Coming full circle by ali zuashkiani and andrew k.s. jardine Life cycle costing is becoming more popular as many organizations understand its role in making long-term optimal decisions. Buying the cheapest is losing attractiveness as more managers learn that the least expensive acquisition rarely coincides with the best value buy in the long run. Option evaluation Companies use life cycle cost analysis to determine the best option (new equipment, new building, etc). However, the meaning of the best depends on a company s objectives. It could mean minimizing the total life cycle costs of an asset or maximizing the asset s total life cycle benefits. The life cycle costs of an asset are the sum of the present values of all the expenditures it incurs and the risks to which it is exposed throughout its life cycle ( cradle to grave ). If the objective is minimizing costs, the best option will be minimum discounted life cycle costs. The example below provides clarification. A contractor requires specialized equipment for a period of three years. Given the costs and salvage values in Figure 1, which is the best alternative? Assume that the costs provided in Figure 1 are the only costs that differ from one asset to another. Without any other information, you might add up all the life cycle costs of each asset to determine which equipment yields minimum total costs. This approach results in Total life cycle costs of owning and operating equipment = purchase price + installation costs + the three operating costs - salvage value Based on the calculations, the best option is to purchase equipment A. This solution is based on the simplified assumption that the value of money does not change over time, a 44 Industrial Engineer
Life cycle costing shows how buying the cheapest equipment doesn t always pay off concept discussed more fully later in the article. Although this might be acceptable for decisions when cash flow is dispersed over a short period, perhaps a few months, it may be too simplistic when options under evaluation have monetary implications spread over a long period, such as years or decades. Time value of money Assume that you have deposited $100 in a bank. Your expectation is that after one year your deposit grows, or, in other words, produces interest. The expected interest depends on many factors such as the current economy, risk, inflation rate, value options Equipment Purchase Installation Operating Salvage Total life cycle costs of owning price ($) cost ($) cost ($) value ($) and operating equipment ($) A 5,000 100 100 100 100 3,000 2,400 B 3,000 100 200 300 400 1,500 2,500 C 6,000 100 50 80 100 3,500 2,830 Figure 1. Life cycle costs of three pieces of equipment. Note that costs are multiplied by 100. April 2010 45
coming full circle etc. If the bank s annual interest rate (usually represented as i) for your deposit is 10 percent, you may expect your deposit to be $100 + ($100 x 0.10) = $110 in one year. If you leave the money in the bank for one more year, you may expect to have 100 + (110 x 0.10) = $121. The associated cash flow is shown in Figure 2. The above calculation can be summarized as $100 x (1 + 0.10)2 = $121 Now assume we will have a payment of $121 to make two years from now. What is its value today (present value)? If we put $100 in a bank, after two years it will grow to $121, so the value of a payment of $121 two years from now is $100 in today s dollars. This is called the net present value of the $121 payment two years from now, assuming the annual discount rate is 10 percent. To find the net present value (NPV) of payment, the reverse calculation needs to be conducted: Calculating the optimum buy option Using the concept of time value of money, let us revisit the previous example. To solve life cycle costing problems, it is useful to draw a cash flow diagram for all alternatives, as this provides a better understanding of what is happening during the life cycle of options under evaluation. The cash flow diagram for equipment A is in Figure 3. In a cash flow diagram, the horizontal axis represents time, and the arrows represent monetary transactions that happen at each point in time. The direction of the arrows indicates with interest Figure 2: Time value of money check direction Figure 3. The cash flow diagram for equipment A whether a monetary transaction is a payment (outflow) or revenue (inflow). It does not matter which direction you choose as long as directionality remains consistent. In Figure 3, the positive direction (up) is reserved for payments (expenses) and the negative direction (down) is used for money received (revenues). Assuming an interest rate of i = 11 percent, the net present value of the cash flow diagram in Figure 3 would be: Continuing with the same calculation, we have NPV (selecting equipment B) = $2,721. Similarly, the NPV of purchasing and operating equipment C is $3,731. Based on the above results, the optimum purchase is equipment B. This shows that the optimum acquisition decision can change easily if the time value of money changes. In determining the best option, items that do not vary in cost from one option to another do not affect the decision, as those costs will be canceled out from the NPVs of all options under evaluation. The focus should be on measuring costs that vary from one option to another. Nevertheless, although costs that do not vary from one option to another do not affect the optimum buy decision, they need to be considered for budgeting purposes. Physical assets usually require similar cost items during their life cycle. Some are more visible at the time of the acquisition; others are less evident or more difficult to measure. A number of these are listed below in decreasing order of visibility: Purchasing price Installation Training Operation Maintenance Disposal Cost of lack of reliability Future development Design and development start before construction or purchase of the asset and sometimes continue throughout the life of the asset with ongoing improvement and modification projects. Maintenance costs are expected to be higher when equipment is new due to infant mortality-related faults in the asset, as well as lack of experience of operators and 46 Industrial Engineer
