   #### Estimate    Estimate - 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, 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 activities 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 required. 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. Although we use years in this discussion, any time interval can be used.

The add-in offers two options for cost estimation: with time and without time. The with time option estimates the cash flow in each year over the analysis period, usually the life of the system. The without time option constructs a form to estimate unit cost as a function of production volume. We illustrate the without time option on another page.

Example

To illustrate, we consider again the assembly line design project described in the capital budgeting page. 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. 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 and time is also limited. The materials and resources are listed by name for the example in the table on the left. Each product uses different amounts of materials and resources. These are shown in the columns labeled units/item. The word unit refers to a unit of raw material, and the word item refers to a single finished item. The table on the right shows the costs per unit for the materials and resources. The table at the bottom shows the revenue per finished item for the products as well as the product mix. The latter is the proportion of the total production devoted to each product.

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

The markets 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 few years and then decline. On this page we use this example to estimate the life-cycle cost of the assembly-line system. We use the capital cost computed earlier, but assume 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.

To create a life-cycle cost worksheet, choose Add Estimate from the menu, and fill out the dialog as below. With only product A, this example has 17 items and four levels of detail in the CBS. Clicking the Life-Cycle button creates the CBS rather than the WBS. For the example we include six time periods. The data for the CBS is similar to the WBS, except in a few details. The structure 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 segment between cost and revenue. Items 3 through 14 are costs, while item 15 is 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, columns G through H in the worksheet, hold numbers that compute the total number of units required for each item of finished good. Usually 1 is used for N1. N2 is the number of level 2 items used for each level 1 item, N3 is the number of level 3 items used in the level 2 item, and so on.

For the present case our data specifies the number of units per item directly and that is entered in column N4. For example, we see that for each item of product 1, 0.63 Board 1 components are required.

The Units/Item column, column K, holds the product of the number columns. The number columns are useful for describing the product structure. We illustrate an interesting case in the Automobile example on another page.

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 amount produced and a variable cost. These are entered in columns L and M respectively. The item cost, computed in column O, is the variable cost multiplied by the number of units per item, so it is the variable cost per unit of production of the system.

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 to compute the total labor cost or any other quantity that might be relevant to the estimation. The subtotal column is not used for other computations on the worksheet unless the subtotals are used explicitly in formulas expressing other data on the worksheet.

In the example, overhead item, 14, is 40% of the labor cost, item 13. Since this is the only labor item on the CBS, the overhead is included as a separate item and the subtotal column is not used.

The Quantity entry in cell H11 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.

Time

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 picture to open a larger version of the cost/time table. The model used for the cost contribution of item i in year k is shown below. The cost/time table describes 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. Although we see mostly 1's in this matrix, 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 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 is indicated by the multipliers.

The other columns are for the 6 years of the product's life. 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 amounts and cash flows for the example. We see that except for time 0, there is a profit for each year in the life. 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 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 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.

Summarize

Two buttons are placed on the life-cycle cost worksheet. One allows the number of items to changed. The second creates a summary form that computes the NPW for each set of items having the same level 2 designation. For the example, the summary shows the breakdown between operating cost, revenue and installation cost. Again since we are using zero 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 Three Product Example

The example has three products: A, B and C. 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. Note that we show the product mix in the N2 column. An item in this case is one unit of product. The figure below adds time to the analysis. The cash flow values are taken from the bottom of the chart.

 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 the total profit is greater than with only one. The flexible data structure the Estimate add-in can be used to estimate the life-cycle cost for a variety of situations.  Operations Management / Industrial Engineering
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by Paul A. Jensen    