LifeCycle
Costs
The lifecycle 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 lifecycle
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 addin. This addin 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 lifecycle cost using the Estimate addin.

Given the product sales for each year in the life cycle,
estimate the cash flow for a system.




Text 

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.


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 lifecycle cost of the assemblyline 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 addin. 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.




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 addin
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.
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. 

LifeCycle Cost 

To obtain the lifecycle 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.
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 addin 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.
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.


Estimate Addin 

The Estimate addin provides the tool for building a CBS and using
it to compute the lifecycle cash flows for a project. You should
learn how to use this addin. Click the icon for instructions.


Summary 


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