Sam Is Considering Buying A New Lawn Mower He Has A Choice Between

For additional practice, please see the problems (with selected solutions) provided on the Student CD-ROM that accompanies this book.

4.1 IQ Computer assembles Unix workstations at its plant. The current product line is nearing the end of its marketing life, and it is time to start production of one or more new products. The data for several candidates are shown below.

The maximum budget for research and development is S300 000. A minimum of S200 000 should be spent on these projects. It is desirable to spread out the introduction of new products, so if two products are to be developed together, they should have different lead times. Resource draw refers to the labour and space that are available to the new products; it cannot exceed 100%.

Potential Product

A

B

C

D

Research and

development costs

S120 000

S60 000

SI50 000

S75 000

Lead time

1 year

2 years

1 year

2 years

Resource draw

60%

50%

40%

30%

On the basis of the above information, determine the set of feasible mutually exclusive alternative projects that IQ Computers should consider.

4.2 The Alabaster Marble Company (AM) is considering opening three new quarries. One, designated T, is in Tusksarelooser County; a second, L, is in Lefant County; the third, M, is in Marxbro Count}-. Marble is shipped mainly within a 500-kilometre range of its quarry because of its weight. The market within this range is limited. The returns that AM can expect from any of the quarries depends on how many quarries AM opens. Therefore, these potential projects are related.

(a) Construct a set of mutually exclusive alternatives from these three potential projects.

(b) The Lefant Count}' quarry has very rich deposits of marble. This makes the purchase of mechanized cutter-loaders a reasonable investment at this quarry. Such loaders would not be considered at the other quarries. Construct a set of mutually exclusive alternatives from the set of quarry projects augmented by the potential mechanized cutter-loader project.

(c) AM has decided to invest no more than $2.5 million in the potential quarries. The first costs are as follows:

Project

First Cost

T quarry

S0.9 million

L quarry

1.4 million

M quarry

1.0 million

Cutter-loader

0.4 million

Construct a set of mutually exclusive alternatives that are feasible, given the investment limitation.

4.3 Angus Automotive has $100 000 to invest in internal projects. The choices are:

Project

Cost

1. Line improvements

$20 000

2. New manual tester

30 000

3. Xew automatic tester

60 000

4. Overhauling press

50 000

Only one tester may be bought and the press will not need overhauling if the line improvements are not made. What mutually exclusive project combinations are available if Angus Auto will invest in at least one project?

4.4 The intersection of King and Alain Streets needs widening and improvement. The possibilities include

1. Widen King

2. Widen Main

3. Add a left-turn lane on King

4. Add a left-turn lane on Alain

5. Add traffic lights at the intersection

6. Add traffic lights at the intersection with advanced green for Alain

7. Add traffic lights at the intersection with advanced green for King

A left-turn lane can be installed only if the street in question is widened. A left-turn lane is necessary if the street has traffic lights with an advanced green. The city cannot afford to widen both streets. How many mutually exclusive projects are there?

4.5 Yun is deciding among a number of business opportunities. She can

(a) Sell the X division of her company, Yunco

(b) Buy Barzoo's company, Barco

(c) Get new financing

(d) Expand into Tasmania

There is no sense in getting new financing unless she is either buying Barco or expanding into Tasmania. She can only buy Barco if she gets financing or sells the X division. She can only expand into Tasmania if she has purchased Barco. The X division is necessary to compete in the Tasmania. What are the feasible projects she should consider?

4.6 Xottawasaga Printing has four printing lines, each of which consists of three printing stations, A, B, and C. They have allocated S20 000 for upgrading the printing stations. Station A costs S7000 and takes 10 days to upgrade. Station B costs S5000 and takes 5 days, and station C costs S3000 and takes 3 days. Due to the limited number of technicians, Xottawasaga can only upgrade one printing station at a time. That is, if they decide to upgrade two Bs, the total downtime will be 10 days. During the upgrading period, the downtime should not exceed 14 days in total. Also, at least two printing lines must be available at all times to satisfy the current customer demand. The entire line will not be available if any of the printing stations is turned off for upgrading. Xottawasaga Printing wants to know which line and which printing station to upgrade. Determine the feasible mutually exclusive combinations of lines and stations for Xottawasaga Printing.

