Homework answers / question archive / IEEN 5329 800 Fall 2014 Homework 4 6

IEEN 5329 800 Fall 2014 Homework 4 6

Economics

Share With

---

IEEN 5329 800

Fall 2014

Homework 4

6.2, 6.6, 6.8 (Calculate by hand and computer), 6.17, 6.22.

 

 

PROBLEM

6.1 Assume that an alternative has a 3-year life and that you calculated its annual worth over its 3-year life cycle. If you were told to provide the annual worth of that alternative for a 4-year study period, would the annual worth value you calculated from the alter-native's 3-year life cycle be a valid estimate of the annual worth over the 4-year study period? Why or why not?

6.2 Machine A has a 3-year life with no salvage value. Assume that you were told that the service provided by these machines would be needed for only 5 years. Alternative A would have to be repurchased and kept for only 2 years. What would its salvage value have to be after the 2 years in order to make its annual worth the same as it is for its 3-year life cycle at an interest rate of 10% per year?

Year	Alternative A, $	Alternative B,$
0	-10,000	-20,000
1	-7,000	-5,000
2	-7,000	-5,000
3	-7,000	-5,000
4		-5,000
5		-5,000

 

Alternatives Comparison

6.3 A consulting engineering firm is considering two models of SUVs for the company principals. A GM model will have a first cost of $26,000, an operating cost of $2000, and a salvage value of $12,000 after 3 years. A Ford model will have a first cost of $29,000, an operating cost of $1200, and a $15,000 resale value after 3 years. At an interest rate of 15% per year, which model should the consulting firm buy? Conduct an annual worth analysis.

6.4 A large textile company is trying to decide which sludge dewatering process it should use ahead of its sludge drying operation. The costs associated with centrifuge and belt press systems are shown below. Compare them on the basis of their annual worth’s, using an interest rate of 10% per year.

	Centrifuge	Belt Press
First cost, $	-250,000	-170,000
Annual operating cost, $/year	-31,000	-35,000
Overhaul in year 2, $	-	-26,000
Salvage value, $	40,000	10,000
Life, years	6	4

 

6.5 A chemical engineer is considering two styles of pipes for moving distillate from a refinery to the tank farm. A small pipeline will cost less to purchase (including valves and other appurtenances) but will have a high head loss and, therefore, a higher pumping cost. The small pipeline will cost $1.7 million installed and will have an operating cost of $12,000 per month. A larger-diameter pipeline will cost $2.1 million installed, but its operating cost will be only $8000 per month. Which pipe size is more economical at an interest rate of 1% per month on the basis of an annual worth analysis? Assume the salvage value is 10% of the first cost for each pipeline at the end of the 10-year project period.

 6.6 Polymer Molding, Inc., is considering two processes for manufacturing storm drains. Plan A involves conventional injection molding that will require making a steel mold at a cost of $2 million. The cost for inspecting, maintaining, and cleaning the molds is expected to be $5000 per month. Since the cost of materials for this plan is expected to be the same as for the other plan, this cost will not be included in the comparison. The salvage value for plan A is expected to be 10% of the first cost. Plant; involves using an innovative process known as virtual engineered composites wherein a floating mold uses an operating system that constantly adjusts the water pressure around the mold and the chemicals entering the process. The first cost to tool the floating mold is only $25,000, but because of the newness of the process, personnel and product-reject costs are expected to be higher than those fora conventional process. The company expects the operating costs to be $45,000 per month for the first 8 months and then to decrease to $10,000 per month thereafter. There will be no salvage value with this plan. At an interest rate of 12% per year, compounded monthly, which process should the company select on the basis of an annual worth analysis over a 3-year study period?

6.7 An industrial engineer is considering two robots for purchase by a fiber-optic manufacturing company. Robot X will have a first cost of $85,000, an annual maintenance and operation (M&O) cost of $30,000, and a $40,000 salvage value. Robot Y will have a first cost of $97,000, an annual M&O cost of $27,000, and a $48,000 salvage value. Which should be selected on the basis of an annual worth comparison at an interest rate of 12% per year? Use a 3-year study period.

6.8 Accurate airflow measurement requires straight unobstructed pipe for a minimum of 10 diameters upstream and 5 diameters downstream of the measuring device. In one particular application, physical constraints compromised the pipe layout, so the engineer was considering installing the airflow probes in an elbow, knowing that flow measurement would be less accurate but good enough for process control. This was plan A, which would be acceptable for only 2 years, after which a more accurate flow measurement system with the same costs as plan A will be available. This plan would have a first cost of $25,000 with annual maintenance estimated at $4000. Plan B involved installation of a recently designed submersible airflow probe. The stainless steel probe could be installed in a drop pipe with the transmitter located in a waterproof enclosure on the handrail. The cost of this system would be $88,000, but because it is accurate, it would not have to be replaced for at least 6 years. Its maintenance cost is estimated to be $1400 per year. Neither system will have a salvage value. Al an interest rate of 12% per year, which one should be selected on the basis of an annual worth comparison?

6.9 A mechanical engineer is considering two types of pressure sensors for a low-pressure steam line. The costs are shown below. Which should be selected based on an annual worth comparison at an interest rate of 12% per year?

	Type X	Type Y
First Cost, $	-7,650	-12,900
Maintenance cost, $/year	-1,200	-900
Salvage value, $	0	2,000
Life, Years	2	4

 

6.10 The machines shown below are under consideration for an improvement to an automated candy bar wrapping process. Determine which should be selected on the basis of an annual worth analysis using an interest rate of 15% per year.

