Case studies Engineering Economics -...

Case studies

Engineering Economics

AAge U. Michelsen

2

Case studies

isBN 978-87-89359-18-2

aage u. Michelsen:engineering economicsBased on the danish edition 24, 2013Publisher: Bodano Publishing & Communication apsCopyright © Bodano 2013

Bodano Publishing & Communication apsBox 63dK3060 espergaerdePhone: +45 3874 7876e-mail: [email protected]

3

Foreword

This collection of case studies is designed to be used as educational material in the teaching of business economics to engineering students.

Many engineering students are primarily interested in the technical disciplines and perceive “economics” as uninteresting and more or less irrelevant to the solution of technical problems. A main objective of this collection of case studies is to illustrate that in business, the economic dimension is highly relevant in the resolution of the vast majority of technical problems. By presenting the economic problems in a tech-nical context, it is hoped that a greater number of engineering students will become interested in economic studies and see the relevance of this.

An emphasis has been placed on making the cases realistic, in that they reflect con-crete problems faced by the companies. At the same time, it has been necessary to simplify some of the problems to make them suitable for educational use. In addi-tion, some of the numerical values have been changed for reasons of confidentiality. Most numerical values, however, have the proper order of magnitude.

Proposed solutions have been prepared for the numerical problems in the cases, designed to complement textbook theories and models. Some cases also contain discussion portions, which include keywords or keyword-like phrases. In addition, because the case studies are based on concrete business situations, they can provide the basis for broader discussions – for example, regarding the given assumptions and the consequences of alternative assumptions.

The author extends a sincere thanks to the employees of the companies that have contributed to the preparation of the case studies. Without their involvement, many of the realistic aspects would have been missing.

4

Case studies

With respect to the next edition, we welcome comments about the level of difficulty of the problems and selection of topics. These comments should be directed to the book’s author:

Civil Engineer Aage U. [email protected]

5

Case studies

Table of Contents

Case Solution

ColoPlast a/sConsiderations about the revision of a product 8 38

daNfoss a/sManufacturing Capacity Constraints 12 41

H. luNdBeCK a/sInsourcing – made possible by the reduction of production costs 15 44

Mt Højgaard a/sInclusion of project earnings in the company’s consolidated financial statement 20 47

a/s storeBæltAnnuities with different payment-interval lengths 26 50

velux a/sCalculations with the introduction of new technology for windows 31 54

8

Case: ColoPlast a/s

Considerations about the revision of a product

Coloplast develops products and services that make life easier for people with very personal and private medical conditions. Coloplast has four business areas: ostomy, urology, continence, and wound and skin care. The story of Coloplast begins back in 1954. Elise Sorensen is a nurse. Her sister, Thora, has undergone ostomy surgery and no longer dares to go out among other people out of fear that her stoma may leak. Elise understands her sister’s problems and invents the world’s first ostomy bag. A bag that makes it possible for Thora - and thousands like her - to return to a normal life.

Today, Coloplast’s values still follow Elise’s example: we listen, we learn, and we act.

Most of our customers have suffered a serious accident or illness, and their life sit-uation is often associated with taboo and stigma. We help them return to a fruitful life without restrictions. By making products that work, which are easy to use and do not look like medical equipment, we hope to remove some of the “patient stigma” that many live with. We can only do this by listening to the customer’s needs and involving them in our product innovation.

Facts about Coloplast:• Coloplasthassubsidiariesin33countriesandsellsproductsinmorethan100 countries • GlobalheadquarterslocatedinHumlebaek,Denmark• Morethan8,000employeesworldwide,ofwhichapproximately1,200arein Denmark• ProductioninDenmark,Hungary,China,USA,andFrance• Coloplasthadaturnoverof11billionDanishKronerin2011/12

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Case: ColoPlast a/s

Coloplast is considering undertaking a radical revision of one of its ostomy care products, Alterna, which is expected to reduce the variable production cost of the product. From the time that such a product revision process begins, it normally takesabout18monthsuntilthesaleoftherevisedproductcanbegin.Tosimplifythe calculations, it is assumed here that the development time is one year.

Table 1 specifies data for the current version of the product, since the revision of the product, where applicable, must begin one year before the beginning of year 1.

Year 1 2 3 4 5 6

expected sales (million units/yr.) 62.6 64.5 65.8 67.1 67.1 65.7

expected sales price (dKK/unit) 16.75 16.58 16.42 16.25 16.09 15.93

expected variable costs (dKK/unit) 2.04 1.98 1.92 1.88 1.84 1.81

Table 1: Data on expected sales, sales price, and variable costs for the current product, if the revised version of the product is not developed and marketed.

If the revised version of the product is developed and marketed, the current product willbegraduallyphasedoutover3years.ExpectedsalesofthecurrentproductarelistedinTable2.Salespriceandvariablecostsareexpectedtoremainasindicatedin Table 1.

Year 1 2 3 4 5 6

expected sales (million units/yr.) 49.1 19.7 9.8 0 0 0

Table 2: Estimated sales for the current product, if the revised version is marketed.

Table3specifiesdatafortherevisedversionoftheproduct.

Year 1 2 3 4 5 6

expected sales (million units/yr.) 14.2 47.5 58.8 71.1 74.7 78.4

expected sales price dKK/unit) 16.75 16.58 16.42 16.25 16.09 15.93

expected variable costs (dKK/unit) 2.14 1.89 1.76 1.72 1.69 1.67

Table 3: Data on expected sales, sales price, and variable costs for the revised version of the product.

10

Case: ColoPlast a/s

Ifitisdecidedtodeveloptherevisedversionoftheproduct,5millionDKKwillbeinvestedinavisionsystemforproductionmonitoring,1millionDKKallocatedtomarketingcosts,and5millionDKKallocatedtodeveloptheproductionsystem.Thecostofproductdevelopmentisallocatedtobe3millionDKK.

Coloplastusesadiscountrateof10%peryear.

QUestion 1Will it be profitable for Coloplast to implement the project to revise the current product?

QUestion 2What is the dynamic payback time for the project?

ThesalesfigureslistedinTable3arebasedonallcurrentcustomersswitchingfromthecurrenttotherevisedproduct,plusanincreaseinsalesof5%,sincetheadhesivein the revised version has new features added.

One risk of changing a product, however, is that some existing customers will not switch to the revised product, but instead purchase a product from a competitor.

QUestion 3By how many percent must the annual sales of the revised product be reduced before the project is no longer profitable?

Another uncertainty in the project is the life span the product will have on the mar-ket. In the above, both the current product and the revised version of the product are based on a 6-year period.

QUestion 4How much will the profitability of developing and marketing the revised version of the product be reduced, if the life span on the market is reduced from 6 to 5 years?

Please find the solution on page 34.

Coloplast – the best kept secret!

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Coloplast develops products and services that make life easier for people with very personal and private medical conditions. Working closely with the people who use our products, we create solutions that are sensitive to their special needs. We call this intimate healthcare. Our business includes ostomy care, urology and continence care and wound and skin care. We operate globally and employ more than 7,000 people.

The Coloplast logo is a registered trademark of Coloplast A/S. © 2012-11. All rights reserved Coloplast A/S, 3050 Humlebæk, Denmark.

