Engineering Economics

Case studies Engineering Economics

Aage U. Michelsen

ISBN 978-87-89359-32-8

Bodano Publishing & Communication ApS Hovedgaden 47 DK 2970 Hørsholm Phone +45 38 74 78 76 www.bodanopub.dk E-mail: [email protected]

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 technical 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 necessary 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 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.

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. Michelsen [email protected]

Table of Contents

Case Solution berendsen textil service A/S Capacity Expansion 8 59 Energinet.dk Social benefits of investment in a Great Belt power link 12 62 Energistyrelsen Investing in a heat pump system 16 65 H. Lundbeck A/S Insourcing – Made Possible by the Reduction of Production Costs 19 68 Haldor Topsøe A/S Economic assessments about a new product 24 71 Hofor A/S Heat pumps for generating district heat 28 74 MT Højgaard A/S Inclusion of Project Earnings in the Company’s Consolidated Financial Statement 34 76 nnit a/S Financial considerations in an IT company 40 79 A/S Storebælt Annuities with Different Payment-Interval Lengths 44 82 Vejdirektoratet Financial considerations regarding the construction of a highway 49 86 Velux A/S Calculations with the Introduction of New Technology for Windows 53 89

Cases

7 CASE: berendsen textil service A/S

Capacity Expansion

Berendsen develops and provides innovative service solutions for the rental of linens, clothing, floor mats and hand hygiene. With an annual turnover of 11 billion DKK and 16,000 employees, Berendsen is the market leading service provider in the B2B market in Europe. In Denmark, Berendsen has 1,200 dedicated employees in 16 branches across the country.

This means that Berendsen provides linens to large hotel chains, for example. Linens, towels, tablecloths and kitchen clothing – it is Berendsen that ensures that all of this is clean and sanitary, allowing Berendsen’s customers to serve their own customers in the best possible way. The same applies to the hospital world, where it is essential that bedding and staff clothing is ready to use and properly washed. Berendsen has several other divisions, and throughout the company, Berendsen cooperates with its customers to develop new and innovative solutions that benefit their business and raise their level.

The following assignment is based on Berendsen’s clothing laundry operation in Aarhus. Demand from the customer segment that consists of food production companies has been soaring in recent years. Today, the demand is 30,000 laundered clothing articles per day, for which the capacity for the treatment of laundry from that segment is 100 % utilized. Demand over the coming years is expected to increase linearly, so that in 10 years, demand will reach 48,000 laundered clothing articles per day.

In the current system, an automated sorting and packaging system is used. The workflow starts with the dirty clothes on a table, which are manually sorted by color and washing temperature, after which they are washed in washing machines. After washing, the washing machines are automatically emptied into a washtub, from which the clothes are then routed to five hanging stations where employees scan the clothes and hang them on hangers. From here, the garments pass into a “steamer” in which they are ironed and dried. Then the clothes move on to a sorting system, where they are scanned and sorted by customer/user and given a rack/shelf sorting

8 CASE: berendsen textil service A/S code. The clothes move on to an automatic folding machine that folds the clothes according to customer specifications. Finally, the clothes are packed - depending on customer size - in cages or bags and delivered to the customer the following day by one of Berendsen’s distribution vans. On average, an employee here can treat 120 pieces of laundry per hour.

The production can also be performed without the automated sorting and packing system. In this case, all sorting and packing processes are performed manually, and an employee can then on average treat only 80 pieces of laundry per hour.

The capacity to treat clothing from the aforementioned segment is, as stated, 100 % utilized, which is why Berendsen is considering two options to expand capacity: A. Expanding only with manual tables, where workers manually sort, fold and pack the laundry. With this solution, the capacity can be gradually increased with increasing demand. B. Expanding capacity by investing in a second automated sorting and packaging system, whereby capacity is doubled.

An employee works 1,700 hours per year and 7.5 hours per day. The hourly wage is 200 DKK/hour. The subsequent 10 years are designated as year 1, year 2, ...., year 10.

Question 1 Calculate the total increase in labor costs for the next 10 years if the capacity is only expanded with manual tables.

Question 2 Calculate how much the total increase in labor costs for the next 10 years will be reduced if capacity is expanded by investing in an automated sorting and packing system.

In the following Question 3, it is assumed that the discount rate is 10 % per annum. Furthermore, the rather modest investment cost of the manual tables is ignored.

Question 3 If the investment’s dynamic payback period is 5 years, what must have been the amount of investment in the automated systems? Calculate based on this the investment’s static payback period.

With the options A and B considered above, work is conducted in one shift. These two options require capacity expansion and therefore a building expansion.

9 CASE: berendsen textil service A/S

As an alternative to these two options, Question 4 deals with a third option, C. This consists of the capacity expansion achieved through a combination of overtime, Saturday work and working a second shift. This avoids the need for an investment in the expansion of the buildings, but in turn increases the hourly wage paid for the expanded capacity. Here it is assumed that the hourly average wage is simplified to be 240 DKK/hour.

Question 4 Calculate the total increase in labor costs for the next 10 years if capacity is expanded using option C.

Question 5 Based on the existing information and calculations, can you say anything about which of the three options you would recommend to Berendsen, based on economic considerations?

Other than economic considerations, are there any other factors that should be considered?

Please find the solution on page 59.

10 CASE: berendsen textil service A/S INVOLVERING OG INDFLYDELSE ER DU KLAR TIL AT FORFØLGE EN INTERNATIONAL LEDERKARRIERE?

Har du et stærkt drive, mod, energi og ambitioner til at tage ansvar for at skabe både forretningsmæssige resultater, trivsel og udvikling for andre mennesker? Så har du en god del af fundamentet for at sætte turbo på din karriere.

Dit Management Trainee-program består Det kræver overblik og evnen at kunne af et introforløb på en måned og 4 efter- strukturere sin tid – samt ikke mindst vil- følgende projektforløb på hver ca. 6 må- jen til at yde en ekstra indsats, hvis det er neder. De efterfølgende projektforløb har nødvendigt for at komme i mål. alle det mål at optimere vores forretning. Der er altså ikke tale om skrivebordsøvel- OM BERENDSEN ser, men om projekter, hvis resultater og Berendsen Textil Service udvikler og til- konklusioner vi vil implementere direkte i byder innovative serviceløsninger inden vores drift. for udlejning af linned, beklædning, måt- ter og håndhygiejne. Med en årlig om- Du løser projekterne i tæt dialog med le- sætning på 11 mia. kr. og 16.000 medar- delsen i de afdelinger, du arbejder i, og bejdere er vi markedsledende service- samtidig har du en mentor, som følger udbyder på B2B-markedet i Europa. I dig hele vejen gennem alle projekter – og Danmark er vi 1.200 engagerede medar- som du derfor altid kan sparre med og bejdere fordelt på serviceafdelinger over søge råd hos. hele landet.

Uddannelsesmæssigt er der flere veje ind Vores Management Trainee-program har som Management Trainee i Berendsen. eksisteret i knap 20 år, og overalt i organi- Uanset baggrund skal du trives med at sationen kan du møde tidligere trainees i blive stillet over for store udfordringer, lederstillinger, herunder også i vores in- som du skal løse under tidspres. ternationale topledelse.

Kunne det være noget for dig? Så kontakt HR Chef Anne Krabbe på 2373 8641 eller læs mere på www.berendsen.dk/management-trainees.11

Annonce_Berendsen_168x238.indd 1 09/06/16 09.21 CASE: Energinet.dk

Social benefits of investment in a Great Belt power link

Energinet.dk must ensure the supply of electricity and natural gas in Denmark, while the transition to green energy occurs in an economically sound and efficient manner. They own the energy motorways and are responsible for ensuring fair competition in the market for electricity and natural gas for the benefit of consumers. Energinet.dk: • ensures that there is always power in electrical outlets and gas in gas taps • establishes the framework for well-functioning markets for electricity and natural gas, so both consumers and energy producers are ensured fair prices • contributes to the green transformation of the energy system and helps ensure that the transition will benefit Danish society • subsidizes environmentally friendly energy.

Energinet.dk is an independent public enterprise owned by the Danish Ministry of Energy, Utilities and Climate, with 900 dedicated and highly skilled employees. Based on the values of business orientation, development, responsibility and com- mitment, they constantly emphasize organizational and personal development. The company is headquartered in Fredericia and has offices in Ballerup, Stenlille, Egtved, Lille Torup, Tjele and Vester Hassing. The company has a turnover of approximately 12 billion DKK annually. The company works with many different interest organizations both within and outside of Denmark.

The following assignment is based on the initial consideration of whether – as part of the further development of the electricity market – there should be built a Great Belt power link of 600 MW, so that East and West could be electrically connected. Such a decision required considerable consideration, and as a means to facilitate the decision-making process, business cases were used to illustrate the benefits and costs of the project. Parts of such business cases illustrate the social benefits and costs of a particular project. The project became a reality and the link was completed in 2010.

12 CASE: Energinet.dk

In the following assignment, imagine that you were employed as a planner in Energinet.dk and that you had been asked to calculate the economic consequences of the Great Belt power link of 600 MW as described above. The project was scheduled to start in early 2007, and the link should be ready for operation in early 2010. Costs for procurement, construction and commissioning of the technical components: cable purchase, laying of cable, expansion of substations etc. were estimated to amount to 820 million DKK in 2007, 400 million DKK in 2008 and 150 million DKK in 2009. The life of the link was estimated to be 20 years, starting in 2010 and ending in 2029.

For simplicity reasons, it is assumed that there are the following four different types of benefits of the Great Belt power link:

1. Operational benefit Operational benefit is an expression of the value of increased trade and thus allows for more optimal dispatching of electricity among generating units with lower total cost of production as a result. Operational benefit was estimated to be 33 million DKK annually.

2. The benefit of sharing reserves A Great Belt power link allows for the sharing of electricity reserves between East and West Denmark. This allows the total Danish demand for reserves to be reduced, providing an estimated cost reduction of 90 million DKK annually.

3. The benefit of potential synergies in regulating This is the benefit of potential synergies in regulating power by equalizing imbalances between the two regions. The cost reduction resulting from synergies was estimated to be 10 million DKK annually.

