Deck 11: Breakeven and Sensitivity Analysis

Question 1

The Metropolitan Transit Authority (MTA) has just opened a new subway line (the Orange Line) in its underground transportation network. The Orange Line had a capital investment of $20 million, expected operating and maintenance expenses are $3 million per year, and the final salvage value at the end of a 40-year life is negligible. If the revenue generated by each customer is $3, how many customers per day will be required before the Orange Line can break even The MTA's hurdle (interest) rate is 5% compounded annually. Assume there are 365 days in a year.

Answer 1

Benefit-cost analysis (BCA) is defined as the concept which summarizes the overall value of money in a particular project. Whenever its value is greater than 1, the project seems to be beneficial and if its value is less than 1, that means project will not be beneficial and involves some risks.
Given the capital investment of orange line to be $20 million, operating and maintenance expenses of $3 million with the required revenue of $3 million from each customer with the life of 40 years. It is required to find out the break even before the orange line.
For Break even, it is important to find out the total annual cost and total annual revenue.
The total annual revenue is given and total annual cost is calculated as: After calculating the total annual costs, break-even is calculated as: This shows the breakeven of customers per year.
Now, to find the breakeven with 365 days in a year which is calculated as: Hence, to make the orange line breakeven at least customers are required per day.

Question 2

Refer to Example 11-2. Assuming gasoline costs $4.00 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.
EXAMPLE 11-2 Two Alternative Breakeven Analysis: Hybrid Vehicles
Gas-electric (so-called hybrid) vehicles save on gasoline consumption by shutting off the vehicle's engine while idling, giving the vehicle a boost of electric power during acceleration, and capturing electrical energy while braking. In addition to environmental benefits, the primary monetary benefit to the owner is reduced fuel cost as a result of improved gasmileage. The trade-off, however, is that the purchase price of the hybrid vehicle is higher than that of a standard gasoline-only fueled vehicle.
Consider a hybrid vehicle with a sticker price of $31,500. This vehicle will average 30 miles per gallon of gasoline. A tax credit of $1,500 for the hybrid vehicle effectively reduces its sticker price to $30,000. A comparably equipped gasoline-only vehicle will cost $28,000 and will average 25 miles per gallon of gasoline. Assuming an interest rate of 3% per year and a study period of five years, find the breakeven cost of gasoline ($/gal) if the vehicle will be driven 18,000 miles each year.

Answer 2

Break even points refers to a point where the value and amount is indifferent between the two alternatives. To find the break-even, the equivalent values of both the projects are taken to be equal.
Given the hybrid vehicle with the price of $30,000 with the average of 30 miles per gallon of gasoline and gasoline- only vehicle with the price of $28,000 with the average mile of 25 miles per gallon of gasoline with the rate of interest rate of 3% and a life of 5 years. The cost of gasoline is $4 per gallon and it is required to find the breakeven mileage per year.
To find the mileage per year, it is needed to develop an equivalent uniform annual cost (EUAC) for both the factors taking X as the breakeven mileage per year.
For Hybrid Vehicle, For Gas-only Vehicle, For Breakeven,
Equating (1) and (2), The breakeven mileage per year between hybrid vehicle and gas-only vehicle is .

Question 3

The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Answer 3

The annual operating expenses of long-haul tractors equipped with the different deflectors are calculated as a function of mileage driven per year, X. If 5% drag reduction means 2% in fuel savings per mile, the annual operating expense for different types of deflectors can be calculated as:
For Windshear For Blowby For Air-Vantage Now need to form equivalent-worth equation ( EUAC ) in terms of X. At , equivalent-worth equations ( EUAC ) for different types of deflectors are: To compute the breakeven values between any two types of deflectors, equate their EUAC equations and solve for X.
Windshear and Blowby : 0
It implies the Universal Postal Service will prefer Blowby if 1
.
Blowby and Air-vantage : 2
Air-vantage and Windshear : 3
The tractor must be driven at least 4
and at most 5
before Wind shear is favoured over the other deflectors.
Air-vantage is the best choice when 6
.