maintainers. Operation costs are expected to follow a similar pattern, but their pattern heavily depends on the type of the equipment. Lack of reliability costs represents operational and safety/environmental consequences of breakdowns, and this cost item is usually very difficult to measure at the time of asset acquisition. Economic life of an asset Assets occasionally are purchased for a fixed time period. If the planning interval (the interval during which the asset is needed) is much shorter than the normal life of the asset, the technique illustrated early in this article can be used to determine the most economical buy during the planning horizon. Assets are commonly purchased to serve for a relatively long period, often several times longer than the asset s normal life. When assets are new, their operation and maintenance costs (O&M costs) are usually low, and assets are more reliable. Over time, as assets age, O&M costs tend to increase. However, due to technological improvements, assets with better performance and lower O&M costs might enter the market. The rate at which technologically improved assets enter a market depends on the type of the industry and pace of technology improvements and innovation. In these situations, it is valid to ask When is the best time to replace the current asset? Or, in other terms, What is the economic life of the current asset? As an asset is used for a longer period, the annual capital cost (also known as ownership cost) spent on the asset decreases. In its simplest form, the ownership cost can be thought of as the purchase price of an asset minus its resale value at the time of replacement, divided by the replacement age. Organizations tend to use an asset as long as possible, thus reducing ownership cost per unit of time. Yet annual operational and keep or replace Figure 4: Economic life trade-off graph maintenance costs, cost of lost production due to equipment breakdowns, consumed energy and other costs tend to increase as assets age. The total cost of keeping and operating an asset is the summation of the two costs (one usually increasing and the other decreasing) and has a minimum point. The age at which the total cost function is minimized is called the economic life of the asset, summarized in Figure 4. Some cost items do not change as an asset ages and are therefore called fixed costs. As shown in the graph, fixed costs do not affect the economic life of an asset and can be discarded in the calculations. However, they need to be included when estimating budgetary requirements as they are part of total costs. Economic life of a steadily used asset Through use, equipment deteriorates. Deterioration manifests itself in higher O&M costs. As equipment incurs more O&M costs, there might be a time when replacing the aging equipment is justified economically. If the equipment is replaced at its economic age, the total discounted life cycle cost of the equipment is minimized. In this section, we assume that the old equipment is replaced with a similar piece of equipment, and the trend of O&M costs of the new asset is similar to that of the old asset. This assumption may be relaxed if the replacing asset has different life cycle costs; the difference in life cycle costs can be due to technological improvements or better maintenance and operation practice. For simplicity, we assume in the following that there is no time value of the money: A is the acquisition cost (purchasing price) of the capital equipment plus any expenses for installation. C i is operation and maintenance costs, loss of production due to equipment breakdowns, etc. in the i th period after equipment installation. Here C i is assumed to be paid at the end of the period, i = 1, 2,, n. For simplicity throughout this article, C i is called O&M costs; however, we know this goes beyond O&M costs to include other life cycle cost items mentioned above. S i is the resale value of the equipment at the end of the i th period of operation, i = 1, 2,, n. D is disposal cost, including any removal costs such as dismantling, cleaning, transportation or loss of production during the dismantling process. N is the age of the equipment when replaced. EAC(n) is called equivalent annual cost associated with replacements occurring at intervals of n periods. A cash flow diagram of life cycle costs of an asset replaced at age n is in Figure 5. The asset is bought and installed at time zero (present time). During the first year of operation, April 2010 47
