Civil Engineering Chapter 8 Homework Nper Function Including The Optional Type Entry

Problem 8.1

The fixed costs at Harley Motors are $1 million annually. The main product has revenue

of $9.90 per unit and $4.50 variable cost. Determine the following:

a. Breakeven quantity per year

b. Annual profit if 150,000 units are sold

c. Annual profit if 480,000 units are sold

Problem 8.2

A professional photographer who specializes in wedding-related activities paid $16,000

for equipment that has a $2000 estimated salvage value after five years. He estimates that

his costs associated with each event amount to $65 per day. If he charges $300 per day

for his services, how many days per year must he be employed in order to break even at

an interest rate of 8% per year?

Problem 8.3

An independent over-the-road (OTR) truck driver-owner paid $98,000 for a used tractor-

trailer. The salvage value of the rig after five more years of use is expected to be $66,000.

The operating cost is $0.60 per mile and the base mileage rate(revenue) is $0.71 per mile.

(a) How many miles per year must the owner drive just to break even at an interest rate of

10% per year?

(b) If the owner drives 550 miles per day, how many days per year will be required for

breakeven?

Problem 8.4

A small consulting engineering company bought an office building for $900,000. The

company has ten engineers and eight support staff. Monthly expenses for salaries,

utilities, grounds maintenance, etc. are $1.1 million. If the average billing rate per

engineer is $90 per hour, how many hours per month must be billed in order for the

company to make a profit of $15,000 per month? Use an interest rate of 1% per month

and assume the building will have a market value of $1.5 million after 10 years.

Problem 8.5

How long will it take to recover an investment of $245,000 in enhanced CNC controls

that include axis control to 8 axes (on the milling model) if the associated income is

$92,000 per year, expenses are 38,000 per year, and the salvage value is assumed to be

15% of the first cost. Use a MARR of 15% per year.

Problem 8.6

A call center in India used by U.S. and U.K. credit card holders has a capacity of

1,500,000 calls annually. The fixed cost of the center is $850,000 with an average

variable cost of $1.95 and revenue of $3.25 per call. Find the percentage of the capacity

that must be placed each year to break even.

Problem 8.7

Benjamin used regression analysis to fit quadratic relations to monthly revenue and cost

data with the following results:

R = -0.007Q2 + 32Q

TC = 0.004Q2 + 2.2Q + 8

(a) Plot R and TC. Estimate the quantity Q at which the maximum profit should occur.

Estimate the profit at this quantity.

(b) The profit relation Profit = R – TC and calculus can be used to determine the quantity

Qp at which the maximum profit will occur, and the amount of this profit. The equations

are:

Profit = aQ2 + bQ + c

Qp = -b/2a

Maximum profit = -b2/4a + c

Use these relations to confirm the graphical estimates you made in (a). (Your

instructor may ask you to derive the relations above.)

Problem 8.8

Brittany is cooping this semester at Regency Aircraft, which customizes the interiors of

private and corporate jets. Her first assignment is to develop the specifications for a new

machine to cut, shape, and sew leather or vinyl covers and trims. The first cost is not

easy to estimate due to many options, but the annual revenue and M&O costs should net

out at $15,000 per year over a 10-year life. Salvage is expected to be 20% of the first

cost. Determine what can be paid for the machine now and recover the cost and an

MARR of 8% per year under two scenarios:

I: No outside revenue will be developed.

II: Outside contracting will occur with estimated revenue of $10,000 the first year,

increasing by $5000 per year thereafter.

Solve using (a) tabulated factors, and (b) a spreadsheet and the GOAL SEEK tool.

Problem 8.9

The National Potato Cooperative purchased a deskinning machine last year for $150,000.

Revenue for the first year was $50,000. Over the total estimated life of 8 years, what

must the annual revenue for years 2 through 8 equal to recover the investment, if costs

are constant at $42,000 and a return of 10% per year is expected? A salvage value of

$20,000 is anticipated.

Problem 8.10

ABB purchased fieldbus communication equipment for a project in South Africa for

$3.15 million. If net cash flow is estimated at $500,000 per year, and a salvage value of

$400,000 is anticipated, determine how many years the equipment must be used to just

break even at interest rates ranging from 8% to 15% per year. Solve using (a) tabulated

factors, and (b) a spreadsheet.

Problem 8.11

A semiautomatic process has fixed costs of $40,000 per year and variable costs of

$30 per unit. An automatic process has fixed costs of $88,000 per year and variable costs

of $22 per unit. At what production level per year will the two alternatives break even?

Problem 8.12

Rent-A-Wreck car rental agency has a contract with PM Warranty, Inc to do major

repairs for $700 per car. The car rental agency estimates that it could repair its own cars

for $300 each if it acquires a facility for $300,000 now. A salvage value of $40,000 after

15 years is estimated for the facility. What is the minimum number of cars that must be

repaired each year to make the acquisition attractive at an interest rate of 10% per year?

Problem 8.13

A rural 2-lane road can be surfaced with concrete for $2.3 million per mile. If signing,

mowing and winter maintenance are not included, the basic maintenance costs for

concrete and asphalt roadways are $483 and $774 per mile per year, respectively. If

concrete lasts 20 years, what is the maximum amount that should be spent on asphalt that

will last only 10 years? Use an interest rate of 8% per year.