Coloplast A/S Holtedam 1

3050 Humlebæk Denmark

www.coloplast.com

CP_Flyer_Aahus Symposium_A4-vers3.indd 1 09/10/12 10.28


Are you motivated by makinglife easier for people withintimate healthcare needs?

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Coloplast - curiosity works here...

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Coloplast – the best kept secret!

curious and


Throw this flyer out!

Are you up for challenging your colleagues in a great way – and maybe even your manager?

Coloplast develops products and services that make life easier for people with very personal and private medical conditions. Working closely with the people who use our products, we create solutions that are sensitive to their special needs. We call this intimate healthcare. Our business includes ostomy care, urology and continence care and wound and skin care. We operate globally and employ more than 7,000 people.

The Coloplast logo is a registered trademark of Coloplast A/S. © 2012-11. All rights reserved Coloplast A/S, 3050 Humlebæk, Denmark.

Coloplast A/S Holtedam 1

3050 Humlebæk Denmark

www.coloplast.com

CP_Flyer_Aahus Symposium_A4-vers3.indd 1 09/10/12 10.28


Are you motivated by makinglife easier for people withintimate healthcare needs?

Turn the page!

Go meet some of our young talents by scanningthe QR code or visit us on coloplast.com/career

Are you a curious and ambitious student?

6.

Coloplast - curiosity works here...

Coloplast2013_210x297mm.pdf - 11:22:06 - July 31, 2013 - Page 1 of 1

12

Case: daNfoss a/s

Manufacturing Capacity Constraints

Danfossisaglobalcorporationwith110salescompaniesandapproximately400resellersanddistributorsworldwide.Danfoss’corporateheadquartersislocatedinDenmark.

Withapproximately23,000employees,anannualrevenueof34billionDKK,andanexportmarketshareof98%,Danfossisoneoftheleadingandlargestindustrialcompanies in its field.

Danfossproducescoolingautomation,industrialautomation,frequencyconverters,comfort automation (e.g. radiator thermostats), automatic controls for remote hea-ting plants, components for oil burners, thermostats for refrigerators and freezers, andcompressorsforairconditioners.Danfosshas79modernfactoriesin25coun-tries,atwhichareproducedapproximately250,000componentsperday.

Inthiscasestudy,oneofDanfoss’productiondepartmentshasbeensimplified,soas to consist of two main areas of capability: a turning department and a milling department. In the production department, two main product types are produced: A and B.

Production data for the two product types are shown in table 1.

Product Selling Price(DKK/unit)

Working Time (hours/unit)Turning Dept. Milling Dept.

Material Usage(DKK/unit)

a 530 0.5 0.5 205

B 640 0.8 0.4 248

Table 1: Production data for the product types A and B.

Thevariablecostsforsalaries,etc.are150DKK/hourand180DKK/hourinthetur-ning and milling departments respectively.

Vi søger mennesker, der vil noget Corporate & Administration Finans Human Resources Supply Chain

Produktion IT Udvikling Salg & Marketing

MAKING MODERN LIVING POSSIBLE

jobs.danfoss.dk

Vi søger mennesker, der vil noget Corporate & Administration Finans Human Resources Supply Chain

Produktion IT Udvikling Salg & Marketing

MAKING MODERN LIVING POSSIBLE

jobs.danfoss.dk

14

Case: daNfoss a/s

Itisassumedthatthecapacitiesinthenextmonthare1,000and800hoursintheturning and milling departments respectively.

PS.: In reality, the numerical values of the capacities are of course much larger, but the use of the small numerical values in this example aims to illustrate an overview and does not change the fundamental problem.

QUestion 1What is the maximum contribution margin earned in this production department in the next month?

Duetoproductionproblemsatasubcontractor,ithasbeendeterminedthattherewillonlybeenoughmaterialstoproduce800unitsofproducttypeAinthenextmonth, while there will be sufficient materials for product type B.

QUestion 2What is the maximum contribution margin that can now be earned in the next month?

It now appears that a foreign supplier can deliver additional materials for the pro-duction of product type A. The price for these materials, however, will be higher thanthe205DKKperunitlistedintable1.

QUestion 3What should the maximum price for these additional materials be, if it is to be pro-fitable to import them?


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Case: H. luNdBeCK a/s

Insourcing – made possible by the reduction of production costs

LundbeckisaDanishresearch-basedpharmaceuticalcompanythatdevelopsandmanufactures products for the treatment of central nervous system disorders. Lundbeck is one of the world’s leading companies within this field.

In2012,thecompanyhadatotalrevenueof14.8billionDKK.Lundbeckcurrentlyemploysapproximately5,800employeesin57countries,ofwhich2,000arebasedinDenmark.

Lundbeck’s ambition is to be a growth company, both financially and professio-nally. Financial growth is considered to be a basic prerequisite for the continued development of the company and its employees. To bring Lundbeck into a new growth period, it is necessary that future expenditures are carefully considered. The company must utilize its resources optimally in the coming years to maintain and develop its professional standard, so Lundbeck continues to be the ideal workplace for highly skilled employees.

The idea behind outsourcing is that companies should concentrate on tasks for which their core competencies are utilized, while secondary tasks should be given to subcontractors, who are specialists in performing such tasks. Particularly since the1990s,manyDanishcompanieshaveincreasinglyoutsourcedtheirproduc-tionactivities.ThiswasalsothecaseforLundbeck,whichin2004hadoutsourcednearly70%ofitsfinishedgoodsproduction.In2006,however,Lundbeckdecidedtofocus on developing the best supply chain in the pharmaceutical industry. Lund-beck therefore launched a series of lean projects, which showed that it was possible to achieve such significant productivity improvements that it became profitable to insource production tasks that were previously outsourced. This case study deals with two of the implemented lean projects.

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Thefollowingquestions1and2relatetosomeconsiderationsmadepriortothestart of a project that aimed to investigate whether it would be profitable to convert a packaging line. The packaging line in question was constructed 5 years ago, and theinvestmentinthelinewasthenat20millionDKK.Thepackaginglineisnowexpected to have a remaining life of 5 years. With the current production, 4 million finished product packages containing ampoules are packed per year. Ampoules are smallglassbottlesapproximately3cm.inlengthcontainingliquid.Theampoulescan be broken at the top, so the liquid can be drawn into a syringe, which is then given by injection to patients. Finished goods production consists of loading the ampoules into cardboard boxes with inserts. This production occupies the pack-aging line in the two shifts that are working on it. The project aimed partly to incre-ase the productivity of the finished product pack with ampoules and to convert the packaging line, so it would be possible to utilize the freed-up capacity for packaging dropcontainers.Dropcontainersarealsosmallglassbottlescontainingliquid.Thedrops are taken orally by the patient. A pipette is incorporated into the container’s lid for measuring the dosage. The finished goods production consists of affixing a label to the drop container, after which it is packed into a cardboard box with an instruction manual. A few years ago, the packaging of drop containers was outsour-cedtoasubcontractorthatpackages3milliondropcontainersperyear.