Question 4

In planning a small two-story office building, the architect has submitted two designs. The first provides foundation and structural details so that two additional stories can be added to the required initial two stories at a later date and without modifications to the original structure. This building would cost $1,400,000. The second design, without such provisions, would cost only $1,250,000. If the first plan is adopted, an additional two stories could be added at a later date at a cost of $850,000. If the second plan is adopted, however, considerable strengthening and reconstruction would be required, which would add $300,000 to the cost of a two-story addition. Assuming that the building is expected to be needed for 75 years, by what time would the additional two stories have to be built to make the adoption of the first design justified MARR is 10% per year.

Question 5

Consider these two alternatives. (Problem)
a. Suppose that the capital investment of Alternative 1 is known with certainty. By how much would the estimate of capital investment for Alternative 2 have to vary so that the initial decision based on these data would be reversed The annual MARR is 15% per year.
b. Determine the life of Alternative 1 for which the AWs are equal.
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 6

An area can be irrigated by pumping water from a nearby river. Two competing installations are being considered.
The MARR is 12% per year and electric power for the pumps costs $0.06 per kWh. Recall that 1 horsepower (hp) equals 0.746 kilowatts. (Problem, Problem 1)
a. At what level of operation (hours per year) would you be indifferent between the two pumping systems If the pumping system is expected to operate 2,000 hours per year, which system should be recommended
b. Perform a sensitivity analysis on the efficiency of Pump A. Over what range of pumping efficiency is Pump A preferred to Pump B Assume 2,000 hours of operation per year, and draw a graph to illustrate your answer.
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)

Question 7

Consider the following two investment alternatives. Determine the range of investment costs for Alternative B (i.e., min. value X B. MARR = 10% per year, and other relevant data are shown in the following table. State clearly any assumptions that are necessary to support your answer. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 8

The Ford Motor Company is considering three mutually exclusive electronic stability control systems for protection against rollover of its automobiles. The investment (study) period is four years, and MARR is 12% per year. Data for the fixture costs of the systems are as follows.
Plot the AW of each alternative against MARR as the MARR varies across this range: 4%, 8%, 12%, 16%, and 20%. What can you generalize about the range of the MARR for which each alternative is preferred (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 9

Your company operates a fleet of light trucks that are used to provide contract delivery services. As the engineering and technical manager, you are analyzing the purchase of 55 new trucks as an addition to the fleet. These trucks would be used for a new contract the sales staff is trying to obtain. If purchased, the trucks would cost $21,200 each; estimated use is 20,000 miles per year per truck; estimated operation and maintenance and other related expenses (year-zero dollars) are $0.45 per mile, which is forecasted to increase at the rate of 5% per year; and the trucks are MACRS (GDS) three-year property class assets. The analysis period is four years; t = 38%; MARR = 15% per year (after taxes; includes an inflation component); and the estimated MV at the end of four years (in year-zero dollars) is 35% of the purchase price of the vehicles. This estimate is expected to increase at the rate of 2% per year.
Based on an after-tax, actual-dollar analysis, what is the annual revenue required by your company from the contract to justify these expenditures before any profit is considered This calculated amount for annual revenue is the breakeven point between purchasing the trucks and which other alternative (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 10

Anationwide motel chain is considering locating a new motel in Bigtown, USA. The cost of building a 150-room motel (excluding furnishings) is $5 million. The firm uses a 15-year planning horizon to evaluate investments of this type. The furnishings for this motel must be replaced every five years at an estimated cost of $1,875,000 (at k = 0, 5, and 10). The old furnishings have no market value. Annual operating and maintenance expenses for the facility are estimated to be $125,000. The market value of the motel after 15 years is estimated to be 207c of the original building cost.
Rooms at the motel are projected to be rented at an average rate of $45 per night. On the average, the motel will rent 607o of its rooms each night. Assume the motel will be open 365 days per year. MARR is 10 % per year. (Problem)
a. Using an annual-worth measure of merit, is the project economically attractive
b. Investigate sensitivity to decision reversal for the following three factors: (1) capital investment, (2) MARR, and (3) occupancy rate (average percent of rooms rented per night). To which of these factors is the decision most sensitive
c. Graphically investigate the sensitivity of the AW to changes in the above three factors. Investigate changes over the interval ±40%. On your graph, use percent change as the x -axis and AW as the y -axis.
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 11

