The ABC corporation is interested in purchasing a small manufacturing firm

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 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.

.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 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) (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 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.

.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 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)