17+1","v":12},"El VAN me indica el valor que un proyecto puede añadir al valor de la compañía. V o F?",null,null,null,null,null,null,null,0,"V"]
[13,"El VAN de un proyecto me dice los euros que ese proyecto genera para la empresa. V o F?",null,null,null,null,null,null,null,0,"F"]
[14,"La cantidad inicial a invertir en un proyecto de inversión me la indica el VAN de ese proyecto. V o F?",null,null,null,null,null,null,null,0,"F"]
[15,"La TIR es la rentabilidad de la cantidad inicial invertida en el año 0. V o F?",null,null,null,null,null,null,null,0,"V"]
[16,"En la compra de una empresa el VA para mi indica lo que debería pagar por ella. V o F?",null,null,null,null,null,null,null,0,"V"]
[17,"El VA depende exclusivamente de los cash flows que promete ese proyecto. V o F?",null,null,null,null,null,null,null,0,"F"]
[18,"VAN y NPV son el mismo concepto. V o F?",null,null,null,null,null,null,null,0,"V"]
[19,"NPV es lo mismo que valor actual VA. V o F?",null,null,null,null,null,null,null,0,"F"]
[null,"Preguntas sobre la Perpetuidad"]
[20,"Fórmula de la perpetuidad. La K indica la rentabilidad que le exiges a la inversión. V o F?",null,null,null,null,null,null,null,0,"V"]
[{"$f":"A27+1","v":21},"Como CF de la perpetuidad debes usar el que sea sostenible durante muchos años futuros. V o F?",null,null,null,null,null,null,null,0,"V"]
[22,"Puedo usar la perpetuidad para calcular la rentabilidad espera en una inversión que dura 5 años. V o F?",null,null,null,null,null,null,null,0,"F"]
[23,"En la perpetuidad, una hipótesis de (K-g) = (3%- 2,5%) es perfectamente razonable. V o F?",null,null,null,null,null,null,null,0,"F"]
[24,"Para usar la fórmula de la perpetuidad es necesario que los CF futuros sean casi iguales. V o F?",null,null,null,null,null,null,null,0,"V"]
[25,"En una startup es lógico usar la perpetuidad para calcular el valor de la empresa. V o F?",null,null,null,null,null,null,null,0,"F"]
[]
[null,null,null,null,null,null,null,"Puntos obtenidos",null,{"$f":"SUM(J6:J32)","v":0}]
[null,null,null,null,null,null,null,"Si tienes menso de 15, deberías repasar"]
[]
[null,"CALCULO FINANCIERO CON EXCEL. Practicar CALCULOS"]
[null,"Para responder (Col. I) haz copy & paste del número que aparece en resultados (G43:G47) en amarillo."]
[null,"Respuesta correcta = 1; error = 0. Solución correcta y comentarios en Col. K"]
[null,"Las fórmulas ya están introducidas en las celdas 43:G47.  Ver los comentarios en cada celda. "]
[]
[null,"DATOS para preguntas 1 a 16",null,"Datos","Unidad","RESULTADOS"]
[null,"Rentabilidad exigida (K)","Required return (K) ",0.04,null,"VA=",{"$f":"PV(D43,D44,D45,D47)","v":-9428.660343181924},"PV"]
[null,"Vencimiento","Maturity",1.5,"años o semestres","VF=",{"$f":"FV(D43,D44,D45,D46)","v":0},"FV"]
[null,"Pago o cupón","Payment PMT",0,"euros","Tasa=",{"$f":"RATE(D44,D45,D46,D47)","v":{"$error":"#NUM!"}},"Rate"]
[null,"Valor actual (VA)","Present value PV",null,null,"Int simple",{"$f":"G45*D48","v":{"$error":"#NUM!"}},"APR"]
[null,"Valor futuro (VF)","Future value FV",10000,"euros","TAE = ",{"$f":"EFFECT(G46,D48)","v":{"$error":"#NUM!"}},"Effect"]
[null,"Periodos de pago por año",null,1]
[null,null,null,null,null,null,null,null,"Tu Res-","Califi-","Respuesta"]
[null,"PREGUNTAS AUTOEVALUACION CAP 5. Cálculos",null,null,null,null,null,null,"puesta","cación","Correcta"]
[1,"Pagaré de empresa a 18 meses. Valor nominal, que obtendremos al vencimiento, 10.000 euros. No paga cupones. ¿Cuánto debes pagar por el pagaré para obtener una rentabilidad del 4 %?",null,null,null,null,null,null,null,{"$f":"IF(I51=K51,1,0)","v":0},-9428.660343181924]
[{"$f":"A51+1","v":2},"¿Cuánto debes pagar si quieres que la rentabilidad sea del 5 %?",null,null,null,null,null,null,null,0,-9294.2864090336498]
[{"$f":"A52+1","v":3},"¿Cuánto debes pagar si quieres que la rentabilidad sea del 4 % y el pagaré tiene un vencimiento de 12 meses?",null,null,null,null,null,null,null,0,-9615.3846153846152]