4.7 Alargaret has a project with a £28 000 first cost that returns £5000 per year over its 10-year life. It has a salvage value of £3000 at the end of 10 years. If the MARR is 15%,

(a) What is the present worth of this project?

(b) What is the annual worth of this project?

(c) What is the future worth of this project after 10 years?

(d) What is the payback period of this project?

(e) W nat is the discounted payback period for this project?

4.8 Appledale Dairy is considering upgrading an old ice-cream maker. Upgrading is available at two levels: moderate and extensive. Moderate upgrading costs S6500 now and yields annual savings of S3 300 in the first year, S3000 in the second year, $2700 in the third year, and so on. Extensive upgrading costs $10 550 and saves $7600 in the first year. The savings then decrease by 20% each year thereafter. If the upgraded ice-cream maker will last for seven years, which upgrading option is better? Use a present worth comparison. Appledale's MARR is 8%.

4.9 Kiwidale Dairy is considering purchasing a new ice-cream maker. Two models, $moothie and Creamy, are available and their information is given below.

(a) WTiat is Kiwidale's MARR that makes the two alternatives equivalent? Use a present worth comparison.

Smoothie

Creamy

First cost

SI5 000

$36 000

Service life

12 years

12 years

Annual profit

$4200

$10 800

Annual operating cost

S1200

$3520

Salvage value

$2250

$5000

(b) It turned out that the sendee life of $moothie was 14 years. MTiich alternative is better on the basis of the MARR computed in part (a)? Assume that each alternative can be repeated indefinitely.

4.10 Xabil is considering buying a house while he is at university. The house costs €100 000 today. Renting out part of the house and living in the rest over his five years at school will net, after expenses, €1000 per month. He estimates that he will sell the house after five years for €105 000. If Xabil's MARR is 18%, compounded monthly, should he buy the house?

4.11 A young software genius is selling the rights to a new video game he has developed. Two companies have offered him contracts. The first contract offers $10 000 at the end of each year for the next five years, and then $20 000 per year for the following 10 years. The second offers 10 payments, starting with $10 000 at the end of the first year, $13 000 at the end of the second, and so forth, increasing by $3000 each year (i.e., the tenth payment will be $10 000 + 9 X $3000). Assume the genius uses a MARR of 9%. Which contract should the young genius choose? Use a present worth comparison.

4.12 Sam is considering buying a new lawnmower. He has a choice between a "Lawn Guy" mower and a Bargain Joe's "Clip Job" mower. Sam has a ALARR of 5%. The salvage value of each mower at the end of its sendee life is zero.

(a) Using the information on the next page, determine which alternative is preferable. Use a present worth comparison and the least common multiple of the sendee lives.

(b) For a four-year study period, what salvage value for the Lawn Guy mower would result in its being the preferred choice? What salvage value for the Lawn Guy would result in the Clip Job being the preferred choice?

Lawn Guy

Clip Job

First cost

S3 50

S120

Life

10 years

4 years

Annual gas

S60

S40

Annual maintenance

S30

S60

4.13 Water supply for an irrigation system can be obtained from a stream in some nearby mountains. Two alternatives are being considered, both of which have essentially infinite lives, provided proper maintenance is performed. The first is a concrete reservoir with a steel pipe system and the second is an earthen dam with a wooden aqueduct. Below are the costs associated with each.

Compare the present worths of the two alternatives, using an interest rate of 8%. Which alternative should be chosen?

Concrete Reservoir

Earthen Dam

First cost

S500 000

S200 000

Annual maintenance costs

S2000

S12 000

Replacing the wood portion

of the aqueduct each 15 years

N/A

S100 000

4.14 CB Electronix needs to expand its capacity. It has two feasible alternatives under consideration. Both alternatives will have essentially infinite lives.

Alternative 1: Construct a new building of 20 000 square metres now. The first cost will be S2 000 000. Annual maintenance costs will be $10 000. In addition, the building will need to be painted every 15 years (starting in 15 years) at a cost of $15 000.

