Fundamentals of Engineering Economics

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Quiz 6 :

Annual-Equivalence Analysis

Quiz 6 :

Annual-Equivalence Analysis

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Consider the following sets of investment projects: img Compute the equivalent annual worth of each project at i = 10%, and determine the acceptability of each project.
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Given information:
Table-1 shows the investment and revenue generated for 4 different projects.
Table-1 img • Interest rate is 10 %.
• Time period (n) is 5 years.
Annual equivalent value of project A:
Annual equivalent value can be calculated by using the following formula: img …… (1)Where,
i = interest
n = time period
AV = annual equivalent value img = cash flow in i th year
Substitute the respective values in Equation (1) to calculate the annual equivalent value of project a. img img The annual equivalent value of project A is img . Since the annual equivalent value is negative the project is not acceptable.
Annual equivalent value of project B:
Substitute the respective values in Equation (1) to calculate the annual equivalent value of project b. img img The annual equivalent value of project B is img . Since the annual equivalent value is negative the project is not acceptable.
Annual equivalent value of project C:
Substitute the respective values in Equation (1) to calculate the annual equivalent value of project c. img img The annual equivalent value of project C is img . Since the annual equivalent value is positive the project is acceptable.
Annual equivalent value of project D:
Substitute the respective values in Equation (1) to calculate the annual equivalent value of project d. img img The annual equivalent value of project D is img . Since the annual equivalent value is positive the project is acceptable.

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Consider manufacturing equipment that has an installed cost of $120,000. The equipment is expected to generate $45,000 of the annual energy savings during its first year of installation. The value of these annual savings is expected to increase by 5% per year (over previous year) because of increased fuel costs. Assume that the equipment has a service life of 10 years (or 5,000 operating hours per year) with $20,000 worth of salvage value. Determine the equivalent dollar savings per each operating hour at i = 10% per year. (a) $6.99 per hour (b) $7.24 per hour (c) $4.45 per hour (d) $4.29 per hour
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Given information:
• Initial cost is $120,000.
• Annual energy savings is $45,000.
• Annual energy saving increases by img 5 percent per year.
• Operating hour per year is 5,000.
• Salvage value is $20,000.
• Time period is 10 years.
• Interest rate is ( i ) 10 percent.
Net annual savings:
Net annual savings can be calculated by using the following formula: img …… (1)Where,
i = Interest rate
n = Time period
Substitute the respective values in Equation (1) to calculate the net annual savings. img img Hence, net annual savings is img .
Savings per operating hour:
Savings per operating hour can be calculated by dividing the net annual savings by the annual operating hour as shown below: img Savings per operating hour is img . Hence, option (b) is the correct answer.

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You are considering buying a 30-HP electric motor which has an efficiency rating of 89%. The motor costs $10,000 and will be used for 10 years. The expected salvage value at that time is $1,000. The cost to run the electric motor is $0.09 per kWh for 2,000 hours a year. (1HP = 0.7457kW.) What is the total equivalent cost (present worth) of owning and operating the motor for 10 years at an interest rate of 12% per year? (a) $35,242 (b) $25,884 (c) $32,426 (d) $22,425
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Given information:
• Price of 30 horse power motor is $10,000.
• Efficiency of the motor is 89 percent.
• Expected salvage value is $1,000.
• Revenue increases by $30,000 each year.
• Cost is $0.09 per kilowatt hour.
• Run time is 2,000 hours per year.
• Time period is 10 years.
• Interest rate is 12 percent.
Total equivalent value:
Total equivalent value can be calculated by using the following formula: img …… (1)Where,
i = Interest rate
n = Time period
Substitute the respective values in Equation (1) to calculate the annual equivalent value. img img Total equivalent value is img . Hence, option (a) is the correct answer.