With the current production, the OEE1onthepackaginglineis40%,butitisexpectedthattheOEEcanbeincreasedto60%byimplementingtheleanproject.This increase must be achieved through improvement suggestions from employees. On the packaging line, the packaging time for a finished product pack containing ampoulesis50%greaterthanthepackagingtimeforadropcontainer.

QUestion 1Ifthepackagingline’sOEEisincreasedfrom40%to60%,whatproportionoftheoutsourced packaging of the drop containers would it be possible to insource, using the freed-up capacity?

It is estimated that the investment in the above modification of the packaging line willbe7millionDKK.Furthermore,itisestimatedthattheincreaseinproductionresulting from the increased OEE would subsequently increase costs for operation andmaintenanceofthepackaginglineby1millionDKKperyear.

1 OEE (Overall Equipment Effectiveness) indicates the percentage of the current production output out of the possible output at 100% efficiency.

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The payment to the subcontractor to which the packaging of the drop containers is outsourcedis1.50DKKperpack.Transportationcoststoandfromthesubcontrac-toris250,000DKKperyear.Inaddition,therewillbeareductionof350,000DKKper year for transportation of finished goods if the packaging of the drop containers is insourced.

Adiscountrateof10%peryearisused.

QUestion 2Would you recommend that Lundbeck implements the conversion of the packaging line, or that Lundbeck continues to produce only the finished product packs of ampoules on the packaging line?

Thefollowingquestions3,4,and5dealwithanotherofLundbeck’spackaginglines.Onthisline,itwaspossibletopackageabout40millionblistercardsin2005.Production here is quantified in the number of blister cards – and not the number ofcompletedproductpacks–asacompletedproductpackmaycontainfrom1to10blister cards. The costs are estimated to be:• Fixedcostsonthepackagingline=3.0millionDKK/year• Salarycosts=1.5millionDKK/year• Variablecosts=750DKKper10,000blistercards

It was considered to outsource the packaging process to a subcontractor, who would performthepackagingfor1,500DKKper10,000blistercards.Additionalcostsfortransportationandadministrationwouldbe500,000DKKperyear.

QUestion 3Would it be profitable to outsource the packaging to the subcontractor in question?

Before the decision on outsourcing was made, Lundbeck implemented a project to determine whether productivity of its packaging line could be increased so much that it would be profitable for Lundbeck to continue to do the packaging. Twenty different products were packaged on the packaging line, and the project was speci-fically focused on reducing changeover times, using the thinking and approach of SMED2.

2 SMED (Single Minute Exchange of Dies), developed by the Japanese Shiego Shingo, aims to ensure that all changeo-vers must be able to be performed in under 10 minutes.

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It is assumed that the fixed costs of the packaging line will not change as a result of the increased production. Labor costs are also expected to remain the same, as working hours will not change.

QUestion 4How many blister cards per year must it be possible to package on the line, if it is to be profitable for Lundbeck to perform the packaging?

In light of the above, Lundbeck decided to continue to do the packaging themselves, and carried out a number of lean projects in order to increase the capacity of the packaging line. These projects led to very significant productivity improvements, asillustratedintable1,whichshowsthecompletedproductionintheperiod2005-2011.

Year 2005 2006 2007 2008 2009 2010 2011

Production 40.0 45.9 49.7 60.5 70.0 84.0 92.2

Table 1: Annual production (in millions of packaged blister cards) in the period 2005-2011.

QUestion 5Whatisthefuturevalueattheendof2011becauseLundbeckdidthepackagingthemselves rather than outsourcing it to the subcontractor? Is this value an expres-sion of the gain Lundbeck realized during the project?


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Case: Mt Højgaard a/s

Inclusion of project earnings in the company’s consolidated financial statement

MTHøjgaardisDenmark’slargestconstructioncompany.In2012,thecompanyrealizedaturnoverof9.7billionDanishKronerandemployedanaverageofnearly5,000employees.

MT Højgaard is organized into a number of business units and subsidiaries within construction and supply work, as well as commercial and residential construction andrenovation.30%ofthecompany’sactivitiestakeplaceoutsideofDenmark.In support of its production, the company has created a number of corporate staff functions, such as Finance, HR, IT, Purchasing, QHSE, and Marketing & Communi-cation. All units are independent profit or cost centers with their own budget and accounting.

MT Højgaard’s corporate result is composed of the sum of the profits generated in the business units and subsidiaries, minus the costs of the corporate staff functions.

MT Højgaard submits quarterly consolidated financial statements to the stock exchange, and the consolidated financial statements provide the basis for external stakeholders’ to assess the company’s ability to manage an economically profitable business.

Until a few years ago, MT Højgaard used the accounting principle called the com-pleted contract method. In this method, the results from a project in a business unit or subsidiary were included in the consolidated financial statement when the developer had received the finished project.

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• Theadvantage of the completed contract method was that at the time of a project’s inclusion, there was no uncertainty about the project’s results. All necessary information appeared in the accounting.• Thedisadvantage was, conversely, that the completed contract method does not necessarily give a true picture of MT Højgaard’s ability to operate a profitable business. The reason was that major projects that extended over several years were only first included in the accounting in the financial year in which they were completed. This meant that in a year with few completed projects, the company could show a loss, while in a year with many completed projects, the company could end up with an excessive profit.

As with other major construction companies, MT Højgaard therefore changed to use the long-term contract method, in which the results of all projects are accounted for on an ongoing and pro rata basis, based on the projects’ degree of completion.

The following data is included in the calculation of the pro rata result:A: The expected revenue from the developerB: The expected project resultC: The posted project costsD:Theproject’sdegreeofcompletionE: The realized project result

The expected project result, B, is calculated as the difference between the expected revenue, A, and the expected project costs. It is therefore true that: A–B=theexpectedprojectcosts

The project’s degree of completion is calculated based on the posted project costs at any given time:D=C/(A–B)

The realized project result, E, is calculated as the degree of completion’s proportion of the total expected project result:E=D∙B

An example with numerical values to illustrate the method shown:A:100millionDKKB:20millionDKKC:40millionDKKD:40/(100–20)=0.50E:0.50∙20=10millionDKK

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Inthisexample,halfoftheexpectedprojectcostsareincurredandposted(D=0.50),sohalfoftheexpectedprojectresult(E=10millionDKK)canbeincludedinthefinancial statement.

The advantage of using the long-term contract method is that it gives a more accu-rate picture of MT Højgaard’s current ability to generate profits.

The disadvantage is, conversely, that there is now a requirement that a project manager must always know his project’s expected financial results quite precisely. If he does not, the method is misleading.

Anexampleprojectisshownintable1.TheamountsareinthousandsofDanishKroner.

Expectations per year Year 1 Year 2 Year 3

1) total revenue 100,000 100,000 100,000

2) total project result 20,000 20,000 20,000

Interim financial statement for Year 1 Year 2 Year 3

3) Posted costs 20,000 20,000 40,000

4) degree of complation

5) Project result

Accumulated financial statement Year 1 Year 2 Year 3

6) Posted costs

7) Project result

Table 1: Example 1 of a project process.

Explanation of table 1:1)and2)indicatetheexpectationsof,respectively,thetotalrevenueandtheoverallproject result the project manager in this case has had at the end of each of the three years.3)indicatesthecostswhicharepostedineachofthethreeyears.