Problem 8.14

A land development company is considering the purchase of earth moving equipment.

The equipment will have a first cost of $190,000 and a salvage value of $70,000 when

the company sells it in 10 years. A service contract for maintenance on the equipment

will cost $40,000 per year. The operating cost is expected to be $260 per day.

Alternatively, the company can rent the necessary equipment for $1100 per day and hire

a driver at $180 per day. If the company’s MARR is 10% per year, how many days per

year must the company need the equipment in order to justify its purchase?

Problem 8.15

The Ascarate Fishing Club, a non-profit organization dedicated to teaching kids how to

fish, is considering two options for providing a heavily stocked pond for kids who have

never caught a fish before. Option 1 is an above- ground swimming pool made of heavy

vinyl plastic that will be assembled and disassembled for each quarterly event. The

purchase price will be $400. Leaks from hooks piercing the fabric will be repaired with a

vinyl repair kit at a cost of $70 per year, but the pool will have to be replaced when too

many repairs have been made. Option 2 is an in-ground pond that will be excavated by

club members at no cost and lined with fabric that costs $1 per square foot. The pond

will be 15 feet in diameter and 3 feet deep. Assume 300 ft2 of liner will be purchased. A

chain link fence at $10 per lineal foot will be installed around the pond (100 ft of fence).

Maintenance inside the fence is expected to cost $20 per year. The park where the pond

will be constructed has committed the land for only 10 years. At an interest rate of 6%

per year, how many years will the above-ground pool have to last for the two options to

just break even?

Problem 8.16

Microsurfacing is part of a pavement restoration and maintenance program that seals the

surface of a street that has minor cracking to prevent water from penetrating into the base

material. The annual cost of the equipment (truck, tank, valves, etc.) is $109,000 per year

and the material cost is $2.75 per square yard. Alternatively, regular street resurfacing

requires equipment that has a first cost of $225,000 with a 15-year life and no salvage

value. The variable cost for regular resurfacing is $13 per square yard. At an interest rate

of 8% per year, how many square yards per year must be resurfaced for the two methods

to break even?

Problem 8.17

Two membrane systems are under consideration for treating cooling tower blowdown to

reduce its volume. A low pressure seawater reverse osmosis (SWRO) system will

operate at 500 psi and produce 720,000 gallons of permeate per day. It will have a fixed

cost of $465 per day and an operating cost of $485 per day. A higher pressure SWRO

system operating at 800 psi will produce 950,000 gallons per day at an operating cost of

$1280 per day. The fixed cost of the high pressure SWRO system will be only $328 per

day because fewer membranes will be required. How many gallons of blowdown water

must require treatment each day for the two systems to break even?

Problem 8.18

Three methods can be used for producing heat sensors for high-temperature furnaces.

Method A will have a fixed cost of $140,000 per year and a production cost of $62 per

part. Method B will have a fixed cost of $210,000 per year and a production cost of $28

per part. Method C will require the purchase of equipment costing $500,000 that will

have a life of five years with a 25% salvage value. The production cost will be $53 per

part. At an interest rate of 10% per year, determine the breakeven annual production rate

between the two lowest cost methods.

Problem 8.19

A Yellow Pages directory company must decide whether it should compose the ads for its

clients in-house or outsource them to a production company. To develop the ads in-

house, the company will have to purchase computers, printers, and other peripherals at a

cost of $12,000. The equipment will have a useful life of 3 years, after which it will be

sold for $2000. The employee who creates the ads will be paid $55,000 per year. In

addition, each ad will have an average cost of $5. Alternatively, the company can

outsource ad development at a flat fee of $21 per ad. At an interest rate of 10% per year,

how many ads must the company sell each year for the alternatives to break even?

Problem 8.20

A plant manager has received two estimates from contractors to improve traffic flow and

repave the parking areas. Proposal A includes new curbs, grading, and paving at an

initial cost of $250,000. The life of the parking lot surface constructed in this manner is

expected to be 4 years with an annual cost of $3000 for maintenance and repainting of

strips. According to proposal B, the pavement has a higher quality and an expected life of

12 years. The annual maintenance cost will be negligible for the paved parking area, but

the markings will have to be repainted every 2 years at a cost of $5000, except in the

final year 12 of ownership. If the company’s current MARR is 12% per year, how much

can it afford to spend on proposal B so the two estimates will break even?

Problem 8.21

Alfred Home Construction is considering the purchase of five dumpsters and the

transport truck to store and transfer construction debris from building sites. The entire rig

is estimated to have an initial cost of $125,000, a life of 8 years, a $5000 salvage value,

an operating cost of $40 per day, and an annual maintenance cost of $2000.

Alternatively, Alfred can obtain the same services from the city as needed at each

construction site for an initial delivery cost of $125 per dumpster per site and a daily

charge of $20 per day per dumpster. An estimated 45 construction sites will need debris

storage throughout the average year. If the minimum attractive rate of return is 12% per

year, how many days per year must the equipment be required to justify its purchase?

Problem 8.22

Process X is estimated to have a fixed cost of $40,000 per year and a variable cost of $60

per unit in year 1, decreasing by $5 per unit per year. Process Y will have a fixed cost of

$70,000 per year and a variable cost of $10 per unit, increasing by $1 per unit per year.