coming full circle it incurs costs represented by C 1. We assume that the total cost incurred in one year is paid at the end of the year; this assumption does not hold true all the time and can change. Depending on circumstances, the location of C i can change from the end of the year to the beginning of the year, middle of the year or be spread evenly throughout the year. The net present value of the life cycle costs of the asset can be parametrically represented as the following, which we ll call Equation 1: Using the above formula, annual costs associated with replacing an asset after n years can be calculated easily. Changing n gives us EAC for different replacement policies. The value of n that minimizes EAC is called economic life of the asset. For a numeral example, let A = $45,000. The estimated O&M costs per year for the next five years would be as follows: Year 1 (C 1 ): $4,500 Year 2 (C 2 ): $9,000 Year 3 (C 3 ): $18,000 Year 4 (C 4 ): $27,000 Year 5 (C 5 ): $36,000 Application An energy company in South America wanted to buy four new combustion engines. The company wanted to know which of the two available engines had lower life cycle costs. It also was interested in learning the expected economic lives of the two engines. The first alternative (Engine A) had an initial purchasing and installation cost of $19 million. Both alternatives had anticipated annual O&M costs up to 15 years of age. After conducting life cycle analysis, the company discovered that the economic life of Engine A was 15 years. Actually, the planning horizon was 15 years, and at 15 years, the cost was still declining. Therefore, in the next 15 years there was no expectation that the engine would need a replacement. Figure 7(a) shows the trend in EAC associated with replacement ages ranging from one to 15 years. Based on available evidence (O&M cost data were obtained from the original equipment manufacturers and from some generic databases accessible to oil and gas manufacturers), the economic life was determined to be 15 years or more. In practice, after several years of operation, enough experience is developed among maintainers of equipment that their knowledge can be used to estimate future O&M costs of the assets they are working with. Engine A was specialized equipment, making it almost impossible to find a customer for a secondmonitoring change Figure 5. A cash flow diagram of life cycle costs of an asset replaced at age n sell at year 2 Figure 6: Total costs calculated for different replacement ages The estimated resale values over the next five years are: Year 1 (S 1 ): $30,000 Year 2 (S 2 ): $21,000 Year 3 (S 3 ): $12,000 Year 4 (S 4 ): $9,500 Year 5 (S 5 ): $7,500 With a disposal cost (D) of $3,000, using Equation 1, we have: EAC for year 1: ($45,000 + $4,500 + $3,000 - $30,000)/1 = $22,500 Repeating that calculation for the other four years gives us the following equivalent annual costs: EAC for year 2: $20,250 EAC for year 3: $22,500 EAC for year 4: $24,250 EAC for year 5: $27,000 As shown in Figure 6, the most economical decision is to replace the equipment when it reaches two years of age. 48 Industrial Engineer
hand engine; therefore, its salvage value was estimated as zero. The associated EAC with replacing Engine A after 15 years was determined to be $5.36 million. The alternate equipment, Engine B, had a purchasing and installation cost of $14.5 million. Like Engine A, estimated O&M costs were only available for its first 15 years of operation. Again, like Engine A, it was specialized equipment, so its salvage value was estimated as zero. Figure 7(b) shows the trend in EAC associated with replacement ages ranging from one to 15 years. The resulting optimum EAC was $ 3.17 million and occurred at age 15 years. Therefore, Engine B is a better choice; it would save the company $2.19 million per annum per engine. Since the company wanted four engines, the total annual savings would be $8.76 million. The savings over the life of the engine would going down Figure 7. (a) EAC trend for combustion Engine A be 15 multiplied by $8.76 million, a total of $131.4 million. Dealing with the problems of replacing capital equipment often involves significant uncertainties associated with future costs, interest rates and demands that will be placed on the equipment. However, the availability of specially designed software enables valuable sensitivity analyses. These what if analyses allow the engineer to examine the effect that various estimates of trade-in values, interest rates and other variables will have on replacement cycles. Since a high degree of confidence can be associated with final recommendations to senior management on an asset s economic life, the chances of obtaining approval for major capital expenditures generally increase significantly. Conclusion This article has described evidence-based life cycle costing analysis; this type of analysis processes both hard and soft evidence using proven mathematical modeling to produce optimum life cycle costing decisions. It is important to remember that life cycle costing is about making the best decision in light of available information. Life cycle costing is not aimed at making accurate and detailed evaluations, as this is too time consuming and costly. Instead, the focus is on collecting enough information at the right level of detail to underpin a decision in a cost-effective manner within a rigorous process. Seeking higher quality data is not the goal; rather, it is to show that a decision largely is insensitive to the vagaries of the available data. This type of approach to making decisions is increasingly acceptable to industry regulators and equity markets. d Ali Zuashkiani has many years of practical and theoretical expertise in optimizing maintenance decisions, or evidence-based asset management. He is the author of Expert Knowledge Based Reliability Models and the director of educational programs at the Centre for Maintenance Optimization and Reliability Engineering (C-MORE) at the University of Toronto. Andrew K.S. Jardine is director of the Centre for Maintenance Optimization and Reliability Engineering (C-MORE) and professor emeritus in the Department of Mechanical and Industrial Engineering at the University of Toronto. He wrote Maintenance, Replacement and Reliability, co-edited Maintenance Excellence: Optimizing Equipment Life Cycle Decisions and co-wrote Maintenance, Replacement & Reliability: Theory and Applications. (b) EAC trend for combustion Engine B April 2010 49
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