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You are considering an investment costing $250,000. If you want to recover the initial investment, and also earn 12% interest while your money is being tied up within three years, what is the required equal annual net revenue that must be generated from the investment?
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Two options are available for painting your house: (1) Oil-based painting, which costs $5,000, and (2) water-based painting, which costs $3,000. The estimated lives are 10 years and 5 years, respectively. For either option, no salvage value will remain at the end of respective service lives. Assume that you will keep and maintain the house for 10 years. If your personal interest rate is 10% per year, which of the following statements is correct? (a) On an annual basis, Option 1 will cost about $850 (b) On an annual basis, Option 2 is about $22 less than Option 1 (c) On an annual basis, both options cost about the same (d) On an annual basis, Option 2 will cost about $820.
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A newly constructed water treatment facility cost $2 million. It is estimated that the facility will need revamping to maintain the original design specification every 30 years at a cost of $1 million. Annual repairs and maintenance costs are estimated to be $100,000. At an interest rate of 8%, determine the capitalized cost of the facility, assuming that it will be used for an indefinite period.
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The city of Atlanta is considering adding new buses for its current mass-transit system that links Hartsfield International Airport to major city destinations on nonstop basis. The total investment package is worth $8 million and is expected to last 10 years with a $750,000 salvage value. The annual operating and maintenance costs for buses would be $2 million. If the system is used for 600,000 trips per year, what would be the fair price to charge per trip? Assume that the city of Atlanta uses 5% interest rate for any city-sponsored projects. (a) $3.50 per trip (b) $4.00 per trip (c) $4.50 per trip (d) $5.00 per trip
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Consider the cash flow series shown below. Determine the required annual deposits (end of year) that will generate the cash flows from years 4 to 7. Assume the interest rate is 8%. img
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Consider an investment project with the following repeating cash flow pattern every four years forever: img What is the annual-equivalence amount of this project at an interest rate of 14%?
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The investment shown in the following figure has an annual equivalent worth of $200 at i = 8%. Determine the cash flows in periods 2, 3, 5 and 6. img
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You purchased a drill press machine for $180,000. It is expected to have a useful life of 10 years. The accounting department tells you that the annual capital cost is $33,895 at i = 15%. What salvage value is used in obtaining the annual capital cost of this machine? (a) $30,100 (b) $35,300 (c) $39,970 (d) $42,000
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An engineering design firm needs to borrow $300,000 from a local bank at an interest rate of 9% over five years. What is the required annual equal payment to retire the loan in five years?
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You are considering a luxury apartment building project that requires an investment of $12,500,000. The building has 50 units. You expect the maintenance cost for the apartment building to be $250,000 in the first year, $300,000 in the second year, and increasing by $50,000 in subsequent years. The cost to hire a manager for the building is estimated to be $80,000 per year. After five years of operation, the apartment building can be sold for $14,000,000. What is the annual rent per apartment unit that will provide a return on investment of 15% per year? Assume the building will remain fully occupied during the five years. (a) $36,445 (b) $38,567 (c) $41,373 (d) $44,980
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You are considering making an $80,000 investment in a process improvement project. Revenues are expected to grow from $50,000 in year 1 by $30,000 each year for next four years ($50,000 first year, $80,000 second year, $110,000 third year, and so forth) while costs are expected to increase from $20,000 in year 1 by $10,000 each year. If there is no salvage value at the end of five years, what is the annual equivalent worth of the project assuming an MARR of 12%? (a) $65,492 (b) $53,300 (c) $47,785 (d) $43,300
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You are considering a project with the following financial data: Required initial investment at n = 0: $50M Project life: 10 years Estimated annual revenue: $X (unknown) Estimated annual operating cost: $15M Required minimum return: 20% per year Salvage value of the project: 15% of the initial investment What minimum annual revenue (in $M) must be generated to make the project worthwhile? (a) X = $26.64M (b) X = $28.38M (c) X = $32.47M (d) X = $35.22M
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Consider the following sets of investment projects: img Compute the equivalent annual worth of each project at i = 13%, and determine the acceptability of each project.
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A consumer product company is considering introducing a new shaving system called DELTA-4 in the market. The company plans to manufacture 75 million units of DELTA-4 a year. The investment at time 0 that is required for building the manufacturing plant is estimated as $500 million, and the economic life of the project is assumed to be 10 years. The annual total operating expenses, including manufacturing costs and overhead, are estimated at $175 million. The salvage value that can be realized from the project is estimated at $120 million. If the company's MARR is 25%, determine the price that the company should charge for a DELTA-4 shaving system to break even. (a) $3.15 (b) $4.15 (c) $5.15 (d) $2.80
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Compute the annual-equivalence amount for the following cash flow series at i = 10%: img
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At i = 15%, what is the annual-equivalence amount for the infinite series shown next? img
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Consider the following cash flows and compute the equivalent annual worth at i = 12%: img
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