At an interest rate of 12% per year, how many units must be produced in year 3 for the

two processes to break even?

Problem 8.23

An effective method to recover water used for regeneration of ion exchange resins is to

use a reverse osmosis system in a batch-treatment mode. Such a system involves

recirculation of the partially-treated water back into the feed tank, causing the water to

heat up. The water could be cooled using a single-pass heat exchanger or a closed-loop

heat exchange system. The single-pass system would require a small chiller costing

$920, plus stainless steel tubing, connectors, valves, etc. costing $360, and it could be

used for 3 years. The cost of water, sewer charges, electricity, etc. will be $3.10 per hour.

The closed-loop system will cost $3850 to buy, have a useful life of 5 years, and will

cost $1.28 per hour of operation. The interest rate is 10% per year and the salvage values

are negligible (a) What is the breakeven number of hours per year that the cooling system

must be needed to justify purchase of the closed-loop system? (b) What is the difference

in annual costs if 400 hours per year is the expected usage level?

Problem 8.24

An engineering practitioner can lease a fully equipped computer and color printer system

for $800 per month or purchase one for $8500 now and pay a $75 per month maintenance

fee. If the nominal interest rate is 15% per year, determine the months of use necessary

for the two to break even using (a) tabulated factors, and (b) a single-cell spreadsheet

function.

Problem 8.25

The Ecology Group wishes to purchase a piece of equipment for various metals

recycling. Machine 1 costs $123,000, has a life of 10 years, an annual cost of $5000, and

requires one operator at a cost of $24 per hour. It can process 10 tons per hour. Machine

2 costs $70,000, has a life of 6 years, an annual cost of $2500, and requires two operators

at a cost of $24 per hour for each operator. It can process 6 tons per hour.

(a) Determine the breakeven tonnage of scrap metal at i = 7% per year and select the

better machine for a processing level of 1000 tons per year.

(b)Calculate and plot the sensitivity of the breakeven tons per year to ± 15% change in

the hourly cost of an operator.

Problem 8.26

Donny and Barbara want to join a sports and exercise club. The HiPro plan has no

upfront charge and the first month is free. It then charges a total of $100 at the end of

each subsequent month. Bally charges a membership fee of $100 per person now and $20

per person per month starting the first month. How many months will it take the two

plans to reach a breakeven point? Solve by hand or spreadsheet, as request by your

instructor.

Problem 8.27

Balboa Industries’ Electronics Division is trying to reduce supply chain risk by making

more responsible make/buy decisions through improved cost estimation. A high-use

component (expected usage is 5000 units per year) can be purchased for $25 per unit

with delivery promised within a week. Alternatively, Balboa can make the component

in-house and have it readily available at a cost of $5 per unit, if equipment costing

$150,000 is purchased. Labor and other operating costs are estimated to be $35,000 per

year over the study period of 5 years. Salvage is estimated at 10% of first cost and

i = 12% per year. Neglecting the element of availability (a) determine the breakeven

quantity, and (b) recommend making or buying at the expected usage level.

Problem 8.28

Claris Water Company makes and sells filters for public water drinking fountains. The

filter sells for $50 per unit. Recently a in-house/outsource analysis was completed based

on the need for new manufacturing equipment. The equipment first cost of $200,000 and

$25,000 annual operation cost comprise the fixed cost, while Claris’s variable cost is $20

per filter. The equipment has a 5-year life, no salvage value, and the MARR is 6% per

year. The decision to make the filter was based on the breakeven point and the historical

sales level of 5000 filters per year.

(a) Determine the breakeven point. Should the filters be made in-house?

(b) An engineer at Claris learned that an outsourcing firm offered to make the filters for

$30 each, but this offer was rejected by the president as entirely too expensive. Perform

the breakeven analysis of the two options and determine if the in-house decision was

correct.

(c) Develop and use the profit relations for both options to verify the preceding answers.

Note: Solve all three parts using a single spreadsheet if requested by your instructor.

Problem 8.29

Josaline, the owner of a construction company, is planning to purchase specialized

equipment to complete a contract awarded to her company. The first cost of the

equipment is $250,000 with a life of 3 years at which time she will not need the

equipment anymore. The operating cost is expected to be $75,000 per year.

Alternatively, a subcontractor can perform the work for $175,000 per year. Because the

equipment is specialized, Josaline is not sure about the salvage value. She estimates a

likely salvage of $90,000, but in might have to be scrapped for as little as $10,000 in

three years. The MARR is15% per year.

(a) Is her decision to buy the equipment sensitive to the salvage value?

(b) Determine the salvage value at which the two alternatives break even.

Problem 8.30

A company planning to borrow $10.5 million for a plant expansion is not sure what the

interest rate will be when it applies for the loan. The rate could be as low as 10% per

year or as high as 12% per year. The company will only move forward with the project if

the annual worth of the expansion is below $5.7 million. If the M&O cost is fixed at

$3.1 million per year and the salvage will be $2 million if the interest rate is 10% and

$2.5 million if it is 12%, is the decision to move forward with the project sensitive to the

interest rate? Use a 5-year study period.

Problem 8.31

A company that manufactures clear PVC pipe is investigating two production options

with the following cash flow estimates.