[4,"Letra del Tesoro, vencimiento 12 meses. No paga cupones. Valor facial 100.000 euros. Pagas 97.327 euros. ¿Qué rentabilidad obtienes al vencimiento?",null,null,null,null,null,null,null,0,2.7464115815755138E-2]
[5,"Con los mismos datos, ¿qué rentabilidad obtienes si el vencimiento es a 18 meses?",null,null,null,null,null,null,null,0,1.8226608811543976E-2]
[6,"Inviertes 10.000 euros en un depósito a plazo a tres años y al 4 %. Los intereses se pagan al final. ¿Cuántos euros recibirás?",null,null,null,null,null,null,null,0,11248.640000000001]
[7,"Con los mismos datos, ¿cuántos euros recibirás si el plazo es cinco años?",null,null,null,null,null,null,null,0,12166.529024000003]
[8,"Bono del Estado con vencimiento diez años. Valor nominal 1.000 euros. Cupón anual del 4 %  ó 40 euros al año. ¿Cuánto debes pagar para obtener una rentabilidad del 4 %?",null,null,null,null,null,null,null,0,-999.99999999999989]
[9,"Mismos datos. ¿Cuánto debes pagar para obtener una rentabilidad del 5%?",null,null,null,null,null,null,null,0,-922.78265070815178]
[10,"Mismos datos que en la pregunta 8. ¿Cuánto debes pagar para obtener una rentabilidad del 3 %?",null,null,null,null,null,null,null,0,-1085.3020283677583]
[11,"Mismo bono 8.  Compras a 950 euros. ¿Qué rentabilidad anual habrás obtenido al vencimiento?",null,null,null,null,null,null,null,0,4.6361305427803895E-2]
[12,"Mismo bono 8. Pagas 900 euros. ¿Qué rentabilidad anual habrás obtenido al vencimiento?",null,null,null,null,null,null,null,0,5.3149258123545221E-2]
[13,"Mismo bono. Pero ahora, el cupón se paga semestralmente (20 euros por semestre). Si pagas 1.000 euros, ¿qué rentabilidad semestral habrás obtenido al vencimiento?",null,null,null,null,null,null,null,0,2.0000000000004917E-2]
[14,"Mismos datos que en la pregunta 13. ¿Cuál es la rentabilidad anual simple que has obtenido?",null,null,null,null,null,null,null,0,4.0000000000009833E-2]
[15,"Mismos datos que en la pregunta 13. ¿Cuál es la rentabilidad anual efectiva o TIR que has obtenido?",null,null,null,null,null,null,null,0,4.0400000000009983E-2]
[16,"Has comprado un piso por 200.000 euros. Esperas obtener un alquiler de 10.000 euros cada año. También esperas que en promedio el piso se revalorice un 2 % anual durante los próximos diez años. ¿Qué rentabilidad habrás obtenido si al cabo de diez años se cumplen tus previsiones y vendes el piso?",null,null,null,null,null,null,null,0,6.6141475800501448E-2]
[]
[null,"Cálculo con Perpetuidad",null,"K =","g =","CF =","VA ="]
[null,null,null,0.1,0.03,1,{"$f":"F69/(D69-E69)","v":14.285714285714285}]
[17,"La acción ABC promete un dividendo de 1 euro anual. No esperas que el precio de la acción suba ni baje en el futuro. Quieres obtener a tu inversión en bolsa una rentabilidad K del 10 %. ¿Qué precio deberías pagar por la acción?",null,null,null,null,null,null,null,{"$f":"IF(I70=K70,1,0)","v":0},10]
[{"$f":"A70+1","v":18},"Mismos datos. Esperas que el dividendo de 1 euro crezca un 3 % cada año. ¿Qué precio deberías pagar por la acción?",null,null,null,null,null,null,null,{"$f":"IF(I71=K71,1,0)","v":0},14.285714285714285]
[19,"Has comprado un piso por 200.000 euros. Esperas obtener un alquiler de 10.000 euros el primer año, con una subida anual del 2%. ¿Qué rentabilidad obtienes?",null,null,null,null,null,null,null,{"$f":"IF(I72=K72,1,0)","v":0},7.0000000000000007E-2]
[20,"Has comprado un piso por 200.000 euros. Esperas obtener un alquiler de 10.000 euros el primer año. ¿Qué tasa de crecimiento g debe tener el alquiler para que tu rentabilidad esperada llegue al 8%?",null,null,null,null,null,null,null,{"$f":"IF(I73=K73,1,0)","v":0},0.03]
[]
[null,null,null,null,null,null,null,"Total Respuestas correctas",null,{"$f":"SUM(J51:J73)","v":0}]
[null,null,null,null,null,null,null,"Máxima puntuación posible",null,20]
[null,"ULTIMA PREGUNTA"]
[21,"Calcular la TIR, el VA y el VAN de las inversiones A, B, C y D, cuyos cash flows esperados y tasa de rentabilidad exigida K figuran en el cuadro inferior."]