A large city in the mid-West needs to acquire a street-cleaning machine to keep its roads looking nice year round. A used cleaning vehicle will cost $85,000 and have a $20,000 market (salvage) value at the end of its five-year life. A new system with advanced features will cost $150,000 and have a $40,000 market value at the end of its five-year life. The new system is expected to reduce labor hours compared with the used system. Current street-cleaning activity requires the used system to operate 8 hours per day for 20 days per month. Labor costs $50 per hour (including fringe benefits), and MARR is 12% per year.
a. Find the breakeven percent reduction in labor hours for the new system.
b. If the new system is expected to be able to reduce labor hours by 17% compared with the used system, which machine should the city purchase

Question 12

Refer to Problem 2. The best estimate for reduction of labor hours for the new system is 20% (compared with the used system). Investigate how sensitive the decision is to
(a) changes in the MARR,
(b) changes in the market value of the new system, and
(c) the productivity improvement of the new system. Graph your results. (Problem)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.
Problem 2
A large city in the mid-West needs to acquire a street-cleaning machine to keep its roads looking nice year round. A used cleaning vehicle will cost $75,000 and have a $20,000 market (salvage) value at the end of its five-year life. A new system with advanced features will cost $150,000 and have a $50,000 market value at the end of its five-year life. The new system is expected to reduce labor hours compared with the used system. Current street-cleaning activity requires the used system to operate 8 hours per day for 20 days per month. Labor costs $40 per hour (including fringe benefits), and MARR is 12% per year compounded monthly. (Problem)
a. Find the breakeven percent reduction in labor hours for the new system.
b. If the new system is expected to be able to reduce labor hours by 207o compared with the used system, which machine should the city purchase

Question 13

A group of private investors borrowed $30 million to build 300 new luxury apartments near a large university. The money was borrowed at 6% annual interest, and the loan is to be repaid in equal annual amounts over a 40-year period. Annual operating, maintenance, and insurance expenses are estimated to be $4,000 per apartment. This expense will be incurred even if an apartment is vacant. The rental fee for each apartment will be $12,000 per year, and the worst-case occupancy rate is projected to be 80%. Investigate the sensitivity of annual profit (or loss) to
(a) changes in the occupancy rate and
(b) changes in the annual rental fee. (Problem 1)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 14

The managers of a company are considering an investment with the following estimated cash flows. MARR is 15% per year.
The company is inclined to make the investment; however, the managers are nervous because all of the cash flows and the useful life are approximate values. The capital investment is known to be within ±5%. Annual expenses are known to be within ±10%. The annual revenue, market value, and useful life estimates are known to be within ±20%. (Problem 1)
a. Analyze the sensitivity of PW to changes in each estimate individually. Based on your results, make a recommendation regarding whether or not they should proceed with this project. Graph your results for presentation to management.
b. The company can perform market research and /or collect more data to improve the accuracy of these estimates. Rank these variables by ordering them in accordance with the need for more accurate estimates (from highest need to lowest need).
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 15

An industrial machine costing $14,000 will produce net cash savings of $5,000 per year. The machine has a five-year useful life but must be returned to the factory for major repairs after three years of operation. These repairs cost $5,000. The company's MARR is 10% per year. What IRR will be earned on the purchase of this machine Analyze the sensitivity of IRR to ± $2,000 changes in the repair cost.