Batch Continuous

First cost, $ -80,000 -130,000

Annual cost, $/year -55,000 -30,000

Salvage value, $ 10,000 40,000

Life, years 3 to 10 5

The chief operating officer (COO) has asked you to determine if the batch option would

ever have a lower annual worth than the continuous flow system using interest rates over

a range of 5% to 15% for the batch option, but only 15% for the continuous flow system.

The batch process can be used anywhere from 3 to 10 years. (Note: The continuous flow

process was previously determined to have its lowest cost over a 5-year life cycle.)

Problem 8.32

Home Automation is considering an investment of $500,000 in a new product line. The

company will make the investment only if it will result in a rate of return of 15% per

year or higher. If the revenue is expected to be between $138,000 and $165,000 per year

for 5 years, use a present worth analysis to determine if the decision to invest is sensitive

to the projected range of revenue.

Problem 8.33

Amphenol manufactures motor power connectors and is considering upgrading the

production equipment to reduce costs over a 6-year planning horizon. The company can

invest $80,000 now (year 0), 1 year from now, or 2 years from now. Depending on when

the investment is made, the savings will vary. The savings estimates are $25,000,

$26,000, and $29,000 per year for investing now, year 1, and year 2, respectively. If the

company’s MARR is 20% per year, use an FW analysis to determine if the timing of the

investment will return at least 20% per year.

Problem 8.34

The equivalent annual worth of the process currently used in manufacturing motion

controllers is AW = $-62,000 per year. A replacement process is under consideration that

will have a first cost of $64,000 and an operating cost of $38,000 per year for the next

3 years. Three different engineers have given their opinion about what the salvage value

of the new process will be 3 years from now as follows: $10,000, $13,000, and $18,000.

Is the decision to replace the process sensitive to the salvage value estimates at the

company’s MARR of 15% per year?

Problem 8.35

Emerson Electric is considering the purchase of equipment that will allow the company

to manufacture a new line of wireless devices for home appliance control. The first cost

will be $80,000, and the life is estimated at 6 years with a salvage value of $10,000.

Three different salespeople have provided estimates regarding the added revenue the

equipment will generate. Salespersons 1, 2 and 3 have made estimates of $10,000,

$16,000, and $18,000 per year, respectively. If the company’s MARR is 8% per year, use

a PW-based relation to determine if these different estimates will change the decision to

purchase the equipment.

Problem 8.36

MAG Industrial needs 1000 square meters of storage space. Purchasing land for $80,000

and then erecting a temporary metal building at $70 per square meter is one option. The

president hopes to sell the land for $100,000 and the building for $20,000 after 3 years.

Another option is to lease space for $30 per square meter per year payable at the

beginning of each year. The MARR is 20%. Perform a present worth analysis of the

building and leasing alternatives to determine the sensitivity of the decision if the

construction cost decreases by 10% to $63 per square meter and the lease cost remains at

$30 per square meter per year.

Problem 8.37

Consider the two air conditioning systems detailed below.

___________________ System 1 System 2

First cost, $ -10,000 -17,000

Annual operating cost, $ -600 -150

Salvage (disposal) value, $ -100 -300

New compressor and motor

cost at midlife, $ -1,750 -3,000

Life, years 8 12

Use AW analysis to determine the sensitivity of the economic decision to MARR

values of 4%, 6%, and 8%. Work this problem (a) by hand and (b) by spreadsheet.

Problem 8.38

Ned Thompson Labs performs tests on superalloys, titanium, aluminum, and most

metals. Tests on metal composites that rely upon scanning electron microscope results

can be subcontracted or the labs can purchase new equipment. Evaluate the sensitivity of

the economic decision to purchase the equipment over a range of ±20% (in 10%

increments) of the estimates for P, AOC, R, n, and MARR (range on MARR is 12% to

18%). Use the AW method and plot the results on a sensitivity graph. For which

parameter(s) is the AW most sensitive? least sensitive?

First cost, P = $-180,000

Salvage, S = $20,000

Life, n = 10 year

Annual operating cost, AOC = $-30,000 per year

Annual revenue, R = $70,000 per year

MARR = 15% per year

Problem 8.39

Determine if the selection of system 1 or 2 is sensitive to variation in the return required

by management. The corporate MARR ranges from 8% to 16% per year on different

projects. Use tabulated factors or a spreadsheet, as requested by your instructor.

____________ System 1 System 2

First cost, $ -50,000 -100,000

AOC, $ per year -6,000 -1,500

Salvage value, $ 30,000 0

Rework at midlife, $ -17,000 -30,000

Life, years 4 12

Problem 8.40

Titan manufactures and sells gas-powered electricity generators. It can purchase a new

line of fuel injectors from either of two companies. Cost and savings estimates are

available, but the savings estimates are unreliable at this time. Use an AW analysis at

MARR = 10% per year to determine if the selection between company A and B changes

when the estimated savings varies as much as ±40% from the best estimates. Use

tabulated factors or a spreadsheet, as requested by your instructor.

______________________________Company A Company B

First cost, $ -50,000 -37,500

AOC, $ per year -7,500 -8,000

Savings best estimate, $ per year 15,000 13,000

Salvage, $ 5,000 3,700

Life, years 5 5

Problem 8.41

A Civil Engineer involved in construction management must decide between two ways

to pump concrete up to the top floors of a seven-story office building under construction.