Alternative 2: Construct a new building of 12 500 square metres now and an additional ".500 square mefres in 10 years. The first cost of the 12 500-square-metre building will be $1 250 000. The annual maintenance costs will be $5000 for the first 10 years (i.e., until the addition is built). The 7500-square-metre addition will have a first cost of $1 000 000. Annual maintenance costs of the renovated building (the original building and the addition) will be $11 000. The renovated building will cost $15 000 to repaint even- 15 years (starting 15 years after the addition is done).

Carn- out an annual worth comparison of the two alternatives. WTiich is preferred if the ALARR is 15%?

4.15 Katie's project has a five-year term, a first cost, no salvage value, and annual savings of $20 000 per year. After doing present worth and annual worth calculations with a 15% interest rate, Katie notices that the calculated annual worth for the project is exactly three times the present worth. What is the project's present worth and annual worth? $hould Katie undertake the project?

4.16 Xighhigh Newsagent wants to replace its cash register and is currently evaluating two models that seem reasonable. The information on the nvo alternatives, CR1000 and CRX, is shown in the table.

CR1000

CRX

First cost

£680

£1100

Annual savings

£245

£440

Annual maintenance

£35 in year 1, increasing by

£60

cost

£10 each year thereafter

Sendee life

4 years

6 years

Scrap value

£100

£250

(a) If Xighhigh Newsagent's MARR is 10%, which type of cash register should they choose? Use the present worth method.

(b) For the less preferred type of cash register found in part (a), what scrap value would make it the preferred choice?

4.17 Midland Metalworking is examining a 750-tonne hydraulic press and a 600-tonne moulding press for purchase. Midland has only enough budget for one of them. If Midland's MARR is 12% and the relevant information is as given below, which press should they purchase? Use an annual worth comparison.

Hydraulic Press

Moulding Press

Initial cost

$275 000

$185 000

Annual savings

S33 000

S24 500

Annual maintenance cost

$2000, increasing by 15% each year thereafter

Si000, increasing bv $350 each year thereafter

Life

15 years

10 years

Salvage value

S19 250

S14 800

4.18 Westmount Waxworks is considering buying a new wax melter for its line of replicas of statues of government leaders. There are two choices of supplier, Finedetail and Simplicity. Their proposals are as follows:

Finedetail

Simplicity

Expected life

7 years

10 years

First cost

$200 000

S350 000

Maintenance

SlOOOO/year +

$0.05/unit

S20 000/year

+ SO.Ol/unit

Labour

$1.25/unit

$0.50/unit

Other costs

$6500/year + $0

.95/unit

S15 500/year

+ $0.55/unit

Salvage value

S5000

S20 000

Management thinks they will sell about 30 000 replicas per year if there is stability in world governments. If the world becomes very unsettled so that there are frequent overturns of governments, sales may be as high as 200 000 units a year. Westmount Waxworks uses a M\RR of 15% for equipment projects.

(a) Who is the preferred supplier if sales are 30 000 units per year? Use an annual worth comparison.

(b) Who is the preferred supplier if sales are 200 000 units per year? Use an annual worth comparison.

(c) How sensitive is the choice of supplier to sales level? Experiment with sales levels between 30 000 and 200 000 units per year. At what sales level will the costs of the two melters be equal?

4.19 The City of Brussels is installing a new swimming pool in the municipal recreation centre. Two designs are under consideration, both of which are to be permanent (i.e., lasting forever). The first design is for a reinforced concrete pool which has a first cost of €1 500 000. Even' 10 years the inner surface of the pool would have to be refin-ished and painted at a cost of €200 000.

The second design consists of a metal frame and a plastic liner, which would have an initial cost of €500 000. For this alternative, the plastic liner must be replaced every 5 years at a cost of €100 000, and even" 15 years the metal frame would need replacement at a cost of €150 000. Extra insurance of €5000 per year is required for the plastic liner (to cover repair costs if the liner leaks). The city's cost of long-term funds is 5%. Determine which swimming pool design has the lower present cost.

4.20 Sam is buying a refrigerator. He has two choices. A used one, at $475, should last him about three years. A new one, at $1250, would likely last eight years. Both have a scrap value of $0. The interest rate is 8%.