QUestion 1Whatnumericalvaluesmustbeinrows4),5),6),and7)?Has the project manager in this case had control of the project economy?

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The construction industry traditionally operates with quite a modest profit margin, which is why it is of paramount importance that the project manager has control over costs.

QUestion 2Bywhatpercentagewouldtherealizedprojectresultinyear3havebeengreateriftheprojectmanagerwasabletoreducethecostsinyear3by5%?

Anotherexampleprojectisshownintable2.TheamountsareinthousandsofDanishKroner.


1) total revenue 100,000 100,000 100,000

2) total project result 20,000 10,000 -5,000


3) Posted costs 20,000 25,000 60,000

4) degree of complation

5) Project result


6) Posted costs

7) Project result

Table 2: Example 2 of a project process.

QUestion 3Question 3.1Whathastheprojectmanager’sestimateofthetotalcostsintable2beenattheendof each of the three years?

Question 3.2What could be the reasons that the assessment of the cost has evolved in this way through the project?

Question 3.2What project result would have been realized in this project process in each of the three years?

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Question 3.3If the project manager already at the beginning of year 1 had foreseen how the project costs would evolve, could the project’s results have been recognized in a more accurate way? Could there be other benefits of early detection of a bad project economy?


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26

Case: a/s storeBælt

annuities with different payment-interval lengths

TheGreatBeltFixedLinkisanessentialpartofmanyDanes’journeyswhentheytravelbetweentheeasternandwesternpartsofthecountry.Atotalof10,894,082vehiclesdroveoverthebridgein2012,andtheaveragedailytrafficwas29,765vehicles.Bycomparison,in1997,thelastfullyearofferryoperations,approxim-ately8,300vehiclesweretransportedacrosstheGreatBeltdaily.Railtraffichasalsobenefitedgreatlyfromthefixedlink.Upto142trainscrossedtheGreatBelteachdayin2012,versustheprevious40-45.

Thelink’ssocietalimportancerequiresthatbothroadandrailwayacrosstheGreatBeltisopenaroundtheclock-allyearround.A/SStorebæltisresponsiblefororga-nizing the operation, so that travelers experience a fast, flexible, and safe transpor-tation option between the eastern and western parts of the country.

TheGreatBeltFixedLinkisdesignedforaservicelifeof100years,butwithtimelyimplementation of necessary maintenance, the basic concrete and steel construc-tioncanensurealifetimeofwellover100years.ForA/SStorebælts’operationsorganization, it is therefore essential to have good access to all concrete and steel surfaces, so regular inspections can be carried out and necessary repairs underta-ken in a timely manner, without inconveniencing travelers.

The operations organization’s needs were only accommodated to a limited extent whenthelinkwasconstructed,andA/SStorebælthasthereforehadtosubsequentlydevelop and acquire several different platform solutions.

The following exercise deals with considerations on the choice of a platform for the inspection and maintenance of the west bridge’s two concrete block girders. The westbridgehasatotalof128bridgespans,supportedby126bridgepilingsandtwo abutments. The bridge spans’ concrete is given a routine inspection every two years. A general inspection is carried out every six years, and this replaces the

27


routine inspection that year. Every year, an inspection of the two bridge bearings found on each bridge piling is also conducted.

The final choice was between two platforms that are conceptually very different:

Type A: In principle, a traditional scaffold which is mounted on vehicles on the top of the bridge.Type B: In principle, a reversed tower crane, which is suspended from a trolley pla-ced on rails which are mounted on the underside of the bridge.

Dataforthetwotypesareshownintable1.Thelastrowintable1includesthecostof moving type A from one side of the bridge to the other.

QUestion 1What is the cost for each of the two types of platforms for implementing a general inspection, a routine inspection of the concrete, and an inspection of the bridge bearings?

An annuity is a series of payments with equal time intervals between the individual payments. If the payments are equal, it is known as a constant annuity.

QUestion 2How can the costs of inspection of concrete and bridge bearings for each type of platform be described by three different constant annuities?

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Type A Type B

investment (millions of dKK):

supporting construction 18 20

equipment (electrical, hydraulics, etc.) 7 10

lifetime (years):

supporting construction 50 50

equipment (electrical, hydraulics, etc.) 25 25

Maintenance costs (dKK/year):

supporting construction *) 1,5% 1%

equipment (electrical, hydraulics, etc.) *) 2,5% 2,5%

Number of operators for operation of platform 2 2

Concrete inspection:

Number of inspectors 3 2

inspection time for general inspection (hours/span) 1,75 2,50

inspection time for routine inspection (hours/span) 0,7 1,0

Bridge bearings inspection:

Number of inspectors 1 1

inspection time (hours/bridge piling) 1,5 1,5

Payroll costs (dKK/hour)

operator 300 300

inspector 600 600

time spent crossing the bridge pilings (hours/bridge piling) 2 0

Cost for moving between road and rail girders (dKK) 250.000 0

*) The costs are indicated as a percentage of the investment amount

Table 1: Data for the two platforms

The time between two consecutive annuity payments is called the “payment interval.” The net present value, NPN, of a constant annuity – as we know – can be calculated as:NPV=a∙[1–(1+i)-n]/i,where:

i=theinterestrateperpaymentinterval.n=thenumberofpaymentintervals.

A/SStorebæltusesadiscountrateof7%peryear.

29

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Den ene dag laver jeg efter syn på Storebæltsbroen. Den næste dag sidder jeg bag computeren. Jeg bliver udfordret både fagligt og fysisk i mit job. Den variation sætter jeg stor pris på i hverdagen.Kim Agersø NielsenIngeniør og teknisk chef for konstruktioner og anlæg, Sund & Bælt

30


QUestion 3Iftheannuitypaymentintervalis2yearsor6years,whatisthenA/SStorebælt’sdiscount rate per payment interval in these two cases?

QUestion 4WhichofthetwotypesofplatformswouldyourecommendthatA/SStorebæltacquires?


31

Case: velux a/s

Calculations with the introduction of new window technology

TheVELUXGroupcreatesbetterlivingenvironmentswithdaylightandfreshairthrough the roof. The product portfolio consists of a wide range of roof windows andskylights,alongwithsolutionsforflatroofs.TheVELUXGroupalsosuppliesmany types of decoration and sun screening, roller shutters, installation products as well as products for remote control.

TheVELUXGroup,whichhasmanufacturingcompaniesin11countriesandsalescompaniesinjustunder40countries,representsoneofthestrongestbrandsintheglobal building materials industry and its products are sold in most of the world. The companyhasabout10,000employees,approximately2,600ofwhicharelocatedinDenmark.TheVELUXGroupisheadquarteredinHørsholm,northofCopenhagen,with production, administration and development departments distributed across Denmark.TheVELUXGroupisownedbyVKRHoldingA/S,alimitedcompanywholly owned by foundations and family. You can read more at www.velux.com.

VELUXGroupengineerstypicallyworkwithproductdevelopment,manufacturing,logistics, testing and quality, or in administrative support functions. Many develop-mentprojectsareundertakenincollaborationwithcolleaguesintheVELUXGroup’sglobal organisation and with external partners.

