Case studies Engineering Economicsbodanopub.dk/wp-content/uploads/2014/09/Casesamling2014_02_en… · Case: ColoPlast a/s Considerations about the Changing of a Product Coloplast

Case studies

Engineering Economics

AAge U. Michelsen

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Case studies

isBN 978-87-89359-26-7

aage u. Michelsen:Virksomhedsøkonomi for ingeniørstudierne25. udgave 2014udgiver: Bodano Publishing & Communication apsCopyright © Bodano 2014

Bodano Publishing & Communication apsPostboks 633060 espergærdetelefon: 38 74 78 76e-mail: [email protected]

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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 concrete problems faced by the companies. At the same time, it has been neces-sary to simplify some of the problems to make them suitable for educational use. In addition, some of the numerical values have been changed for reasons of confi-dentiality. 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.

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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:

Master of Science in Engineering Aage U. [email protected]

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Case studies

Table of Contents

Case Solution

ColoPlast a/sConsiderations About the Changing of a Product 8 40

daNfoss a/sManufacturing Capacity Constraints 12 43

H. luNdBeCk a/sInsourcing - Made Possible by the Reduction of Production Costs 15 46

Mt Højgaard a/sInclusion of Project Earnings in the Company’s Consolidated Financial Statement 20 49

siMCorP a/sSales of SimCorp System Solutions with Related Services 25 52

a/s storeBæltAnnuities with Different Payment Interval Lengths 29 54

Velux a/sCalculations with the introduction of new window technology 34 58

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Case studies

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Case studies

CasEs

8

Case: ColoPlast a/s

Considerations about the Changing 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 situation 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:• Coloplast has subsidiaries in 36 countries and sells products in more than 100 countries • Global headquarters located in Humlebaek, Denmark• More than 8,500 employees worldwide, of which approximately 1,200 are in Denmark• Production in Denmark, Hungary, China, USA, and France• Coloplast had a turnover of 11.635 billion Danish Kroner in 2012/13

Coloplast is considering undertaking a radical change to 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 change process begins, it normally

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Case: ColoPlast a/s

takes about 18 months until the sale of the revised product can begin. To simplify the 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 will be gradually phased out over 3 years. Expected sales of the current product are listed in Table 2. Sales price and variable costs are expected to remain as indicated in 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.

Table 3 specifies data for the revised version of the product.

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.

If it is decided to develop the revised version of the product, 5 million DKK will be invested in a vision system for production monitoring, 1 million DKK allocated to marketing costs, and 5 million allocated to develop the production system. The cost of product development is allocated to be 3 million DKK.

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Case: ColoPlast a/s

Coloplast uses a discount rate of 10% per year.

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?

The sales figures listed in Table 3 are based on all current customers switching from the current to the revised product, plus an increase in sales of 5%, since the adhesive in 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 market. 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 40

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Case: daNfoss a/s

Manufacturing Capacity Constraints

Danfoss is a global corporation with 58 sales companies in 46 counties and approxi-mately 400 resellers and distributors worldwide. Danfoss’ corporate headquarters is located in Denmark.

With approximately 22,500 employees, an annual revenue of 33.6 billion DKK, and an export market share of 98%, Danfoss is one of the leading and largest industrial companies in its field.

Danfoss produces cooling automation, industrial automation, frequency converters, com-fort automation (e.g. radiator thermostats), automatic controls for remote heating plants, components for oil burners, thermostats for refrigerators and freezers, compressors for air conditioners, and hydraulics for agricultural and construction machinery.

Danfoss has 59 modern factories in 18 countries, at which are produced approxi-mately 250,000 components per day.

In this case study, one of Danfoss’ production departments has been simplified, so as 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.

ProductSelling 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.

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

The variable costs for salaries, etc. are 150 DKK/hour and 180 DKK/hour in the turning and milling departments respectively.

It is assumed that the capacities in the next month are 1,000 and 800 hours in the turning 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?

Due to production problems at a subcontractor, it has been determined that there will only be enough materials to produce 800 units of product type A in the next month, 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 production of product type A. The price for these materials, however, will be higher than the 205 DKK per unit listed in table 1.

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


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Case: H. luNdBeCk a/s

Insourcing - Made Possible by the Reduction of Production Costs

Lundbeck is a Danish research-based pharmaceutical company that develops and manufactures products for the treatment of central nervous system disorders. Lundbeck is one of the world’s leading companies within this field.

In 2013, the company had a total revenue of 15.2 billion DKK. Lundbeck currently employs approximately 5,500 employees in 57 countries, of which 2,000 are based in Denmark.

Lundbeck’s ambition is to be a growth company, both financially and professionally. 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 subcon-tractors, who are specialists in performing such tasks. Particularly since the 1990s, many Danish companies have increasingly outsourced their production activities. This was also the case for Lundbeck, which in 2004 had outsourced nearly 70% of its finished goods production. In 2006, however, Lundbeck decided to focus on developing the best supply chain in the pharmaceutical industry. Lundbeck 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.