[]
[null,"Proyecto","A","B","C","D"]
[null,"Rent exigida K",0.1,0.1,0.1,0.1]
[null,0,-100,-100,-40,-100]
[null,1,10,-20,-20,-20]
[null,2,10,0,-10,0]
[null,3,10,10,0,10]
[null,4,10,20,10,20]
[null,5,10,30,15,30]
[null,6,10,30,20,40]
[null,7,10,30,20,40]
[null,8,10,20,20,40]
[null,9,10,20,15,50]
[null,10,110,100,20,50]
[]
[null,"Suma de cash flows",100,140,50,160]
[null,"TIR o IRR = "]
[null,"VA o PV = "]
[null,"VAN o NPV = "]
[]
[null,"RESPUESTAS CORRECTAS"]
[null,"Suma de cash flows",{"$f":"SUM(C82:C92)","v":100},{"$f":"SUM(D82:D92)","v":140},{"$f":"SUM(E82:E92)","v":50},{"$f":"SUM(F82:F92)","v":160}]
[null,"TIR o IRR = ",{"$f":"IRR(C82:C92,0.1)","v":0.10000000000000009},{"$f":"IRR(D82:D92,0.1)","v":0.11333692491236147},{"$f":"IRR(E82:E92,0.1)","v":8.5700450414291307E-2},{"$f":"IRR(F82:F92,0.1)","v":0.13059962361886357}]
[null,"VA o PV = ",{"$f":"NPV(C81,C83:C92)","v":99.999999999999943},{"$f":"NPV(D81,D83:D92)","v":110.31462898940565},{"$f":"NPV(E81,E83:E92)","v":34.652792041864721},{"$f":"NPV(F81,F83:F92)","v":123.86686115614312}]
[null,"VAN o NPV = ",{"$f":"C102+C82","v":0},{"$f":"D102+D82","v":10.314628989405648},{"$f":"E102+E82","v":-5.3472079581352787},{"$f":"F102+F82","v":23.866861156143116}]

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[null,"CAP. 5 PREGUNTAS DE AUTOEVALUACION (Conceptos)"]
[null,"Son las mismas que tienes en el Cap 5. Para estas preguntas no necesitas hacer ningún cálculo, pero sí tener claros los conceptos. "]
[null,"Responder V o F en columna \"I\". Respuesta correcta en columna K. Repuesta correcta = +1. Incorrecta = -1. En blanco = 0. ",null,null,null,null,null,null,null,-1]
[null,"Preguntas sobre VA, VF, TIR y K",null,null,null,null,null,null,"Tu Res-","Califi-","Respuesta"]
[null,"Bono A. Vencimiento 3 años. Cupón de 5€ año. Al vencimiento recibes 100€. Precio 100€.",null,null,null,null,null,null,"puesta","cación","Correcta"]
[1,"Bono A. Tu rentabilidad esperada es de 5%. V o F?",null,null,null,null,null,null,null,{"$f":"IF(I6=K6,1,IF(I6=\"\",0,$J$3))","v":0},"V"]
[2,"Ahora lo compras por 95€, tu rentabilidad esperada será menor que 5%. V o F?",null,null,null,null,null,null,null,{"$f":"IF(I7=K7,1,IF(I7=\"\",0,$J$3))","v":0},"F"]
[3,"Mismo bono A, pero paga 2,5€ de cupón cada semestre. La TAE del bono o TIR será la misma, es decir 5%. V o F?",null,null,null,null,null,null,null,0,"F"]
[4,"Igual que pregunta 3. La rentabilidad simple anual será del 5%. V o F?",null,null,null,null,null,null,null,0,"V"]
[5,"Mismo bono A. Quieres obtener una rentabilidad superior al 5%, por tanto deberías pagar más de 100€. V o F?",null,null,null,null,null,null,null,0,"F"]
[6,"Bono A. Han bajado los tipos de interés en el mercado y el bono A cotiza al 4%. Su precio de mercado seguro que es mayor que 100€ V o F?",null,null,null,null,null,null,null,0,"V"]
[7,"Si bajan los tipos de interés o rentabilidad exigida K del bono, este sube de precio. V o F?",null,null,null,null,null,null,null,0,"V"]
[8,"Bono cupón cero (no paga cupones). A vencimiento te pagan 100€. Para obtener una rentabilidad del 5% deberías pagar más que su valor par (100€). V o F?",null,null,null,null,null,null,null,0,"F"]
[9,"Cuando suben los tipos de interés baja el precio de los bonos y de casi todos los activos. V o F?",null,null,null,null,null,null,null,0,"V"]
[null,"Preguntas sobre VAN, VA y TIR"]
[10,"Si un proyecto tiene un VAN positivo, su TIR es mayor que la rentabilidad exigida K. V o F?",null,null,null,null,null,null,null,0,"V"]
[{"$f":"A16+1","v":11},"El VAN nos dice la rentabilidad que un proyecto promete, pero expresada en euros y no en porcentaje. V o F?",null,null,null,null,null,null,null,0,"F"]
[{"$f":"A17+1","v":12},"El VAN me indica el valor que un proyecto puede añadir al valor de la compañía. V o F?",null,null,null,null,null,null,null,0,"V"]
