__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).

**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** where

* V, C = PC * V , T= F * (R-C-D)

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 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.

**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).

**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** where

* V, C = PC * V , T= F * (R-C-D)

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 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.

**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)