The following questions 1 and 2 relate to some considerations made prior to the start 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

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the investment in the line was then at 20 million DKK. The packaging line is now expected 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 small glass bottles approximately 3 cm. in length containing liquid. The ampoules can 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 packaging line in the two shifts that are working on it. The project aimed partly to increase 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 drop containers. Drop containers are also small glass bottles containing liquid. The drops 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 outsourced to a subcontractor that packages 3 million drop containers per year.

With the current production, the OEE1 on the packaging line is 40%, but it is expected that the OEE can be increased to 60% by implementing the lean project. This increase must be achieved through improvement suggestions from employees. On the packaging line, the packaging time for a finished product pack containing ampoules is 50% greater than the packaging time for a drop container.

QUestion 1If the packaging line’s OEE is increased from 40% to 60%, what proportion of the outsourced 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 will be 7 million DKK. Furthermore, it is estimated that the increase in production resulting from the increased OEE would subsequently increase costs for operation and maintenance of the packaging line by 1 million DKK per year.

1OEE (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 outsourced is 1.50 DKK per pack. Transportation costs to and from the subcontractor is 250,000 DKK per year. In addition, there will be a reduction of 350,000 DKK per year for transportation of finished goods if the packaging of the drop containers is insourced.

A discount rate of 10% per year is used.

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?

The following questions 3, 4, and 5 deal with another of Lundbeck’s packaging lines. On this line, it was possible to package about 40 million blister cards in 2005. Production here is quantified in the number of blister cards - and not the number of completed product packs - as a completed product pack may contain from 1 to 10 blister cards. The costs are estimated to be:• Fixed costs on the packaging line = 3.0 million DKK/year• Salary costs = 1.5 million DKK/year• Variable costs = 750 DKK per 10,000 blister cards

It was considered to outsource the packaging process to a subcontractor, who would perform the packaging for 1,500 DKK per 10,000 blister cards. Additional costs for transportation and administration would be 500,000 DKK per year.

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 specifically focused on reducing changeover times, using the thinking and approach of SMED2.

2SMED (Single Minute Exchange of Dies), developed by the Japanese Shiego Shingo, aims to ensure that all change-overs 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, as illustrated in table 1, which shows the completed production in the period 2005-2011.

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 5What is the future value at the end of 2011 because Lundbeck did the packaging themselves rather than outsourcing it to the subcontractor? Is this value an expression 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

MT Højgaard aims to be the most productive company in the building and construction industry. In 2013, the company realized a turnover of 7.4 billion Danish Kroner and employed an average of about 4,500 employees.

MT Højgaard is organized into a number of business units and subsidiaries within facilities & concrete, commercial and residential construction, offshore & steel bridges, as well as renovation. A small part of the company’s activities take place outside of Denmark. In support of its production, the company has created a num-ber of corporate staff functions called Production Support, Purchasing, Customers & Markets, Work Environment & Quality, BIM / VDC, and Design & Engineering. 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.

The advantage 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.

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The disadvantage 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: The project’s degree of completion E: 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 = the expected project costs

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: 100 million DKKB: 20 million DKKC: 40 million DKKD: 40 / (100 - 20) = 0.50E: 0.50 ∙ 20 = 10 million DKK

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In this example, half of the expected project costs are incurred and posted (D = 0.50), so half of the expected project result (E = 10 million DKK) can be included in the financial statement.The advantage of using the long-term contract method is that it gives a more accurate 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.

An example project is shown in table 1. The amounts are in thousands of Danish Kroner.

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) and 2) indicate the expectations of, respectively, the total revenue and the overall project result the project manager in this case has had at the end of each of the three years.

3) indicates the costs which are posted in each of the three years.

QUestion 1What numerical values must be in rows 4), 5), 6), and 7)?Has the project manager in this case had control of the project economy?

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.

As employees of MT Højgaard, we share an exciting and varied working day. We are good at making use of one another across departments, and therefore the professional and social network plays a big role.Morten Arbirk, Project Engineer and Lise Rasmussen, Graduate Engineer

Read more at mth.comFollow us on Facebook and LinkedIn

MTH_168x238+5_DTU.indd 2 31-07-2014 09:30:18

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QUestion 2By what percentage would the realized project result in year 3 have been greater if the project manager was able to reduce the costs in year 3 by 5%?Another example project is shown in table 2. The amounts are in thousands of Danish Kroner.


1) Total revenue 100,000 100,000 100,000

2) Total project result 20,000 10,000 -5,000Interim financial statement for Year 1 Year 2 Year 3

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

4) Degree of complation

5) Project resultAccumulated financial statement Year 1 Year 2 Year 3

6) Posted costs

7) Project result

Table 2: Example 2 of a project process.

QUestion 3Question 3.1What has the project manager’s estimate of the total costs in table 2 been at the end of 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?

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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Case: siMCorP a/s

sales of simCorp system solutions with Related services

SimCorp develops, sells, and delivers software solutions to the international financial sector. The company has a global workforce of around 1,200, at the head office in Copenhagen and at subsidiaries in Europe, North America, Asia, and Australia. Listed on the NASDAQ OMX in Copenhagen, SimCorp reported 2013 revenue of EUR 225 million and earnings before interest, tax, depreciation, and amortization (EBITDA) of EUR 57 million.