Question 16

You have decided to purchase a new automobile with a hybrid-fueled engine and a six-speed transmission. After the trade-in of your present car, the purchase price of the new automobile is $30,000. This balance can be financed by the auto dealer at 2.9% APR (compounded monthly) and repaid over 48 monthly payments. Alternatively, you can get an instant rebate on the purchase price if you finance the loan balance at an APR of 8.9% (compounded monthly) over 48 months. Determine the amount of the instant rebate that would make you indifferent between the financing plans. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 17

Two traffic signal systems are being considered for an intersection. One system costs $32,000 for installation and has an efficiency rating of 78%, requires 28 kW power (output), incurs a user cost of $0.24 per vehicle, and has a life of 10 years. A second system costs $45,000 to install, has an efficiency rating of 90%, requires 34 kW power (output), has a user cost of $0.22 per vehicle, and has a life of 15 years. Annual maintenance costs are $75 and $100, respectively. MARR = 10% per year. How many vehicles must use the intersection to justify the second system when electricity costs $0.08/kWh (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 18

An office building is considering converting from a coal-burning furnace to one that burns either fuel oil or natural gas. The cost of converting to fuel oil is estimated to be $80,000 initially; annual operating expenses are estimated to be $4,000 less than that experienced when using the coal furnace. Approximately 140,000 Btus are produced per gallon of fuel oil; fuel oil is anticipated to cost $2.20 per gallon.
The cost of converting to natural gas is estimated to be $60,000 initially; additionally, annual operating and maintenance expenses are estimated to be $6,000 less than that for the coal-burning furnace. Approximately 1,000 Btus are produced per cubic foot of natural gas; it is estimated that natural gas will cost $0.04 per cubic foot.
A planning horizon of 20 years is to be used. Zero market values and a MARR of 10% per year are appropriate. Perform a sensitivity analysis for the annual Btu requirement for the heating system. (Problem 1)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 19

Suppose that, for a certain potential investment project, the optimistic, most likely, and pessimistic estimates are as shown in the accompanying table. (Problem 1)
a. What is the AW for each of the three estimation conditions
b. It is thought that the most critical factors are useful life and net annual cash flow. Develop a table showing the net AW for all combinations of the
estimates for these two factors, assuming all other factors to be at their most likely values.
Problem 1
In planning a small two-story office building, the architect has submitted two designs. The first provides foundation and structural details so that two additional stories can be added to the required initial two stories at a later date and without modifications to the original structure. This building would cost $1,400,000. The second design, without such provisions, would cost only $1,250,000. If the first plan is adopted, an additional two stories could be added at a later date at a cost of $850,000. If the second plan is adopted, however, considerable strengthening and reconstruction would be required, which would add $300,000 to the cost of a two-story addition. Assuming that the building is expected to be needed for 75 years, by what time would the additional two stories have to be built to make the adoption of the first design justified MARR is 10% per year. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 20

Abridge is to be constructed now as part of a new road. Engineers have determined that traffic density on the new road will justify a two-lane road and a 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 two-lane bridge will cost $200,000 and the four-lane bridge, if built initially, will cost $350,000. The future cost of widening a two-lane bridge to four lanes will be an extra $200,000 plus $25,000 for every year that widening is delayed. The MARR used by the highway department is 12% per year. The following estimates have been made of the times at which the four-lane bridge will be required:
In view of these estimates, what would you recommend What difficulty, if any, do you have in interpreting your results List some advantages and disadvantages of this method of preparing estimates. (Problem 1)
Problem 1
In planning a small two-story office building, the architect has submitted two designs. The first provides foundation and structural details so that two additional stories can be added to the required initial two stories at a later date and without modifications to the original structure. This building would cost $1,400,000. The second design, without such provisions, would cost only $1,250,000. If the first plan is adopted, an additional two stories could be added at a later date at a cost of $850,000. If the second plan is adopted, however, considerable strengthening and reconstruction would be required, which would add $300,000 to the cost of a two-story addition. Assuming that the building is expected to be needed for 75 years, by what time would the additional two stories have to be built to make the adoption of the first design justified MARR is 10% per year. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 21