Introduction of new technology Over the years, several pane variants have been developed to be able to offer custo-mers a variety of features such as better insulation properties, sun protection and laminated glass. A new technology now makes it possible to add a coating to the pane that resists adhesion of dirt and makes it self-cleaning when it rains.

VELUXGroupsalescompaniesaroundtheworldconsideritofgreatvaluetobeableto offer this coating to their customers and studies have shown that customers are willing to pay extra for the feature. Technologically, it is possible to apply the new

32

Case: velux a/s

coatingtothepanesif-incooperationwiththeglasssupplier-10DKKmisinve-stedinnewequipment.TheVELUXGroupwillpaytheexpensesoftheinvestment.Raw materials for the finished window will increase the window’s sales price by 15 DKK.Whenthepanewiththenewcoatingisfittedinthesash,itmustbehandledmore carefully and requires additional quality control before and after this process. Labourcostswillconsequentlyincreaseby12DKKperwindow.

Calculation for an ordinary window without the new coating:

Materials 800 dKK 57.1%

labour costs 200 dKK 14.3%

additional costs 100 dKK 7.1%

depreciation and interest 40 dKK 2.9%

Cost price 1,140 DKK 81.4%

sales costs 100 dKK 7.1%

Marketing 90 dKK 6.4%

Profit 70 dKK 5.0%

Selling price 1,400 DKK 100.0%

Thenumberofsoldwindowsisestimatedtobe200,000unitsperyear,andaninternalrateofreturnof7%perannumisused.

QUestion 1If investment in the new equipment is financed and depreciated over two years, how much would this increase the item ”depreciation and interest” in the above calculation?

QUestion 2IftheVELUXGroupwishestomaintaina5%profitmargin,howmuchshouldthewindow’s sales price increase as a result of the new coating?

Based on market estimates, the sales companies will increase the sales price of the windowswiththenewcoatingby45DKK.Basedontheanswertoquestion2,thiswillresultinaprofitmarginreductionperwindowfortheVELUXGroup.

QUestion 3Can a reduction in the profit margin per window be perceived as an indication that the investment in the new technology is not profitable?

If you like working with people who take pride in their job, you’ll be in great company

As an employee in the VELUX Group, you will follow your projects from A to Z. To us there is no such thing as just a window, and our products are renowned as hallmarks of invention and creativity. Your job will be to help set new standards for innovative daylight and ventilation solutions. We take our responsibility as a market leader very seriously and never forget that the curiosity of our employees is what keeps us going. Light up your career at velux.com/jobs

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34

Case: velux a/s

QUestion 4Calculate the profitability of the investment in the new technology if the investment must yield interest and be paid over a five-year period.

QUestion 5What is the minimum increase in sales price in order for the investment to be profi-table over a five-year period?


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Case: velux a/s

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Case: velux a/s

soluTIons

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solutioN: ColoPlast a/s

Considerations about the revision of a product

solUtion QUestion 1The most profitable alternative is that which has the greatest net present value (NPV)oftheearnedcontributionmargin.

The annual earned contribution margin, CON, is:CON=SalesVolume∙(SalesPrice–VariableCosts)

From the data in table 1, it can be calculated that if the revised version of the pro-duct is not developed, then the current version will earn annually the CONcu listed in table 4.

Year 1 2 3 4 5 6

CoNcu (million dKK./year) 920.8 941.7 954.1 964.2 956.2 927.7

Table 4: Annual earned contribution margin for the current version of the product.

TheNPVoftheearnedCONcu,calculatedatthebeginningofyear1,NPVCONcu, can be obtained as:NPVCONcu=920.8∙1.10

-1+941.7∙1.10-2+954.1∙1.10-3+964.2∙1.10-4+956.2∙1.10-5+927.7∙1.10-6

NPVCONcu=837.1+778.3+716.8+658.6+593.7+523.6=4,108.1millionDKK.

If the revised version is marketed, the current and the revised versions will earn respectively CONcu and CONre, and the total earned contribution margin is CONtot=CONcu+CONre.Dataforthesecontributionmarginsaregivenintable5.

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Year 1 2 3 4 5 6

dBnu 722.3 287.6 142.1 0 0 0

dBre 207.5 697.8 862.0 1,033.1 1,075.7 1,118.0

dBtot 929.8 985.4 1,004.1 1,033.1 1,075.7 1,118.0

Table 5: Annual earned contribution margin if the revised product is marketed.

TheNPVoftheearnedCONtot,NPVCONtot, can be obtained as:NPVCONtot=929.8∙1.10

-1+985.4∙1.10-2+1,004.1∙1.10-3+1,033.1∙1.10-4+1,075.7∙1.10-5+1,118.0∙1.10-6

NPVCONtot=845.3+814.4+754.4+705.6+667.9+631.1=4,418.7millionDKK.

In the development year, there must be:• Invested5millionDKKinthevisionsystem• Invested5millionDKKinthedevelopmentoftheproductionsystem• Allocated1millionDKKformarketingcosts• Allocated3millionDKKforproductiondevelopmentcosts

Traditionally, one year’s payments are attributed to the beginning of the year, whe-reasthepaymentsreferredtointheabovecalculations,NPVCONcuandNPVCONre, are attributedtotheyear-end.TheNPVofinvestmentsandcostsinthedevelopmentyear, cu, becomes, at the beginning of year 1:NPVu=(5+5+1+3)∙1.10=15.4millionDKK.

ThetotalNPVoftheprojectcanbecalculatedas:NPV=-NPVu+(NPVCONtot-NPVCONcu)=-15.4+(4,418.7–4,108.1)=295.2millionDKK.

On this basis, the development project appears to be highly profitable.

solUtion QUestion 2The dynamic payback time is an expression of how long it will take before the pro-jectachievesacapitalvalueof0DKK,takingintoaccountinterestrates.

The capital value of the project is referred to as Cx,s, if the project is assumed to stop at the end of the year x.

C0,s=-15.4millionDKK.C1,s=-15.4∙1.10+(929.8–920.8)=-16.9+9.0=-7.9millionDKK.C2,s=-7.9∙1.10+(985.2–941.7)=-8.7+43.5=34.8millionDKK.

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The dynamic payback time is only one year and a few months. From this perspec-tive, the project is therefore particularly attractive.

solUtion QUestion 3InthesolutionofQuestion1,itiscalculatedthattheNPVoftheprojectis295.2mil-lionDKK.TheNPVoftheearnedCONoftherevisedproductmustthereforedeclineby this amount before the project is no longer profitable.

Table 5 lists the expected annual earned CON of the revised product, CONre.TheNPVhereof,NPVCONre, is:NPVCONre=207.5∙1.10

-1+697.8∙1.10-2+862.0∙1.10-3+1,033.1∙1.10-4+1,075.7∙1.10-5+1,118.0∙1.10-6 NPVCONre=188.6+576.7+647.6+705.6+667.9+631.1=3,417.5millionDKK.