SimCorp’s flagship product is SimCorp Dimension, an internationally recognized and acclaimed one-stop software solution for professional asset managers. A so-called enterprise solution, SimCorp Dimension supports all the essential asset management process activities.

Whether analysis of investment opportunities, ordering, order management, risk monitoring and control, performance measurement, reconciliation, accounting, or reporting, SimCorp Dimension integrates all these activities on a single platform. This integrated approach empowers the entire asset management organization to work with consistent real-time data.

SimCorp Dimension is one of the most comprehensive standard systems of its kind. It is delivered with related services as a total solution for the client’s asset manage-ment business. SimCorp’s market units handle the sale, delivery, and consultancy services relating to the implementation, application, and integration in the client’s business, while product development is primarily at the Copenhagen head office.

SimCorp bases its business on financial expertise and software know-how. Some 90% of its employees have an academic education - primarily in finance, economics, computer science, or engineering. In-depth knowledge of financial theory and software development - combined with extensive experience and insight into business processes - is crucial for SimCorp to continue developing and offering clients competitive, high-quality solutions.

26

Case: siMCorP a/s

SimCorp’s business model rests on three pillars: Sale of software licenses, main-tenance services, and consulting. Sale of the right to utilize SimCorp’s software provides licensing revenue; maintenance revenue derives from the right to ongoing system upgrades and user assistance; and consulting revenue is generated through the work provided in connection with implementing, introducing, and expanding software installations.

If the price of the software license for SimCorp Dimension is set at an index of 100, then the consultancy services for implementing a typical system solution would be 50. The next five years would represent SimCorp’s revenue from maintenance, upgrades, user assistance, etc., at a respective 29, 35, 37, 40, and 43.

For the following Question 1, it is assumed that such a system is implemented for a client in the year 0, and that the client pays for the license and implementation by the end of this year, i.e. at the start of year 1. Payments for services over the next five years, i.e. in years 1-5, take place at the end of each year.

QUestion 1If a client applies a discount rate of 10% per annum, what percentage of the net current value of the client’s total cost is made up of the price of the software license?

In the following Question 2, it is assumed that the client acquires SimCorp Dimension and that the license fee amounts to EUR 2 million. Index figures for the stated subsequent expenses in Question 1 above are also assumed to apply. For the client, this means that the system acquisition results in reduced costs and increased earnings.

QUestion 2How substantial must the client’s average annual financial benefits be if the acquisition of the system - over a five-year period - is to be profitable for the client?

In the following Question 3, it is assumed that the client’s financial benefits are calculated at EUR 2 million per year.

QUestion 3What are the net present value (NPV) and the dynamic payback period for inve-sting in the system?

FINANCIAL DISTRICT, NEW YORK

Meet other SimCorpemployees at simcorp.com/meetouremployeesor follow us on facebook

“It’s great to experience how my education helps me create the right solutions – also in a computerscientific perspective.”Anders, System Developer

Working at SimCorp means making a difference. At SimCorp, you help create the tools that shape the global financial industry of tomorrow. SimCorp provides integrated software solutions that can turn investment management companies into winners. With SimCorp, you make the most of your ambitions, realizing your full potential in a challenging, empowering, and stimulating work environment.

Are you among the best qualified in finance, economics, computer science, or mathematics?

Find your next challenge at www.simcorp.com/careers

The Financial Industry Needs a Strong Software PlatformThat’s why we need you

ad_new_york_168x238_bodano_june_2014.indd 1 27-Jun-14 11:26:01

FINANCIAL DISTRICT, NEW YORK

Meet other SimCorpemployees at simcorp.com/meetouremployeesor follow us on facebook

“It’s great to experience how my education helps me create the right solutions – also in a computerscientific perspective.”Anders, System Developer

Working at SimCorp means making a difference. At SimCorp, you help create the tools that shape the global financial industry of tomorrow. SimCorp provides integrated software solutions that can turn investment management companies into winners. With SimCorp, you make the most of your ambitions, realizing your full potential in a challenging, empowering, and stimulating work environment.

Are you among the best qualified in finance, economics, computer science, or mathematics?

Find your next challenge at www.simcorp.com/careers

The Financial Industry Needs a Strong Software PlatformThat’s why we need you

ad_new_york_168x238_bodano_june_2014.indd 1 27-Jun-14 11:26:01

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Case: siMCorP a/s

In the following Question 4, it is assumed that the license revenue for a system solution accruing to SimCorp is on average EUR 2 million. The system solution leads to the subsequent years’ revenues, which can be calculated from the given indices in Question 1 above. It is also assumed that these revenues are calculated in current prices with inflation at an annual rate of 5%.

QUestion 4How many systems must SimCorp sell annually on average to generate annual revenues in real terms of EUR 150 million?


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Case: a/s storeBælt

annuities with Different Payment Interval Lengths

The Storebælt link is an essential part of many Danes’ journeys when they travel between the eastern and western parts of the country. A total of 10,883,248 vehicles drove over the bridge in 2013, and the average daily traffic was 29,817 vehicles. By comparison, in 1997, the last full year of ferry operations, approximately 8,300 vehicles were transported across Storebælt daily. Rail traffic has also benefited greatly from the fixed link. An average of 142 trains crossed Storebælt each day in 2013 com-pared to 40-45 before the bridge opened.

