Deck 12: Probabilistic Risk Analysis

Question 1

A large mudslide caused by heavy rains will cost Sabino County $1,000,000 per occurrence in lost property tax revenues. In any given year, there is one chance in 100 that a major mudslide will occur.
A civil engineer has proposed constructing a culvert on a mountain where mudslides are likely. This culvert will reduce the likelihood of a mudslide to near zero. The investment cost would be $50,000, and annual maintenance expenses would be $2,000 in the first year, increasing by 5% per year thereafter. If the life of the culvert is expected to be 20 years and the cost of capital to Sabino County is 7% per year, should the culvert be built (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Answer 1

To determine whether this culvert should be built, we proceed as follows:
The equivalent uniform annual cost for the large mudslide caused by heavy rains for Sabino County is $1,000,000 per occurrence for any given year, and there is one chance in 100, that is 0.01 chance, that it will occur: …… (1)
An equivalent uniform annual cost for the culvert that costs $50,000 and the annual maintenance cost of $2,000 in the first year are increasing by 5%: thereafter, the culvert life of 20 years with MARR of 7% per year will be given as: (2)
Substitute 0.2584 for , 2.6533 for , and 0.0944 for in equation (2) from the interest chart. …… (3) Now, from equation (1) and (3), .
Thus, this culvert should be built.

Question 2

A bridge is to be constructed now as part of a new road. An analysis has shown that traffic density on the new road will justify a two-lane bridge at the present time. Because of uncertainty regarding future use of the road, the time at which an extra two lanes will be required is currently being studied. The estimated probabilities of having to widen the bridge to four lanes at various times in the future are as follows:
The present estimated cost of the two-lane bridge is $2,000,000. If constructed now, the four-lane bridge will cost $3,500,000. The future cost of widening a two-lane bridge will be an extra $2,000,000 plus $250,000 for every year that widening is delayed. If money can earn 12% per year, what would you recommend (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Answer 2

The present estimated cost of the two-lane bridge is $2,000,000.
If the four-lane bridge is constructed now, it will cost $3,500,000.
The cost of widening the two-lane bridge in the future will be an extra $2,000,000 plus $250,000 for every year the widening is delayed.
Present worth ( PW ) of expansion in the future is calculated as: Where,
PW is the present worth,
k is the year in which the expansion takes place, and
i is the interest rate.
The following table calculates the cost of widening if the expansion takes place in the 3 rd , 4 th , 5 th or 6 th year. The expected present worth of expansion in the future is: It can be seen that the present worth of constructing the four-lane bridge now is less than the expected present worth of constructing the four-lane bridge in future. That is,

Question 3

A new snow making machine utilizes technology that permits snow to be produced in ambient temperature of 70 degrees Fahrenheit or below. The estimated cash flows for the ski resort contemplating this investment are uncertain as shown below (note: pr. = probability).
The machine is expected to have a useful life of 12 years, and the MARR of the ski resort is 8% per year. What is the expected present worth of this investment

Answer 3

Present worth of an investment project is the current value of all the future cash flows associated with the project discounted at appropriate rate.
It is given that the cash flows for the company are uncertain. An investment is made in a machine which produces snow in 70 degree Fahrenheit or below. The following information is given:
Capital Investment is $120,000 with probability 1.0. Annual revenues are given to be $140,000 with probability 0.6 or $135,000 with probability 0.4. Annual expenses are given to be $60,000 with probability 0.6 or $50,000 with probability 0.4. Salvage value is given to be $40,000 with probability 0.5 or $35,000 with probability 0.5.The life expectancy of the machine is 12 years with MARR 8%.
It is required to compute the Expected present worth for which expected revenues, expenses and salvage value needs to be known.
Expected Revenues can be computed as shown below: Expected Expenses can be computed as shown below: Expected Salvage Value can be computed as shown below: Expected Present Worth can be computed as shown below: Hence, the expected present worth is . This investment is recommended.

Question 4

It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 5

Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 6

A very important levee spans a distance of 10 miles on the outskirts of a large metropolitan area. Hurricanes have hit this area twice in the past 20 years, so there is concern over the structural integrity of this particular levee. City engineers have proposed reinforcing and increasing the height of the levee by various designs to withstand the storm surge of numerous strength categories of hurricanes.
Study results regarding the probability that high flood water from a hurricane in any one year will exceed the increased height of the levee, and the cost of construction of the levee for each storm category, are summarized next.
A panel of experts suggests that the average property damage will amount to $100,000,000 if a storm surge causes the levee to overflow. The capital investment to rebuild the levee for each hurricane category will be financed with 30-year municipal bonds earning 6% per year. These bonds will be retired as annuity payments each year. What is the most economical way to rebuild the levee to protect the city from flooding during a hurricane What other factors might affect the decision in this situation What if the average damage from a flood is $200,000,000 (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 7