Plan 1 requires the purchase of equipment for $6000 which costs between $0.40 and

$0.75 per metric ton to operate, with a most likely cost of $0.50 per metric ton. The asset

is able to pump 100 metric tons per day. If purchased, the asset will last for 5 years, have

no salvage value, and be used 50 days per year. Plan 2 is an equipment-leasing option and

is expected to cost the company $2500 per year for equipment with a low cost estimate

of $1800 and a high estimate of $3200 per year. In addition, an extra $5 per hour labor

cost will be incurred for operating the leased equipment each 8-hour day. Use I = 12%

per year. (a) Which plan should the engineer recommend on the basis of the most likely

estimates of costs?(b) Will the decision above change if the pessimistic estimates are

used?

Problem 8.42

When the country’s economy is expanding, AB Investment Company is optimistic and

expects a MARR of 15% for new investments. However, in a receding economy the

expected return is 8%. Normally a 10% return is required. An expanding economy

causes the estimates of asset life to go down about 50%, and a receding economy makes

the n values increase about 20%. Which plan should be selected if the company president

expects the economy to be (a) expanding, and (b) receding.

Plan M Plan Q

Initial investment, $ -200,000 -240,000

Net cash flow, $/year 65,000 71,000

Life, years 10 10

Problem 8.43

In evaluating two environmental chambers at Holly Farms, the AW of the 409G model is

determined to be $-135,143 with a high degree of certainty. The cost estimates for the

D103 model are less certain. The manager requested a ‘worst case’ analysis with three

estimates for P and n as shown below. The annual operating cost is fixed at $4000 and the

salvage value of the chamber is expected to be 10% of the first cost. Perform the analysis

using (a) tabulated factors, and (b) a spreadsheet to determine if D103 is favored under

any of the first cost and life scenarios indicated? The company’s MARR is 10% per year.

__________________Pessimistic Most Likely Optimistic

First cost, $ -500,000 -400,000 -300,000

Life, years 1 3 5

Problem 8.44

State why payback analysis is best used as a supplemental analysis tool when an

economic study is performed.

Problem 8.45

The process for producing a fruit-tree pesticide has a first cost of $200,000 with annual

costs of $50,000 and revenue of $90,000 per year. What is the payback period at

(a) i = 0%, and (b) i = 12% per year?

Problem 8.46

Two machines can be used to produce an aircraft part from titanium. The costs and other

cash flows associated with each alternative are shown. The salvage values are zero

regardless of when the machines are replaced. Use the estimates to preliminarily

determine which alternative(s) should be selected for further analysis provided they must

pay back in 5 years or less. Perform the analysis with (a) i = 0% and (b) i = 10% per year.

Machine 1 Machine 2

First cost, $ -40,000 -90,000

Net cash flow, $ per year 10,000 15,000

Maximum life, years 10 10

Salvage value, $ 0 0

Problem 8.47

Laura’s grandparents helped her purchase a small self-serve laundry business to make

extra money during her five college years. When she completed her electrical

engineering degree, she sold the business and her grandparents told her to keep the

money as a graduation present. For the net cash flows (NCF) listed, determine:

(a) if the total income exceeded the total amount invested in 5 years (i = 0%).

(b) the actual rate of return over the 5-year period.

(c) how long it took to pay back the $75,000 investment plus a 7% per year return.

(d) answers to all three questions above using a spreadsheet.

Year 0 1 2 3 4 5

NCF, $1000 per year -75 -10.5 18.6 -2 28 105

Problem 8.48

A company that manufactures diaphragm seals has identified the cash flows shown

below with a certain part of the manufacturing and sales functions. Determine the no-

return payback period.

First cost of equipment, $ -130,000

Annual expenses, $/year -45,000

Annual revenue, $/year 75,000

Problem 8.49

In desalting ground waters that contain a significant amount of sulfates, the concentrate

that is generated during the desalting process can sometimes be treated with lime to

recover gypsum and other salts. Because the high pH process is tough on equipment, the

equipment’s useful life is uncertain. A treatment train with an initial cost of $90,000 has

an operating cost of $20,000 per month. The revenue from the sale of calcium sulfate is

$22,000 per month. Determine how many months the equipment must last to recover the

investment at i = 0.5% per month using (a) hand solution, (b) a calculator, and (c) a

single-cell spreadsheet function.

Problem 8.50

Ellis Equipment sold a used Massey Ferguson tractor for $55,000 to a South- Kansas

farmer 10 years ago. (a) What is the uniform net cash flow that the farmer had to receive

each year to realize payback and a return of 5% per year on his investment over a period

of 3 years? 5 years? 8 years? All 10 years? (b) If the net cash flow was actually $6000

per year, what is the amount the farmer should have paid for the tractor to realize

payback plus the 5% per year return over these 10 years?

Problem 8.51

CMS Express has historically owned and maintained its own delivery trucks. Leasing is

an option being seriously considered because costs for maintenance, fuel, insurance, and

some liability issues will be transferred to United Leasing, the truck leasing company.

The study period is no more than 24 months for either alternative. The annual lease cost

is paid at the beginning of each year and is not refundable for partially used years.

Purchase: P = $30,000 now; monthly cost = $1200; monthly revenue = $4500

Lease: P = $10,000 at the beginning of each year (months 0 and 12);

monthly cost = $2800; monthly revenue = $4500

(a) Use the first cost and net cash flow estimates to determine the payback in months with

a nominal 9% per year return for the purchase and lease options.