The link’s importance to society requires that both road and railway across Storebælt are open around the clock - all year round. A/S Storebælt is responsible for organising the operation, so that travellers experience a fast, flexible, and safe transport facility between the eastern and western parts of the country.

The Storebælt link is designed for a service life of 100 years, but with timely implementation of necessary maintenance, the basic concrete and steel structures can ensure a lifetime of well over 100 years. For A/S Storebælt’s operations organisation, it is therefore essential to have good access to all concrete and steel surfaces, so regular inspections can be carried out and necessary repairs undertaken in a timely manner, without inconveniencing travellers.

The operations organisation’s needs were only accommodated to a limited extent when the link was constructed, and A/S Storebælt has therefore had to subsequently develop 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 box girders. The West Bridge has a total of 128 bridge spans, supported by 126 bridge piers and two 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

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routine inspection that year. Every year, an inspection of the two bridge bearings found on each bridge pier 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 placed on rails which are mounted on the underside of the bridge.

Data for the two types are shown in table 1. The last row in table 1 includes the cost of moving type A from one side of the bridge to the other.

QUestion 1What is the cost of 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 (dkk million):

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 pier) 1.5 1.5

Payroll costs (dkk/hour)

operator 300 300

inspector 600 600

time spent crossing the bridge piers (hours/bridge pier) 2 0

Cost of moving between road and rail girder (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, NPV, of a constant annuity, a, - as we know - can be calculated as:NPV = a ∙ [1 - (1 + i)-n]/i, where:

i = the discount rate per payment interval.n = the number of payment intervals.

A/S Storebælt uses a discount rate of 7% per annum.

32


QUestion 3If the annuity payment interval is 2 years or 6 years, what is then A/S Storebælt’s discount rate per payment interval in these two cases?

QUestion 4Which of the two types of platforms would you recommend that A/S Storebælt acquires?


Sund & Bælt’s most important objective is to make travelling easier. Customers use our traffic facilities every day, i.e. the Storebælt link, the Øresund motorway and the Øresund rail line with associated stations as well as the ports at Odden, Ebeltoft, Spodsbjerg and Tårs.

We are also undertaking the planning work for a fixed link across the Fehmarnbelt with associated Danish landworks. Moreover, we own BroBizz A/S, which offers comprehensive electronic payment for driving on toll roads in Scandinavia and Austria.

Sund & Bælt will be recruiting engineers for construction, operation and maintenance work over the next few years – one of them could be you.

At Sund & Bælt, you will enjoy a career of professional challenges and freedom with responsibility. Great colleagues and ongoing training are also part of the package.

Read more about your future career here:www.sundogbaelt.dk

Martin Duus HansenOperations Manager, Construction Structural Engineer, Steel

One moment I’m out inspecting the Storebælt Bridge. The next, I’m sitting at my desk. My work challenges me both professionally and physically. I like this variety in my working day.

We bring Denmark togetherWhy not join our team?

34

Case: Velux a/s

Calculations with the introduction of new window technology

For more than 70 years, the VELUX Group has created better living environments for people around the world. Making the most of daylight and fresh air through the roof. Our product programme includes roof windows and modular skylights as well as a range of decoration and sun screenings, roller shutters, installation solutions and intelligent home controls.

These products help to ensure a healthy and sustainable indoor climate. For work and learning. For play and pleasure.

We work globally - with sales and manufacturing operations in more than 40 countries and around 10,000 employees worldwide. The VELUX Group is owned by VKR Holding A/S, a limited company wholly owned by foundations and family. For more information, visit www.velux.com.

VELUX Group engineers typically work with product development, manufacturing, logistics, testing and quality, or in administrative support functions. Many develop-ment projects are undertaken in collaboration with colleagues in the VELUX Group’s global 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 selfcleaning when it rains.

35

Case: Velux a/s

VELUX Group sales companies around the world consider it of great value to be able to 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 coating to the panes if - in cooperation with the glass supplier - 10 DKKm is inve-sted in new equipment. The VELUX Group will pay the expenses of the investment. Raw materials for the finished window will increase the window’s sales price by 15 DKK. When the pane with the new coating is fitted in the sash, it must be handled more carefully and requires additional quality control before and after this process. Labour costs will consequently increase by 12 DKK per window.

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%

The number of sold windows is estimated to be 200,000 units per year, and an internal rate of return of 7% per annum is used.

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 2If the VELUX Group wishes to maintain a 5% profit margin, how much should the window’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 windows with the new coating by 45 DKK. Based on the answer to question 2, this will result in a profit margin reduction per window for the VELUX Group.

36

Case: Velux a/s

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

V0011947-063-001_image_ad_168x238.indd 1 08-06-2012 13:52:54

Velux2013_168x238mm.PDF - 11:16:51 - July 31, 2013 - Page 1 of 1

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?

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 profitable over a five-year period?


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

V0011947-063-001_image_ad_168x238.indd 1 08-06-2012 13:52:54

Velux2013_168x238mm.PDF - 11:16:51 - July 31, 2013 - Page 1 of 1

38

Case: Velux a/s

39

Case: Velux a/s

soLuTIons

w

40

solutioN: ColoPlast a/s

Considerations about the Changing of a Product

solUtion QUestion 1The most profitable alternative is that which has the greatest capital value of the earned contribution margin.