(a) Which refrigerator has a lower cost? (Use a present worth analysis with repeated lives. Assume operating costs are the same.)

(b) If Sam knew that he could resell the new refrigerator after three years for $1000, would this change the answer in part (a)? (LTse a present worth analysis with a three-year study period. Assume operating costs are the same.)

4.21 Yal is considering purchasing a new video plasma display panel to use with her notebook computer. One model, the XJ3, costs $4500 new, while another, the Y19, sells for $3200. Val figures that the XJ3 will last about three years, at which point it could be sold for $1000, while the Y19 will last for only two years and will also sell for $1000. Both panels give similar sendee, except that the Y19 is not suitable for client presentations. If she buys the Y19, about four times a year she will have to rent one similar to the XJ3, at a total year-end cost of about $300. LTsing present worth and the least common multiple of the sendee lives, determine which display panel Val should buy. Val's MARR is 10%.

4.22 For Problem 4.21, Val has determined that the salvage value of the XJ3 after two years of sendee is $1900. Which display panel is the better choice, on the basis of present worth with a two-year study period?

4.23 Tom is considering purchasing a £24 000 car. After five years, he will be able to sell the vehicle for £8000. Petrol costs will be £2000 per year, insurance £600 per year, and parking £600 per year. Maintenance costs for the first year will be £1000, rising by £400 per year thereafter.

The alternative is for Tom to take taxis everywhere. This will cost an estimated £6000 per year. Tom will rent a vehicle each year at a total cost (to year-end) of £600 for the family vacation, if he has no car. If Tom values money at 11 % annual interest, should he buy the car? Use an annual worth comparison method.

4.24 A new gizmo costs R10 000. Maintenance costs R2000 per year, and labour savings are R6567 per year. What is the gizmo's payback period?

4.25 Building a bridge will cost S65 million. A round-trip toll of $12 will be charged to all vehicles. Traffic projections are estimated to be 5000 per day. The operating and maintenance costs will be 20% of the toll revenue. Find the payback period (in years) for this project.

4.26 A new packaging machine will save Greene Cheese Pty. Ltd. $3000 per year in reduced spoilage, $2500 per year in labour, and $1000 per year in packaging material. The new machine will have additional expenses of $700 per year in maintenance and $200 per year in energy. If it costs $20 000 to purchase, what is its payback period? Assume that the savings are earned throughout the year, not just at year-end.

4.27 Diana usually uses a three-year payback period to determine if a project is acceptable. A recent project with uniform yearly savings over a five-year life had a payback period of almost exactly three years, so Diana decided to find the project's present worth to help determine if the project was truly justifiable. However, that calculation didn't help either since the present worth was exactly 0. What interest rate was Diana using to calculate the present worth? The project has no salvage value at the end of its five-year life.

4.28 The Biltmore Garage has lights in places that are difficult to reach. Management estimates that it costs about $2 to change a bulb. $tandard 100-watt bulbs with an expected life of 1000 hours are now used. $tandard bulbs cost $1. A long-life bulb that requires 90 watts for the same effective level of light is available. Long-life bulbs cost $3. The bulbs that are difficult to reach are in use for about 500 hours a month. Electricity costs $0.08/kilowatt-hour payable at the end of each month. Biltmore uses a 12% ALARR (1% per month) for projects involving supplies.

(a) V\ nat minimum life for the long-life bulb would make its cost lower?

(b) If the cost of changing bulbs is ignored, what is the minimum life for the long-life bulb for them to have a lower cost?

(c) If the solutions are obtained by linear interpolation of the capital recover}' factor, will the approximations understate or overstate the required life?

4.29 A chemical recovery system costs 300 000 yuan and saves 52 800 yuan each year of its seven-year life. The salvage value is estimated at 75 000 yuan. The ALARR is 9%. What is the net annual benefit or cost of purchasing the chemical recover}' system? Use the capital recovery formula.

4.30 $avings of $5600 per year can be achieved through either a $14 000 machine (A) with a seven-year service life and a $2000 salvage value, or a $25 000 machine (B) with a ten-year service life and a $10 000 salvage value. If the ALARR is 9%, which machine is a better choice, and for what annual benefit or cost? Use annual worth and the capital recovery formula.

