Life-Cycle Costs

The life-cycle cost, LCC, is the sum of all expenditures less receipts from origination of the project to disposal of the system. In additional to the capital costs considered in the last lesson, the LCC includes the operating costs and revenues for each year of the life cycle as well as the disposal cost. When an interest rate is defined, the LCC is the net present worth rather than the sum.

For this analysis we need a new structural definition, the cost breakdown structure or CBS. This structure is similar to the WBS in that it uses a numerical classification system. Rather than enumerate the tasks in a project, however, this structure enumerates the cost and revenue components of the life-cycle cost.

There are two problems associated with LCC. The first is estimating the annual operating cost and revenue. For systems with some complexity, this is not a small problem since there are usually a great number of parts associated with a typical product and a corresponding large number of individual estimates necessary. The second problem is estimating the variation of these costs (and revenues if appropriate) over time. The life of a typical life cycle may be several years and the factors that affect cost estimates may well change over time.

The figures on this page were developed with the Estimate add-in. This add-in will be useful for solving the small problems related to this course and also larger problems that arise in practice.

 Goals
 Be able to construct a CBS for a simple system. Compute item costs and revenues based on a given CBS and the fixed and variable costs. Be able to estimate the life-cycle cost using the Estimate add-in. Given the product sales for each year in the life cycle, estimate the cash flow for a system.
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We referred to Chapter 4 in the last lesson, but review it again for its discussion of the CBS.

 4.4 Developing the LCC Model
 Cost Terminology

In the examples throughout this course we use economic terminology that is common but may not be familiar to the student. The following link opens a document that defines some terms used in this lesson.

 Cost Terms
 Example

To illustrate, we consider again the assembly line design project described in the capital cost lesson. Here we describe the products that the assembly line will produce once installation is complete. The line produces three products: A, B and C. The characteristics of the products are shown in the tables below. Manufacturing the products uses materials and resources. Materials include the parts and supplies that go into the product. Resources describe the machines and labor that are used for production. Materials must be replenished after use. Resources use time, which is limited in amount for a specified duration. The materials and resources are listed by name for the example in the table on the left. We use the term component to represent either a material or resource. Thus a product will consist of a collection of various components. We use the term product to refer to a single individual finished product.

Each product uses different amounts of each component. These are shown in the columns labeled units. The numbers in this table show the amount or number of components required for a single finished product. The table on the right shows the costs per unit for the components. The table at the bottom left shows the revenue obtained when a finished product is sold, as well as the product mix. The latter is the proportion of the total production devoted to each product.

Component units may not be measured using the same dimensions. For example, resource usage is typically measured in a time dimension such as hours, while material usage is typically measured in quantity dimensions such as pounds or part count. The cost for the first board type, for example, is \$20/board, while the cost for labor is \$20/hour. To compute the cost for a component we multiply the number of units by cost/unit so the dimension of the measurement cancels out. It is important that the dimensions be consistent. The result of the multiplication is the cost of the component for a single finished product.

The demand for the products are expected to last six years. The anticipated annual sales for all three products are in the table below. We see that production is expected to grow in the first three years and then decline.

In this lesson we use this example to estimate the life-cycle cost of the assembly-line system. We use the capital cost computed earlier, but assume that the disposal or salvage value of the line is zero. We first analyze a single product, A, to keep the example small, but then we consider all three products.

 Cost Breakdown Structure

To illustrate the CBS, we consider a simpler case consisting only of the first product, A. Click on the icon to see the structure created by the CBS option of the Estimate add-in. We call the individual rows of the form items of which there are 17 (including one called "Finish" at the end). Items is a generic term that includes the individual components, aggregations of components, overhead costs, revenues for the products sold, and in this case, the installation cost of the line.

 1-Product CBS

The CBS identifies levels of the product structure. The system is assigned to level 1 with the index 1. We use level 2 for the product definition and to distinguish between cost and revenue. Items 3 through 14 are costs, while item 15 is the revenue from sales (entered as a negative cost). Level 3 is used to divide the cost components into material, resources and overhead. Level 4 identifies the individual cost elements. Each line in the CBS is unique with respect to the indices assigned to the levels. Item 16 holds the installation cost computed on the capital budgeting page.

The columns N1 through N4 hold values that are used to compute the total number of units required for each finished product. Usually 1 is used for N1. N2 is the number of level 2 units used for each level 1 unit, N3 is the number of level 3 units used in the level 2 item, and so on.

The Units column holds the product of the number columns; i.e., N1*N2*N3*N4. For a particular item it is the number of units of that item for each unit of product described by the CBS. The number columns are useful for describing the product structure. We illustrate an interesting case in the Automobile example in the next lesson.

For the current case, our data specifies the number of units directly, which is entered in column N4. For example, we see that for each product A, 0.63 Board 1 components are required. The example was construct by the Process add-in and the fractional numbers are due to scrap and discarded material.