A diesel generator is needed to provide auxiliary power in the event that the primary source of power is interrupted. Various generator designs are available, and more expensive generators tend to have higher reliabilities should they be called on to produce power. Estimates of reliabilities, capital investment costs, operating and maintenance expenses, market value, and damages resulting from a complete power failure (i.e., the standby generator fails to operate) are given in Table for three alternatives. If the life of each generator is 10 years and MARR = 10% per year, which generator should be chosen if you assume one main power failure per year Does your choice change if you assume two main power failures per year (Operating and maintenance expenses remain the same.) (Problem)
Table
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 8

The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating and maintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates that there is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 9

Refer to Problem 1. Assume the following changes: the study period is eight years; the ski lift will be depreciated lay using the MACRS Alternative Depreciation System (ADS); the ADS recovery period is seven years; MARR = 15% per year (after-tax); and the effective income tax rate ( t ) is 40%. Based on this information, what is the E (PW) and SD(PW) of the ATCF Interpret the analysis results and make a recommendation on installing the ski lift. (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.
Problem 1
The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating and maintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates that there is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed (Problem)

Question 10

An energy conservation project is being evaluated. Four levels of performance are considered feasible. The estimated probabilities of each performance level and the estimated before-tax cost savings in the first year are shown in the following table:
Assume the following:
• Initial capital investment: $100,000 [80% is depreciable property and the rest (20%) are costs that can be immediately expensed for tax purposes].
• The ADS under MACRS is being used. The ADS recovery period is four years.
• The before-tax cost savings are estimated to increase 6% per year after the first year.
• MARR at = 12% per year; the analysis period is five years; MV 5 = 0.
•The effective income tax rate is 40%.
Based on E (PW) and after-tax analysis, should the project be implemented (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 11

The purchase of a new piece of electronic measuring equipment for use in a continuous metalforming process is being considered. If this equipment were purchased, the capital cost would be $418,000, and the estimated savings are $148,000 per year. The useful life of the equipment in this application is uncertain. The estimated probabilities of different useful lives occurring are shown in the following table. Assume that MARR = 15% per year before taxes and the market value at the end of its useful life is equal to zero. Based on a before-tax analysis,
a. What are the E (PW), V (PW), and SD(PW) associated with the purchase of the equipment
b. What is the probability that the PW is less than zero Make a recommendation and give your supporting logic based on the analysis results. (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 12

The tree diagram in Figure describes the uncertain cash flows for an engineering project. The analysis period is two years, and MARR = 15% per year. Based on this information,
a. What are the E (PW), V (PW), and SD(PW) of the project
b. What is the probability that PW 0 (12.3)

Question 13

A potential project has an initial capital investment of $100,000. Net annual revenues minus expenses are estimated to be $40,000 (A$) in the first year and to increase at the rate of 6.48% per year. The useful life of the primary equipment, however, is uncertain, as shown in the following table:
Assume that i m = MARR = 15% per year and f = 4% per year. Based on this information,
a. What are the E (PW) and SD(PW) for this project
b. What is the Pr{PW 0}
c. What is the E ( AW ) in R$
Do you consider the project economically acceptable, questionable, or not acceptable, and why (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 14

A hospital administrator is faced with the problem of having a limited amount of funds available for capital projects. He has narrowed his choice down to two pieces of x-ray equipment, since the radiology department is his greatest producer of revenue. The first piece of equipment (Project A) is a fairly standard piece of equipment that has gained wide acceptance and should provide a steady flow of income. The other piece of equipment (Project B), although more risky, may provide a higher return. After deliberation with his radiologist and director of finance, the administrator has developed the following table:
Figure
Discovering that the budget director of the hospital is taking courses in engineering, the hospital administrator has asked him to analyze the two projects and make his recommendation. Prepare an analysis that will aid the budget director in making his recommendation, in this problem, do risk and reward travel in the same direction (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 15

In an industrial setting, process steam has been found to be normally distributed with an average value of 25,000 pounds per hour. There is an 80% probability that steam flow lies between 20,000 and 30,000 pounds per hour. What is the variance of the steam flow (Problem 1)
Problem 1
Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 16

Suppose that a random variable (e.g., market value for a piece of equipment) is normally distributed, with mean = $175 and variance = 25$ 2. What is the probability that the actual market value is at least $171 (Problem 1)
Problem 1
Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 17

