Problem #1 (16)
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).
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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
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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 µ corresponding to a 98% confidence level. (where µ is
the true mean yearly cash flow)
3). If a yearly cash flow of less than ½ 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 geologists 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 States 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.
.gif”> 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 Oilcos 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) (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). .gif">
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
.gif”>
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 µ corresponding to a 98% confidence level. (where µ is
the true mean yearly cash flow)
3). If a yearly cash flow of less than ½ 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 geologists 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 States 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.
.gif”> 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 Oilcos 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)