The annual earned contribution margin, CON, is:CON = Sales ∙ (sales price - variable costs)

From the data in table 1, it can be calculated that if the revised version of the product 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.

The net present value of the earned CONcu is: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 = 4,108.1 million DKK.

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. Data for these contribution margins are given in table 5.

41


Year 1 2 3 4 5 6

Concu 722.3 287.6 142.1 0 0 0

Conre 207.5 697.8 862.0 1,033.1 1,075.7 1,196.4

Contot 929.8 985.4 1,004.1 1,033.1 1,075.7 1,196.4

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

The net present value of the earned CONtot, is: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 = 4,418.7 million DKK.

In the development year, there must be:• Invested 5 million DKK in the vision system• Invested 5 million DKK in the development of the production system• Allocated 1 million DKK for marketing costs• Allocated 3 million DKK for production development costs

Traditionally, one year’s payments are attributed to the beginning of the year, whereas the payments referred to in the above calculations, CCONcu and CCONre, are attributed to the year-end. The present value of investments and costs in the development year, PVu, becomes, at the beginning of year 1:PVu = (5 + 5 + 1 + 3) ∙ 1.10 = 15.4 million DKK.

The net present capital value of the project, NPV, can be obtained as:NPV = -Cu + (CCONtot - CCONcu) = -15.4 + (4,418.7 - 4,108.1) = 295.2 million DKK.

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 project achieves a future value of 0 DKK, taking into account interest rates.

The future value of the project is referred to as FVx, if the project is assumed to stop at the end of the year x.

FV0 = -15.4 million DKK.FV1 = -15.4 ∙ 1.10 + (929.8 - 920.8) = -16.9 + 9.0 = -7.9 million DKK.FV2 = -7.9 ∙ 1.10 + (985.2 - 941.7) = -8.7 + 43.5 = 34.8 million DKK.

42


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

solUtion QUestion 3In the solution of Question 1, it is calculated that the net present value, NPV, of the project is 295.2 million DKK. The present value of the earned CON of the revised product must therefore decline by this amount before the project is no longer profitable.

Table 5 lists the expected annual earned CON of the revised product, CONre. The net present value hereof, CCONre, 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 = 3,417.5 million DKK.

It is clear from the equation for NPVCONre that if the annual earned CON is reduced by y%, then NPVCONre will also be reduced by y%. The condition that the project is profitable can be expressed as:3.417.5 ∙ y/100 ≤ 295.2

From this we get:y ≤ 8.6 %

solUtion QUestion 4If year 6 is deleted, then the last term in the equations for NPVCONcu og NPVCONtot are also deleted. This reduces NPV with 631.1 -523.6 = 107.5 million DKK. The percen-tage reduction of NPV, ∆NPV, is as follows:∆NPV0 = 107.5/295.2 ∙ 100 = 36.4 %

If year 6 is deleted, then the profitability of the project is thus reduced by approximately 36%.

43

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 (turning department)0.5 ∙ x + 0.4 ∙ y ≤ 800 (milling department)

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

These two limiting lines are plotted in Fig. 1.

x

1.600 2.0000

2.000

1.250

y

Milling Dept.

Turning 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”.

44


The contribution margins (CM = sales - cost of materials - salary costs) for the two product types are:CMA = 530 - 205 - (0.5 ∙ 150 + 0.5 ∙ 180) = 160 DKK/unit.CMB = 640 - 248 - (0.8 ∙ 150 + 0.4 ∙ 180) = 200 DKK/unit.

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

A total contribution margin of K DKK/month can be achieved by the combination possibilities 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 achieves the greatest CM can be found for a given value of K1 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 = 1,200 units/month y1 = 500 units/month

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

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

45


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 = 278,000 DKK/month.

The material limitation leads to a reduction in the CM of:∆CM = 292,000 - 278,000 = 14,000 DKK/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 + 250,000 DKK/month.

(Check - as a control - if this is in accordance with the solutions to questions 1 and 2!).

Increasing x thus gives a growth in the CM of:dCM/dx = 35 DKK/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 not exceed = limit CM = 35 DKK/unit of A. Since the limit CM is constant, it can - if the incremental price is < 35 DKK /unit of A - be worthwhile to import materials to 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.

If the additional cost of materials is = 35 DKK/unit of A, then the CM is not increased by the import of additional materials. This can be illustrated by the fact that the marginal CM for product type A with this additional cost is = 160 - 35 = 125 DKK/unit. The slope of the CM line becomes in this case = -125 / 200 = -0.625. The CM 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.

46

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 OEE from 40% to 60%, that is, a 50% increase, will free up capacity for packaging an additional 2 million finished product packs per year. Since the time for finished product packaging is 50% greater than the time for packaging of drop containers, the increase in OEE will therefore mean that capacity for packaging 3 million drop containers will be freed up. The entire packaging of drop containers can therefore be insourced.

solUtion QUestion 2It is stated that the investment in the packaging line 5 years ago was 20 million DKK. This investment has already taken place, so it is “sunk cost” and thereby irrelevant 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.