4.31 Ridgley Custom Aletal Products (RCAIP) must purchase a new tube bender. RCA IP's ALARR is 11%. They are considering two models:

Model

First Cost

$100 000

150 000

Economic Life

5 years

5 years

Yearly Net Savings

S50 000

60 000

Salvage Value

$20 000

30 000

(a) Using the present worth method, which tube bender should they buy?

(b) RCMP has discovered a third alternative, which has been added to the table below. Now which tube bender should they buy?

Model First Economic Yearly Salvage

Cost Life Net Savings Value

T $100 000 5 years S50 000 S 20 000

A 150 000 5 years 60 000 30 000

X 200 000 3 years 75 000 100 000

4.32 RCMP (see Problem 4.31, part (b)) can forecast demand for its products for only three years in advance. The salvage value after three years is S40 000 for model T and $80 000 for model A. Using the study period method, which of the three alternatives is best?

4.33 Using the annual worth method, which of the three tube benders should RCMP buy? The MARR is 11%. Use the data from Problem 4.31, part (b).

4.34 VTiat is the payback period for each of the three alternatives from the RCMP problem? Use the data from Problem 4.31, part (b).

4.35 Data for two independent investment opportunities are shown below.

Machine A

Machine B

Initial cost

¥1 500 000

¥2 000 000

Revenues (annual)

¥ 900 000

¥1 100 000

Costs (annual)

¥ 600 000

¥ 800 000

Scrap value

¥ 100 000

¥ 200 000

Service life

5 years

10 years

(a) For a ALARR of 8%, should either, both, or neither machine be purchased? Use the annual worth method.

(b) For a ALARR of 8%, should either, both, or neither machine be purchased? Use the present worth method.

(c) What are the payback periods for these machines? Should either, both, or neither machine be purchased, based on the payback periods? The required payback period for investments of this type is three years.

4.36 Xaviera is comparing two mutually exclusive projects, A and B, that have the same initial investment and the same present worth over their sendee lives. Wolfgang points out that, using the annual worth method, A is clearly better than B. What can be said about the sendee lives for the nvo projects?

4.37 Xaviera noticed that two mutually exclusive projects, A and B, have the same payback period and the same economic life, but A has a larger present worth than B does. What can be said about the size of the annual savings for the two projects?

4.38 Tvo plans have been proposed for accumulating money for capital projects at Bobbin Bay Lighting. One idea is to put aside 100 000 rupees per year, independent of growth. The second is to start with a smaller amount, 80 000 rupees per year, but to increase this in proportion to the expected company growth. The money will accumulate interest at 10%, and the company is expected to grow about 5% per year. Which plan will accumulate more money in 10 years?

4.39 Cleanville Environmental Sendees is evaluating two alternative methods of disposing of municipal waste. The first involves developing a landfill site near the city. Costs of the site include Si 000 000 start-up costs, Si00 000 closedown costs 30 years from now, and operating costs of S20 000 per year. Starting in 10 years, it is expected that there will be revenues from user fees of S30 000 per year. The alternative is to ship the waste out of the region. An area firm will agree to a long-term contract to dispose of the waste for S13 0 000 per year. Using the ammal worth method, which alternative is economically preferred for a ALARR of 11%? Would this likely be the actual preferred choice?

4.40 Alfredo Auto Parts is considering investing in a new forming line for grille assemblies. For a five-year study period, the cash flows for two separate designs are shown below. Create a spreadsheet that will calculate the present worths for each project for a variable ALARR. Through trial and error, establish the ALARR at which the present worths of the two projects are exactly the same.