ItisclearfromtheequationforNPVCONre that if the annual earned CON is reduced byy%,thenNPVCONrewillalsobereducedbyy%.Theconditionthattheprojectisprofitable can be expressed as:3.417.5∙y/100≤295.2

From this we get:y≤8.6%

solUtion QUestion 4Ifyear6isdeleted,thenthelasttermintheequationsforNPVCONcuogNPVCONtot are alsodeleted.ThisreducesNPVwith631.1–523.6=107.5millionDKK.Thepercen-tagereductionofNPV,∆NPV,isasfollows:∆NPV=107.5/295.2∙100=36.4%

If year 6 is deleted, then the profitability of the project is thus reduced by approxi-mately36%.

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solutioN: daNfoss a/s

Manufacturing Capacity Constraints

solUtion QUestion 1With next month’s production volumes of product types A and B designated as x and y respectively, the capacity constraints can be expressed as:0.5∙x+0.8∙y≤1,000(turningdepartment)0.5∙x+0.4∙y≤800(millingdepartment)

By rewriting these two equations for the capacity constraints, we obtain:y=-0.625∙x+1,250(turningdepartment)y=-1.25∙x+2,000(millingdepartment)

These two limiting lines are plotted in Fig. 1.

.

.

y (units/month)

2,000

1,250

00 1,600 2,000

x (units/month)

Turning Dept.

Milling Dept.

Fig. 1: Limiting lines for the capacity of the two production departments.

The shaded area in fig. 1 indicates the available production possibilities, that is, the technical possibilities. The task is now to find the optimal option from among these possibilities. The criterion is ”maximizing the contribution margin”.

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Thecontributionmargins(CM=sales-costofmaterials–salarycosts)forthetwoproduct types are:CMA=530–205–(0.5∙150+0.5∙180)=160DKK/unit.CMB=640–248–(0.8∙150+0.4∙180)=200DKK/unit.

The total CM can be expressed as:CM=CMA∙x+CMB∙y

AtotalcontributionmarginofKDKK/monthcanbeachievedbythecombinationpossibilities of x and y that satisfy the condition:K=160∙x+200∙y

This line is known as the iso-CM-line, as ”iso” means ”same”, and exactly the same CM is obtained at all points along the line.

By rewriting the equation, we get:y=-0.8∙x+K1

From among the technical possibilities (the shaded area in fig. 1), the option which achievesthegreatestCMcanbefoundforagivenvalueofK1 by plotting a line in fig. 1 and the parallel displacement of this line as much as the constraints allow. Since the size of the slope coefficient on the CM line lies between the sizes of the slope coefficients of the two limiting lines, the greatest CM is obtained where these two lines intersect. The greatest CM can be found by solving two equations with two unknowns:y=-0.625∙x+1,250y=-1.25∙x+2,000

This gives us:x1=1,200units/monthy1=500units/month

The greatest CM which can be generated is as follows:CMmax=160∙1,200+200∙500=292,000DKK

solUtion QUestion 2The material shortage results in a new limiting line:x=800units/month.

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The maximum CM is now obtained where this limiting line intersects the limiting line for turning capacity. The intersection point of these two lines is:(x2, y2)=(800,750)

From which we now get:CMmax=160∙800+200∙750=278,000DKK/month.

The material limitation leads to a reduction in the CM of:∆CM=292,000–278,000=14,000DKK/month.

solUtion QUestion 3Referring to the solution for question 1, CM can generally be expressed as:CM=160∙x+200∙y

The acquisition of additional materials for the production of product type A will maximize the CM by constantly moving down the limiting line for the turning capacity. The relationship between x and y can therefore be expressed as:y=-0.625∙x+1,250

Inserting this context into the CM equation, we get:CM=35∙x+250,000DKK/month.

(Check-asacontrol-ifthisisinaccordancewiththesolutionstoquestions1and2!).

Increasing x thus gives a growth in the CM of:dCM/dx=35DKK/unit.

Marginal CM expresses the ”added value” (also called ”shadow price”) by increasing x by one unit. This means that the additional price for materials for product A shall notexceed=limitCM=35DKK/unitofA.SincethelimitCMisconstant,itcan–iftheincrementalpriceis<35DKK/unitofA–beworthwhiletoimportmaterialsto increase production, until the limit of the milling capacity is reached, i.e. for the production that is calculated in the solution of question 1.

Iftheadditionalcostofmaterialsis=35DKK/unitofA,thentheCMisnotincre-ased by the import of additional materials. This can be illustrated by the fact that themarginalCMforproducttypeAwiththisadditionalcostis=160–35=125DKK/unit.TheslopeoftheCMlinebecomesinthiscase=-125/200=-0.625.TheCM line now has the same slope as the limiting line for the turning capacity. Thus, the CM is not changed now by moving up or down this limitation.

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solutioN: H. luNdBeCK a/s

Insourcing – made possible by the reduction of production costs

solUtion QUestion 1Currently, 4 million finished product packages are packaged per year. An increased OEEfrom40%to60%,thatis,a50%increase,willfreeupcapacityforpackaginganadditional2millionfinishedproductpacksperyear.Sincethetimeforfinishedproductpackagingis50%greaterthanthetimeforpackagingofdropcontainers,theincreaseinOEEwillthereforemeanthatcapacityforpackaging3milliondropcontainers will be freed up. The entire packaging of drop containers can therefore be insourced.

solUtion QUestion 2Itisstatedthattheinvestmentinthepackagingline5yearsagowas20millionDKK.Thisinvestmenthasalreadytakenplace,soitis”sunkcost”andtherebyirre-levant to the decision on the conversion of the packaging line. Subsequently, a differential consideration is applied: Invest in redevelopment rather than continuing the current finished product packaging of ampoules. Since the packaging line in both alternatives will be used, the differential consideration can exclude the present value of the packaging line.

Thedifferentialinvestmentforconversionis7millionDKK,andthisinvestmentincreasesthecostofoperationandmaintenanceby1millionDKKperyear.

Thecostsforthesubcontractorarereducedby1.5∙3=4.5millionDKK/year,andthecostsfortransportarereducedby250,000+350,000=600,000DKK/year≈0.6millionDKK/year.

Thecostsarethusreducedby-1+4.5+0.6=4.1millionDKK/year.

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The packaging line’s remaining lifetime is given to be 5 years. If this is assumed to be the lifetime of the investment, the investment’s net present value, NPN, is calcu-lated as:NPN=-7+4.1∙(1–1.10-5)/0.10=-7+15.5=8.5millionDKK.

The investment in redevelopment is therefore extremely profitable.

The investment’s static payback time, PTs, is calculated as:PTs=7/4.1=1.7years.

The investment is thus paid back very quickly.

solUtion QUestion 3The costs of insourced production, Ci, are:Ci=(3+1.5)+750/10,000∙40=7.5millionDKK/year.

If the packaging is outsourced, the costs, Co, become:Co=0.5+1,500/10,000∙40=6.5millionDKK.