[13,"El VAN de un proyecto me dice los euros que ese proyecto genera para la empresa. V o F?",null,null,null,null,null,null,null,0,"F"]
[14,"La cantidad inicial a invertir en un proyecto de inversión me la indica el VAN de ese proyecto. V o F?",null,null,null,null,null,null,null,0,"F"]
[15,"La TIR es la rentabilidad de la cantidad inicial invertida en el año 0. V o F?",null,null,null,null,null,null,null,0,"V"]
[16,"En la compra de una empresa el VA para mi indica lo que debería pagar por ella. V o F?",null,null,null,null,null,null,null,0,"V"]
[17,"El VA depende exclusivamente de los cash flows que promete ese proyecto. V o F?",null,null,null,null,null,null,null,0,"F"]
[18,"VAN y NPV son el mismo concepto. V o F?",null,null,null,null,null,null,null,0,"V"]
[19,"NPV es lo mismo que valor actual VA. V o F?",null,null,null,null,null,null,null,0,"F"]
[null,"Preguntas sobre la Perpetuidad"]
[20,"Fórmula de la perpetuidad. La K indica la rentabilidad que le exiges a la inversión. V o F?",null,null,null,null,null,null,null,0,"V"]
[{"$f":"A27+1","v":21},"Como CF de la perpetuidad debes usar el que sea sostenible durante muchos años futuros. V o F?",null,null,null,null,null,null,null,0,"V"]
[22,"Puedo usar la perpetuidad para calcular la rentabilidad espera en una inversión que dura 5 años. V o F?",null,null,null,null,null,null,null,0,"F"]
[23,"En la perpetuidad, una hipótesis de (K-g) = (3%- 2,5%) es perfectamente razonable. V o F?",null,null,null,null,null,null,null,0,"F"]
[24,"Para usar la fórmula de la perpetuidad es necesario que los CF futuros sean casi iguales. V o F?",null,null,null,null,null,null,null,0,"V"]
[25,"En una startup es lógico usar la perpetuidad para calcular el valor de la empresa. V o F?",null,null,null,null,null,null,null,0,"F"]
[]
[null,null,null,null,null,null,null,"Puntos obtenidos",null,{"$f":"SUM(J6:J32)","v":0}]
[null,null,null,null,null,null,null,"Si tienes menso de 15, deberías repasar"]
[]
[null,"CALCULO FINANCIERO CON EXCEL. PREGUNTAS Y RESPUESTAS CAP 5. "]
[null,"Para responder (Col. I) haz copy & paste del número que aparece en resultados (G43:G47) en amarillo."]
[null,"Respuesta correcta = 1; error = 0. Solución correcta y comentarios en Col. K"]
[null,"Las fórmulas ya están introducidas en las celdas 43:G47.  Ver los comentarios en cada celda. "]
[]
[null,"DATOS para preguntas 1 a 16",null,"Datos","Unidad","RESULTADOS"]
[null,"Rentabilidad exigida (K)","Required return (K) ",0.04,null,"VA=",{"$f":"PV(D43,D44,D45,D47)","v":-9428.660343181924},"PV"]
[null,"Vencimiento","Maturity",1.5,"años o semestres","VF=",{"$f":"FV(D43,D44,D45,D46)","v":0},"FV"]
[null,"Pago o cupón","Payment PMT",0,"euros","Tasa=",{"$f":"RATE(D44,D45,D46,D47)","v":{"$error":"#NUM!"}},"Rate"]
[null,"Valor actual (VA)","Present value PV",null,null,"Int simple",{"$f":"G45*D48","v":{"$error":"#NUM!"}},"APR"]
[null,"Valor futuro (VF)","Future value FV",10000,"euros","TAE = ",{"$f":"EFFECT(G46,D48)","v":{"$error":"#NUM!"}},"Effect"]
[null,"Periodos de pago por año",null,1]
[null,null,null,null,null,null,null,null,"Tu Res-","Califi-","Respuesta"]
[null,"PREGUNTAS AUTOEVALUACION CAP 5. Cálculos",null,null,null,null,null,null,"puesta","cación","Correcta"]
[1,"Pagaré de empresa a 18 meses. Valor nominal, que obtendremos al vencimiento, 10.000 euros. No paga cupones. ¿Cuánto debes pagar por el pagaré para obtener una rentabilidad del 4 %?",null,null,null,null,null,null,null,{"$f":"IF(I51=K51,1,0)","v":0},-9428.660343181924]
[{"$f":"A51+1","v":2},"¿Cuánto debes pagar si quieres que la rentabilidad sea del 5 %?",null,null,null,null,null,null,null,0,-9294.2864090336498]
[{"$f":"A52+1","v":3},"¿Cuánto debes pagar si quieres que la rentabilidad sea del 4 % y el pagaré tiene un vencimiento de 12 meses?",null,null,null,null,null,null,null,0,-9615.3846153846152]
[4,"Letra del Tesoro, vencimiento 12 meses. No paga cupones. Valor facial 100.000 euros. Pagas 97.327 euros. ¿Qué rentabilidad obtienes al vencimiento?",null,null,null,null,null,null,null,0,2.7464115815755138E-2]