The use of three estimates (defined here as H = high, L = low, and M = most likely) for random variables is a practical technique for modeling uncertainty in some engineering economy studies. Assume that the mean and variance of the random variable, X k , in this situation can be estimated by E(X k ) = (1/6)( H + 4 M + L ) and V ( X k ) = [ (H - L) /6] 2. The estimated net cash-flow data for one alternative associated with a project are shown in Table.
The random variables, X k , are assumed to be statistically independent, and the applicable MARR = 15% per year. Based on this information,
a. What are the mean and variance of the PW
b. What is the probability that PW 0 (state any assumptions that you make)
c. Is this the same as the probability that the IRR is acceptable Explain. (Problem 1)
Table
Problem 1
Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 18

Two mutually exclusive investment alternatives are being considered, and one of them must be selected.
Alternative A requires an initial investment of $13,000 in equipment. Annual operating and maintenance costs are anticipated to be normally distributed, with a mean of $5,000 and a standard deviation of $500. The terminal salvage value at the end of the eight-year planning horizon is anticipated to be normally distributed, with a mean of $2,000 and a standard deviation of $800.
Alternative B requires end-of-year annual expenditures over the eight-year planning horizon, with the annual expenditure being normally distributed with a mean of $7,500 and a standard deviation of $750. Using a MARR of 15% per year, what is the probability that Alternative A is the most economic alternative (i.e., the least costly) (Problem 1)
Problem 1
Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 19

Two investment alternatives are being considered. The data below have been estimated by a panel of experts, and all cash flows are assumed to be independent. Life is not a variable.
With MARR = 15% per year, determine the mean and standard deviation of the incremental PW [i.e., ( B - A )]. (Problem 1)
Problem 1
Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 20

The market value of a certain asset depends upon its useful life as follows:
a. The asset requires a capital investment of $120,000, and MARR is 15% per year. Use Monte Carlo simulation and generate four trial outcomes to find its expected equivalent AW if each useful life is equally likely to occur. (Problem 2)
b. Set up an equation to determine the variance of the assets AW. (Problem 1)
Problem 1
Annual profit ( P ) is the product of total annual sales ( S ) and profit per unit sold ( X ); that is, P = X S. It is desired to know the probability distribution of the random variable P when X and S have the following assumed probability mass functions ( X and S are independent):
What are the mean, variance, and standard deviation of the probability distribution for annual profit, P (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.
Problem 2
Problem 2
A very important levee spans a distance of 10 miles on the outskirts of a large metropolitan area. Hurricanes have hit this area twice in the past 20 years, so there is concern over the structural integrity of this particular levee. City engineers have proposed reinforcing and increasing the height of the levee by various designs to withstand the storm surge of numerous strength categories of hurricanes.
Study results regarding the probability that high flood water from a hurricane in any one year will exceed the increased height of the levee, and the cost of construction of the levee for each storm category, are summarized next.
A panel of experts suggests that the average property damage will amount to $100,000,000 if a storm surge causes the levee to overflow. The capital investment to rebuild the levee for each hurricane category will be financed with 30-year municipal bonds earning 6% per year. These bonds will be retired as annuity payments each year. What is the most economical way to rebuild the levee to protect the city from flooding during a hurricane What other factors might affect the decision in this situation What if the average damage from a flood is $200,000,000

Question 21

A company that manufactures automobile parts is weighing the possibility of investing in an FMC (Flexible Manufacturing Cell). This is a separate investment and not a replacement of the existing facility. Management desires a good estimate of the distribution characteristics for the AW. There are three random variables i.e., they have uncertainties in their values.
An economic analyst is hired to estimate the desired parameter, AW. He concludes that the scenario presented to him is suitable for Monte Carlo simulation (method of statistical trials) because there are uncertainties in three variables and the direct analytical approach is virtually impossible.
The company has done a preliminary economic study of the situation and provided the analyst with the following estimates:
All the elements subject to variation vary independently. Use Monte Carlo simulation to generate 10 AW outcomes for the proposed FMC. What is the standard deviation of the outcomes (Problem 1 and 2)
Problem 1
A very important levee spans a distance of 10 miles on the outskirts of a large metropolitan area. Hurricanes have hit this area twice in the past 20 years, so there is concern over the structural integrity of this particular levee. City engineers have proposed reinforcing and increasing the height of the levee by various designs to withstand the storm surge of numerous strength categories of hurricanes.
Study results regarding the probability that high flood water from a hurricane in any one year will exceed the increased height of the levee, and the cost of construction of the levee for each storm category, are summarized next.
A panel of experts suggests that the average property damage will amount to $100,000,000 if a storm surge causes the levee to overflow. The capital investment to rebuild the levee for each hurricane category will be financed with 30-year municipal bonds earning 6% per year. These bonds will be retired as annuity payments each year. What is the most economical way to rebuild the levee to protect the city from flooding during a hurricane What other factors might affect the decision in this situation What if the average damage from a flood is $200,000,000 (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.
Problem 2
A diesel generator is needed to provide auxiliary power in the event that the primary source of power is interrupted. Various generator designs are available, and more expensive generators tend to have higher reliabilities should they be called on to produce power. Estimates of reliabilities, capital investment costs, operating and maintenance expenses, market value, and damages resulting from a complete power failure (i.e., the standby generator fails to operate) are given in Table for three alternatives. If the life of each generator is 10 years and MARR = 10% per year, which generator should be chosen if you assume one main power failure per year Does your choice change if you assume two main power failures per year (Operating and maintenance expenses remain the same.) (Problem)
Table

