OPS MGMT – The ABC corporation is interested in purchasing a small manufacturing firm

Problem #1 (16)The ABC corporation is interested in purchasing a small manufacturing firm (making car seats). Aninitial Investment of $15 million is required. Let us assume that the sale price of the car seat is normallydistributed with a mean of $65, and standard deviation of $4.00 per unit. Also we assume that the salesvolume is governed by the following empirical distributionYearly Sales Volume (in 1000)Probability———————————————————–90 1200.25120 — 1500.47150 1800.28The cost (of production) is uniformly distributed between $20-$50. We want to accurately estimate theyearly net cash flow assuming a corporate (composite )tax rate (T) which is 45% now but there is a60% Probability that it will jump to 55% starting next year. Use the following notations and equations tothe 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 volumeEquations:SCF = R-C-T,R=P * V, C = PC * V , T= F * (R-C-D) where D= depreciation per year. Usestraight line depreciation for n=15 yearsWhat is required:Assume D=depreciation (linear deprecistion for 10 years), develop the simulation mode, run it 60times and determine:1). The expected value (mean) of the yearly cash flow2). Determine the limits of corresponding to a 98% confidence level. (where isthe 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 TotalLoss, 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 companybuilds at city D, however, and an earthquake occurs (at that city) during the next 5 years, constructionwill be terminated and the company will loose $10 million.(and will still have to build at city C). Thecompany, from historical data, believes that there is 20% chance that an earthquake will occur in city Dduring the next 5 years. For $1 million, a geologist can be hired to analyze the fault structure in CityD. He will either predict that an earthquake will occur or will not occur. The geologists past recordindicates 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. Usethis information and answer the following questions:a). develop the decision tree of the situation. (Make sure the Tree has all the relevantinformation 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. Thecompany uses regression analysis to predict the market condition for the next 12 months beforedetermining to invest in stock or the alternative, invest in Bonds and CDs ( with only 2.5% fixed andsure return/year). They have decided that The United States stock market index (Y) fluctuations isrelated to a number of overseas market indexes, including, European Market Index (X1), Asian Marketindex (X2), Far East market index (X3), and South American market index. For the past 10 years, theaverage semiannual market index are available and are presented in the following table.Year1345678910X135314560756050382738613273667465808464X224212425242525232625232427272325252528X391908887889190897989918792958991878698X41009511088110105100981128798101109102103949796853162Y24023627027426727628828124525627523231030626830130029630772269999A). Determine the relationship between Y and X1, X2,X4. Interpret the resulting equationB). Test the significance of regression coefficients using =0.05C). Determine a 95% confidence interval for mean value of Y when X1=75, X2= 24, X3 = 90, andX4=104D). 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 theEstimate for the index for the next year, should the company invest in stock or buy bond andrealize arate of return of 2.5%. . At that point, what is the probability that buying stock will be moreprofitablethan 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 Oilis discovered , its value is estimated to be $600000. Oilco believes there is a 45% chance that the fieldcontain oil. Before making decision on drilling, Oilco can hire (for $10000) a consultant to obtain moreinformation 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 afavorable report, there is 80% chance that the field contain oil. Given an unfavorable report, there isThere is only w % chance that the field contains Oil.1) Assuming Y=50% and W= 10%, Determine Oilcos Optimum course of action.2) the historical information shows that ; Y >30 , and W <25. Conduct a sensitivity analysis, graph atornado (type) diagram and interpret the results (best course of action under different conditions)