4. The benefit of better market functioning This is the benefit of better market functioning by reducing the possibility of abuse of market dominance. This reduces the so-called deadweight losses, since com petition will increase. The gain from such improvements was estimated to be 31 million DKK annually.

Operating cost is a maintenance cost that should be expected each year. It was estimated that it would cost 12 million DKK annually to maintain the power link. Once the link was put into operation, there would be electrical losses on the network, which was estimated to be 12 million DKK annually.

13 CASE: Energinet.dk

All annual amounts of the costs, savings, gains and benefits were assigned to the end of the year and an interest rate of 6 % per year was used.

Question 1 What was - established at the beginning of the year 2010 - the total social surplus or deficit from the Great Belt power link?

Energinet.dk estimated that there was a risk that the project could be delayed a year, so the link would first become operational in early 2011. In this case, it was expected that in the year 2010, additional construction costs would amount to 50 million DKK. The link’s life was still projected to be 20 years from the start of operations.

Question 2 If the project was delayed in this way, what would then - calculated at the beginning of the year 2010 – be the total social surplus or deficit from the Great Belt power link?

It is often discussed what demands should be placed on the return of public investments.

Question 3 What is the answer to question 2, if an interest rate of 5 % per year instead of 6 % per year is used?

The values of the four benefit values used in the solution of question 1 are all subject to uncertainty, especially the value of the reduction in market dominance. The Board of Energinet.dk therefore considered the following question:

Question 4 If the assumptions underlying question 1 are taken to be valid, how much should the value of the reduction of market dominance be changed, such that the social benefit of the project will be equal to 0 DKK?

Please find the solution on page 62.

14 vær med til at bygge højspændings- forbindelser til udlandet - så danskerne har strøm i stikkontakten både kl. 20.50 og i 2050

Energinet.dk’s eltransmissionsnet er forbundet til nabolandene Norge, Sverige og Tyskland, og nye forbindelser er på vej. Udlandsforbindelserne fungerer bl.a. som handelsforbindelser mellem landene. Dermed er det muligt at handle overskydende strøm fra fx vindmøller i situationer, hvor Danmark ikke selv kan forbruge strømmen. Derudover er udlandsforbindelserne en vigtig del af den daglige drift, hvor balancen mellem produktion og forbrug konstant skal opretholdes.

Viking Link skal forbinde Danmark og Storbritannien 650 1,4 mio km søkabel husstande Viking Link er en 740 km lang Forbindelsen er på 1400 MW og Læs mere om vores jævnstrømsforbindelse (HVDC) kan transportere elektricitet til komplekse projekter og med ca. 650 km søkabel og to 1,4 mio. husstande. Vi forventer, dine karrieremuligheder konverterstationer. at forbindelsen går i drift i 2022. på www.energijob.dk CASE: Energistyrelsen

Investing in a heat pump system

The Danish Energy Agency (DEA) is a major contributor to Denmark’s role as a pioneer in the cost-effective transformation of the energy sector – for the benefit of both the climate and the Danish economy. The DEA undertakes assignments related to energy production, supply and consumption and efforts to reduce CO2 emissions. The DEA also participates in international collaboration on energy transition in countries such as China, Mexico, Ukraine, Indonesia and South Africa, among others.

The DEA is responsible for supporting the economic efficiency of the supplysector, which in addition to energy, comprises societally vital areas such as water, waste and telecommunications. The DEA sets a solid professional fingerprint on the policies pursued in this area and ensures the best possible conditions for the Danes to have delivery of a stable supply.

The DEA has existed since 1976 and is part of a group jointly organized under the Danish Ministry of Energy, Utilities and Climate. The DEA emphasizes a high level of professionalism and knowledge sharing among many disciplines and prides itself on having good colleagues and being a flexible workplace where there is room for individual needs. There are nearly 400 employees in the DEA, divided into offices in Esbjerg and Copenhagen.

In connection with the implementation of the energy reserves for the 2016 budget, funds have been set aside for initiatives over a three-year period 2016-2018 that will help to propagate large heat pumps. The funds are earmarked for a traveling team that will advise district heating plants and other stakeholders on concrete options for the establishment of large heat pumps.

The DEA’s traveling team aims to help district heating plants and other stakeholders, such as processing companies, with the implementation of heat pump solutions. The team advises on specific opportunities for the establishment of large heat pumps.

16 CASE: Energistyrelsen

The advice is based on available energy resources and other technical conditions that determine the possibilities in the individual surrounding areas.

The following assignment is based on the premise that the DEA has carried out a technical and economic evaluation of utilizing excess heat in the cooling towers of a company that produces industrial gases. Instead of cooling the industrial process by using electricity and water, cooling is proposed to be done by using a heat pump system that draws heat out of the cooling towers and uses it to heat the district heating plant network. It is expected that the company will reduce the cost of electricity and water for cooling by 2 million DKK per year.

The proposed heat pump system is powered by electricity and produces 5½ MW of thermal power. The facility’s COP (Coefficient Of Performance), which is an expression of the relationship between the energy of the heat pump’s output and input, is 4, which means that if the input to the heat pump is 1 kWh of electricity, the output will be 4 kWh of heat. A COP of 4 is a relatively high value for a heat pump, and can be achieved here because in this case, 3-4 heat pumps are linked together. The price of the heat supplied to the district heating network is 337 DKK/MWh. The price of the electricity that drives the heat pump is 1.10 DKK/kWh.

The company works in three shifts, seven days a week, year round, but the heat pump system is only expected to be in operation for 360 days a year.

The investment in the heat pump itself is 12 million DKK. In addition, connection to pipelines, a transformer, a building for the transformer and design work cost 3 million DKK. The lifetime of the investment is assumed to be 15 years and a discount rate is 8 % per annum is used.

The largest expense in the operating costs is the cost of electricity to operate the heat pump. In addition, maintenance, etc. will cost 2 million DKK per year.

Question 1 Calculate the total operating expenses.

Most often, the capital value method is used for assessing the profitability of investments, but in the solution of Question 2, the annuity method should be used.

Question 2 Transcribe all cash expenditures and cash receipts to a constant annuity over the life of the investment.

17 CASE: Energistyrelsen

Question 3 Calculate the investment’s net present value, based on your answer to Question 2.

Question 4 Calculate the investment’s dynamic payback period.

The EU Commission believes that the Danish PSO tax is contrary to the EU Treaty, since it excludes the green electricity produced in other member states and thus favors Denmark. This means that the government must find a new model. If the PSO tax is abolished, the company’s electricity price will be immediately reduced to 0.85 DKK per kWh.

Question 5 How much will the profitability of the heat pump system improve, if the PSO tax is abolished and the company’s electricity price is not increased by new taxes?

Please find the solution on page 65.

18 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 2015, the company had a total revenue of 14.6 billion DKK. Lundbeck currently employs approximately 5,500 employees in 57 countries, of which 1,700 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 subcontractors, 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.

19 CASE: H. Lundbeck A/S

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 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, but 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 1 If 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.

20 CASE: H. Lundbeck A/S

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 2 Would 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 3 Would 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.

21 CASE: H. Lundbeck A/S

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 4 How 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 5 What 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?

Please find the solution on page 68.

22 CASE: H. Lundbeck A/S

23 CASE: Haldor Topsøe A/S

Economic assessments about a new product

Haldor Topsoe A/S (Topsoe) is the leader in heterogeneous catalysis and supplies catalysts and process design to oil refineries, power plant exhaust gas treatment systems and clean energy processes. The environment plays a significant role in the company’s research and production, and through the introduction of new technologies, Topsoe supports a more sustainable use of the world’s resources. Approximately 2,600 employees work at the company’s headquarters in Lyngby and subsidiaries in the USA, Russia, India, China, Bahrain, Argentina, Brazil, Malaysia, South Africa and Canada, as well as manufacturing facilities in Frederikssund, Houston, USA and Tianjin, China. The annual turnover in 2015 amounted to 5.7 billion kroner.

Over the past decade, Topsoe’s sale of process technology and catalysts for oil refineries has increased sharply. One reason for this was a strategic focus on the development of catalysts for the production of fuel with ultra-low sulfur content (ULSD – Ultra-Low Sulphur Diesel) and a global trend toward environmental legis- lation that tightens requirements for allowable sulfur content.

Topsoe has developed and delivered catalysts for oil refineries worldwide. Catalysts, called “TK series”, are used for cleaning oil and for the production of refinery products - mainly gasoline, kerosene, diesel, fuel oil and asphalt. In addition, raw materials for a variety of other products were also produced. More than 2,000 different products can be produced from crude oil.

To refine products that meet environmental regulations, products such as gasoline and diesel must first be cleansed of contaminants such as sulfur compounds and nitrogen. This is done by mixing the products with hydrogen and then directing them through the vessels containing the TK catalysts. The catalysts induce the vari- ous compounds in the oil to react with the hydrogen to produce the desired product.

24 CASE: Haldor Topsøe A/S

After several years of research work, Topsoe was able to develop a new catalyst, TK- new, which is even more efficient than the previous catalyst, TK. During the part of the refining process where the catalyst is employed, a semi-processed product, LCO (Light Cycle Oil), is recovered. LCO is important in the production of ULSD. By using the TK-new, the amount of recovered LCO increased from 25.0 % to 29.2 % of the amount of oil flowing into the catalyst. This added value in the production of LCO is set to be 60 DKK per barrel.

The basis of the following calculations is a refinery that processes 30,000 barrels of oil a day and produces 365 days a year. For a refinery of this size, 110 tons of catalyst must be used. After 2.5 years, the catalyst must be replaced.

Before Topsoe can attempt to sell the TK-new to refiners, they must first establish a selling price. A common method is to use a specific margin for the variable manufacturing costs. In a research-intensive company such as Topsoe, this method is not suitable, because the variable manufacturing costs are relatively small in com parison to the considerable development costs. To determine the selling price based on the development costs is also not economically rational, as already incurred costs (sunk cost) should never influence future decisions.

A sense of what will be an upper limit for the selling price can be obtained from an assessment of the product’s usefulness to the customer: EVC (Economic Value for the Customer).

Question 1 If the refinery has previously used TK, what is the absolute highest additional cost for TK-new the refinery should be expected to accept?