The differential investment for conversion is 7 million DKK, and this investment increases the cost of operation and maintenance by 1 million DKK per year.

The costs for the subcontractor are reduced by 1.5 ∙ 3 = 4.5 million DKK / year, and the costs for transport are reduced by 250,000 + 350,000 = 600,000 DKK / year ≈ 0.6 million DKK / year.

The costs are thus reduced by -1 + 4.5 + 0.6 = 4.1 million DKK / year.

47


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, NPV, is calculated as:NPV = -7 + 4.1 ∙ (1 - 1.10-5)/0.10 = -7 + 15.5 = 8.5 million DKK.

The investment in redevelopment is therefore extremely profitable.

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

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 = 7.5 million DKK / year.

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

The costs should therefore be able to be reduced by 1 million DKK if the packaging is outsourced.

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

From this, we get x = 53.3 million blister cards per year. The production on the pack-aging line must therefore increase by (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

48


The future value of the savings, FV2012, calculated at the end of 2011, is:FV2012 = -1.00∙1.106 - 0.55∙1.105 - 0.27∙1.104 + 0.54∙1.103 + 1.75∙1.102 + 2.30∙1.10 + 2.91FV2012 = -1.77 - 0.89 - 0.40 + 0.72 + 2.12 + 2.53 + 2.91 = 5.22 million DKK.

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.

49

solutioN: Mt Højgaard a/s

Inclusion of Project Earnings in the Company’s Consolidated Financial statement

solUtion QUestion 1In year 1, the posted costs are 20,000 thousand DKK, as shown in table 1 in the case text. Because the total project costs are expected to be 100,000 thousand DKK - 20,000 thousand DKK = 80,000 thousand DKK, then the assessed degree of project completion is 20,000 / 80,000 = 0.25. On this basis, the realized project result in year 1 is 0. 25 ∙ 20,000 = 5,000 thousand DKK.

In year 2, 20,000 thousand DKK in project costs were also posted. For years 1 and 2, a total of 40,000 thousand DKK were posted. Therefore, it is estimated that the project is half completed (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

50


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.

solUtion QUestion 2The cost in year 3 was 40,000 thousand DKK. A reduction of these costs by 5% corresponds to 2,000 thousand DKK. Whereas in year 3 without cost reduction would result in a project result of 10,000 thousand DKK, a cost reduction of 2,000 thousand DKK would result in a project result of 10,000 + 2,000 = 12,000 thousand DKK. A cost reduction of 5% in year 3 would therefore have resulted in an increase of 20% in the project result for year 3.

solUtion QUestion 3By the end of year 1, the total project cost is estimated to be 80,000 thousand DKK. After 2 years they are estimated to be 90,000 thousand DKK, and after 3 years to be 105,000 thousand DKK.

The reasons for this could be, for example:• That the project manager from the beginning has underestimated the costs.• That the project manager throughout the project did not have a sufficiently tight

control on the costs.

At the end of year 1, the total project costs are estimated to be 100,000 - 20,000 = 80,000 thousand DKK. Since the posted costs after year 1 are 20,000 thousand DKK, the degree of completion is calculated to be 0.25, which results in a project result of 5,000 thousand DKK for year 1.

At the end of year 2, the project’s total costs are estimated to be 100,000 - 10,000 = 90,000 thousand DKK. Since the total posted costs for year 1 and 2 are 45,000 thousand DKK, the degree of completion is now calculated to be 0.50, and the accumulated project result is now calculated to be 0.50 ∙ 10.000 = 5.000 thousand DKK. The project result for year 2 is therefore 0.

At the end of year 3, the accumulated project result was -5,000 thousand DKK. For year 3, the realized project result was -10,000 thousand DKK.

51



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

An accumulated realized project result of 5,000 thousand DKK in years 1 and 2, fol-lowed by a realized project result of -10,000 thousand DKK in year 3 does not give an accurate picture of the situation. If the total project result of -5,000 thousand DKK had been recognized as early as year 1, MT Højgaard would have accommo-dated this in year 1. The project result for years 2 and 3 would then have been 0.

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.

52

solutioN: siMCorP a/s

sales of simCorp system solutions with Related services

solUtion QUestion 1Based on the above indices, an index (I1) can be calculated for the net present value of the client’s costs as follows:I1 = 100 + 50 + 29 ∙ 1.10-1 + 35 ∙ 1.10-2 + 37 ∙ 1.10-3 + 40 ∙ 1.10-4 + 43 ∙ 1.10-5 I1 = 150 + 26.4 + 28.9 + 27.8 + 27.3 + 26.7 = 287.1

The price of the software license hence amounts to 100/287.1 = 0.35, or 35%.

solUtion QUestion 2Based on the solution to Question 1, the net present value (NPV) of the client’s costs associated with the system can be calculated as:NPV = 2 ∙ 2.871 = EUR 5.742 million

Rewriting NPV as an annual annuity (a) over the subsequent five years, we get:a = 5.742 ∙ 0.10/(1 - 1.10-5) = EUR 1.515 million per year