Thecostsshouldthereforebeabletobereducedby1millionDKKifthepackagingisoutsourced.

solUtion QUestion 4The production size, x, where the costs of insourcing the packaging will be the same as the costs of outsourcing the packaging, can be calculated from:4.5+750/10,000∙x=0.5+1,500/10,000∙x

Fromthis,wegetx=53.3millionblistercardsperyear.Theproductiononthepackaginglinemustthereforeincreaseby(53.3–40)/40∙100=33.3%.

solUtion QUestion 5

Year 2005 2006 2007 2008 2009 2010 2011

Production 40.0 45.9 49.7 60.5 70.0 84.0 92.2

Cost of outsourcing 6.50 7.39 7.96 9.58 11.50 13.10 14.33

Cost of insourcing 7.50 7.94 8.23 9.04 9.75 10.80 11.42

savings with insourcing

-1.00 -0.55 -0.27 0.54 1.75 2.30 2.91

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Thefuturevalueofthesavings,FV2012,calculatedattheendof2011,is:FV2012=-1.00∙1.10

6–0.55∙1.105–0.27∙1.104+0.54∙1.103+1.75∙1.102+2.30∙1.10+2.91

FV2012=-1.77–0.89–0.40+0.72+2.12+2.53+2.91=5.22millionDKK.

FV2012 is not an expression of the gains Lundbeck has achieved through the imple-mentation of lean projects in this packaging line. Lundbeck has also incurred costs. The majority of these costs resulted from employees having spent time on the project. These costs can be difficult to quantify - not least because employees have acquired new skills and the lean culture of the company has been reinforced, which can form the basis for many improvement projects in the future.

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solutioN: Mt Højgaard a/s

Inclusion of project earnings in the company’s consolidated financial statement

solUtion QUestion 1Inyear1,thepostedcostsare20,000thousandDKK,asshownintable1inthecasetext.Becausethetotalprojectcostsareexpectedtobe100,000thousandDKK–20,000thousandDKK=80,000thousandDKK,thentheassesseddegreeofprojectcompletionis20,000/80,000=0.25.Onthisbasis,therealizedprojectresultinyear1is0.25∙20,000=5,000thousandDKK.

Inyear2,20,000thousandDKKinprojectcostswerealsoposted.Foryears1and2,atotalof40,000thousandDKKwereposted.Therefore,itisestimatedthattheprojectishalfcompleted(40,000/80,000=0.50).


1) total revenue 100,000 100,000 100,000

2) total project result 20,000 20,000 20,000


3) Posted costs 20,000 20,000 40,000

4) degree of complation 0,25 0.50 1.00

5) Project result 5,000 5,000 10,000


6) Posted costs 20,000 40,000 80,000

7) Project result 5,000 10,000 20,000

The project manager here has had control of the economy. The originally expected revenue and the expected project result have been realized, which is why a correct project result has been calculated in each of the three years.

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solUtion QUestion 2Thecostinyear3was40,000thousandDKK.Areductionofthesecostsby5%cor-respondsto2,000thousandDKK.Whereasinyear3withoutcostreductionwouldresultinaprojectresultof10,000thousandDKK,acostreductionof2,000thou-sandDKKwouldresultinaprojectresultof10,000+2,000=12,000thousandDKK.Acostreductionof5%inyear3wouldthereforehaveresultedinanincreaseof20%intheprojectresultforyear3.

solUtion QUestion 3Bytheendofyear1,thetotalprojectcostisestimatedtobe80,000thousandDKK.After2yearstheyareestimatedtobe90,000thousandDKK,andafter3yearstobe105,000thousandDKK.

The reasons for this could be, for example:• thattheprojectmanagerfromthebeginninghasunderestimatedthecosts.• thattheprojectmanagerthroughouttheprojectdidnothaveasufficientlytight control on the costs.

Attheendofyear1,thetotalprojectcostsareestimatedtobe100,000–20,000=80,000thousandDKK.Sincethepostedcostsafteryear1are20,000thousandDKK,thedegreeofcompletioniscalculatedtobe0.25,whichresultsinaprojectresultof5,000thousandDKKforyear1.

Attheendofyear2,theproject’stotalcostsareestimatedtobe100,000–10,000=90,000thousandDKK.Sincethetotalpostedcostsforyear1and2are45,000thou-sandDKK,thedegreeofcompletionisnowcalculatedtobe0.50,andtheaccumu-latedprojectresultisnowcalculatedtobe0.50∙10.000=5.000thousandDKK.Theprojectresultforyear2istherefore0.

Attheendofyear3,theaccumulatedprojectresultwas-5,000thousandDKK.Foryear3,therealizedprojectresultwas-10,000thousandDKK.

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1) total revenue 100,000 100,000 100,000

2) total project result 20,000 10,000 -5,000


3) Posted costs 20,000 25,000 60,000

4) degree of complation 0.25 0.50 1.00

5) Project result 5,000 0 -10,000


6) Posted costs 20,000 45,000 105,000

7) Project result 5,000 5,000 -5,000

Anaccumulatedrealizedprojectresultof5,000thousandDKKinyears1and2,fol-lowedbyarealizedprojectresultof-10,000thousandDKKinyear3doesnotgiveanaccuratepictureofthesituation.Ifthetotalprojectresultof-5,000thousandDKKhadbeenrecognizedasearlyasyear1,MTHøjgaardwouldhaveaccommo-datedthisinyear1.Theprojectresultforyears2and3wouldthenhavebeen0.

Another advantage of early recognition of bad project economy could have been that there might have been opportunities to allocate resources toward correcting the project.

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solutioN: a/s storeBælt

annuities with different payment-interval lengths

solUtion QUestion 1

Type A: Generalinspectionofconcrete: Inspectiontime:1.75∙128=224hours Crossingofbridgepilings:2∙126=252hours Payrollcosts:(224+252)∙(3∙600+2∙300)=1.142.400DKK Movingofplatform=250,000DKK Totalcosts=1,142,400+250,000=1,392,400DKK

Routine inspection of concrete: Inspectiontime:0.7∙128=89,6hours Crossingofbridgepilings:2∙126=252hours Payrollcosts:(89.6+252)∙(3∙600+2∙300)=819.840DKK Movingofplatform=250,000DKK Totalcosts=819,840+250,000=1,069,840DKK

Inspection of bridge bearings: Inspectiontime:1.5∙126=189hours Crossingofbridgepilings:2∙126=252hours Payrollcosts:(189+252)∙(1∙600+2∙300)=529,200DKK/year Movingofplatform=250,000DKK Totalcosts=529,200+250,000=779,200DKK

Type B:Generalinspectionofconcrete: Inspectiontime:2.50∙128=320hours Crossingofbridgepilings:0∙126=0hours Payrollcosts:320∙(2∙600+2∙300)=576,000DKK

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Routine inspection of concrete: Inspectiontime:1.0∙128=128hours Crossingofbridgepilings:0∙126=0hours Payrollcosts:128∙(2∙600+2∙300)=230,400DKK

Inspection of bridge bearings: Inspectiontime:1.5∙126=189hours Crossingofbridgepilings:0∙126=0hours Payrollcosts:189∙(1∙600+2∙300)=226,800DKK/year

solUtion QUestion 2Every sixth year, a general inspection is carried out, and this replaces the routine inspection that year. If the costs of a general inspection are composed of the costs of a routine inspection plus an additional amount, then the costs of the concrete inspections can be described by two constant annuities:• anannuitywithanamountequaltothecostofaroutineinspectionevery2nd year.• anannuitywithanamountequaltotheaforementioned“additionalamount” every 6th year.

