Decisiones en Proyectos de Inversión: El Promedio y la Variancia del NPV y el IRR - Prof. , Apuntes de Administración de Empresas

¡Descarga Decisiones en Proyectos de Inversión: El Promedio y la Variancia del NPV y el IRR - Prof. y más Apuntes en PDF de Administración de Empresas solo en Docsity! es» Universidad Rey Juan Carlos e ú Financial Management BUSINESS AND ADMINISTRATION DEGREE Vicalvaro, 2017  Topic 5. Investment Project decisions based on the average and the variance of NPV and IRR Financial Management l Introduction In case of similar Average of NPV go ahead with the project with the lowest variance. In case of similar variances go ahead with the project with the highest Average. Financial Management l www.urjc.es Average of NPV AM (C0 ) = C0 rP∑ 0 r AM (CFt ) = CFt rPt r∑ C0 r = Capital expenditure r of period 0 P0 r=Probability of C0 r CFt r=Cash Flow r of period t P0 r = Probability of CFt r Financial Management l www.urjc.es Average of NPV NPV = −C0 + CF1 (1+ k) + CF2 (1+ k)2 +...+ CFt (1+ k)t AM (NPV ) = −AM (C0 )+ AM (CF1) (1+ k) + AM (CF2 ) (1+ k)2 +...+ AM (CFt ) (1+ k)t CF = Cash Flow AM = Arithmetic mean k = Cost of capital t = Period Financial Management l www.urjc.es Example 1 —  Assuming the following project finance, choose the best one according with the Average and Variance of NPV. Project A and B have similar AM (NPV) but Variance of NPV (B) is much lower than Variance of NPV (A), it means that the risk of variability of FCF is lower in project B. Project Arithmetic Mean (NPV) Variance (NPV) A 15.000 5.000 B 14.500 1.000 Financial Management l www.urjc.es Example 2 —  Assuming the following project finance, choose the best one according with the Average and Variance of NPV. Project C and D have similar variances, it means that the risk of variability of FCF are similar, both project finance have similar risk. However AM (NPV project D) is much higher than AM (NPV project C). Project Arithmetic Mean Variance C 15.000 5.000 D 30.000 5.250 Financial Management l www.urjc.es NPV and normal distribution ª  Based on the Central Limit theorem we can assume that probability of the NPV follows the normal distribution. ª  The central limit theorem estates that the mean of a large number of random variables independently drawn from the same distribution is distributed approximately normally. ª  Normal distribution can be used to estimate the probability of a sum of random variables. ª  We can assume that “a large number of random variables” is with 10 or more. However, investment analyst usually takes the normal distribution. The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough. Financial Management l www.urjc.es Tables of the Normal Distribution $ Probability Content from -oo JA 0.04 0.05 0.06 0.07 0.08 0 O” 2 -5319 0.5359 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 O 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.9987(0.9987)0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 Summery Ø NPV is the sum of random variables. Ø The NPV of an investment, calculated on the basis of the average cash flows, must be accompanied by the variance. Ø The highest average of NPV and the lowest variance are keys that the investment project to be accepted. Ø  Normal distribution can be used to estimate the probability of a sum of random variables (>10). Financial Management l www.urjc.es Quiz 1 —  If the company know that the mathematical expectation of the Cash flow (10,000) is identical to its value, the variance of this cash flow will be: —  A) 10,000 C) <10,000 —  B) 0 D) None 25 50 75 100%Resp. Votos F E D C B A 3209876315432131098763054321300987629543212909876285432281 2809876275432127098762654321260987625543212509876245432241 2409876235432123098762254321220987621543212109876205432201 2009876195432119098761854321180987617543211709876165432161 1609876155432115098761454321140987613543211309876125432121 120987611543211109876105432110098769543219098768543281 8098767543217098766543216098765543215098764543241 40987635432130987625432120987615432110987654321 1 180179178177176175174173172171170169168167166165164163162161160159158157156155154153152151 150149148147146145144143142141140139138137136135134133132131130129128127126125124123122121 120119118117116115114113112111110109108107106105104103102101100999897969594939291 908988878685848382818079787776757473727170696867666564636261 605958575655545352515049484746454443424140393837363534333231 302928272625242322212019181716151413121110987654321 605958575655545352515049484746 454443424140393837363534333231 302928272625242322212019181716 15141312111098765432 329282726524232221 20191817161514131211 1098765321 100999897969594939291908988878685848382818079787776 75747372717069686766656463626160595857565554535251 504948474645444342410393837363534333233029282726 25242322212019181716151413121110987654321 A vanzar siguiente Cancelar Votac. Prórroga T iempo Fin Votación Restante 0 Ver Gráfica 0 0 0 T iempo Participantes Votos Inicio Votación Financial Management l www.urjc.es —  Which of the following methods of selecting a strategy is consistent with risk averting behavior? —  A) If two strategies have