(b) Spreadsheet question: Write the single-cell NPER function, including the optional

‘type’ entry, that will display payback for the lease option, where lease costs are paid at

the beginning of the year. Explain how you developed the function.

Problem 8.52

Fidelity Life Insurance has a document imaging system that needs replacement. A local

salesperson quoted a cost of $10,000 with an estimated salvage of $900 after 5 or more

years. If the system is expected to save $1700 per year in clerical time, find the payback

time at 8% per year. As a practice, the office manager purchases equipment only when

the payback is less than 6 years. Otherwise, he prefers to lease. Should the imaging

system be purchased or leased?

Problem 8.53

Darrell, an engineer with TAGHeuer Watches, is considering two alternative processes to

waterproof the new line of scuba-wear watches. Estimates follow.

Process 1: P = $50,000; n = 5 years; NCF = $24,000 per year; no salvage value.

Process 2: P = $120,000; n = 10 years; NCF = $42,000 for year 1, decreasing by

$2500 per year thereafter; no salvage value.

Darrell first decided to use no-return payback to select the process, because his boss told

him most investments at TAGHeuer must pay back in 3 to 4 years. Determine which

process Darrell will select.

Problem 8.54

Darrell, an engineer with TAGHeuer Watches, is considering two alternative processes to

waterproof the new line of scuba-wear watches. Estimates follow.

Process 1: P = $50,000; n = 5 years; NCF = $24,000 per year; no salvage value.

Process 2: P = $120,000; n = 10 years; NCF = $42,000 for year 1, decreasing by

$2500 per year thereafter; no salvage value.

Next Darrell decided to use the AW method at the corporate MARR of 12% per year that

he used previously on another evaluation. Now what process will he select?

Problem 8.55

Darrell, an engineer with TAGHeuer Watches, is considering two alternative processes to

waterproof the new line of scuba-wear watches. Estimates follow.

Process 1: P = $50,000; n = 5 years; NCF = $24,000 per year; no salvage value.

Process 2: P = $120,000; n = 10 years; NCF = $42,000 for year 1, decreasing by

$2500 per year thereafter; no salvage value.

Finally, Darrell decided to calculate the rate of return for the cash flows of each process

over its respective life. (a) What process does this analysis indicate as better? (b) Explain

the fundamental assumptions and errors made when this approach is used. (Hint: Before

answering, review Sections 6.3 and 6.4 on ROR.)

Problem 8.56

Darrell, an engineer with TAGHeuer Watches, is considering two alternative processes to

waterproof the new line of scuba-wear watches. Estimates follow.

Process 1: P = $50,000; n = 5 years; NCF = $24,000 per year; no salvage value.

Process 2: P = $120,000; n = 10 years; NCF = $42,000 for year 1, decreasing by

$2500 per year thereafter; no salvage value.

Of the evaluations presented in problems 8.53 through 8.55 (see below), which is the

correct method upon which to base the final economic decision? Why is this method the

only correct one?

8.53 Darrell first decided to use no-return payback to select the process, because his boss

told him most investments at TAGHeuer must pay back in 3 to 4 years. Determine which

process Darrell will select.

8.54 Next Darrell decided to use the AW method at the corporate MARR of 12% per

year that he used previously on another evaluation. Now what process will he select?

8.55 Finally, Darrell decided to calculate the rate of return for the cash flows of each

process over its respective life. (a) What process does this analysis indicate as better?

(b) Explain the fundamental assumptions and errors made when this approach is used.

(Hint: Before answering, review Sections 6.3 and 6.4 on ROR.)

Problem 8.57

In linear breakeven analysis, if a company expects to operate at a point below the

breakeven point, the alternative to select is:

a. the one with the lower fixed cost.

b. the one with the higher fixed cost.

c. the one with the lower variable cost.

d. the one with the higher variable cost.

Problem 8.58

A process can be completed using either Alternative X or Y, where Y is an automated

version of X. X has fixed costs of $10,000 per year with a variable cost of $50 per unit. If

the process is automated, the fixed cost for Y will be $5,000 per year and its variable cost

will be only $30 per unit. The minimum number of units that must be produced each year

for alternative Y to be favored is closest to:

a. Alternative Y will be favored for any level of production

b. 125

c. 375

d. Alternative X will be favored for any level of production

Problem 8.59

A company is considering two alternatives for automating a certain process.

Alternative A will have fixed costs of $42,000/year and will require 2 laborers at $48/day

each. Together, these laborers can generate 100 units of product.

Alternative B will have fixed costs of $56,000/year, but with this alternative, the 3

laborers will generate 200 units of product. In determining the breakeven number of units

Q, the total cost per year for Alternative B is represented as:

a. [2(48)/100]Q

b. [3(48)/200]Q

c. [3(48)/200]Q + 56,000

d. [2(48)/100]Q + 42,000

Problem 8.60

The price of a car that you want is $70,000 today. Its price is expected to increase by

$3300 per year. You now have $35,000 in an investment which is earning 15% per year.