An aerodynamic three-wheeled automobile (the Dart) runs on compressed natural gas stored in two cylinders in the rear of the vehicle. The $13,000 Dart can cruise at speeds up to 80 miles per hour, and it can travel 100 miles per gallon of fuel. Another two-seater automobile costs $10,000 and averages 50 miles per gallon of compressed natural gas. If fuel costs $8.00 per gallon and MARR is 10% per year, over what range of annual miles driven is the Dart more economical Assume a useful life of five years for both cars. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 22

Extended Learning Exercise
Consider these two alternatives for solid-waste removal (Problem 1):
Alternative A: Build a solid-waste processing facility. Financial variables are as follows:
Alternative B: Contract with vendors for solid-waste disposal after intermediate recovery. Financial variables are as follows:
Related Data:
a. How much more expensive (in terms of capital investment only) could Alternative B be in order to breakeven with Alternative A
b. How sensitive is the after-tax PW of Alternative B to cotermination of both alternatives at the end of year 10
c. Is the initial decision to adopt Alternative B in Part (a) reversed if our company's annual operating expenses for Alternative B ($2.10 million per year) unexpectedly double Explain why (or why not).
d. Use a computer spreadsheet available to you to solve this problem.
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 23

Extended Learning Exercise Construct the spreacisheet used in Example. Use this spreadsheet as a starting point to answer the following questions. Be sure to clearly state your assumptions. (Problem 1)
a. How sensitive is the decision to the amount of the down payment for the purchase option If a down payment of less than 20% is used, you will need to account for monthly mortgage insurance (about $56 /month).
b. How sensitive is the decision to the type of mortgage acquired You can look at different repayment periods (15 or 20 years) as well as the impact of points paid on the loan. One point is equal to 1% of the loan value and is paid as part of the closing costs.
c. Interest paid on a mortgage is tax deductible if you itemize deductions on your personal income tax return. Discuss how you would incorporate this and what impact it would have on the decision to purchase versus rent a home.
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 24

We know the standard means of cutting the high cost of driving our automobiles-slow down your speed, no jack rabbit starts, inflate tires properly, clean air filters regularly, and so on. Another way to reduce the cost of driving is to join every big-rigger in the United States and half of Europe-go diesel. Diesels are inherently more efficient than gasoline engines because they deliver a third better fuel mileage. They also offer a reliable high-torque engine!
The initial extra sticker price of a diesel-fueled car is about $1,200. A gallon of diesel fuel costs about the same as a gallon of gasoline. Assu me your gasoline-fueled car averages 24-27 miles per gallon. You drive an average of 20,000 miles per year, and your personal MARR is in the 12-15% per year ballpark. Develop a spreadsheet to compare the economics of driving 100,000 miles in your car fueled by gasoline versus diesel. Explore various what if questions that you have regarding this comparison. (Problem 1)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 25

It is desired to determine the most economical thickness of insulation for a large cold-storage room. Insulation is expected to cost $150 per 1,000 square feet of wall area per inch of thickness installed, and to require annual property taxes and insurance of 5% of the capital investment. It is expected to have $0 market value after a 20-year life. The following are estimates of the heat loss per 1,000 square feet of wall area for several thicknesses:
The cost of heat removal (loss) is estimated at $0.04 per 1,000 Btu. The MARR is 20% per year. Assuming continuous operation throughout the year, develop a spreadsheet to analyze the sensitivity of the optimal thickness to errors in estimating the cost of heat removal. Use the AW technique. (Problem)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 26