[5,"Con los mismos datos, ¿qué rentabilidad obtienes si el vencimiento es a 18 meses?",null,null,null,null,null,null,null,0,1.8226608811543976E-2]
[6,"Inviertes 10.000 euros en un depósito a plazo a tres años y al 4 %. Los intereses se pagan al final. ¿Cuántos euros recibirás?",null,null,null,null,null,null,null,0,11248.640000000001]
[7,"Con los mismos datos, ¿cuántos euros recibirás si el plazo es cinco años?",null,null,null,null,null,null,null,0,12166.529024000003]
[8,"Bono del Estado con vencimiento diez años. Valor nominal 1.000 euros. Cupón anual del 4 %  ó 40 euros al año. ¿Cuánto debes pagar para obtener una rentabilidad del 4 %?",null,null,null,null,null,null,null,0,-999.99999999999989]
[9,"Mismos datos. ¿Cuánto debes pagar para obtener una rentabilidad del 5%?",null,null,null,null,null,null,null,0,-922.78265070815178]
[10,"Mismos datos que en la pregunta 8. ¿Cuánto debes pagar para obtener una rentabilidad del 3 %?",null,null,null,null,null,null,null,0,-1085.3020283677583]
[11,"Mismo bono 8.  Compras a 950 euros. ¿Qué rentabilidad anual habrás obtenido al vencimiento?",null,null,null,null,null,null,null,0,4.6361305427803895E-2]
[12,"Mismo bono 8. Pagas 900 euros. ¿Qué rentabilidad anual habrás obtenido al vencimiento?",null,null,null,null,null,null,null,0,5.3149258123545221E-2]
[13,"Mismo bono. Pero ahora, el cupón se paga semestralmente (20 euros por semestre). Si pagas 1.000 euros, ¿qué rentabilidad semestral habrás obtenido al vencimiento?",null,null,null,null,null,null,null,0,2.0000000000004917E-2]
[14,"Mismos datos que en la pregunta 13. ¿Cuál es la rentabilidad anual simple que has obtenido?",null,null,null,null,null,null,null,0,4.0000000000009833E-2]
[15,"Mismos datos que en la pregunta 13. ¿Cuál es la rentabilidad anual efectiva o TIR que has obtenido?",null,null,null,null,null,null,null,0,4.0400000000009983E-2]
[16,"Has comprado un piso por 200.000 euros. Esperas obtener un alquiler de 10.000 euros cada año. También esperas que en promedio el piso se revalorice un 2 % anual durante los próximos diez años. ¿Qué rentabilidad habrás obtenido si al cabo de diez años se cumplen tus previsiones y vendes el piso?",null,null,null,null,null,null,null,0,6.6141475800501448E-2]
[]
[null,"Cálculo con Perpetuidad",null,"K =","g =","CF =","VA ="]
[null,null,null,0.1,0.03,1,{"$f":"F69/(D69-E69)","v":14.285714285714285}]
[17,"La acción ABC promete un dividendo de 1 euro anual. No esperas que el precio de la acción suba ni baje en el futuro. Quieres obtener a tu inversión en bolsa una rentabilidad K del 10 %. ¿Qué precio deberías pagar por la acción?",null,null,null,null,null,null,null,{"$f":"IF(I70=K70,1,0)","v":0},10]
[{"$f":"A70+1","v":18},"Mismos datos. Esperas que el dividendo de 1 euro crezca un 3 % cada año. ¿Qué precio deberías pagar por la acción?",null,null,null,null,null,null,null,{"$f":"IF(I71=K71,1,0)","v":0},14.285714285714285]
[19,"Has comprado un piso por 200.000 euros. Esperas obtener un alquiler de 10.000 euros el primer año, con una subida anual del 2%. ¿Qué rentabilidad obtienes?",null,null,null,null,null,null,null,{"$f":"IF(I72=K72,1,0)","v":0},7.0000000000000007E-2]
[20,"Has comprado un piso por 200.000 euros. Esperas obtener un alquiler de 10.000 euros el primer año. ¿Qué tasa de crecimiento g debe tener el alquiler para que tu rentabilidad esperada llegue al 8%?",null,null,null,null,null,null,null,{"$f":"IF(I73=K73,1,0)","v":0},0.03]
[]
[null,null,null,null,null,null,null,"Total Respuestas correctas",null,{"$f":"SUM(J51:J73)","v":0}]
[null,null,null,null,null,null,null,"Máxima puntuación posible",null,20]
[null,"ULTIMA PREGUNTA"]
[21,"Calcular la TIR, el VA y el VAN de las inversiones A, B, C y D, cuyos cash flows esperados y tasa de rentabilidad exigida K figuran en el cuadro inferior."]