The client’s financial benefits must therefore be greater than EUR 1.5 million per year if the acquisition based on these assumptions is to be profitable.

solUtion QUestion 3In the following table, amounts are shown in millions of euros calculated at year-end. In the table, the second row lists the index for each year’s payments accruing to SimCorp. Based on a license fee of EUR 2 million, the third row lists the annual payments. With annual savings of EUR 2 million (row 4), the fifth row shows the calculated annual net deposits (= savings - payments). The last row lists the net present value of net deposits and payments over time. The net present value is calculated as follows:Net present value year x = Net present value year (x-1) + (Net deposit year x) ∙ 1.10-x

53

solutioN: siMCorP a/s

Year 0 1 2 3 4 5

index 150 29 35 37 40 43

Payment 3.00 0.58 0.70 0.74 0.80 0.86

savings 2 2 2 2 2

Net deposit -3.00 1.42 1.30 1.26 1.20 1.14

Net present value -3.00 -1.71 -0.64 0.31 1.13 1.84

It can be seen that after five years, the net present value (NPV) of the investment is EUR 1.84 million. This net present value can alternatively be calculated as follows:NPV = -3.00 + 1.42 ∙ 1.10-1 + 1.30 ∙ 1.10-2 + 1.26 ∙ 1.10-3 + 1.20 ∙ 1.10-4 + 1.14 ∙ 1.10-5 NPV = -3.00 + 1.29 + 1.07 + 0.95 + 0.82 + 0.71 = EUR 1.84 million

It can be seen in the sixth row of the table that the net current value becomes 0 during Year 3. The dynamic payback period is hence less than three years.

solUtion QUestion 4Adjusting for inflation results in an index (I2) for the total income from a system solution:I2 = 100 + 50 + 29 ∙ 1.05-1 + 35 ∙ 1.05-2 + 37 ∙ 1.05-3 + 40 ∙ 1.05-4 + 43 ∙ 1.05-5 I2 = 150 + 27.6 + 31.7 + 32.0 + 32.9 + 33.7 = 307.9

Measured in real terms, SimCorp’s total revenue from the sale of the system solution amounts to 2 ∙ 3.079 = EUR 6.158 million. To achieve an annual turnover of EUR 150 million, SimCorp needs to sell an average of around 25 system solutions annually.

54

solutioN: a/s storeBælt

annuities with Different Payment Interval Lengths

solUtion QUestion 1Type A:General inspection of concrete:

Inspection time: 1.75 ∙ 128 = 224 hoursCrossing of bridge piers: 2 ∙ 126 = 252 hoursPayroll costs: (224 + 252) ∙ (3 ∙ 600 + 2 ∙ 300) = 1,142,400 DKKMoving of platform = 250,000 DKKTotal costs = 1,142,400 + 250,000 = 1,392,400 DKK

Routine inspection of concrete:Inspection time: 0.7 ∙ 128 = 89.6 hoursCrossing of bridge piers: 2 ∙ 126 = 252 hoursPayroll costs: (89.6 + 252) ∙ (3 ∙ 600 + 2 ∙ 300) = 819,840 DKKMoving of platform = 250,000 DKKTotal costs = 819,840 + 250,000 = 1,069,840 DKK

Inspection of bridge bearings:Inspection time: 1.5 ∙ 126 = 189 hoursCrossing of bridge piers: 2 ∙ 126 = 252 hoursPayroll costs: (189 + 252) ∙ (1 ∙ 600 + 2 ∙ 300) = 529,200 DKK/yearMoving of platform = 250,000 DKKTotal costs = 529,200 + 250,000 = 779,200 DKK

Type B:General inspection of concrete:

Inspection time: 2.50 ∙ 128 = 320 hoursCrossing of bridge piers: 0 ∙ 126 = 0 hoursPayroll costs: 320 ∙ (2 ∙ 600 + 2 ∙ 300) = 576,000 DKK

55


Routine inspection of concrete:Inspection time: 1.0 ∙ 128 = 128 hoursCrossing of bridge piers: 0 ∙ 126 = 0 hoursPayroll costs: 128 ∙ (2 ∙ 600 + 2 ∙ 300) = 230,400 DKK

Inspection of bridge bearings:Inspection time: 1.5 ∙ 126 = 189 hoursCrossing of bridge piers: 0 ∙ 126 = 0 hoursPayroll costs: 189 ∙ (1 ∙ 600 + 2 ∙ 300) = 226,800 DKK/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 comprise the costs of a routine inspection plus an additional amount, then the costs of the concrete inspections can be described by two constant annuities:

• An annuity with an amount equal to the cost of a routine inspection every 2nd year• An annuity with an amount equal to the aforementioned “additional amount” every 6th year

The costs of 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:The costs of 1,392,400 DKK for the general inspection every 6th year comprise the costs of 1,069,840 DKK for the routine inspection plus an additional payment of 1,392,400 - 1,069,840 = 322,560 DKK. Hereby the costs of the inspection of the concrete can be described by the two annuities:

• An annuity with a payment of 1,069,840 DKK every 2nd year• An annuity with a payment of 322,560 DKK every 6th year

In addition, there is the annual annuity of 779,200 DKK for the inspection of the bridge bearings.