The development of TK-new has taken 3 years and the development cost is cal culated to be 3.5 million DKK per year.

The price of TK-new has now been established, and on that basis, sales of TK-new in the next 5 years will be: Year 1: 400 tons Year 2: 700 tons Year 3: 2,400 tons Year 4: 3,800 tons Year 5: 4,200 tons

25 CASE: Haldor Topsøe A/S

For the next 5 years, the marketing costs for TK-new are planned to be 200,000 DKK per year. Assume that the gross margin on TK-new at the established selling Topsoe careers price is 30,000 DKK per ton. Further, assume that Topsoe uses an interest rate of 20 % per annum.

One problem in assessing profitability in developing a new technology (here TK- Global challenges new) that replaces an existing technology (here TK), is that the assessment should be based on assumptions about what would have happened if the new technology had solved by you not been developed. At Topsoe, we encourage the engineers of tomorrow Question 2 to not only develop next generation products, but also solve global challenges. Working in areas from What is the payback period for the development of TK-new, if it is assumed that it atsmospheric pollution to renewable energy production, would not have been possible to sell TK in years 1-5? we help our customers get more out of their raw materials while at the same time using less energy – we call this optimal performance.

When marketing TK-new, it is likely that Topsoe will acquire new customers With multiple opportunities to work in di erent who previously used competing products. In this case, TK-new will contribute to industries and regions of the world within one company, there are no limits to where your increased sales of catalysts. However, when TK-new replaces TK, it is expected that abilities could take you. existing customers will switch over from TK to TK-new, with reference to Question Contact us at [email protected] 1. In this case, the contribution of TK-new will only be an additional gross profit and start your career today. with respect to TK.

Question 3 Assuming that the TK-new does not contribute to increased sales, but merely replaces a similar sale of TK that could be achieved over the five years, what should the additional gross profit on TK-new be for the project payback period to be 3 years?

Please find the solution on page 71.

26 topsoe.com Topsoe careers

Global challenges solved by you

At Topsoe, we encourage the engineers of tomorrow to not only develop next generation products, but also solve global challenges. Working in areas from atsmospheric pollution to renewable energy production, we help our customers get more out of their raw materials while at the same time using less energy – we call this optimal performance.

With multiple opportunities to work in di erent industries and regions of the world within one company, there are no limits to where your abilities could take you.

topsoe.com CASE: hofor a/S

Heat pumps for generating district heat

HOFOR, the Capital region’s utility company, supplies cities with water, wastewater treatment, district heating, natural gas and cooling and constructs windmills. The company is owned by eight municipalities: Albertslund, Broendby, Dragoer, Herlev, Hvidovre, Copenhagen, Roedovre and Vallensbaek. HOFOR ensures that residents of the Capital region are supplied with clean drinking water from the tap, and handles treatment of sewage and rainwater. In addition, HOFOR supplies residents with district heating, natural gas and cooling. The company also constructs wind turbi- nes and owns “Amagervaerket,” which produces district heating and electricity.

HOFOR shares a common vision - HOFOR will create sustainable cities based on climate friendly and environmentally friendly supply solutions. Everything HOFOR does every day is about creating sustainable cities. Part of HOFOR’s strategy focuses on providing green heat to Copenhagen at a reasonable price and with the highest possible reliability of supply. Today, the country’s largest district heating plant covers about 99 percent of Copenhagen’ heating demand, and more than half of that heat comes from fossil-free fuels. Internationally, this is in a class of its own, and each year delegations from around the world make pilgrimages to the city to learn about green heating.

One of the owners, the City of Copenhagen, has a goal of becoming the world’s first

CO2 neutral capital. An important prerequisite for achieving this ambitious goal is that the Copenhagen district heating plant is powered by CO2 neutral production. HOFOR has already started with the transition, for which one important step will be to rebuild “Amagervaerket,” so that from 2020 it is only fired with sustainable biomass from wood pellets and chips.

Concurrently, HOFOR is working to exploit new technologies that can help to make the overall heating system even more efficient and sustainable. HOFOR is investigating technologies such as geothermal heat storage and large heat pumps.

28 CASE: hofor a/S

Accordingly, the company has started several pilot projects in which large heat pumps will be tested in the coming years to determine how they can help to optimize the overall district heating system.

The following case is based on HOFOR’s activities in Nordhavn (Copenhagen’s North Harbor), located on the Oeresund coast. This harbor system was created in the late 1800s by the filling in of the Svanemoelle Bay north of Copenhagen’s Free Harbor. The area is over 2 km2 in size. Most of the land is owned by the Copenhagen City & Port Development Authority, which has initiated a gradual development of the area. It is expected that when the entire North Harbor is fully developed around 2050, there will be space for 40,000 residents and 40,000 jobs in offices, shops, etc.

In the first phase of development, part of the area is being developed with a mix- ture of residential and commercial uses, and this area will provide 7,000 jobs and housing for 2,000 people. As a basis for the following case, it is assumed that planning now needs to be done for phase 2, which is expected to include 90 buildings with an average of 6,000 square meters, and the total number of square meters is assumed here to be equally divided between housing and jobs. The case deals with some of HOFOR’s considerations of how this fictitious phase 2 can be supplied with district heating. It should be noted that the following indicated numerical values are of a realistic scale, and that the said data center is “invented” for this case.

HOFOR is considering two options to supply the area with district heating for both hot water as well as for space heating via radiators or underfloor heating: 1. Establishment of a distribution network in the area connected to the existing network that already supplies the rest of Copenhagen with district heating. 2. Establishment of a local distribution network in the area, in which the water is heated by means of two heat pumps:

a. A heat pump, HPA, which draws energy from the surrounding seawater (“water to water”).

b. A heat pump, HPB, which draws energy from the cooling air from a data center (“air to water”).

A heat pump works in principle in the same way as a refrigerator. Whereas the purpose of a refrigerator is to transport heat out of the refrigerator, so the temperature is kept low, the purpose of a heat pump is, however, the opposite, in that a medium is heated by transporting heat in from another medium. The heat pump, HPA must therefore draw energy out of the nearby seawater, and upgrade this energy so it can be used to heat the district heating water. Similarly, the heat pump HPB, draws energy from the cooling air from the data center.

29 CASE: hofor a/S

A heat pump is powered by electricity, and the efficiency of a heat pump is expressed by the factor COP (Coefficient Of Performance), which is a measure of the ratio of the energy output of the heat pump and its electricity input. The COP depends on, among other factors, the temperature before and after the heat pump. On average, for example, to achieve a COP of 3.0, then the energy output by the heat pump is on average 3 times as great as the electricity input to the heat pump.

The electricity networks in the Scandinavian countries are interconnected so that electricity can be continuously bought and sold between countries, and this takes place through an energy exchange market, the Nord Pool energy market. HOFOR buys its electricity on Nord Pool, where the price varies over the day and over the year, as the price is determined by supply and demand. Generally, the price is highest during the day when demand is high, and lowest at night when demand is low.

In order to simplify the calculations, it is assumed here to be very simplified that the cost of electricity over each day follows the curve shown in Fig. 1.

DKK/kW

0,48

0,09 Tim

00 06 22 24

Fig. 1: Daily market price on Nord Pool from 00:00 to 24:00.

Fig. 1 shows the simplified assumption that the market price during the night is 0.09 DKK per kWh, while during the day it is 0.48 DKK per kWh. In addition to the electricity for the heat pumps, 0.80 DKK per kWh is added for taxes, tariffs and fees.

Question 1 What is the average market price of electricity on Nord Pool?

30 CASE: hofor a/S

Because the planned buildings must comply with Building Regulation 2020 (BR20), the energy consumption for heating must be relatively small. According to BR20, the total expected energy consumption for space heating and hot water must not exceed 23 kWh/m2 per year for residences and 15 kWh/m2 per year for workplaces.

Question 2 What is the expected total energy consumption for the area in phase 2?

Data for the two heat pumps are listed in Table 1.

Investment (DKK) Operation & maintenance (DKK/year) Lifetime COP

HPa 10 million 0.1 million 25 years 2.8

HPb 15 million 0.2 million 25 years 3.0

Table 1: Data for the two heat pumps.

The cooling air temperature from the data center is assumed to be 350C, and it is expected that the amount of heat extracted by the heat pump will yield a total heat output of 6 GWh /year. The remaining energy needs must then be supplied by the seawater heat pump.

Question 3 What is the expected annual cost of electricity for operation of the two heat pumps, if it is assumed that heat pumps produce evenly over the day?

It is assumed that the investment in the distribution networks will be largely the same for the two solution options, and therefore this investment can be disregarded when the two options are compared. For investment calculations, HOFOR uses a discount rate of 6 % per annum.

Question 4 What is the expected average cost of delivery of 1 kWh of heat over the heat pumps’ life expectancy with solution option 2?

In Question 4, the cost for supplying district heating is calculated for solution option 2. Calculated in a corresponding manner, HOFOR’s cost for supplying district heating in Copenhagen is 0.60 DKK per kWh. The situation, however, is that the technology for heat pumps is undergoing rapid development, as heat pumps’ COP

31 CASE: hofor a/S is increasing and their price is decreasing. If the investment in the two heat pumps is first expected to be made in 2020, then the amount of the investment in the heat pumps will therefore in 2020 be less than assumed above.

Question 5 By how many percent should the total investment in the two heat pumps be less, if the cost of option 2 must be less than the cost of option 1?

Please find the solution on page 74.

32 ILDSJÆLE MED PRIORITETERNE I ORDEN

VI skaber fremtidens bæredygtige byer og sikrer forsyninger til en million forbrugere i hovedstadsområdet.

DU ønsker et afvekslende og udfordrende job, der samtidig giver dig mulighed for at prioritere et liv ved siden af arbejdet.

Hver eneste dag er rigtig mange borgere afhængige af HOFORs forsyninger. Derfor er det ikke for sjov, når vi siger, at vi ønsker de dygtigste medarbejdere.

Som ny medarbejder vil du opleve at være omgivet af ildsjæle. Vi arbejder dedikeret på, at vores projekter lykkes, men vi har også fokus på at skabe sund balance mellem arbejde og fritid.

Se mere på www.hofor.dk/job, hvor du også kan oprette en JobAgent.