The number of years before you have enough to buy the car without borrowing any

money is closest to:

a. 3 years

b. 5 years

c. 7 years

d. 9 years

Problem 8.61

In conducting a sensitivity analysis, the only parameter that represents a measure of

worth is:

a. the future worth.

b. the breakeven point.

c. a cost index.

d. a sinking fund equation.

Problem 8.62

When conducting a sensitivity analysis using multiple estimates, the three estimates are

usually:

a. probabilistic, authentic, most likely

b. deterministic, most likely, optimistic

c. pessimistic, strategic, realistic

d. optimistic, pessimistic, most likely

Problem 8.63

A process for making a laboratory-grade sodium phosphate will have a first cost of

$320,000 with annual costs of $40,000 and revenue of $98,000 per year. At a return

requirement of 20% per year, the payback period is closest to:

a. 3 years

b. 5 years

c. 7 years

d. ∞; it will never pay off

Problem 8.64

When the variable cost is reduced for linear total cost and revenue lines, the breakeven

point decreases. This is an economic advantage because:

a. the revenue per unit will increase.

b. the two lines will now cross at zero.

c. the profit will increase for the same revenue per unit.

d. the total cost line becomes nonlinear.

Problem 8.65

The profit relation for the following estimates at a quantity that is 10% above

breakeven is:

Fixed cost = $500,000 per year

Cost per unit = $200

Revenue per unit = $250

a. Profit =200(11,000) – 250(11,000) – 500,000

b. Profit =250(11,000) – 500,000 – 200(11,000)

c. Profit =250(11,000) – 200(11,000) + 500,000

d. Profit =250(10,000) – 200(10,000) – 500,000

Problem 8.66

For these two AW relations, the breakeven point QBE in miles per year is closest to:

AW1 = -23,000(A/P,10%,10) + 4000(A/F,10%,10) – 5000 – 4QBE

AW2 = -8,000(A/P,10%,4) – 2000 – 6QBE

a. 1984

b. 1224

c. 1090

d. 655

Problem 8.67

To make an item in-house, equipment costing $250,000 must be purchased. It will have a

life of 4 years, an annual cost of $80,000, and each unit will cost $40 to manufacture.

Buying the item externally will cost $100 per unit. At i = 15% per year, it is cheaper to

make the item in-house if the number per year needed is:

a. above 1047 units

b. above 2793 units

c. equal to 2793 units

d. below 2793 units

Problem 8.68

The sensitivity of two parameters (P and n) for one project is evaluated by graphing the

AW values versus percentage variation from the most likely estimates. The curve for n

has a slope very close to zero, while the P curve has a significant negative slope. One

good conclusion from the graph is that:

a. both PW and AW values are more sensitive to variations in P than n.

b. the project should be rejected, since AW values vary with P and n.

c. a better estimate of P needs to be made.

d. the ROR is equally sensitive for both parameters.

Problem 8.69

Four mutually exclusive alternatives are evaluated using three estimates or strategies

(pessimistic, most likely, and optimistic) for several parameters. The resulting PW values

over the LCM are determined as shown.

PW Values Over LCM, $ ___

Strategy 1 2 3 4__

Pessimistic (P) 4,500 -6,000 3,700 -1,900

Most likely (ML) 6,000 -500 5,000 -100

Optimistic (O) 9,500 2,000 10,000 3,500

The best alternative to select under the stated condition is:

a. pessimistic: select alternative 2

b. optimistic: select alternative 2

c. pessimistic: select alternative 1

d. optimistic: select alternative 4

Problem 8.70

Four mutually exclusive alternatives are evaluated using three estimates or strategies

(pessimistic, most likely, and optimistic) for several parameters. The resulting PW values

over the LCM are determined as shown.

PW Values Over LCM, $ ___

Strategy 1 2 3 4__

Pessimistic (P) 4,500 -6,000 3,700 -1,900

Most likely (ML) 6,000 -500 5,000 -100

Optimistic (O) 9,500 2,000 10,000 3,500

If no one of the strategies is more likely than any other strategy, the alternative to

select is:

a. 2

b. 1 and 2 are equally acceptable

c. 1

d. 3

Solution 8.1

(a) QBE = 1,000,000/(9.90 – 4.50)

Solution 8.2

Let x = days per year to break even

Solution 8.3

(a) Let x = miles per year to break even

Solution 8.4

Let x = hours per month billed to realize a profit of $15,000

Solution 8.5

Solution 8.6

Solution 8.7

(a) Plot shows maximum quantity at about 1350 units. Profit is about $20,000.

Solution 8.8

(a) Develop PW = 0 relation and solve for first cost P.

(b) Spreadsheet solution uses GOAL SEEK for each scenario to find P. Set PW

values (cells B13 and D13) to 0 and change values in cells B2 and D2.

Solution 8.9

Let R = revenue for years 2 through 8. Set up PW = 0 relation.

(Extra: Spreadsheet solution uses GOAL SEEK to find R = $72,141 with

remaining revenue cells set equal to this value.)

Solution 8.10

(a) Using the relation PW = 0, select different i values and solve for n. Details for

i = 8% and 15% are shown.

(b) Retention ranges from 8 to 20 years for varying i values. This is a perfect

example where the spreadsheet is easier. Use the NPER function.

