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##### stats problems with solution fall 2014

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Question;Problem;#1 (16);The ABC corporation is interested;in purchasing a small manufacturing firm (making car seats). An initial Investment of $15 million is;required. Let us assume that the sale;price of the car seat is normally distributed with a mean of $65, and standard deviation of;$4.00 per unit. Also we assume that the;sales volume is governed by the following empirical distribution;Yearly;Sales Volume (in 1000);Probability;--------------------------------------- ----------------------;90 ? 120 0.25;120 -- 150 0.47;150 ? 180 0.28;The cost (of production) is uniformly distributed between $20-$50. We want to accurately estimate the yearly net;cash flow assuming a corporate (composite;tax rate (T) which is 45% now but there;is a 60% Probability that it will jump to 55% starting next year. Use the;following notations and equations to the questions asked (See what is required;below).;Notations;YCF = Annual cash Flow, R= annual Revenue, C = annual cost;PC= production cost per;unit, T = annual tax, F= corporate tax rate;P= Sale Price per;unit, V= sales volume;Equations;SCF = R-C-T, R=P;* V, C = PC * V, T= F * (R-C-D) where;D= depreciation per year. Use straight;line depreciation for n=15 years;What is required;Assume D=depreciation (linear;deprecistion for 10 years),develop the simulation;mode, run it 60 times and determine;1). The expected value (mean) of;the yearly cash flow;2). Determine the limits of ? corresponding to a 98% confidence level. (where ? is;the true mean yearly cash flow);3). If a yearly cash flow of less than ? of the above average (determined;in part 1) is considered a Total;Loss, determine the probability that the company will be in ?Total Loss? situation.;Problem;#2 (16Points);A nuclear power company is deciding;whether or not to build a power plant at;city ?D? or city? R?. The cost of building the power plant is $10;million at city D and $20 Million at city C. IF the company builds at city D;however, and an earthquake occurs (at that city) during the next 5 years;construction will be terminated and the company will loose $10 million.(and will;still have to build at city C). The;company, from historical data, believes;that there is 20% chance that an earthquake will occur in city D during the;next 5 years. For $1 million, a;geologist can be hired to analyze the;fault structure in City D. He will;either predict that an earthquake will occur or will not occur. The geologist?s past record indicates that he;will predict an earthquake on 95% of the;occasions for which an earthquake will occur. He will also predict no earthquake;on 90% of the occasions for which an earthquake will not occur. Use this;information and answer the following questions;a). develop the decision tree of the situation. (Make sure the Tree has all the relevant;information on it);b)- Determine Pr(the geologist;will say Earthquake);c)- Should the power plant hire;the geologist.;D). What is the least attractive;alternative available for the company now.;Problem #3. (18 Poimts);The;Nestle Financial Services Company, is considering investing $20 million in;stock market. The company uses;regression analysis to predict the market condition for the next 12 months;before determining to invest in stock or the alternative, invest in Bonds and;CDs (with only 2.5% fixed and sure return/year). They have decided that The United State?s stock market index (Y) fluctuations is related to a number of;overseas market indexes, including, European Market Index (X1), Asian Market;index (X2), Far East market index (X3), and South American market index. For the past 10 years, the average semiannual;market index are available and are presented in the following table.;Year Y X1 X2 X3 X4;1 240 35 24 91 100;236 31 21 90 95;2 270 45 24 88 110;274 60 25 87 88;3 267 75 24 88 110;276 60 25 91 105;4 288 50 25 90 100;281 38 23 89 98;5 245 27 26 79 112;256 38 25 89 87;6 275 61 23 91 98;232 32 24 87 101;7 310 73 27 92 109;306 66 27 95 102;8 268 74 23 89 103;301 65 25 91 94;9 300 80 25 87 97;296 84 25 86 96;10 307 64 28 98 85;316 72 26 99 99;A). Determine the relationship between Y and X1;X2,?X4. Interpret the resulting equation;B). Test the significance of regression;coefficients using?=0.05;C). Determine a 95% confidence interval for mean value of Y when X1=75, X2= 24;X3 = 90, and;X4=104;D). It is;estimated that, Total gain in value of stock (in one year) is determined;from the equation;Yearly;gain = (Y-280)/10) * 1.05 Million.;If the condition stated in part C above;represent the;Estimate for the index for the;next year, should the company invest in stock or buy bond and realize a;rate of return of 2.5%.. At that point, what is the probability that;buying stock will be more profitable;than the alternative (ie., buying Bond;CDs).;Problem #4 (16 Points);Oilco must decide whether or not;to drill for oil in the South China sea or not.;It cost $100000 and if Oil is discovered, its value is estimated to be;$600000. Oilco believes there is a 45%;chance that the field contain oil.;Before making decision on drilling, Oilco can hire (for $10000) a consultant to;obtain more information about the likelihood that the field contain oil.;There is Y % chance that the consultant will issue a;favorable report (saying there is oil).;Given a favorable report, there is 80% chance that the field contain;oil. Given an unfavorable report, there;is;There is only w % chance that the field contains Oil.;1) Assuming Y=50% and W=;10%, Determine Oilco?s Optimum course of;action.;2) the historical information;shows that, Y >30, and;W <25. Conduct a sensitivity analysis, graph a tornado (type) diagram and;interpret the results (best course of action under different conditions)

Paper#61288 | Written in 18-Jul-2015

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