Jobannonce268x238.indd 1 07-06-2016 13:22:04 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 2015, the company realized a turnover of 6.5 billion Danish Kroner and employed an average of about 4,000 employees.

MT Højgaard is organized into a number of business units and subsidiaries within facilities & concrete, commercial and residential construction, high rises, reno vation, as well as offshore & steel bridges. A small part of the company’sactivities takes place outside of Denmark. In support of its production, the company has created a number 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 completed 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.

34 CASE: MT Højgaard A/S

• 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.

• 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 developer B: The expected project result C: The posted project costs D: 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 DKK B: 20 million DKK C: 40 million DKK

35 CASE: MT Højgaard A/S

D: 40 / (100 – 20) = 0.50 E: 0.50 ∙ 20 = 10 million DKK

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 1 What numerical values must be in rows 4), 5), 6), and 7)?

36 CASE: MT Højgaard A/S

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.

Question 2 By 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.

Expectations per year Year 1 Year 2 Year 3 1) Total revenue 100,000 100,000 100,000 2) Total project result 20,000 10,000 -5,000 Interim financial statement for Year 1 Year 2 Year 3 3) Posted costs 20,000 25,000 60,000 4) Degree of complation 5) Project result Accumulated financial statement Year 1 Year 2 Year 3 6) Posted costs 7) Project result

Table 2: Example 2 of a project process.

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

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

Question 3.3 What project result would have been realized in this project process in each of the three years?

37 CASE: MT Højgaard A/S

Question 3.4 If 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?

Please find the solution on page 76.

38 

My tasks vary throughout the entire construction process. In collaboration with the architect, I currently work on ensuring the durability of the supporting structures at the New Psychiatric Department in Vejle. Merdzan Ismaili, Design Engineer

Read more at mth.com Follow us on Facebook, LinkedIn and Twitter

MTH_168x238+5_DTU.indd 2 01-06-2015 12:52:18 CASE: nnit a/S

Financial considerations in an IT company

NNIT is one of Denmark’s leading IT service providers. The company develops, implements and operates IT services for regulated industries. NNIT became publicly traded in 2015, but was previously 100 % owned by Novo Nordisk A/S. With deep roots in the pharmaceutical industry, NNIT provides solutions that meet the highest standards of quality, safety and standardization.

Over the last ten years, NNIT has had high annual revenue growth rates and currently employs over 2,500 employees. The majority of employees work in localities close to Copenhagen, but the company is growing internationally and also has employees in China, the Philippines, Switzerland, the Czech Republic, Germany, Britain and the United States.

NNIT’s methods and expertise are widely sought after in the market. NNIT’s sales outside the Novo Nordisk Group are increasing and account for approximately 50 % of total revenue. Customers are all characterized by the fact that they set high standards for safety, quality and documentation, and belong to one of the following sectors: Life Sciences (pharmaceutical industry), Public (public institutions and publicly owned companies), Finance (banks, pension funds and insurance com panies) and Enterprise (transport, food and manufacturing companies).

Despite NNIT’s considerable organic growth, the company has achieved average earnings before interest and tax (EBIT) of over 10 % the last 5 years, which is con sidered very satisfactory and among the best in the market. This level of success can only be achieved by continuously optimizing business processes and having focus on the profitability of all projects and deliverables.

Some of NNIT’s employees only work part time, which is why an employee at NNIT is on average equivalent to 97 % of an FTE (Full Time Employee). It is planned that 30 % of an FTE’s work hours are not billable, due to illness, meetings and vacation.

40 CASE: nnit a/S

In addition, it is expected that an average of 2 % of FTEs are on maternity leave. One FTE is expected to work 160 hours per month. Production capacity (billing capacity) per FTE per month is expressed as:

P1= Number of billable hours per month Number of FTEs

In addition, NNIT provides server capacity available to operate customers’ portals and applications. With a monthly server capacity, D, NNIT’s total production capacity can be expressed as: Production capacity = P1 ∙ FTE + D

Question 1 What is the P1 value for NNIT?

It is assumed that NNIT’s monthly revenue per FTE can be described by:

Revenue/month = P1 ∙ P3 - P1 ∙ P3 ∙ Co + Do, where

P3 = the hourly rate at which customers are billed

Co = the correlation factor between the hourly rate and the number of allocated hours = 0.0005 ∙ P3

Do = the monthly revenue NNIT achieves by operating customer portals and applications

Do is set to 300 DKK per billable hour.

It is assumed that virtually all of NNIT’s costs are fixed, that is to say, independent of the number of hours sold.

Question 2 What is the optimal hourly rate at which NNIT should bill their customers, and what annual revenue will NNIT hereby achieve?

NNIT has a subsidiary in China, where 700 people currently work. It is assumed that in China – as in Denmark – an employee is on average 97 % of an FTE. NNIT is not certain that their office in China contributes positively to NNIT’s bottom line, in that there are only 50 hours each month billed per FTE. The low billing rate is because some of the staff is inexperienced, and due to linguistic and cultural con ditions, a lot of time is wasted.

41 CASE: nnit a/S

The annual fixed costs for buildings, administration and travel are 44.2 million DKK per year. The hourly wage for a Chinese FTE is 100 DKK, and NNIT can bill a Chinese FTE at 280 CNY per hour, where CNY/DKK = 0.70.

Question 3 In the current situation, does the office in China positively contribute to NNIT’s bottom line?

With the information underlying the answer to Question 3, the China office is assessed based on a short-term economic assessment. If NNIT should decide whether the China office should be maintained, then it might be relevant to include many other conditions.

Question 4 Discuss what arguments could be made for and against NNIT maintaining its China office.

Please find the solution on page 79.

42 CASE: nnit a/S

GRADUATE at a fast-growing IT company

Come make your mark on challenging projects. Kick-start your IT career and be part of a passionate team. Join the NNIT Graduate Program – we open for applications in 2017.

www.nnit.com/graduate

Pernillae Brøndum Junior Consultant David Shahmiri Junior Consultant

43 www.nnit.com/graduate CASE: A/S Storebælt

Annuities with Different Payment-Interval Lengths

The Great Belt Fixed Link is an essential part of many Danes’ journeys when they travel between the eastern and western parts of the country. A total of 11,880,022 vehicles drove over the bridge in 2015, and the average daily traffic was 32,548 vehicles. By comparison, in 1997, the last full year of ferry operations, approximately 8,300 vehicles were transported across the Great Belt daily. Rail traffic has also benefited greatly from the fixed link. An average of 133 trains crossed the Great Belt each day in 2015, versus 40-45 before the bridge opened.

The link’s societal importance requires that both road and railway across the Great Belt is open around the clock - all year round. A/S Storebælt is responsible for organizing the operation, so that travelers experience a fast, flexible, and safe transportation option between the eastern and western parts of the country.

The Great Belt Fixed Link is designed for a service life of 100 years, but with timely implementation of necessary maintenance, the basic concrete and steel construction can ensure a lifetime of well over 100 years. For A/S Storebælts’ operations organization, it is therefore essential to have good access to all concrete and steel surfaces, so regular inspections can be carried out and necessary repairs under taken in a timely manner, without inconveniencing travelers.

The operations organization’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 pilings and two abut- ments. The bridge spans’ concrete is given a routine inspection every two years.

44 CASE: A/S Storebælt

A general inspection is carried out every six years, and this replaces the 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 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 1 What 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 2 How can the costs of inspection of concrete and bridge bearings for each type of platform be described by three different constant annuities?

45 CASE: A/S Storebælt

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

Table 1: Data for the two platforms *)The costs are indicated as a percentage of the investment amount

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

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

46 Vi skaber forbindelser i Danmark. Vil du med på holdet?

Den ene dag har jeg eftersyn 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.

Martin Duus Hansen Uddannet bygningsingeniør Driftsleder

I de kommende år får Sund & Bælt brug for ingeniører, Sund & Bælt vil gøre det der er kvalificeret til at løse opgaver inden for konstruktion, nemmere at være rejsende drift og vedligehold ligesom Martin Duus Hansen gør det. Vores primære opgave er at eje og drive Måske er det dig? de faste forbindelser over Storebælt og Øresund samt med tiden tillige Hos Sund & Bælt lægger vi vægt på, at du får en hverdag Femern Bælt-forbindelsen. Opgaverne med faglige udfordringer og frihed under ansvar. Gode skal løses under hensyn til opretholdelse kollegaer og løbende efteruddannelse følger også med, af en høj tilgængelighed og et højt når du bliver ansat hos os. sikkerhedsniveau på forbindelserne. Ligeledes ejer vi BroBizz A/S, som Læs mere om din fremtidige arbejdsplads her tilbyder en samlet elektronisk afregning for kørsel på betalingsveje i Skandinavien www.sundogbaelt.dk og Østrig. CASE: A/S Storebælt

Question 3 If 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 4 Which of the two types of platforms would you recommend that A/S Storebælt acquires?

Please find the solution on page 82.

48 CASE: Vejdirektoratet

Financial considerations regarding the construction of a highway

The Danish Road Directorate is responsible for the national road network, consisting of highways, a number of main roads and many of the country’s bridges - a total of about 3.800 km of roadway. The national road network accounts for about five percent of the total public road network of nearly 75,000 km and almost half of all traffic in Denmark uses the network. The Road Directorate’s work consists primarily of planning, construction and operation of roads and bridges as well as traffic flow and traffic management.

In the planning of the roads, the Road Directorate’s ambition is to create solutions that impact the environment as little as possible and allow both private vehicles and public transport to work together. As a basis for planning, data on traffic, safety and the environment are collected and processed.

In the construction and operation of roads and bridges, the Danish Road Directorate’s goal is to create safe and effective solutions that are both sustainable and financially responsible, so that Denmark gets the best possible roads for the money. The Danish Road Directorate does not build roads and bridges itself, but acts as the main contractor when road construction work is competitively bid and undertaken by private suppliers and contractors.

When roads are constructed, the Danish Road Directorate’s responsibility is to ensure their optimum use. This is partly achieved with the help of efficient traffic flow and intelligent traffic information, so all traffic flows easily and safely.