Solution 8.11

Solution 8.12

Let N = number of cars per year

Solution 8.13

Let Pasp = maximum $/mile for asphalt

Solution 8.14

Let x = days per year to just break even

Solution 8.15

Let n = number of years for pool to last for breakeven

Solution 8.16

Let x = square yards per year to break even

Solution 8.17

Let x = gallons per day to breakeven

Solution 8.18

Method A has a higher fixed cost and higher variable cost than Method C.

Solution 8.19

Solution 8.20

Set AWA = AWB, with PB = first cost of Proposal B. The The final term in AWB removes

Solution 8.21

Let x = breakeven days per year

Solution 8.22

Let x = production in year 3

Solution 8.23

(a) Let x = number of hours per year

(b) At x = 400 hours per year, select the closed-loop system. Determine difference

in annual costs.

Solution 8.24

(a) Solve AWlease – AWbuy = 0 for N = number of months. Monthly i = 1.25%

Solution 8.25

(a) Let T = number of tons. Solve relation AW1 = AW2 for T.

20.4

2.04T

6.8T

4.76T = 5327

27.6

2.76T

9.2T

6.44T = 5327

(b) Set up the VC relation for each machine and solve for T in AW1 = AW2 .

Solution 8.26

Let N = number of months

Spreadsheet solution:

% change

Cost,

$/hour

VC1

VC2

AW1 = AW2

relation

Breakeven

T value, tons

Solution 8.27

(a) Solve AWbuy = AWmake for Q = breakeven number of units per year.

Solution 8.28

(a) Solve relation Revenue – Cost = 0 for Q = number of filters per year

A spreadsheet can be used to answer all three questions.

Solution 8.29

(b) Let S = salvage value; set AW = $ -175,000

S = $32,971

Solution 8.30

Solution 8.31

Lowest cost for batch will occur when the interest rate is the lowest (5%)

and life is longest (10 years)

Solution 8.32

Solution 8.33

Invest now: FW25,000 = -80,000(F/P,20%,6) + 25,000(F/A,20%,6)

Solution 8.34

AWcurrent = $-62,000

Solution 8.35

SP1: PW1 = –80,000 + 10,000(P/F,8%,6) + 10,000(P/A,8%,6)

Solution 8.36

PWLease = – 30(1000) – 30(1000)(P/A,20%,2)

Solution 8.37

(a) AW1 = -10,000(A/P,i%,8) – 600 – 100(A/F,i%,8) – 1750(P/F,i%,4)(A/P,i%,8)

(b) Spreadsheet solution requires that the PW value is first determined using the

NPV function over the LCM of 24 years and then converting it to an AW value

using the PMT function. Spreadsheet follows.

Solution 8.38

Spreadsheet for -20% to +20% changes in P, AOC, R, n and MARR follows. The PMT

function for a +20% change is detailed at the bottom of the spreadsheet.

Solution 8.39

Hand analysis: Determine AW at different MARR values between 8% and 16%.

Selection changes for MARR values of 14% and 16%.

Solution 8.40

Hand solution: Determine AW values at different savings, s.

= -17,286 + s

Selection changes when s is +40% of best estimate. Table follows:

Spreadsheet solution: PMT functions display AW values with savings variation

added to end of function.

Solution 8.41

Plan 1 – Purchase

Percent

variation

Savings for A,

$ per year

AWA

Savings for B,

$ per year

AWB

Selection

-40%

9,000

$-10,871

7,800

$-9,486

B

18,000

-1,871

15,600

-1,686

B

21,000

1,129

18,200

914

A

Solution 8.42

(a) Expanding: MARR = 15%; n = 0.5(10) = 5 years

(b) Receding: MARR = 8%; n = 1.2(10) = 12 years

Solution 8.43

(a) Set up the general AW relation for D103 and determine AW for the three

scenarios.

(b) Spreadsheet solution.

Solution 8.44

Payback analysis should be used only as a supplemental analysis tool because it only

Solution 8.45

Solution 8.46

(a) Machine 1:

(b) Machine 1:

Solution 8.47

(c) Calculate PW at 7% by year to determine when PW turns positive. Start with

(d) A spreadsheet solution for all three parts follows.

Solution 8.48

Let np = number of years until payback at 0%

Solution 8.49

(a) Let np = number of months at 0.5% per month

Solution 8.50

(b) For payback with 5% return in np = 10 years, find PW. He should have paid

Solution 8.51

Monthly i = 9/12 = 0.75%. Solve PW relations for np

Solution 8.52

Set up the PW relation and use trial and error or spreadsheet for np.

Solution 8.53

Process 1: np = 50,000/24,000 = 2.1 years

Process 2: Interpolate for np = 3.04 years

Solution 8.54

Solution 8.55

(a) Determine i* from AW relations

(b) First of all, an ROR analysis always requires an incremental analysis over the

Solution 8.56

The AW method with evaluation at MARR = 12% is correct. Problem 8.54 correctly

Solution 8.57

Solution 8.58

Solution 8.59

Solution 8.60

Solve for n by trial and error or spreadsheet

Solution 8.61

Solution 8.62

Solution 8.63

There is no P/A factor this large for any n value, that is, n → ∞. From observation,, the

Solution 8.64

Solution 8.65

Solution 8.66

2QBE = 23,000(0.16275) – 4000(0.06275) – 8000(0.31547) + 3000

Solution 8.67

Solution 8.68

Solution 8.69

Solution 8.70