the same expected profit, select the one with the smaller standard deviation. —  B) If two strategies have the same standard deviation, select the one with the smaller expected profit. —  C) Select the strategy with the larger coefficient of variation. —  D) All of the above are correct. Quiz 4 25 50 75 100%Resp. Votos F E D C B A 3209876315432131098763054321300987629543212909876285432281 2809876275432127098762654321260987625543212509876245432241 2409876235432123098762254321220987621543212109876205432201 2009876195432119098761854321180987617543211709876165432161 1609876155432115098761454321140987613543211309876125432121 120987611543211109876105432110098769543219098768543281 8098767543217098766543216098765543215098764543241 40987635432130987625432120987615432110987654321 1 180179178177176175174173172171170169168167166165164163162161160159158157156155154153152151 150149148147146145144143142141140139138137136135134133132131130129128127126125124123122121 120119118117116115114113112111110109108107106105104103102101100999897969594939291 908988878685848382818079787776757473727170696867666564636261 605958575655545352515049484746454443424140393837363534333231 302928272625242322212019181716151413121110987654321 605958575655545352515049484746 454443424140393837363534333231 302928272625242322212019181716 15141312111098765432 329282726524232221 20191817161514131211 1098765321 100999897969594939291908988878685848382818079787776 75747372717069686766656463626160595857565554535251 504948474645444342410393837363534333233029282726 25242322212019181716151413121110987654321 A vanzar siguiente Cancelar Votac. Prórroga T iempo Fin Votación Restante 0 Ver Gráfica 0 0 0 T iempo Participantes Votos Inicio Votación Financial Management l www.urjc.es —  Why do you need a measure of variability? —  A) to describe how far the data are spread around the mean. —  B) to calculate the mean. —  C) to understand the lowest and highest points in the data. —  D) to calculate the median. Quiz 5 25 50 75 100%Resp. Votos F E D C B A 3209876315432131098763054321300987629543212909876285432281 2809876275432127098762654321260987625543212509876245432241 2409876235432123098762254321220987621543212109876205432201 2009876195432119098761854321180987617543211709876165432161 1609876155432115098761454321140987613543211309876125432121 120987611543211109876105432110098769543219098768543281 8098767543217098766543216098765543215098764543241 40987635432130987625432120987615432110987654321 1 180179178177176175174173172171170169168167166165164163162161160159158157156155154153152151 150149148147146145144143142141140139138137136135134133132131130129128127126125124123122121 120119118117116115114113112111110109108107106105104103102101100999897969594939291 908988878685848382818079787776757473727170696867666564636261 605958575655545352515049484746454443424140393837363534333231 302928272625242322212019181716151413121110987654321 605958575655545352515049484746 454443424140393837363534333231 302928272625242322212019181716 15141312111098765432 329282726524232221 20191817161514131211 1098765321 100999897969594939291908988878685848382818079787776 75747372717069686766656463626160595857565554535251 504948474645444342410393837363534333233029282726 25242322212019181716151413121110987654321 A vanzar siguiente Cancelar Votac. Prórroga T iempo Fin Votación Restante 0 Ver Gráfica 0 0 0 T iempo Participantes Votos Inicio Votación Financial Management l www.urjc.es Quiz 6 If a random variable is normally distributed, A) The random variable cannot assume negative numbers. B) The distribution of the random variable is defined by a mean and standard deviation. 25 50 75 100%Resp. Votos F E D C B A 3209876315432131098763054321300987629543212909876285432281 2809876275432127098762654321260987625543212509876245432241 2409876235432123098762254321220987621543212109876205432201 2009876195432119098761854321180987617543211709876165432161 1609876155432115098761454321140987613543211309876125432121 120987611543211109876105432110098769543219098768543281 8098767543217098766543216098765543215098764543241 40987635432130987625432120987615432110987654321 1 180179178177176175174173172171170169168167166165164163162161160159158157156155154153152151 150149148147146145144143142141140139138137136135134133132131130129128127126125124123122121 120119118117116115114113112111110109108107106105104103102101100999897969594939291 908988878685848382818079787776757473727170696867666564636261 605958575655545352515049484746454443424140393837363534333231 302928272625242322212019181716151413121110987654321 605958575655545352515049484746 454443424140393837363534333231 302928272625242322212019181716 15141312111098765432 329282726524232221 20191817161514131211 1098765321 100999897969594939291908988878685848382818079787776 75747372717069686766656463626160595857565554535251 504948474645444342410393837363534333233029282726 25242322212019181716151413121110987654321 A vanzar siguiente Cancelar Votac. Prórroga T iempo Fin Votación Restante 0 Ver Gráfica 0 0 0 T iempo Participantes Votos Inicio Votación C) The variance of the random variable must be greater than one. Financial Management l www.urjc.es