The Danish Road Directorate employs about 800 employees distributed among six service centers: Aalborg, Skanderborg, Middelfart, Copenhagen, Floeng and Naestved.

49 CASE: Vejdirektoratet

The following assignment is based on the Danish Parliament’s passage of a law on the construction of a highway south of Regstrup, also known as the second phase of the Kalundborg highway. This phase consists of an approximately 6 km long stretch between Regstrup, where the existing Kalundborg highway ends, and continuing south of Regstrup connecting to Skovvejen near Dramstrup. The following data is of realistic magnitude, but they are not all the actual data.

The project is budgeted to cost approximately 295 million DKK, and the road is expected to open for traffic on April 1, 2019. In 2016, the Road Directorate will complete the detailed design of the road, and construction is expected to begin in early 2017. Nemt og The following data are given: 2106: Project Planning + land acquisition: 25 million DKK sikkert frem 2017: Construction work: 125 million DKK 2018: Construction work: 120 million DKK 2019: Construction work: 25 million DKK Total: 295 million DKK

To simplify the calculations, the annual amounts are attributable to the middle of the year. For 2019, however, the annual amounts are attributable to the beginning of the year. A discount rate of 5 % per annum is used, and fixed costs are assumed.

Question 1 What is the present value of the project at the beginning of 2019? I Vejdirektoratet planlægger og styrer vi ler vi innovative løsninger til fremtidens auto- Since motorists are not charged for the use of the road, the project does not produce nogle af landets største infrastrukturprojek- matiserede transport og andre nye trafikale actual income, but with public projects, income is often based on their societal ter, og vi benytter de nyeste teknologier til udfordringer. value. The main elements of the societal value of establishing a highway are the at hjælpe danskerne nemt og sikkert frem. Som arbejdsplads dækker vi hele landet. value of the time saved by motorists, as well as the economic value of the reduction Vi leverer trafikinformation 24/7, og vi bruger Hos os arbejder du med opgaver, der ska- in the number of accidents, in that accident frequency is lower on highway than on avancerede modeller til at beskrive trafiks- ber værdi i danskernes hverdag og har country roads. trømme her og nu og forudsige morgenda- store perspektiver for vækst og samfunds- gens trafikmønstre. Vi udfører vores opgaver udvikling. Suppose that the societal value of the relevant stretch of highway amounts to 88 i tæt samarbejde med naboer, kommuner og million DKK per year. To simplify the calculations, the annual societal value is transportsektoren. Hensynet til omgivelser, Du bliver en del af et stort hold af kompetente trafiksikkerhed og økonomi er således dybt og vidt forskellige mennesker – med plads attributable to the end of the year. forankret i vores arbejde. til at udvikle din faglighed i flere retninger. Du får tillid og ansvar fra begyndelsen og Vi har stærke netværk internationalt, og har gode muligheder for at tilrettelægge din sammen med de skarpeste hoveder udvik- arbejdsdag og personlige udvikling.

Følg os på linkedin.com/company/vejdirektoratet eller vejdirektoratet.dk 50 Nemt og sikkert frem

I Vejdirektoratet planlægger og styrer vi ler vi innovative løsninger til fremtidens auto- nogle af landets største infrastrukturprojek- matiserede transport og andre nye trafikale ter, og vi benytter de nyeste teknologier til udfordringer. at hjælpe danskerne nemt og sikkert frem. Som arbejdsplads dækker vi hele landet. Vi leverer trafikinformation 24/7, og vi bruger Hos os arbejder du med opgaver, der ska- avancerede modeller til at beskrive trafiks- ber værdi i danskernes hverdag og har trømme her og nu og forudsige morgenda- store perspektiver for vækst og samfunds- gens trafikmønstre. Vi udfører vores opgaver udvikling. i tæt samarbejde med naboer, kommuner og transportsektoren. Hensynet til omgivelser, Du bliver en del af et stort hold af kompetente trafiksikkerhed og økonomi er således dybt og vidt forskellige mennesker – med plads forankret i vores arbejde. til at udvikle din faglighed i flere retninger. Du får tillid og ansvar fra begyndelsen og Vi har stærke netværk internationalt, og har gode muligheder for at tilrettelægge din sammen med de skarpeste hoveder udvik- arbejdsdag og personlige udvikling.

Følg os på linkedin.com/company/vejdirektoratet eller vejdirektoratet.dk CASE: Vejdirektoratet

Question 2 What is the dynamic payback period of the road, calculated from project inception at the beginning of 2016?

In Question 1, the present value of the project was calculated at the beginning of the year 2019.

Question 3 What is the present value of the project on April 1, 2019, when the road is opened for traffic?

The above calculations do not take into account that the road needs to be maintained. On top of the asphalt road, a wear layer is applied. This layer creates friction and comfort and provides special optical properties (it reflects light). It is assumed here that the wear layer on the relevant stretch of motorway of 6 km will need to be replaced/renewed every 15 years. The width of each of the two lanes is 8 m, and the cost of replacement of the wear layer is 70 DKK/m2.

Question 4 What is the expected average annual disbursement for replacement of the wear layer?

Please find the solution on page 86.

52 CASE: Velux A/S

Calculations with the Introduction of New Technology for Windows

For more than 70 years, the VELUX Group has created better housing for people worldwide by bringing daylight and fresh air through the roof.

Our product portfolio consists of both skylights and skylight modules, as well as a wide range of decoration and sun-screening products, roller shutters, installation products, and intelligent remote controls. These are products that contribute to a healthy indoor environment and sustainable solutions - for playing and learning, working, and pleasure.

With sales offices and factories in more than 40 countries, we operate globally and have approximately 10,000 employees worldwide.

The VELUX Group is owned by VKR Holding A/S, a foundation and family owned limited liability company.

You can read more at www.velux.com.

Engineers in the VELUX Group typically work with product development, manufacturing, logistics, testing, and quality, or in administrative support functions. Many development projects are undertaken in collaboration with colleagues in the VELUX Group’s global organization and with Danish and foreign partners.

Introduction of new technology Over the years, many different window pane variants have been developed, to be able to offer customers a variety of features such as better insulation properties, sun protection, and laminated glass. A new technology now makes it possible to put a coating on the window pane which resists the adhesion of dirt and debris, giving the window a self-cleaning effect in the rain.

53 CASE: Velux A/S

The VELUX Group sales subsidiaries around the world see great value in being able to offer this coating to their customers, and studies have shown that customers are willing to pay extra for this feature. Technologically, it is possible to apply this coating to the window panes, if in cooperation with the glass supplier 10 million DKK is invested in new equipment. This investment is to be borne by the VELUX Group. In addition, the raw materials for the finished window will be 15 DKK more expensive. When the window with the new coating is mounted in the frame, it must be handled more carefully and requires additional quality control before and after this process. This means that labor costs will increase by 12 DKK per window.

Calculation for a normal window without the new coating: Materials: 800 DKK 57.1 % Salary: 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 sales of windows are assumed to be 200,000 units per year, and a discount rate of 7 % per annum is used.

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

Question 2 If the VELUX Group wishes to continue to have a profit margin of 5 %, by how much should the selling price of a window be increased as a result of the new coating?

Based on market research, the sales subsidiaries raise the selling price of the windows with the new coating by 45 DKK. Based on the answer to question 2, it is shown that this will result in a reduction in the profit margin per window for the VELUX Group.

54 CASE: Velux A/S

I’m proud of working for a company that was sustainable even before the term was invented

Bringing light to life... That’s what the VELUX Group is all about. In more than one sense.

Our products create healthy indoor environments. And our workplace gives people the chance to grow. velux.com/careers

V0011947-063-022_Ad_168x238.indd 1 17-06-2015 13:39:38 CASE: Velux A/S

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

Question 4 Calculate the profitability of the investment in the new technology if the investment shall accrue interest and be paid off over a five year period.

Question 5 What is the minimum amount by which the selling price can be increased, in order for the investment to be profitable over a five year period?

Please find the solution on page 89.

56 CASE: Velux A/S

57 CASE: Velux A/S

solutions

58 w Solution: berendsen textil service A/S

Capacity Expansion

Solution Question 1 If there are only manual tables, an employee can treat 80 pieces of laundry per hour. With a daily working time of 7.5 hours, an employee can thus treat 7.5 ∙ 80 = 600 pieces of laundry per day.

By the end of the 10th year, production increased by 48,000 - 30.000 = 18.000 pieces per day. If this increase must be performed by staff at the manual tables, there will at that time be a need for 18,000 / 600 = 30 new employees. On average per year, there will thus be the need for ½ ∙ 30 new employees over the next 10 years.

The annual labor cost is 1,700 ∙ 200 = 340,000 DKK per employee. The total increase in labor costs over the next 10 years will then be ½ ∙ 30 ∙ 10 ∙ 340,000 = 51 million DKK.

Solution Question 2 With the help of the automated system, an employee can treat 120 pieces of laundry per hour, that is, 7.5 ∙ 120 = 900 pieces of laundry per day.

By the end of the 10th year, production increased by 18,000 pieces per year, which at that time in this situation will require 18,000 / 900 = 20 new employees. The total increase in labor costs over the next 10 years would then be ½ ∙ 20 ∙ 10 ∙ 340,000 = 34 million DKK.

By investing in the automated system, total labor costs over the 10 year period would thereby be reduced by 51 million - 34 million = 17 million DKK.

Solution Question 3 By the end of the 10th year, the investment in the automated system implies the need for 30 - 20 = 10 fewer employees. As this reduction in staffing levels is linearly increasing, one employee is saved the first year, and this saving increases by one employee per year. The discounted savings obtained after each of the five years that make up the investment’s dynamic payback period are:

59 w Solution: berendsen textil service A/S

Year 1: 1 ∙ 340,000 ∙ 1.10-1 = 309,091 DKK Year 2: 2 ∙ 340,000 ∙ 1.10-2 = 561,983 DKK Year 3: 3 ∙ 340,000 ∙ 1.10-3 = 766,341 DKK Year 4: 4 ∙ 340,000 ∙ 1.10-4 = 928,898 DKK Year 5: 5 ∙ 340,000 ∙ 1.10-5 = 1,055,566 DKK ∑ discounted savings = 3,621,879 DKK

The investment must have thus been just over 3.6 million DKK.