Cash Flows for Grille Assembly Project

Automated Line

Manual Line

Year

Disbursements

Receipts

Net Cash Flow

Disbursements

Receipts

Net Cash Flow

0

€1 500 000

€ 0

- € 1 500 000

€1 000 000

€ 0

- € 1 000 000

1

50 000

300 000

250 000

20 000

200 000

180 000

2

60 000

300 000

240 000

25 000

200 000

175 000

3

70 000

300 000

230 000

30 000

200 000

170 000

4

80 000

300 000

220 000

35 000

200 000

165 000

5

90 000

800 000

710 000

40 000

200 000

160 000

4.41 Stayner Catering is considering setting up a temporary division to handle demand created by their city's special tourist promotion during the coming year. They will invest in tables, sendng equipment and trucks for a one-year period. Labour is employed on a monthly basis. Warehouse space is rented monthly, and revenue is generated monthly. The items purchased will be sold at the end of the year, but the salvage values are somewhat uncertain. Given below are the known or expected cash flows for the project.

Month

Purchase

Labour Expenses

Warehouse Expenses

Revenue

January (beginning)

S200 000

January (end)

S 2000

S3000

S 2000

February

2000

3000

2000

March

2000

3000

2000

April

2000

3000

2000

May

4000

3000

10 000

June

10 000

6000

40 000

July

10 000

6000

110 000

August

10 000

6000

60 000

September

4000

3000

30 000

October

2000

3000

10 000

November

2000

3000

5000

December

Salvage?

2000

3000

2000

For an interest rate of 12% compounded monthly, create a spreadsheet that calculates and graphs the present worth of the project for a range of salvage values of the purchased items from 0% to 100% of the purchase price. Should Stayner Catering go ahead with this project?

4.42 Alfredo Auto Parts has two options for increasing efficiency. They can expand the current building or keep the same building but remodel the inside layout. For a five-year study period, the cash flows for the two options are shown below. Construct a spreadsheet that will calculate the present worth for each option for a variable ALARR. By trial and error, determine the ALARR at which the present worths of the two options are equivalent.

Expansion Option

Remodelling Option

Year

Disbursements

Receipts

Net Cash Flow

Disbursements

Receipts

Net Cash Flow

0

€850 000

€ 0

-€8 50 000

€230 000

€ 0

-€230 000

1

25 000

200 000

175 000

9000

80 000

71 000

2

30 000

225 000

195 000

11 700

80 000

68 300

5

35 000

250 000

215 000

15 210

80 000

64 790

4

40 000

275 000

235 000

19 773

80 000

60 227

5

45 000

300 000

255 000

25 705

80 000

54 295

4.43 Derek has two choices for a heat-loss prevention system for the shipping doors at Kirkland Manufacturing. He can isolate the shipping department from the rest of the plant, or he can curtain off each shipping door separately. Isolation consists of building a permanent wall around the shipping area. It will cost S60 000 and will save $10 000 in heating costs per year. Plastic curtains around each shipping door will have a total cost of about S5000, but will have to be replaced about once every two years. Savings in heating costs for installing the curtains will be about S3000 per year. Use the payback period method to determine which alternative is better. Comment on the use of the payback period for making this decision.

4.44 Assuming that the wall built to isolate the shipping department in Problem 4.43 will last forever, and that the curtains have zero salvage value, compare the annual worths of the two alternatives. The MARR for Kirkland Manufacturing is 11%. Which alternative is better?

4.45 Cleanville Environmental Services is considering investing in a new water treatment system. On the basis of the information given below for two alternatives, a fully automated and a partially automated system, construct a spreadsheet for computing the annual worths for each alternative with a variable MARR. Through trial and error, determine the MARR at which the annual worths of the two alternatives are equivalent.

Fully Automated System

Partially Automated System

Year

Disbursements

Receipts

Net Cash Flow

Disbursements

Receipts

Net Cash Flow

0

SI 000 000

s o

-SI 000 000

S650 000

S 0

- S650 000

1

30 000

300 000

270 000

30 000

220 000

190 000

2

30 000

300 000

270 000

30 000

220 000

190 000

1

80 000

300 000

220 000

35 000

220 000

185 000

4

30 000

300 000

270 000

35 000

220 000

185 000

5

30 000

300 000

270 000

40 000

220 000

180 000

6

80 000

300 000

220 000

40 000

220 000

180 000

7

30 000

300 000

270 000

45 000

220 000

175 000

8

30 000

300 000

270 000

45 000

220 000

175 000

9

80 000

300 000

220 000

50 000

220 000

170 000

10

30 000

300 000

270 000

50 000

220 000

170 000

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