Type B:The costs of 576,000 DKK for the general inspection every 6th year comprise the costs of 230,400 DKK for the routine inspection plus an additional payment of 576,000 - 230,400 = 345,600 DKK. Hereby the costs of the inspection of the concrete can be described by the two annuities:

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• An annuity with a payment of 230,400 DKK every 2nd year• An annuity with a payment of 345,600 DKK every 6th year

In addition, there is the annual annuity of 226,800 DKK for the inspection of the bridge bearings.

solUtion QUestion 3A discount rate, i, of 7% per year corresponds to a discount rate, i2, over 2 years of:1 + i2 = (1 + 0.07)2

From this, we get:i2 = 0.1449, that is = 14.49% over 2 years.

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

i6 = 0.5007, that is = 50.07% over 6 years.

solUtion QUestion 4The supporting construction has a lifetime of 50 years for both types of platforms. Since the lifetime is the same, the choice of the type of platform can be made based on the criterion: Maximum net present value (NPV).

Type A:The investment amounts to 18 + 7 = 25 million DKK plus a payment of 7 million DKK after 25 years. The present value of this, PVA,I, is:PVA,I = -25,000,000 - 7,000,000 ∙ 1.07-25 = DKK -26,289,744

Based on the answers to questions 2 and 3, the present value of the payments for the concrete inspections, PVA,C, can be obtained, since the number of payments over the 50 years of the annuity with payments every 2 years is 25, while the number of payment years of the annuity with payments every 6 years is 8:PVA,C = -1,069,840 ∙ (1 - 1.1449-25)/0.1449 - 322,560 ∙ (1- 1.5007-8)/0.5007 = -7,132,652 - 619,175 = -7,751,827 DKK

The present value of the payments for the inspection of bridge bearings, PVA,B is:PVA,B = -779,200 ∙ (1 - 1.07-50)/0.07 = -10,753,542 DKK

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

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The present value of this, PVA,M, is:PVA,M = -445,000 ∙ (1 - 1.07-50)/0.07 = -6,141,332 DKK

The net present value of investing in type A, NPVA, is therefore:NPVA = -26,289,744 - 7,751,827 - 10,753,542 - 6,141,332 = -50,936,445 DKK

Type B:The investment amounts to 20 + 10 = 30 million DKK plus a payment of 10 million DKK after 25 years. The present value of this, PVB,I, is:PVB,I = -30,000,000 - 10,000,000 ∙ 1.07-25 = -31,842,492 DKK

Based on the answers to questions 2 and 3, the present value of the payments for the concrete inspections, PVB,C, can be obtained, since the number of payments over the 50 years of the annuity with payments every 2 years is 25, while the number of payment years of the annuity with payments every 6 years is 8:PVB,C = -230,400 ∙ (1 - 1.1449-25)/0.1449 - 345,600 ∙ (1- 1.5007-8)/0.5007 = -1,536,083 - 663,402 = -2,199,485 DKK

The present value of the payments for the inspection of bridge bearings, PVB,B is:PVB,B = -226,800 ∙ (1 - 1.07-25)/0.07 = -2,643,033 DKK

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

The present value of this, PVB,M, is:PVB,M = -450,000 ∙ (1 - 1.07-50)/0.07 = -6,210,336 DKK

The net present value of investing in type B, NPVB, is therefore:NPVB = -31,842,492 - 2,199,485 - 2,643,033 - 6,210,336 = -42,895,346 DKK

Since NPVB > NPVA, A/S Storebælt should select type B.

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solutioN: Velux a/s

Calculations with the introduction of new window technology

solUtion QUestion 1Rewriting the investment of 10 DKKm to an annuity, a, over two years, we get:a = 10,000,000 ∙ 0.07/(1 - 1.07-2) = 5,530,918 DKK/yr.

With annual sales of 200,000 units, we get an increase in “depreciation and interest” of:5,530,918/200,000 = 27.65 DKK per window

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 DKK 100.0 %

PS.: The total cost of production, sales and marketing amounts to 1,385 DKK. As the profit must be 5% of the sales price, it must be 1,385 / 0.95 = 1,458 DKK per window. The profit is thus 1,458-1,385 = 73 DKK per window.

The sales price of a window must therefore be increased by 1,458-1,400 = 58 DKK

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solutioN: 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 ≥ 0 DKK. The investment of 10 DKKm in the new technology results in:

• An increase in labour costs of 12 DKK per window• An increase in material costs of 15 DKK per window • An increase in the sales price of 45 DKK

Overall, this results in a net cash flow of 45 - 12 - 15 = 18 DKK per window, which corresponds to 18 ∙ 200,000 = 3,600,000 DKK/year.

Net present value of the investment, NPV, thus becomes:NPV = -10,000,000 + 3,600,000 ∙ (1 - 1.07-5)/0.07 = 4,760,710 DKK

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 ≥ 0 DKK

From this, we get:NCF ≥ 2,438,907 DKK/yr. or 2,438,907/200,000 = 12.19 DKK per window.

Therefore, the sales price of a window must be increased by minimum 12.19 + 12 + 15 = approximately 39 DKK, if the investment in the new technology is to be profitable.

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