	Machine C	Machine D
First cost, $	-40,000	-65,000
Annual cost, $/year	-10,000	-12,000
Salvage value, $	12,000	25,000
Life, years	3	6

 

6.11 Two processes can be used for producing a polymer that reduces friction loss in engines. Process K will have a fast cost of $160,000, an operating cost of $7000 per month, and a salvage value of $40,000 after its 2-year life. Process L will have a first cost of $210,000, an operating cost of $5000 per month, and a $26,000 salvage value after its 4-year life. Which process should be selected on the basis of an annual worth analysis at an interest rate of 12% per year, compounded monthly?

6.12 Two mutually exclusive projects have the estimated cash flows shown below. Use an annual worth analysis to determine which should be selected at an interest rate of 10% per year.

	Project Q	Project R
First cost, $	-42,000	-80,000
Annual cost, $/year	-6,000	-7,000 year 1, increasing by $1000 per year
Salvage value, $	0	4,000
Life, years	2	4

 

6.13 An environmental engineer is considering three methods for disposing of a nonhazardous chemical sludge: land application, fluidized-bed incineration, and private disposal contract. The details of each method are shown below. Determine which has the least cost on the basis of an annual worth comparison at 12% per year.

	Land Application	Incineration	Contract
First cost, $	-110,000	-800,000	0
Annual cost, $/year	-95,000	-60,000	-190,000
Salvage value, $	15,000	250,000	0
Life, years	3	6	2

 

6.14 A state highway department is trying to decide whether it should "hot-patch" a short section of an existing county road or resurface it. If the hot-patch method is used, approximately 300 cubic meters of material would be required at a cost of $700 per cubic meter (in place). Additionally, the shoulders will have to be improved at the same time at a cost of $24,000. These improvements will last 2 years, at which time they will have to be redone. The annual cost of routine maintenance on the patched up road would be $5,000. Alternatively, the state can resurface the road at a cost of $850,000. This surface will last 10 years if the road is maintained at a cost of $2000 per year beginning 3 years from now. No matter which alternative is selected, the road will be completely rebuilt in 10 years. At an interest rate of 8% per year, which alternative should the state select on the basis of an annual worth analysis?

Permanent Investments and Projects

6.15 How much must you deposit in your retirement account starting now and continuing each year through year 9 (i.e., 10 deposits) if you want to be able to withdraw $80,000 per year forever beginning 30 years from now? Assume the account earns interest at 10% per year.

6.16 What is the difference in annual worth between an investment of $100,000 per year for 100 years and an investment of $100,000 per year forever at an interest rate of 10% per year?

6.17 A stockbroker claims she can consistently earn 15% per year on an investor's money. If she invests $20,000 now, $40,000 two years from now, and $10,000 per year through year 11 starting 4 years from now, how much money can the client withdraw every year forever, beginning 12 years from now, if the stockbroker delivers what she said and the account earns 6% per year from year 12 forward? Disregard taxes.

6.18 Determine the perpetual equivalent annual worth (in years 1 through infinity) of an investment of $50,000 at time 0 and $50,000 per year thereafter (forever) at an interest rate of 10% per year.

6.19 The cash How associated with landscaping and maintaining a certain monument in Washington, D.C., is $100,000 now and $50,000 every 5 years forever. Determine its perpetual equivalent annual worth (in, years 1 through infinity) at an interest rate of 8% per year.

6.20 The cost associated with maintaining rural highways follows a predictable pattern. There are usually no costs for the first 3 years, but thereafter maintenance is required for restriping, weed control, light replacement, shoulder repairs, etc. For one section of a particular highway, these costs are projected to be $6000 in year 3, $7000 in year 4, and amounts increasing by $1000 per year through the highway's expected 30-year life. Assuming it is replaced with a similar roadway, what is its perpetual equivalent annual worth (in years 1 through infinity) at an interest rate of 8% per year?

6.21 A philanthropist working to set up a permanent endowment wants to deposit money each year, starting now and making 10 more (i.e., 11) deposits, so that money will be available for research related to planetary colonization. If the size of the first deposit is $1 million and each succeeding one is $100,000 larger than the previous one, how much will be available forever beginning in year 11, if the fund earns interest at a rate of 10% per year?

 

6.22 For the cash flow sequence shown below  (in thousands of dollars), determine the amount of money that can be withdrawn annually for an infinite period of time, if the first withdrawal is to be made in year 10 and the interest rate is 12% per year.

Year	0	1	2	3	4	5	6
Deposit amount, $	100	90	80	70	60	50	40

 

6.23 A company that manufactures magnetic membrane switches is investigating three production options that have the estimated cash flows below. (a) Determine which option is preferable at an interest rate of 15% per year. (b) If the options are independent, determine which are economically acceptable. (All dollar values are in millions.)

	In-house	License	Contract
First cost, $	-30	-2	0
Annual cost, $ year	-5	-0.2	-2
Annual income, $/year	14	1.5	2.5
Salvage value, $	7	-	-
Life, years	10	∞	5

 

FE REVIEW PROBLEMS

The sign convention on the FE exam may be opposite of that used here. That is, on the FE exam, costs may be positive and receipts negative.

6.24 For the mutually exclusive alternatives shown below, determine which one(s) should be selected.

Alternative	Annual Worth
A	-25,000
B	-12,000
C	10,000
D	15,000

 

 (a) Only A (b) Only D (c) Only A and B (d) Only C and D

 

6.25 The annual worth (in years 1 through infinity) of $50,000 now, $10,000 per year in years 1 through 15, and $20,000 per year in years 16 through infinity at 10% per year is closest to

(a) Less than $16,900 (b) $16,958 (c) $17,394 (d) $19,573

6.26 An alumnus of West Virginia University wishes to start an endowment that will provide scholarship money of $40,000 per year beginning in year 5 and continuing indefinitely. The donor plans to give money now and for each of the next 2 years. If the size of each donation is exactly the same, the amount that must be donated each year at i = 8% per year is closest to