Suppose that, for an engineering project, the optimistic, most likely, and pessimistic estimates are as shown in the accompanying table.
Develop a spreacisheet to determine the AW for each of the three estimate conditions. It is thought that the
most critical elements are useful life and net annual cash flow. Include in your spreadsheet a table showing the AW for all combinations of the estimates for these two factors, assuming that all other factors remain at their most likely values. (Problem 1)
Problem 1
In planning a small two-story office building, the architect has submitted two designs. The first provides foundation and structural details so that two additional stories can be added to the required initial two stories at a later date and without modifications to the original structure. This building would cost $1,400,000. The second design, without such provisions, would cost only $1,250,000. If the first plan is adopted, an additional two stories could be added at a later date at a cost of $850,000. If the second plan is adopted, however, considerable strengthening and reconstruction would be required, which would add $300,000 to the cost of a two-story addition. Assuming that the building is expected to be needed for 75 years, by what time would the additional two stories have to be built to make the adoption of the first design justified MARR is 10% per year. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 27

The world's largest carpet maker has just completed a feasibility study of what to do with the 16,000 tons of overruns, rejects, and remnants it produces every vear. The company s CEO launched the feasibility study by asking, Why pay someone to dig coal out of the ground and then pay someone else to put our waste into a landfill Why not just burn our own waste The company is proposing to build a $10-million power plant to burn its waste as fuel, thereby saving $2.8 million a year in coal purchases. Company engineers have determined that the wasteburning plant will be environmentally sound, and after its four-year study period the plant can be sold to a local electric utility for $5 million.
The firm's MARR is 15%. Develop a spreadsheet to investigate the sensitivity of the proposal s IW to changes in the estimates of
(a) initial investment amount,
(b) annual savings of fuel cost, and
(c) future resale value of the plant. To which factor is the decision most sensitive Include in your solution the specific values of these factors that would cause decision reversal. Use the charting feature to create a spiderplot. (Problem 1)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 28

Refer to Problem 2. Disposing of incandescent light bulbs is just like getting rid of and recycling glassware in general. However, this is not the case for CFLs. Disposing of CFLs is complicated by the fact that each lamp contains a small amount of mercury, which is a very environmentally dangerous substance. Write a brief report of your findings for your boss for each of the following scenarios (Problem 1):
a. Develop an Excel spreadsheet to investigate the sensitivity of choice of lighting systems when the CFL disposal cost varies from $1.00 to $5.00 per lamp.
b. Use your spreadsheet to explore the sensitivity of bulb or lamp choice as the cost of electricity varies from $0.04 per kWh to $0.16 per kWh.
c. Use your spreadsheet to quantify the sensitivity of bulb or lamp choice when CFLs last 5,6,7, 8,9, and 10 times as long as incandescent bulbs.
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.
Problem 2
Your boss has asked you to evaluate the economics of replacing 1,000 60-Watt incandescent light bulbs (ILBs) with 1,000 compact fluorescent lamps (CFLs) for a particular lighting iapplication. During your investigation you discover that 13-Watt CFLs costing $2.00 each will provide the same illumination as standard 60-Watt ILBs costing $0.50 each. Interestingly, CFLs last, on average, eight times as long as incandescent bulbs. The average life of an TLB is one year over the anticipated usage of 1,000 hours each year. Each incandescent bulb costs $2.00 to install/replace. Installation of a single CFL costs $3.00, and it will also be used 1,000 hours per year.
Electricity costs $0.12 per kiloWatt hour (kWh), and you decide to compare the two lighting options over an 8-year study period. If the MARR is 12% per year, compare the economics of the two alternatives and write a brief report of your findings for the boss. Problem
Problem 3
Three mutually exclusive design alternatives are being considered. The estimated sales and cost data for each alternative are given below. The MARR is 20% per year.
Annual revenues are based on the number of units sold and the selling price. Annual expenses are based on fixed and variable costs. Determine which selection is preferable based on AW. State your assumptions.