The savings, ∆O(t), as a function of time, t, can be described by: ∆O(t) = 340,000 ∙ t DKK/year, as the unit of t is years.

The total savings, ∑O(t), as a function of time can be found by the integration of ΔO(t): ∑O(t) = ½ ∙ 340,000 ∙ t2 = 170,000 ∙ t2 DKK.

The static payback period, PPS, can then be calculated by setting I = ∑O(t), to give:

PPS = (3,621,879 /170,000)½ = 4.6 years.

Solution Question 4 For the capacity expansion in option C, the annual salary cost will be 1,700 ∙ 240 = 408,000 DKK per employee.

With option C, the current automated sorting and packing system could be used, so that the situation in terms of process is similar to that dealt with in Question 2 - except that the annual salary cost per employee now has increased from 340,000 to 408,000 DKK per year.

The total increase in labor costs over the next 10 years would then be ½ ∙ 20 ∙ 10 ∙ 408,000 = 40,800,000 DKK.

Solution Question 5 The total increases in labor costs for the next 10 years are calculated to be: Option A: 51,000,000 DKK Option B: 34,000,000 DKK Option C: 40,800,000 DKK

A complete economic comparison requires information about the investment in the building expansion for options A and B as well as the investment in the automated sorting and packing system for option B.

60 Solution: berendsen textil service A/S

It should be noted that the above total increases in labor costs were generated by a direct summation of annual increases. If the increases are to be included in investment calculations, then the total increases should be calculated by a summation of the discounted annual increases. In order to simplify the calculations, this has been omitted.

The answer to Question 3 shows that the investment in the automated sorting and packaging system has been just over 3.6 million DKK. Comparing this with the above total increases in labor costs strongly indicates that option B is preferable to option A, based on economic considerations.

Other, non-economic considerations might be, for example, that option C would require a change in working hours, including overtime, weekend work and working a second shift – something that Berendsen would like to avoid.

Furthermore, it could be noted that an investment in the automated sorting and packing system in option B achieves high capacity and thus great flexibility to meet future customer needs.

The purpose of the above examples is to illustrate that even though economic con siderations are the main basis for choosing between alternatives, in certain situations a number of other considerations could be extremely relevant to include.

61 Solution: Energinet.dk

Social benefits of investment in a Great Belt power link

Solution question 1 The discounted value (DV) of the payments made for the establishment of the link,

DVe, calculated at the end of the year 2009 (= the beginning of the year 2010), is: 2 1 DVe,2009 = 820 ∙ 1.06 + 400 ∙ 1.06 + 150 = 921.352 + 424.0 + 150.0 = about 1,495 million DKK.

PS.: If an investment starts at the beginning of year 1, the discounted value

calculated at this time is called DV0. Therefore, the discounted value calculated at the beginning of 2010 is designated DV2009.

The annual social benefit value is represented as 33 + 90 + 10 + 31 = 164 million DKK/year throughout the link’s 20-year life. This must exclude operating costs and the value of the net loss, i.e. 12 + 12 = 24 million DKK/year. The net value of the benefits to society are thus 164 – 24 = 140 million DKK/year.

The discounted value of this net value, DVn, calculated at the beginning of 2010, is: –20 DVn,2009 = 140 ∙ [1 – 1.06 ] / 0.06 = about 1,606 million DKK.

The total social surplus resulting from the establishment of the link, calculated at the beginning of 2010, is as follows:

DV2009 = DVn,2009 – DVe,2009 =1,606 – 1,495 = about 111 million DKK.

This is the net present value (NPV) of the project and when NPV is positive, the project will – based on the underlying assumptions – increase the benefits to society if the project is implemented.

62 Solution: Energinet.dk

Solution question 2 If the project is delayed a year, then the discounted value of the payments for the establishment of link, DVe, calculated at the end of the year 2010 (= the beginning of year 2011), is: 3 2 1 DVe,2010 = 820 ∙ 1,06 + 400 ∙ 1.06 + 150 ∙ 1,06 + 50 = 976.633 + 449.44 + 159.0 + 50 = about 1,635 million DKK.

The discounted value of the net value of the social benefit, DVn, calculated at the beginning of 2011, is: -20 DVn,2010 = 140 ∙ [1 – 1.06 ] / 0.06 = about 1,606 million DKK.

The total social benefit of establishing the link, calculated at the beginning of the year 2011, is thus now:

DV2010 = 1,606 – 1,635 = -29 million DKK.

Calculated at the beginning of year 2010, the social benefit is: -1 DV2009 = -29 ∙ 1.06 = -27.4 million DKK.

If the project is delayed, there will thus be a social loss resulting from the implementation of the project.

Solution question 3

The discounted value of payments for the establishment of the link, DVe, calculated at the end of the year 2010 (= the beginning of the year 2011) now becomes: 3 2 1 DVe,2010 = 820 ∙ 1.05 + 400 ∙ 1.05 + 150 ∙ 1.05 + 50 = 949.253 + 441.0 + 157.5 + 50 = about 1,598 million DKK.

The discounted value of the net value of the social benefit, DVn, calculated at the beginning of 2011, is now: -20 DVn,2010 = 140 ∙ [1 – 1.05 ] / 0.05 = about 1,745 million DKK.

The total social benefit of establishing the link, calculated at the beginning of the year 2011, is thus now:

DV2010 = DVn,2010 - DVe,2010 = 1,745 – 1,598 = 147 million DKK.

Calculated at the beginning of year 2010, the social benefit is: -1 DV2009 = 147 ∙ 1.05 = 140 million DKK.

63 Solution: Energinet.dk

By using an interest rate of 6 % per annum in question 2, the social benefit is calculated as -27.4 million DKK, whereas by using an interest rate of 5 % per annum in this question, it is calculated as 140 million DKK. The social benefit of long-term public investment is therefore very dependent on the requirements for return on such investments.

Solution question 4 The gain from reduced market dominance amounts to 31 million DKK year. The

discounted value of this, DVm, calculated at the beginning of 2010 is: -20 DVm,2009 = 31 ∙ [1 – 1.06 ] / 0.06 = about 356 million DKK.

In question 1, it was calculated that the total discounted value of the project at the beginning of the year 2010 is 111 million DKK. If DVm,2009 is reduced by this amount, i.e. if DVm,2009 is only 356 – 111 = 245 million DKK., then the NPV of the project = 0 DKK.

If the project is to have a positive discounted value , then the value of the annual reduction in market dominance must therefore be at least:

31 ∙ 245 / 356 = about 21 million DKK. If the value of the annual reduction in market dominance is 10 million DKK lower than the estimated 31 million DKK, then there will not be a social benefit resulting from the implementation of the project.

64 Solution: Energistyrelsen

Investing in a heat pump system

Solution Question 1 The proposed heat pump system produces 5½ MW of thermal power. The heat pump is running around the clock for 360 days a year, thus producing: 5½ ∙ 24 ∙ 360 = 47,520 MWh/year.

Operation of the heat pump with a COP of 4 requires a power consumption of: 47,520/4 = 11,880 MWh/year.

The cost of electricity, UE, will then be: 3 UE = 11,880 ∙ 1.10 ∙ 10 = 13,068,000 DKK/year.

Total operating expenses, UD, then become:

UD = 13,068,000 + approx. 2 million ≈ 15 million DKK/year.

Solution Question 2

With a price of 337 DKK/MWh, there is thus obtained an income, IV, from the sale of heat to the district heating network of:

IV = 47,520 ∙ 337 = 16,014,240 DKK/year ≈ 16 million DKK/year.

The investment entails the following cash expenditures: • I = plant investment = 15 million DKK

• UD = operational costs = 15 million DKK/year.

The investment entails the following cash receipts:

• IV = cash receipts from the sale of heat = 16 million DKK/year.

• IE&V = savings on electricity and water = 2 million DKK/year.

The annual income annuity, ai, is then: ai = IV + IE&V - UD = 16 + 2 – 15 = 3 million DKK/year.

65 Solution: Energistyrelsen

The investment is written for a constant payout annuity over 15 years: -15 au = 15,000,000 ∙ [0.08/(1 – (1 + 0.08) )] = 1,752,443 DKK/year ≈ 1.75 million DKK/ year.

For the annual net cash flow, a, we get: a = ai – au = 3.00 – 1.75 =1.25 million DKK > 0, which is why the investment is profitable.

Solution Question 3 The investment’s net present value, NPV, can now be calculated as the present value of the annuity, a: NPV = 1.25 ∙ [(1 – (1 + 0.08)-15)/0.08] = 10.7 million DKK.

Control: If the net present value is calculated using the capital value method, the same result should be obtained: -15 NPV = -I + ai ∙ [(1 – (1 + 0.08) )/0.08] = -15 + 25.7 = 10,7 million DKK.

Solution Question 4 The dynamic payback period is the time that will pass before the sum of the discounted net cash flow, ∑NBx years, is equal to the amount of investment.

-6 ∑NB6 years = 3 ∙ [(1 – (1 + 0.08) )/0.08] = 13.8 -7 ∑NB7 years = 3 ∙ [(1 – (1 + 0.08) )/0.08] = 15.6

This shows that the present value of net cash flow after 6 years is 13.8 million DKK, and after 7 years is 15.6 million DKK, which is slightly more than the amount invested. The dynamic payback period is thus a little less than 7 years.

Solution Question 5 The price of electricity is now assumed to be reduced by 1.10 - 0.85 = 0.25 DKK per kWh. This will mean a reduction in the company’s cost of electricity of 11,880 ∙ 0.25 ∙ 103 = 2,970,000 million DKK per year ≈ 3 million DKK per year.

The net annual net cash flow, a, of 1.25 million DKK calculated in Question 2 will thus be increased to 1.25 + 3 = 4.25 million DKK. The profitability of the investment in the heat pump system is thus extremely sensitive to developments in the price of electricity.

66 Solution: Energistyrelsen

The dynamic payback period for the new annual net cash flow is now calculated to be: -4 ∑NB4 years = 4.25 ∙ [(1 – (1 + 0.08) )/0.08] = 13.9 -5 ∑NB5 years = 4.25 ∙ [(1 – (1 + 0.08) )/0.08] = 16.8

The dynamic payback period is thus now between 4 and 5 years.