Question 22

Simulation results are available for two mutually exclusive alternatives. A large niunber of trials have been run with a computer, with the results shown in Figure.
Figure
Discuss the issues that may arise when attempting to decide between these two alternatives. (Problem 1 and 2)
Problem 1
A very important levee spans a distance of 10 miles on the outskirts of a large metropolitan area. Hurricanes have hit this area twice in the past 20 years, so there is concern over the structural integrity of this particular levee. City engineers have proposed reinforcing and increasing the height of the levee by various designs to withstand the storm surge of numerous strength categories of hurricanes.
Study results regarding the probability that high flood water from a hurricane in any one year will exceed the increased height of the levee, and the cost of construction of the levee for each storm category, are summarized next.
A panel of experts suggests that the average property damage will amount to $100,000,000 if a storm surge causes the levee to overflow. The capital investment to rebuild the levee for each hurricane category will be financed with 30-year municipal bonds earning 6% per year. These bonds will be retired as annuity payments each year. What is the most economical way to rebuild the levee to protect the city from flooding during a hurricane What other factors might affect the decision in this situation What if the average damage from a flood is $200,000,000 (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.
Problem 2
A diesel generator is needed to provide auxiliary power in the event that the primary source of power is interrupted. Various generator designs are available, and more expensive generators tend to have higher reliabilities should they be called on to produce power. Estimates of reliabilities, capital investment costs, operating and maintenance expenses, market value, and damages resulting from a complete power failure (i.e., the standby generator fails to operate) are given in Table for three alternatives. If the life of each generator is 10 years and MARR = 10% per year, which generator should be chosen if you assume one main power failure per year Does your choice change if you assume two main power failures per year (Operating and maintenance expenses remain the same.) (Problem)
Table

Question 23

If the interest rate is 8% per year, what decision would you make based on the decision tree diagram in Figure (Problem 1)
Figure
Problem 1
The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating and maintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates that there is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 24

Extended Learning Exercise The additional investment in a new computer system is a certain $300,000. It is likely to save an average of $100,000 per year compared to the old, outdated system. Because of uncertainty, this estimate is expected to be normally distributed, with a standard deviation of $7,000. The market value of the system at any time is its scrap value, which is $20,000 with a standard deviation of $3,000. MARR on such investments is 15% per year.
What is the smallest value of N (the life of the system) that can exist such that the probability of getting a 15% internal rate of return or greater is 0.90 Ignore the effects of income taxes. Also note that market value is independent of N. (Problem)
Problem
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.

Question 25

Extended Learning Exercise A firm must decide between constructing a new facility or renting a comparable office space. There are two random outcomes for acquiring space, as shown in Figure. Each would accommodate the expected growth of this company over the next 10 years. The cost of rental space is expected to escalate over the 10 years for each rental outcome.
The option of constructing a new facility is also defined in Figure. An initial facility could be constructed with tire costs shown. In five years, additional space will be required. At that time, there will be an option to build an office addition or rent space for the additional space requirements.
The probabilities for each alternative are shown. MARR for the situation is 10% per year. A PW analysis is to be conducted on the alternatives. Which course of action should be recommended Note: At [2], the PW(10%) of the upper branch is -$5,111.14 k and the PW(10%) for the lower branch is -$4,119.06 k.
Figure

Question 26

After additional research, the range of probable useful lives has been narrowed down to the following three possibilities:
How does this affect E (PW) and SD(PW) What are the benefits associated with the cost of obtaining more accurate estimates (Problem 1)
Problem 1
It costs $250,000 to drill a natural gas well. Operating expenses will be 10% of the revenue from the sale of natural gas from this particular well. If found, natural gas from a highly productive well will amount to 260,000 cubic feet per day. The probability of locating such a productive well, however, is about 10%.
a. If natural gas sells for $8 per thousand cubic feet, what is the E (PW) of profit to the owner/operator of this well The life of the well is 10 years and MARR is 15% per year.
b. Repeat Part (a) when the life of the well is seven years.
c. Perform one-at-a-time sensitivity analyses for ±20% changes in daily well production and selling price of natural gas. Use a 10-year life for the well.