Question 29

Refer to Problem 2. Set up a spreadsheet to answer various "what if" questions such as "How does the IRR vary as the cost of gasoline takes on these values: $3.00 per gallon, $4 per gallon, and $5.00 per gallon" Also, how does IRR change when the ownership period changes across this range. 3 years, 4 years, 5 years, 6 years, and 7 years How does the IRR vary when the differential resale value is $1,000, $2,000, $3,000, and $4,000 (Problem 1)
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.
Problem 2
Are you thinking of bypassing a gasoline-fueled car in favor of a hybrid (gasoline and electric) automobile Let's take a look at the relative economics of your possible choice. The gasoline-fueled car sells for $20,000 and gets 25 miles per gallon (mpg) of fuel. The alternative hybrid vehicle sells for $25,000 and averages 46 mpg. The resale value of the hybrid car is $2,000 more than that of the gasoline-only car after five years of anticipated ownership. Tf you drive 15,000 miles per year and gasoline costs $4.00 per gallon, what is the internal rate of return on the incremental investment in the hybrid automobile Problem
Problem 3
Three mutually exclusive design alternatives are being considered. The estimated sales and cost data for each alternative are given below. The MARR is 20% per year.
Annual revenues are based on the number of units sold and the selling price. Annual expenses are based on fixed and variable costs. Determine which selection is preferable based on AW. State your assumptions.

Question 30

A highway bridge is being considered for replacement. The new bridge would cost $ X and would last for 20 years. Annual maintenance costs for the new bridge are estimated to be $24,000. People will be charged a toll of $0.25 per car to use the new bridge. Annual car traffic is estimated at 400,000 cars. The cost of collecting the toll consists of annual salaries for five collectors at $10,000 per collector. The existing bridge can be refurbished for $1,600,000 and would need to be replaced in 20 years. There would be additional refurbishing costs of $70,000 every five years and regular annual maintenance costs of $20,000 for the existing bridge. There would be no toll to use the refurbished bridge. If MARR is 12% per year, what is the maximum acceptable cost ( X ) of the new bridge (Problem)
(a) $1,943,594
(b) $2,018,641
(c) $1,652,425
(d) $1,570,122
(e) $2,156,209
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 31

An analysis of accidents in a rural state indicates that widening a highway from 30 ft to 40 ft will decrease the annual accident rate from 1,250 to 710 per million vehicle-miles. Calculate the average daily number of vehicles that should use the highway to justify widening on the basis of the following estimates:
(i) the average loss per accident is $1,200;
(ii) the cost of widening is $117,000 per mile;
(iii) the useful life of the widened road is 25 years;
(iv) annual maintenance costs are 3% of the capital investment; and
(v) MARR is 12% per year. (Problem)
(a) 78
(b) 63
(c) 34
(d) 59
(e) 27
A supermarket chain buys loaves of bread from its supplier at $0.50 per loaf. The chain is considering two options to bake its own bread.
Neither machine has a market value at the end of seven years, and MARR is 12% per year. Use this information to answer Problems. Select the closest answer. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.
Problem 2
What is the minimum number of loaves that must be sold per year to justify installing Machine A instead of buying the loaves from the supplier
(a) 7,506
(b) 22,076
(c) 37,529
(d) 75,059
(e) 15,637
Problem 3
What is the minimum number of loaves that must be sold per year to justify installing Machine B instead of buying the loaves from the supplier
(a) 37,529
(b) 15,637
(c) 22,076
(d) 75,059
(e) 7,506
Problem 4
If the demand for bread at this supermarket is 35,000 loaves per year, what strategy should be adopted for acquiring bread Both Machine A and Machine B are capable of meeting annual demand.
(a) Continue buying from the supplier.
(b) Install Machine A.
(c) Install Maclaine B.
(d) Install both Machine A and Machine B.
Answer Problems 5, 6, 7, 8, 9 on the basis of the figure on page 476 and the most likely estimates given as follows:
Problem 5
If the initial investment is increased by more than 9%, the project is profitable.
(a) True
(b) False
Problem 6
If the profit ( R E ) is decreased by 5%, this project is not profitable.
(a) True
(b) False
Problem 7
Variations in the profit and useful life of the project are inversely related.
(a) True
(b) False
Problem 8
This project (based upon the most likely estimates) is profitable.
(a) True
(b) False
Problem 9
An initial investment of $5,500 is profitable.
(a) True
(b) False