67 Solution: H. Lundbeck A/S

Insourcing – Made Possible by the Reduction of Production Costs

Solution question 1 Currently, 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 of ampoules 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 2 It 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 capital costs 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.

68 Solution: H. Lundbeck A/S

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 cal culated 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 3

The 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 4 The 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 packaging 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 -1.00 -0.55 -0.27 0.54 1.75 2.30 2.91 insourcing

69 Solution: H. Lundbeck A/S

The future value of the savings, FV2012, calculated at the end of 2011, is: 6 5 4 2 FV2012 = -1.00∙1.10 – 0.55∙1.10 – 0.27∙1.10 + 0.54∙1.103 + 1.75∙1.10 + 2.30∙1.10 + 2.91

FV2012 = -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 implementation 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.

70 Solution: Haldor Topsøe A/S

Economic assessments about a new product

Solution Question 1 The annual production of the refinery is: 30,000 · 365 = 10,950,000 barrels.

By using the TK-new, the annual volume of LCO can be increased by: (0.292 – 0.250) · 10,950,000 = 459,900 barrels.

The added value of this annual additional production of LCO is: 60 · 459,900 = 2,759,400 DKK.

Since the lifetime of the catalyst is 2.5 years, it should be expected that the refinery would pay a maximum of: 2.5 · 2,759,400 = 6,898,500 DKK for the 110 tons of TK-new, that is, a maximum additional charge for TK-new of: 6,898,500/110 = 62,714 DKK/ton TK-new.

For an additional price of 62,714 DKK/ton TK-new, the refinery - apart from the stated assumptions - will not have a financial incentive to switch from TK to TK- new. The price of TK-new should therefore probably be set so the additional price is lower.

Solution Question 2 If development costs in each of the three years is attributable to the year-end, the net present value of the project after three years of development time, that is, at the beginning of year 1: 1 2 V0 = -3.5 – 3.5 · 1.20 – 3.5 · 1.20 = -3.5 – 4.2 – 5.04 = -12.74 million DKK

71 Solution: Haldor Topsøe A/S

In year 1, the expected earned gross profit is:

GP1 = 400 · 30,000 – 200,000 = 11.8 million DKK

Attributing this to the year-end, the net present value of the project by the end of year 1 is: 1 V1 = -12.74 · 1.20 + 11.8 = -15.288 + 11.8 = -3.488 million DKK

In year 2, the expected earned gross profit is:

GP2 = 700 · 30,000 – 200,000 = 20.8 million DKK

Attributing this to the year-end, the net present value of the project by the end of year 2 is: 1 V2 = -3.488 · 1.20 + 20.8 = -4.1856 + 20.8 = about 16.6 million DKK

It is thus seen that the project, with the expected sales figures, is already repaid at the beginning of year 2, assuming that it had not had been possible to sell TK as an alternative.

Solution Question 3 In Question 2, the net present value of the development costs is estimated to be:

V0 = -12.74 million DKK

Designated as the additional gross profit from TK-new, x DKK/ton, gives the expected gross profit earned in the first three years:

GP1 = 400 · x – 200,000

GP2 = 700 · x – 200,000

GP3 = 2,400 · x – 200,000

The discounted value calculated to the end of year 3 is then: 6 3 2 1 V3 = -12.74 · 10 · 1.20 + (400 · x – 200,000) · 1.20 + (700 · x – 200,000) · 1.20 + 2,400 · x – 200,000

6 V3 = -22.015 · 10 + 576 · x – 288,000 + 840 · x – 240,000 + 2,400 · x – 200,000

If the project is to be repaid after 3 years, then V3 should = 0. This means that: 3,816 · x = 22,743 · 106

This gives: x = 5,960 DKK/ton.

72 Solution: Haldor Topsøe A/S

If TK-new does not contribute to increased sales, then the gross profit for TK-new should thus be 5,960 DKK/ton higher than for TK for the project to have a payback period of 3 years.

The assumptions behind Question 2 (TK could not be sold in the five years) can be perceived as very pessimistic. In contrast, the assumptions behind Question 3 (that TK could alternatively achieve the same sales figures as TK-new) can be perceived as very favorable. The reality would probably lie somewhere in between these two extremes.

One problem with the assessment of profitability in developing new technology is that it cannot - as in the above - be made from short-term, partial considerations alone. Such calculations can help to illustrate profitability, but a company’s focus on new development projects are to a greater extent based more on long-term strategic decisions.

73 Solution: hofor a/S

Heat pumps for generating district heat

Solution Question 1

Based on the price curve in Fig. 1, the average market price, pG, on Nord Pool is expected to be: pG = [(06-00) ∙ 0.09 + (22-06) ∙ 0.48 + (24-22) ∙ 0.09] / 24 = [0.54 + 7.68 + 0.18] / 24 = 0.35 DKK/kWh.

Solution Question 2 The expected annual energy demand: Residences: 90 ∙ 0.5 ∙ 6,000 ∙ 23 = 6,210,000 kWh/year ≈ 6.21 GWh/year Offices, etc.: 90 ∙ 0.5 ∙ 6,000 ∙ 15 = 4,050,000 kWh/year ≈ 4.05 GWh/year Total: 0.26 GWh/year

Solution Question 3

The heat pump HPb is expected to produce 6 GWh/year. With a COP = 3.0, the electricity used for heat pump operation = 6/3.0 = 2 GWh/year.

The heat pump HPa must cover the remaining heat demand, i.e. produce 10.26 – 6 = 4.26 GWh/year. With a COP = 2.8, the electricity needed to operate the heat pump

HPa = 4.26/2.8 ≈ 1.52 GWh/year.

The total electricity consumption for operation of the two heat pumps = 2.00 + 1.52 = 3.52 GWh/year. With the calculated (in Question 1) electricity price of 0.35 per kWh + 0.80 per kWh for taxes, etc., the cost, Ce, for electricity is: 6 Ce = 3.52 ∙ 10 ∙ (0.35 + 0.80) = 4,048,000 DKK/year ≈ 4.05 million DKK/year.

Solution Question 4 The investment, I, in the two heat pumps = 10 + 15 = 25 million DKK. Rewriting this investment as an annuity, aI, over 25 years, yields: -25 aI = 25 ∙ 0.06/(1 – 1.06 ) = 1.96 million DKK/year.

74 Solution: hofor a/S

Table 1 shows that the expected annual costs for operation and maintenance, CO&M, are:

CO&M = 0.1 + 0.2 = 0.3 million DKK/year

For the average total costs over the 25 years, C, we now get:

C = Ce + aI + CO&M = 4.05 + 1.96 + 0.30 = 6.31 million DKK/year

For the total cost of delivered kWh of heat, CkWh, we get:

CkWh = 6.31/10.26 = 0.62 DKK/kWh

Solution Question 5 The cost of option 2 must be reduced by at least 0.62 – 0.60 = 0.02 DKK/kWh, if this option is to have the lowest cost. With a total energy consumption of 10.26 GWh/ year, such a reduction requires a reduction in annual costs of 10,260,000 ∙ 0.02 ≈ 205,200 DKK/year.

Assuming that the calculated (in Question 4) costs for electricity, Ce, and for operation and maintenance, CO&M do not change, then the annuity for the investment in the two heat pumps, aI, must be reduced by at least 205,200 DKK/year. In Question

4, aI is calculated to be 1.96 million DKK/year. For the cost reduction to be achieved, then the investment in the two heat pumps must thus be reduced by ΔI: ∆I = (0.205200/1.96) ∙ 100 ≈ 10 %.

The total investment in the heat pumps must only be 10 % less for the two options to be economically equal. It should be noted that HOFOR not only evaluates investments based on economic considerations, but also based on the emission of green- house gases such as CO2 and air pollutants such as SO2 and NOx. If two alternatives are largely economically equal, the difference in emissions can therefore be decisive in HOFOR’s choice.

P.S. Note that this case has been developed specifically for this assignment, and the data are therefore not actual values.

75 Solution: MT Højgaard A/S

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

Solution question 1 In 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).

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 0.25 0.50 1.00 5) Project result 5,000 5,000 10,000 Accumulated financial statement Year 1 Year 2 Year 3 6) Posted costs 20,000 40,000 80,000 7) Project result 5,000 10,000 20,000

76 Solution: MT Højgaard A/S

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 2 The 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 3 By 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.

77 Solution: MT Højgaard A/S

Expectations per year Year 1 Year 2 Year 3 1) Total revenue 100,000 100,000 100,000 2) Total project result 20,000 10,000 -5,000 Interim financial statement for Year 1 Year 2 Year 3 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 Accumulated financial statement Year 1 Year 2 Year 3 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, followed 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 accommodated 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.

78 Solution: nnit a/S

Financial considerations in an IT company

Solution question 1 With 2,500 employees, this amounts to 2,500 ∙ 0.97 = 2,425 FTEs. On average, 2 % of those are on maternity leave, and only 70 % of the number of FTE hours worked can be billed. With a working time of 160 hours per month, we get: Number of billable hours per month = 2,425 ∙ 0.98 ∙ 0.70 ∙ 160 = 266,168 hours/month.

From this, we get: P1 = 266,168/2,425 = 110 billable hours per month per FTE

Solution Question 2 Since all costs are assumed to be fixed, then the optimal hourly rate is that which results in maximum revenue.

Inserted into the equation for the monthly revenue per FTE, we obtain for NNIT’s total revenue per month: Revenue/month = R = (P1 ∙ P3 – 0.0005 ∙ P1 ∙ P32 + P1 ∙ 300) ∙ FTE

The optimal hourly rate can be found by the differentiation: dR/dP3 = P1 – 0.0005 ∙ P1 ∙ 2 ∙ P3 = 0

From this, we determine the optimal hourly rate to be:

P3opt = 1.000 DKK/hour

Inserting this hourly rate, as well as the values for the other parameters, into the equation for revenue per month, R, gives: R = (110 ∙ 1,000 – 0.0005 ∙ 110 ∙ 1,0002 + 110 ∙ 300) ∙ 2,425 = (110,000 – 55,000 + 33,000) ∙ 2,425

79 Solution: nnit a/S

R = 88,000 ∙ 2,425 = 213,400,000 DKK/month.