[]
[null,"Proyecto","A","B","C","D"]
[null,"Rent exigida K",0.1,0.1,0.1,0.1]
[null,0,-100,-100,-40,-100]
[null,1,10,-20,-20,-20]
[null,2,10,0,-10,0]
[null,3,10,10,0,10]
[null,4,10,20,10,20]
[null,5,10,30,15,30]
[null,6,10,30,20,40]
[null,7,10,30,20,40]
[null,8,10,20,20,40]
[null,9,10,20,15,50]
[null,10,110,100,20,50]
[]
[null,"Suma de cash flows",100,140,50,160]
[null,"TIR o IRR = "]
[null,"VA o PV = "]
[null,"VAN o NPV = "]
[]
[null,"RESPUESTAS CORRECTAS"]
[null,"Suma de cash flows",{"$f":"SUM(C82:C92)","v":100},{"$f":"SUM(D82:D92)","v":140},{"$f":"SUM(E82:E92)","v":50},{"$f":"SUM(F82:F92)","v":160}]
[null,"TIR o IRR = ",{"$f":"IRR(C82:C92,0.1)","v":0.10000000000000009},{"$f":"IRR(D82:D92,0.1)","v":0.11333692491236147},{"$f":"IRR(E82:E92,0.1)","v":8.5700450414291307E-2},{"$f":"IRR(F82:F92,0.1)","v":0.13059962361886357}]
[null,"VA o PV = ",{"$f":"NPV(C81,C83:C92)","v":99.999999999999943},{"$f":"NPV(D81,D83:D92)","v":110.31462898940565},{"$f":"NPV(E81,E83:E92)","v":34.652792041864721},{"$f":"NPV(F81,F83:F92)","v":123.86686115614312}]
[null,"VAN o NPV = ",{"$f":"C102+C82","v":0},{"$f":"D102+D82","v":10.314628989405648},{"$f":"E102+E82","v":-5.3472079581352787},{"$f":"F102+F82","v":23.866861156143116}]

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[null,"Exercício 5.1",null,null,null,null,null,"Exercício 5.2",null,null,null,null,null,"Exercício 5.3",null,null,null,null,null,"Exercício 5.4",null,null,null,null,"Exercício 5.5",null,null,null,null,"Exercício 5.6",null,null,null,null,"Exercício 5.7",null,null,null,null,"Exercício 5.8",null,null,null,null,null,null,"Exercício 5.9",null,null,null,null,null,null,"Exercício 5.10",null,null,null,null,null,null,"Exercício 5.11",null,null,null,null,null,null,"Exercício 5.12",null,null,null,null,null,null,"Exercício 5.13",null,null,null,null,null,null,"Exercício 5.13",null,null,null,null,null,"Exercício 5.16",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Exercício 5.17",null,null,null,null,null,null,"Exercício 5.18",null,null,null,null,null,null,"Exercício 5.19",null,null,null,null,null,null,null,"Exercício 5.20"]
[]
[null,"n  = ",18,"meses",null,null,null,"n  = ",18,"meses",null,null,null,"n  = ",12,"meses",null,null,null,"n  = ",12,"meses",null,null,"n  = ",18,"meses",null,null,"n  = ",3,"anos",null,null,"n  = ",5,"anos",null,null,"n  = ",10,"anos",null,null,null,null,"n  = ",10,"anos",null,null,null,null,"n  = ",10,"anos",null,null,null,null,"n  = ",10,"anos",null,null,null,null,"n  = ",10,"anos",null,null,null,null,"n  = ",10,"anos",null,null,null,null,"Taxa Efetiva",{"$f":"BX15","v":2.0000000000760965E-2},"ao semestre",null,null,null,"Projeto","A",null,null,"B",null,null,"C",null,null,"D",null,null,null,null,null,"Ação ABC",null,null,null,null,null,null,"Ação ABC",null,null,null,null,null,null,"Preço apto",200000,"euros",null,null,null,null,null,"Preço apto",200000,"euros"]
[null,"VF = ",10000,"(inclui os juros)",null,null,null,"VF = ",10000,"(inclui os juros)",null,null,null,"VF = ",10000,"(inclui os juros)",null,null,null,"VF = ",100000,null,null,null,"VF = ",100000,null,null,null,"r = ",0.04,"ao ano",null,null,"r = ",0.04,"ao ano",null,null,"VF = ",1000,"ao ano",null,null,null,null,"VF = ",1000,"ao ano",null,null,null,null,"VF = ",1000,"ao ano",null,null,null,null,"VF = ",1000,"ao ano",null,null,null,null,"VF = ",1000,"ao ano",null,null,null,null,"VF = ",1000,null,null,null,null,null,null,null,null,null,null,null,"Taxa",null,0.1,null,null,0.1,null,null,0.1,null,null,0.1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Aluguel",10000,"euros / mês",null,null,null,null,null,"Aluguel",10000,"euros / mês"]