Question 32

What is the minimum number of loaves that must be sold per year to justify installing Machine A instead of buying the loaves from the supplier
(a) 7,506
(b) 22,076
(c) 37,529
(d) 75,059
(e) 15,637

Question 33

What is the minimum number of loaves that must be sold per year to justify installing Machine B instead of buying the loaves from the supplier
(a) 37,529
(b) 15,637
(c) 22,076
(d) 75,059
(e) 7,506

Question 34

If the demand for bread at this supermarket is 35,000 loaves per year, what strategy should be adopted for acquiring bread Both Machine A and Machine B are capable of meeting annual demand.
(a) Continue buying from the supplier.
(b) Install Machine A.
(c) Install Maclaine B.
(d) Install both Machine A and Machine B.
Answer Problems 1, 2, 3, 4, 5 on the basis of the figure on page 476 and the most likely estimates given as follows:
Problem 1
If the initial investment is increased by more than 9%, the project is profitable.
(a) True
(b) False
Problem 2
If the profit ( R E ) is decreased by 5%, this project is not profitable.
(a) True
(b) False
Problem 3
Variations in the profit and useful life of the project are inversely related.
(a) True
(b) False
Problem 4
This project (based upon the most likely estimates) is profitable.
(a) True
(b) False
Problem 5
An initial investment of $5,500 is profitable.
(a) True
(b) False

Question 35

If the initial investment is increased by more than 9%, the project is profitable.
(a) True
(b) False

Question 36

If the profit ( R E ) is decreased by 5%, this project is not profitable.
(a) True
(b) False

Question 37

Variations in the profit and useful life of the project are inversely related.
(a) True
(b) False

Question 38

This project (based upon the most likely estimates) is profitable.
(a) True
(b) False

Question 39

An initial investment of $5,500 is profitable.
(a) True
(b) False

Question 40

Two electric motors are being economically evaluated for use in a submersible robotic device. Each is capable of delivering 90 horsepower to a necessary application that the device performs. Data for the mutually exclusive motors are as follows.
The MARR is 12% per year. If the expected usage of the motor is 500 hours per year, what would the cost of electric power have to be before the Phillips motor is favored over the General Electric motor Recall that 1 horsepower = 0.746 kilowatts. Choose the closest answer from those below. (Problem 1)
(a) $0.02 per kWh
(b) $0.19 per kWh
(c) $0.09 per kWh
(d) $0.05 per kWh
Problem 1
The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long-haul tractors. Three types of deflectors, with the following characteristics, are being considered (MARR =10% per year):
If 5% in drag reduction means 2% in fuel savings per mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other deflectors Over what range of miles driven per year is air-vantage the best choice ( Note: Fuel cost is expected to be $3.00 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) State any assumptions you make. (Problem)
Problem
Refer to Example 11-2. Assuming gasoline costs $3.50 per gallon, find the breakeven mileage per year between the hybrid vehicle and the gas-only vehicle. All other factors remain the same.

Question 41

A carpet manufacturer in Georgia plans to expand its plant for a capital investment of $500,000. The extra capacity will permit the company to produce 400,000 yards of carpet each year during the plant's fiveyear life. Each yard of carpet will produce a revenue of $2.00, and the plant's incremental operating expenses are expected to be $150,000 each year. Assume the expansion has no salvage value at the end of year five. If the manufacturer's MARR is 18% per year, what is the minimum annual production rate to make the expansion a worthwhile investment
(a) 103,400 yards
(b) 310,000 yards
(c) 154,950 yards
(d) 250,350 yards

Question 42

Acentrifuge is required in a chemical separation process. Two centrifuges (A and B) are available and summarized below. The net annual revenues for centrifuge B are not known. If the MARR is 10% per year and salvage values can be ignored, what is the minimum value of X to make centrifuge B the better choice Select the closest answer below.
(a) $500
(b) $6,700
(c) $8,000
(d) $9,800