The annual revenue, Ry, is thus:

Ry = 213,400,000 ∙ 12 = 2,560,800,000 DKK/year

Solution Question 3 The billing rate in China is at 280 CNY per hour, corresponding to 280/0.70 = 400 DKK/hour. To cover the fixed costs of 44.2 million DKK/year with an hourly rate of 100 DKK, there should be billed 44,200,000/(400 – 100) = 147,333 hours/year.

The number of billable FTEs in China is 250 ∙ 0.97 = 242.5

In China, there should therefore be billed: (147,333/242.5)/12 = 51 hours/month per FTE.

Since there are currently billed only 50 hours/month per FTE, the China office is not positively contributing to NNIT’s bottom line.

Solution Question 4 The answer to Question 3 shows that the China office currently does not positively contribute to NNIT’s bottom line, which could indicate that the office should be abolished. There are many other factors, however, that should be evaluated before making such a decision. The following are a few examples that can hopefully provide inspiration for further discussion.

Examples of arguments for maintaining the China office could include: • It ought to be possible to increase the billing rate significantly, so the office becomes profitable. • China is a large and growing market, where NNIT could have a very high revenue in the long term. • NNIT’s Danish division could possibly outsource IT work to the China office, where the hourly wage is much lower than in Denmark. They could also possibly exploit the fact that working hours are time-shifted, so in practice it could act as two shifts. • Many Danish companies are setting up production in China, and for these companies, the China office could exploit the fact that NNIT is a known and reputable company.

80 Solution: nnit a/S

Examples of arguments for abolishing the China office could include: • The office will need to become much larger before it obtains sufficient capacity and expertise to become competitive in the Chinese market. • It will burden NNIT in Denmark if leaders and experts need to be transferred to the China office.

81 Solution: A/S Storebælt

Annuities with Different Payment-Interval Lengths

Solution question 1 Type A: General inspection of concrete: Inspection time: 1.75 ∙ 128 = 224 hours Crossing of bridge pilings: 2 ∙ 126 = 252 hours Payroll costs: (224 + 252) ∙ (3 ∙ 600 + 2 ∙ 300) = 1.142.400 DKK Moving of platform = 250,000 DKK Total costs = 1,142,400 + 250,000 = 1,392,400 DKK

Routine inspection of concrete: Inspection time: 0.7 ∙ 128 = 89,6 hours Crossing of bridge pilings: 2 ∙ 126 = 252 hours Payroll costs: (89.6 + 252) ∙ (3 ∙ 600 + 2 ∙ 300) = 819.840 DKK Moving of platform = 250,000 DKK Total costs = 819,840 + 250,000 = 1,069,840 DKK

Inspection of bridge bearings: Inspection time: 1.5 ∙ 126 = 189 hours Crossing of bridge pilings: 2 ∙ 126 = 252 hours Payroll costs: (189 + 252) ∙ (1 ∙ 600 + 2 ∙ 300) = 529,200 DKK/year Moving of platform = 250,000 DKK Total costs = 529,200 + 250,000 = 779,200 DKK

Type B: General inspection of concrete: Inspection time: 2.50 ∙ 128 = 320 hours Crossing of bridge pilings: 0 ∙ 126 = 0 hours Payroll costs: 320 ∙ (2 ∙ 600 + 2 ∙ 300) = 576,000 DKK

82 Solution: A/S Storebælt

Routine inspection of concrete: Inspection time: 1.0 ∙ 128 = 128 hours Crossing of bridge pilings: 0 ∙ 126 = 0 hours Payroll costs: 128 ∙ (2 ∙ 600 + 2 ∙ 300) = 230,400 DKK

Inspection of bridge bearings: Inspection time: 1.5 ∙ 126 = 189 hours Crossing of bridge pilings: 0 ∙ 126 = 0 hours Payroll costs: 189 ∙ (1 ∙ 600 + 2 ∙ 300) = 226,800 DKK/year

Solution question 2 Every 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: • 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 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: The costs of 1,392,400 DKK for the general inspection every 6th year are composed of 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 for 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 are composed of 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 for the inspection of the concrete can be described by the two annuities:

83 Solution: A/S Storebælt

• 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 3

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

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

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

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

Solution question 4 The 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: -25 PVA,I = -25,000,000 – 7,000,000 ∙ 1.07 = -26,289,744 DKK

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 payments years of the annuity with payments every 6 years is 8: -25 -8 PVA,C = -1,069,840 ∙ (1 – 1.1449 )/0.1449 – 322,560 ∙ (1- 1.5007 )/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: -50 PVA,B = -779,200 ∙ (1 – 1.07 )/0.07 = -10,753,542 DKK

84 Solution: A/S Storebælt

The costs for maintenance, CA,M, are:

CA,M = 18,000,000 ∙ 0.015 + 7,000,000 ∙ 0.025 = 270,000 + 175,000 = 445,000 DKK/ year.

The present value of this, PVA,M, is: -50 PVA,M = -445,000 ∙ (1 – 1.07 )/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: -25 PVB,I = -30,000,000 – 10,000,000 ∙ 1.07 = -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 payments years of the annuity with payments every 6 years is 8: -25 -8 PVB,C = -230,400 ∙ (1 – 1.1449 )/0.1449 – 345,600 ∙ (1- 1.5007 )/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: -25 PVB,B = -226,800 ∙ (1 – 1.07 )/0.07 = -2,643,033 DKK

The costs for 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: -50 PVB,M = -450,000 ∙ (1 – 1.07 )/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.

85 Solution: Vejdirektoratet

Financial considerations regarding the construction of a highway

Solution question 1 Disbursements for design and construction have the following payment schedule:

2016 2017 2018 2019 Years

25 25

120 125

Fig. 1: Payment schedule for disbursements for design and construction.

The present value of the project at the beginning of 2019 can be found by forward discounting the amounts for the years 2016, 2017 and 2018, with 2½, 1½ and ½ years, respectively. The discount rate is 5 % per annum.

The present value of the project, PV2018, calculated at the end of 2018 (= beginning of 2019): 2,5 1,5 0,5 PV2018 = -25 ∙ 1.05 - 125 ∙ 1.05 - 120 ∙ 1.05 - 25

PV2018 = -28.2 – 134.5 - 123.0 - 25 = -310.7 million DKK.

Solution Question 2 Table 1 shows the present value at the end of the years 2018 to 2023: 2018 2019 2020 2021 2022 2023 Societal value 66 88 88 88 88 Present value, end of year -310.7 -260.2 -185.2 -106.5 -23.8 63.0

Table 1: The present value of the project, calculated at the end of 2018 to 2023.

86 Solution: Vejdirektoratet

Explanation of Table 1: • The societal value in the year 2019 is only 66 million DKK, because the road first opens on April 1, 2019, so there is only traffic on the road for three quarters of this year.

• The present value at the end of year x, PVx, is calculated by:

PVx = PVx-1 ∙ 1.05 + the year’s societal value.

It is seen from Table 1 that the present value becomes 0 in the year 2023. Calculated from the start of the project in 2016, the project’s payback period is therefore 7-8 years.

Solution Question 3

The present value on April 1, 2019, PV1. April 2019, can be calculated by forward

discounting the present value at the beginning of 2019, PV2018, with 1/4 years.

Since the annual discount rate is 5 %, the quarterly discount rate, i1/4 can be cal culated by: 4 (1 + i1/4) = 1.05.

From this, we get: i1/4 = 0.012 ≈ 1.2 % for each quarter.

From this, we get:

PV1. April 2019 = PV2018 ∙ (1 + 0.012) = -310.7 ∙ 1.012 = -314.4 mio. kr.

PS.: This Question is included only for educational purposes, since in practice it is irrelevant whether the project’s present value is calculated a quarter sooner or later.

Solution Question 4 The total road area amounts to 6 km at 2 ∙ 8 m width, corresponding to 96,000 m2.

With a cost of 70 DKK/m2, we thus obtain a disbursement of 70 ∙ 96,000 ≈ 6.72 million DKK every 15 years.

Disbursements for resurfacing every 15 years can be described by a constant annuity with 15 years between payments. The present value of this annuity can be calculated with a discount rate for 15 years, i15, that can be derived from: 15 1 + i15 = (1 + 0.05)

87 Solution: Vejdirektoratet

From this, we get: i15 = 1.08, which is 108 % for 15 years.

Assuming that the road’s lifespan is ∞, the present value of disbursements for replacement of the wear layer, PVs, is: -∞ PVs = -6.72 ∙ (1 – 2.08 )/1.08 = -6.22 million DKK.

This can be rewritten to a constant infinite annual annuity, sa : -∞ as = -6.22 ∙ [0.05/(1 – (1 – 1.05 ))] = -6.22 ∙ 0.05 = -0.311 million DKK/year.

Since the societal value is assessed to be 88 million DKK per year, the average annual disbursement for the resurfacing of 0.311 million DKK has only a very small impact on the profitability of the project.

88 Solution: Velux A/S

Calculations with the Introduction of New Technology for Windows

Solution question 1 Rewriting the investment of 10 million DKK 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 2 Calculation for a window with the new coating: Materials: 815 DKK 55.9 % Salary: 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 for production, sales, and marketing comes to 1,385 DKK. Since the profit must be 5 % of the selling price, it must be 1,385 / 0.95 = 1,458 DKK per window. The profit is hereby 1,458-1,385 = 73 DKK per window.

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

89 Solution: Velux A/S

Solution question 3 The profitability of investments resulting in changes in the costs and selling price cannot be judged by how the profit margin in a full-cost calculation changes.

Solution question 4 The general criterion for an investment to be profitable is that its net present value must be ≥ 0 DKK. The investment of 10 million DKK in the new technology results in: • An increase in salary costs of 12 DKK per window • An increase in material costs of 15 DKK per window • An increase in the selling 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.

The investment’s net present value, NPV, thus becomes: NPV = -10,000,000 + 3,600,000 ∙ (1 – 1.07-5)/0.07 = 4,760,710 DKK

Solution question 5 If 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 selling price of a window must be increased by a minimum of 12.19 + 12 + 15 = approximately 39 DKK, if the investment in the new technology is to be profitable.