[null,"r = ",0.04,"ao ano",null,null,null,"r = ",0.05,"ao ano",null,null,null,"r = ",0.04,"ao ano",null,null,null,"PV = ",97327,null,null,null,"PV = ",97327,null,null,null,"PV = ",10000,null,null,null,"PV = ",10000,null,null,null,"Cupom = ",0.04,"ao ano",{"$f":"AO5*AO4","v":40},"por ano",null,null,"Cupom = ",0.04,"ao ano",{"$f":"AV5*AV4","v":40},"por ano",null,null,"Cupom = ",0.04,"ao ano",{"$f":"BC5*BC4","v":40},"por ano",null,null,"Cupom = ",0.04,"ao ano",{"$f":"BJ5*BJ4","v":40},"por ano",null,null,"Cupom = ",0.04,"ao ano",{"$f":"BQ5*BQ4","v":40},"por ano",null,null,"Cupom = ",0.04,"ao ano, pagos semestralmente",null,null,null,null,"APR (taxa simples)",{"$f":"CE3*2","v":4.0000000001521929E-2},"ao ano",null,null,null,"Período","FC","Fator Desc.","VP","FC","Fator Desc.","VP","FC","Fator Desc.","VP","FC","Fator Desc.","VP",null,null,null,"Dividendo (euro)",null,1,"anual",null,null,null,"Dividendo (euro)",null,1,"anual",null,null,null,"g aluguel",0.05,"ao ano",null,null,null,null,null,"g aluguel",0.05,"ao ano"]
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[null,"2 métodos:",null,null,null,null,null,"2 métodos:",null,null,null,null,null,"2 métodos:",null,null,null,null,null,"2 métodos:",null,null,null,null,"2 métodos:",null,null,null,null,"2 métodos:",null,null,null,null,"2 métodos:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"r = ",0.04,"ao ano",null,null,null,null,null,null,null,null,null,null,1,10,1.1000000000000001,9.0909090909090899,-20,1.1000000000000001,-18.18181818181818,-20,1.1000000000000001,-18.18181818181818,-20,1.1000000000000001,-18.18181818181818,null,null,null,null,null,null,null,null,null,null,"g",null,0.03,"ao ano",null,null,null,"K = ",{"$f":"DO4/DO3+DO5","v":0.1},null,null,null,null,null,null,"Periodo","Aluguel","Valorização","FC",null,"Fator Desc.","PV"]
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[null,null,null,null,null,null,null,"Para obter mais rentabilidade, deve ",null,null,null,null,null,"Se o prazo é menor, vc deve pagar menos.",null,null,null,null,null,null,null,null,null,null,"Se vc paga o mesmo e o prazo",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"+AN19+1","v":2},{"$f":"AO19","v":40},1.0816000000000001,36.982248520710058,null,null,null,{"$f":"+AU19+1","v":2},{"$f":"AV19","v":40},1.1025,36.281179138321995,null,null,null,{"$f":"+BB19+1","v":2},{"$f":"BC19","v":40},1.0609,37.703836365350178,null,null,null,8,40,1.4369887527000234,27.835986833468379,null,null,null,8,40,1.5132804074248241,26.432642492258726,null,null,null,"Período","FC","Fator Desc.","PV",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,1,2.1435888100000011,0.46650738020973315,null,null,null,8,1.2298738654248702,2.1435888100000011,0.57374523494777419,null,null,null,8,14071.004226562502,1.9925626416901929,7061.7625424447187,null,null,null,null,null,null,"TIR",{"$f":"IRR(DY8:DY18)","v":9.1164429559469573E-2},null,"Taxa Desc.","Soma PVs"]
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{"sheet":"Perpetuity","index":8,"n_rows":46,"n_cols":11,"rows_kept":46,"cut":false,"hidden":false,"merged":[]}
["Number of Cash Flows and use of the Perpetuity",null,null,null,null,null,null,null,"NOT TO BE PRINTED IN THE BOOK. "]
[]
["Present Value PV of 100€ received at year \"n\"",null,null,null,null,null,"PV of 100€ received each year, during n years"]
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[8,46.650738020973314,32.690177384616753,23.256803936137786,16.777215999999999,null,8,533.49261979026642,448.73215076922185,383.71598031931109,332.89113600000002]
[9,42.409761837248467,28.426241204014573,19.380669946781488,13.421772799999999,null,9,575.90238162751484,477.15839197323641,403.09665026609258,346.3129088]
[10,38.554328942953148,24.718470612186586,16.150558288984573,10.73741824,null,10,614.45671057046798,501.876862585423,419.24720855507718,357.05032704000001]
[11,35.049389948139222,21.494322271466597,13.458798574153812,8.5899345920000005,null,11,649.50610051860724,523.37118485688961,432.70600712923101,365.64026163200003]
[12,31.863081771035656,18.690715018666612,11.215665478461512,6.8719476736000003,null,12,681.36918228964294,542.06189987555626,443.92167260769253,372.51220930560004]
[13,28.966437973668778,16.252795668405746,9.346387898717925,5.4975581388799997,null,13,710.33562026331174,558.31469554396199,453.26806050641045,378.00976744448002]
[14,26.333125430607975,14.132865798613693,7.788656582264939,4.3980465111039999,null,14,736.66874569391973,572.44756134257568,461.05671708867538,382.407813955584]