The costs for the inspection of the bridge bearings are an annuity with an annual payment.

For the two types, the annuities are thus obtained by:

Type A:Thecostsof1,392,400DKKforthegeneralinspectionevery6thyeararecomposedofthecostsof1,069,840DKKfortheroutineinspectionplusanadditionalpaymentof1,392,400–1,069,840=322,560DKK.Herebythecostsfortheinspectionoftheconcrete can be described by the two annuities:• anannuitywithapaymentof1,069,840DKKevery2ndyear• anannuitywithapaymentof322,560DKKevery6thyear Inaddition,thereistheannualannuityof779,200DKKfortheinspectionofthebridge bearings.

Type B:Thecostsof576,000DKKforthegeneralinspectionevery6thyeararecomposedofthecostsof230,400DKKfortheroutineinspectionplusanadditionalpaymentof

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576,000–230,400=345,600DKK.Herebythecostsfortheinspectionofthecon-crete can be described by the two annuities:• anannuitywithapaymentof230,400DKKevery2ndyear• anannuitywithapaymentof345,600DKKevery6thyear

Inaddition,thereistheannualannuityof226,800DKKfortheinspectionofthebridge bearings.

solUtion QUestion 3Adiscountrate,i,of7%peryearcorrespondstoadiscountrate,i2,over2yearsof:1+i2=(1+0.07)

2

From this, we get:i2=0.1449,thatis=14.49%over2years.

Correspondingly, if the payment interval length is 6 years:1+i6=(1+0.07)

6

i6=0.5007,thatis=50.07%over6years.

solUtion QUestion 4Thesupportingconstructionhasalifetimeof50yearsforbothtypesofplatforms.Since the lifetime is the same, the choice of the type of platform can be made based onthecriterion:Maximumnetpresentvalue(NPV).

Type A:Theinvestmentamountsto18+7=25millionDKKplusapaymentof7millionDKKafter25years.Thepresentvalueofthis,PVA,I, is:PVA,I=-25,000,000–7,000,000∙1.07

-25=-26,289,744DKK

Basedontheanswerstoquestions2and3,thepresentvalueofthepaymentsfortheconcreteinspections,PVA,C, can be obtained, since the number of payments over the50yearsoftheannuitywithpaymentsevery2yearsis25,whilethenumberofpaymentsyearsoftheannuitywithpaymentsevery6yearsis8:PVA,C=-1,069,840∙(1–1.1449

-25)/0.1449–322,560∙(1-1.5007-8)/0.5007=-7,132,652–619,175=-7,751,827DKK

Thepresentvalueofthepaymentsfortheinspectionofbridgebearings,PVA,B is:PVA,B=-779,200∙(1–1.07

-50)/0.07=-10,753,542DKK

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The costs for maintenance, CA,M, are:CA,M=18,000,000∙0.015+7,000,000∙0.025=270,000+175,000=445,000DKK/year.

Thepresentvalueofthis,PVA,M, is:PVA,M=-445,000∙(1–1.07

-50)/0.07=-6,141,332DKK

ThenetpresentvalueofinvestingintypeA,NPVA, is therefore:NPVA=-26,289,744–7,751,827–10,753,542–6,141,332=-50,936,445DKK

Type B:Theinvestmentamountsto20+10=30millionDKKplusapaymentof10millionDKKafter25years.Thepresentvalueofthis,PVB,I, is:PVB,I=-30,000,000–10,000,000∙1.07-25=-31,842,492DKK

Basedontheanswerstoquestions2and3,thepresentvalueofthepaymentsfortheconcreteinspections,PVB,C, can be obtained, since the number of payments over the50yearsoftheannuitywithpaymentsevery2yearsis25,whilethenumberofpaymentsyearsoftheannuitywithpaymentsevery6yearsis8:PVB,C=-230,400∙(1–1.1449

-25)/0.1449–345,600∙(1-1.5007-8)/0.5007=-1,536,083–663,402=-2,199,485DKK

Thepresentvalueofthepaymentsfortheinspectionofbridgebearings,PVB,B is:PVB,B=-226,800∙(1–1.07

-25)/0.07=-2,643,033DKK

The costs for maintenance, CB,M, are:CB,M=20,000,000∙0.010+10,000,000∙0.025=200,000+250,000=450,000DKK/year.

Thepresentvalueofthis,PVB,M, is:PVB,M=-450,000∙(1–1.07

-50)/0.07=-6,210,336DKK

ThenetpresentvalueofinvestingintypeB,NPVB, is therefore:NPVB=-31,842,492–2,199,485–2,643,033–6,210,336=-42,895,346DKK

SinceNPVB>NPVA,A/SStorebæltshouldselecttypeB.

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Case: velux a/s

Calculations with the introduction of new window technology

solUtion QUestion 1Rewritingtheinvestmentof10DKKmtoanannuity,a,overtwoyears,weget:a=10,000,000∙0.07/(1–1.07-2)=5,530,918DKK/yr.

Withannualsalesof200,000units,wegetanincreasein”depreciationandinterest” of:5,530,918/200,000=27.65DKKperwindow

solUtion QUestion 2Calculation for a window with the new coating:

Materials 815 dKK 55.9%

labour costs 212 dKK 14.5%

additional costs 100 dKK 6.9%

depreciation and interest 68 dKK 4.6%

Cost price 1,195 DKK 81.9%

sales costs 100 dKK 6.9%

Marketing 90 dKK 6.2%

Profit 73 dKK 5.0%

Selling price 1,458 kr. 100.0%

PS.:Thetotalcostofproduction,salesandmarketingamountsto1,385DKK.Astheprofitmustbe5%ofthesalesprice,itmustbe1,385/0.95=1,458DKKperwindow.Theprofitisthus1,458-1,385=73DKKperwindow.

Thesalespriceofawindowmustthereforebeincreasedby1,458-1,400=58DKK

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Case: velux a/s

solUtion QUestion 3The profitability of investments resulting in changes in both costs and sales price cannot be estimated by the change in the profit margin in a full-cost calculation.

solUtion QUestion 4The general criterion for a profitable investment is that its net present value must be ≥0DKK.Theinvestmentof10DKKminthenewtechnologyresultsin:Anincreaseinlabourcostsof12DKKperwindowAnincreaseinmaterialcostsof15DKKperwindowAnincreaseinthesalespriceof45DKK

Overall,thisresultsinanetcashflowof45–12–15=18DKKperwindow,whichcorrespondsto18∙200,000=3,600,000DKK/year.

Netpresentvalueoftheinvestment,NPV,thusbecomes:NPV=-10,000,000+3,600,000∙(1–1.07-5)/0.07=4,760,710DKK

solUtion QUestion 5If the investment is to be profitable, then the minimum requirement for the net cash flow, NCF, can be calculated as:NPV=-10,000,000+NCF∙(1–1.07-5)/0.07≥0DKK

From this, we get:NCF≥2,438,907DKK/yr.or2,438,907/200,000=12.19DKKperwindow.

Therefore,thesalespriceofawindowmustbeincreasedbyminimum12.19+12+15=approximately39DKK,iftheinvestmentinthenewtechnologyistobeprofi-table.

Case studies Engineering Economics -...

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