The cost of production for a given period depends on the production volume of the product. The model includes a fixed cost that is independent of the volume and a variable cost. The item cost is the variable cost multiplied by the number of units for the item. It is the variable cost contribution of an item to a single unit of the product described by the CBS.

Sometimes the variable cost of some item depends on the costs of several other items. For example, it is common for the overhead cost to be a percentage of total labor costs. We include the subtotal column (Sub Total) to compute the total labor cost or any other quantity that might be relevant to the estimation. In the example, overhead item 14 is 40% of the labor cost, item 13 (that is, overhead = 40% * labor cost = 0.4*0.375 = 0.15). Since this is the only labor item on the CBS, it is unnecessary to use the subtotal column.

The Quantity entry at the top of the figure is useful when the estimate is to be for a production lot of an integer number of finished items. Here we use the default value of 1. When it is not 1, the variable cost in column M is the cost to produce the amount specified by the Quantity value.

As indicated at the beginning of the page, the assembly line can produce three products. The CBS for this case lists the costs and revenues for all three products. Click on the icon to see the CBS in a separate window.

 3-Product CBS

We have included the product mix in the column for N2. Because we are producing three products on the same assembly line, they must share the line. Our assumption here is that the total production volume is divided with 10% devoted to A, 40% to B, and 50% to C.

 Life-Cycle Cost

To obtain the life-cycle cost we construct a table that has a column for each year of the life cycle and also a column for time 0. An entry in the table is a multiplier that indicates how much a particular item contributes to the cost for that year. We compute the cash flow for the years of the life cycle with this table. Click the icon to open the figure that shows the cost/time table for product A.

 1-Product LCC

The model used for the cost contribution of item i in year k is shown below. The cost/time table holds the multipliers. The fixed cost is in column L and the variable cost is column O. The result of the computation is not shown directly on the worksheet but is used to find the cash flow for each year and the NPW for each item. The add-in includes the quantity variable in these equations, but we have left it out to keeps things simple.

Although we see mostly 1's in the cost/time table, the coefficients can be altered to represent changes with time. For instance, if the costs are increasing with inflation, the numbers in the columns will grow as the year index increases.

A column is included for time 0. This is the start of the life cycle and any initial investments can be placed in this column. For the example we see a lone 1 for item 16, representing the capital cost of the assemply line. Although the capital cost is spread over several months as illustrated on the capital budgeting page, for this larger time horizon we usually place the capital cost at time 0. If, in fact, the capital cost spreads over several years, the contribution in each year would be indicated by the multipliers.

The other columns are for the 6 years of the life cycle. At the top of each year we see the production volume for that year. The data indicates that this quantity varies with time. The cash flow at the bottom of each column is found by summing the item contributions for the year.

The table below summarizes production volumes and cash flows for the example. We see that except for time 0, there is a profit (indicated by the red text) in each of the 6 years. This cash flow is typical for a profitable investment. The total cash flow indicates that this system does yield a profit over its life.

 Year Prod. Cash Flow 0 0 \$308,000 1 5,000 61,539 2 8,000 98,463 3 12,000 147,695 4 7,000 86,155 5 4,000 49,232 6 1,000 12,308 Total 37,000 147,392

The NPW column computes the present worth for each item. The present worth computation combines the individual cash flows into a single equivalent value at time 0. It depends on the discount (interest) rate that must be given. When the discount rate is 0, the NPW is simply the sum of the cash flows for an item. The formulas computing the quantities in the NPW column are below.

The NPW worth is used to evaluate the profitability of an investment. When the NPW is greater than 0, the rate of return for the investment is greater than the discount rate. When the NPW is less than 0, the rate of return for the investment is less than the discount rate. For this lesson we choose the interest rate to be zero. Then, NPW is the sum of the cash flow values.

For the example, the summary shows the breakdown between operating cost, revenue and installation cost. Again, since we are using 0 for the discount rate, the NPW values are the sums of the costs. The total cost estimate is shown at the right. Because the value is colored red, it is negative. This means that the assembly line yields a profit over its life.

The CBS for the full example lists the costs and revenues for all three products: A, B and C. Click on the icon to see the CBS and LCC computations in a separate window. Recall that the product mix is given in the N2 column. An item in this case is one unit of product.

 3-Product LCC

The following cash flow values, with the exception of the entries in the row labeled "Total," are taken from the bottom right of the Cost/Time table.

 Year Prod. Cash Flow 0 0 \$308,000 1 5,000 67,042 2 8,000 107,267 3 12,000 160,900 4 7,000 93,858 5 4,000 53,633 6 1,000 13,408 Total 37,000 188,109

The summary for this system is below. With three products being produced, the total profit is greater than with only one.