[15,23.93920493691634,12.28944852053365,6.4905471518874487,3.5184372088832001,null,15,760.60795063083606,584.73700986310928,467.54726424056281,385.9262511644672]
[16,21.762913579014853,10.686476974377088,5.4087892932395416,2.81474976710656,null,16,782.37086420985088,595.42348683748639,472.95605353380233,388.74100093157375]
[17,19.784466890013501,9.2925886733713821,4.5073244110329513,2.2517998136852482,null,17,802.15533109986438,604.71607551085776,477.46337794483526,390.99280074525899]
[18,17.985878990921364,8.0805118898881592,3.7561036758607926,1.8014398509481984,null,18,{"$f":"H24+B25","v":820.14121009078576},612.79658740074592,481.21948162069606,392.7942405962072]
[19,16.350799082655783,7.0265320781636174,3.1300863965506602,1.4411518807585588,null,19,836.4920091734416,619.82311947890958,484.34956801724672,394.23539247696579]
[20,14.864362802414348,6.1100278940553201,2.6084053304588837,1.1529215046068471,null,20,851.35637197585595,625.93314737296487,486.9579733477056,395.38831398157265]
[21,13.513057093103951,5.3130677339611481,2.1736711087157365,0.92233720368547756,null,21,864.8694290689599,631.246215106926,489.13164445642133,396.31065118525811]
[22,12.284597357367227,4.6200588990966507,1.8113925905964472,0.73786976294838202,null,22,877.15402642632716,635.86627400602265,490.94303704701775,397.04852094820649]
[23,11.167815779424751,4.01744252095361,1.5094938254970394,0.59029581035870571,null,23,888.32184220575186,639.88371652697629,492.45253087251479,397.63881675856521]
[24,10.152559799477048,3.4934282790900961,1.2579115212475329,0.47223664828696454,null,24,898.47440200522897,643.37714480606633,493.71044239376232,398.11105340685219]
[25,{"$f":"100/(1+B$6)^$A32","v":9.229599817706406},3.0377637209479098,1.0482596010396106,0.3777893186295716,null,25,{"$f":"H31+B32","v":907.70400182293542},646.41490852701429,494.75870199480192,398.48884272548179]
[]
["Present Value",{"$f":"SUM(B8:B32)","v":907.70400182293542},{"$f":"SUM(C8:C32)","v":646.41490852701429},{"$f":"SUM(D8:D32)","v":494.75870199480192},{"$f":"SUM(E8:E32)","v":398.48884272548179}]
["Perpetuity",{"$f":"100/B6","v":1000},{"$f":"100/C6","v":666.66666666666674},{"$f":"100/D6","v":500},{"$f":"100/E6","v":400}]
["Perpetuity / PV",{"$f":"B35/B34","v":1.1016807219002089},{"$f":"C35/C34","v":1.0313293488013762},{"$f":"D35/D34","v":1.0105936449102682},{"$f":"E35/E34","v":1.0037922197875919}]
[null,null,null,null,null,null,null,"Overvaluation using perpetuity"]
[null,null,null,null,null,null,"For a (K-g) = ",{"$f":"H6","v":0.1},{"$f":"I6","v":0.15},{"$f":"J6","v":0.2},{"$f":"K6","v":0.25}]
[null,null,null,null,null,null,"Value using Perpetuity",{"$f":"B35","v":1000},{"$f":"C35","v":666.66666666666674},{"$f":"D35","v":500},{"$f":"E35","v":400}]
[null,null,null,null,null,null,"\"Real\" PV for 10 year project",{"$f":"H17","v":614.45671057046798},{"$f":"I17","v":501.876862585423},{"$f":"J17","v":419.24720855507718},{"$f":"K17","v":357.05032704000001}]
[null,null,null,null,null,null,"Overvaluation of perpetuity vs real PV for 10 year project",{"$f":"H$39/H40-1","v":0.62745394882511674},{"$f":"I$39/I40-1","v":0.32834708345056529},{"$f":"J$39/J40-1","v":0.19261378441429544},{"$f":"K$39/K40-1","v":0.12029024960167134}]
[null,null,null,null,null,null,"\"Real\" PV for 20 year project",{"$f":"H27","v":851.35637197585595},{"$f":"I27","v":625.93314737296487},{"$f":"J27","v":486.9579733477056},{"$f":"K27","v":395.38831398157265}]
[null,null,null,null,null,null,"Overvaluation for 20 year project",{"$f":"H$39/H42-1","v":0.17459624772545834},{"$f":"I$39/I42-1","v":6.5076469371625478E-2},{"$f":"J$39/J42-1","v":2.6782653465213802E-2},{"$f":"K$39/K42-1","v":1.1663688215737933E-2}]
[]
[null,null,null,null,null,null,"N of years, so that the perpetuity exceeds no more than 10% the PV",25,17,13,11]
[null,null,null,null,null,null,"PV that is 10% lower than the perpetuity",{"$f":"H39/1.1","v":909.09090909090901},{"$f":"I39/1.1","v":606.06060606060612},{"$f":"J39/1.1","v":454.5454545454545},{"$f":"K39/1.1","v":363.63636363636363}]