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Need for understanding Cost behavior:
Cost management
- 1) identify underlying activities that drive costs, require to control "cost creep" 2) need to know cost behavior for forecasting purposes
Pricing
-determine marginal cost for purposes of training
Risk Assessment
- understand how sensitive profits are to changes in sales
Typical cost behavior patterns
Variable
Fixed
Step
Mixed
Variable
cost that varies in direct proportion to changes in activity (unit of analysis): Straight diagonal line from (0,0)
Fixed
cost that does not vary over a wide range of activity (unit of analysis): horizontal line
Step
cost that is constant over discrete range of activity, then shifts to different level at some new activity level (unit of analysis): step up line
Mixed
cost that contains elements of fixed and variable costs: straight line diagonal up, above 0
Economies of scale
at low levels of activity, fixed resources, volume discounts and learning effects lead to costs increasing at a decreasing rate as output rises
Economies of scope
because of the reusability of some resources, additional products can be produced with cost savings by sharing resources. Thus, multiple products can be produced together at a lower cost than they can be produced separately
Congestion costs
at high levels of activity, congestion occurs, driving up costs at an increasing rate as output rises (diseconomies of
scale
)
Complexity
as firms get more complicated, costs go up to at an increasing rate (diseconomies of
scope
)
Cost Concept: maintained assumption in our cost estimation models
over a relevant range, costs are well-behaved and can be estimated as a mixed cost linear function
Relevant range
Curvy line middle
Resource Flexibility
engineered vs committed vs discretionary cost
Engineered Cost
distinct physical relationship to cost object
-Direct Materials
Committed Costs
necessary incurred costs for providing good/service. Related to capacity and other required support inputs
-machinery
-building
Discretionary Costs
Costs that can be delayed for short periods
-training
-advertising
-preventative maintenance
Periodicity Assumption
All costs are variable over a long enough time period. So cost behavior is related to time interval, as the period of time lengthens more costs become more variable. Examples of fixed costs that could be changed over longer time intervals
Sticky Costs
Firms are reluctant to cut costs when sales decline. Thus costs are sticky when sales fall
Pool of costs Key assumption
Pool of costs can be approximately by a mixed cost function
y=mx+b where m is variable cost per unit of x and b is fixed cost
Cost estimation techniques
1) Engineering/work measurement
2) Account analysis
3) Fitting the data
a) visual fit/scattergraph
b) high-low (use high and low activity points)
c) Simple regression (one explanatory variable)
d) Multiple regression (more explanatory variables- not covered)
Account Analysis
manager would go through the account line items and try to
intuitively
build a cost function.
Visual Fit/Scattergraph
-Draw a line through the data points
-The fixed cost estimate is where line meets the y axis
-Pick one other point on the line and note cost and activity
-Solve for slope as change in cost/change in activity. Slope is your VC estimate
High-Low
-Identify high and low activity data points
-Note costs and activity at both high and low activity data points
-Solve for slope as VC = change in cost/change in activity
-Solve for fixed cost at
high or low point
:
---- Fixed = Total Cost high - VC *Activity high
----Fixed = total Cost low - VC *Activity low
High-low
identify high and low activity data points. Maximize variation in X
Regression
-Conduct a least squares analysis of the data. This approach selects parameters a and b of the line, +BX that minimizes the squared prediction errors
-Minimize the sum of the sqared error terms
-Fixed costs are the A parameter and the variable cost per unit is the B parameter. X is activity for observation i, Y is total cost of i.
Costs and activities measured without error
Many times there are recording errors that impact the period of cost recognition or activities undertaken
Estimating a pool of costs that can be assumed to be a mixed cost over the relevant range that is driven by one activity variable
Cost are probably not strictly linear, and probably driven by many factors
Production technology is stable across time or units
Through time, production tech may change as more machinery is added, processes are rearranged and new investment in IT. Also, no learning is occurring that would change relation between inputs and outputs
Planned activity approximates actual activity
This is clearly a problem because we believe costly resources are set based on planned activity, not actual activity. This probably flattens the cost function.
Planned Output--> Resources --> Observed Costs
planned output drives resources (labor, supplies, capital) that drive costs. Planned output is what we expect to product in current period, and costs are set based on planned output.
However, we only observe actual output. We tend to estimate the link between actual output and costs. Some of those costs related more to planned output that actual output.
Actual Output --> Observed Costs
Attributes of a good cost model
1. Does the hypothesized causal relationship (x causes y) seem reasonable
2. Are the parameter estimates (fixed and variable cost per activity) consistent with your intuition
3. Does your model fit the existing data?
4. Does your model do a good job of predicting future costs
Multiple Regression
Conduct a least squares analysis of the data with 2 independent variables. This approach also selects parameters that minimizes the squared prediction errors.
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