1. Identifying Cost Relationships High-Low Method
Principles of Cost Analysis and Management
The 21st Century Soldier Competencies are essential to ensure Soldiers and leaders are fully prepared to prevail in complex, uncertain environments. This lesson reinforces the following 21st Century Soldier Competencies:
Communication and Engagement (Oral, written, and negotiation)
Critical thinking, intergovernmental, and multinational competence
Tactical and Technical Competence
Throughout the lesson discussion seek opportunities to link the competencies with the lesson content through the student’s experiences.
Safety Requirements: In a training environment, leaders must perform a risk assessment in accordance with DA PAM , Risk Management. Leaders will complete a DD Form 2977 RISK MANAGEMENT WORKSHEET during the planning and completion of each task and sub-task by assessing mission, enemy, terrain and weather, troops and support available-time available and civil considerations, (METT-TC). Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the work/rest cycles and water replacement guidelines IAW TRADOC Regulation

2. How can we determine which costs are fixed and which are variable?
Introduction
How can we determine which costs are fixed and which are variable? We know that total cost increases as output increases, but some of our cost elements may be mixed, or even semi-variable. Utilities, for example are generally a mixed cost. There is a fixed component and a variable component in the utility bill itself. There is probably a fixed component in the usage as well: a certain amount of electricity is needed to keep the building habitable, and then as occupancy and productive output increases, more electricity is used. How do we determine the fixed and variable component of the utility cost?

3. Terminal Learning Objective
Task: Determine the Fixed and Variable Components of a Mixed Cost Using the High-Low Method
Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors
Standard: with at least 80% accuracy
Calculate fixed and variable cost components from mixed cost data
Describe High-low method
Task: Determine the Fixed and Variable Components of a Mixed Cost Using the High-Low Method
Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors
Standard: with at least 80% accuracy
Calculate fixed and variable cost components from mixed cost data
Describe High-low method

4. Need for High-Low Method
Fixed and variable components of cost are not always identifiable
This is especially true in service activities
Sometimes costs aren’t strictly fixed and variable but mixed or semi-variable
The High-Low Method permits further analysis by finding an approximate value for variable and fixed costs
Introduction
Fixed and variable components of cost are not always identifiable, as we described in our leadoff example.
This is especially true in service activities. It is generally more difficult to identify variable costs when the unit of output is not a tangible product.
Sometimes costs aren’t strictly fixed and variable but mixed or semi-variable. It is important to recognize that fact, especially when incremental cost is relevant to the decision. However, multivariate and semi-variable costs complicate analysis because they represent equations with multiple variables.
The High-Low Method permits further analysis by finding an approximate value for variable and fixed costs. By definition this cost will be an average. It’s important to understand the limitations of an average. It is useful when all units are homogeneous in nature because they simplify the equations and analysis. They are misleading when units of output are dissimilar. Before applying the High-Low method, it’s important to question whether the units are homogeneous.

5. High-Low Assumptions
The relationship between the cost at the highest level of output and the cost at the lowest level of output is linear
This linear relationship reasonably represents the relationship between costs at other levels of output
The change in cost from the highest level to the lowest level is due to the change in units from the highest level to the lowest:
Change in cost / change in units = VC/unit
Introduction
The relationship between the cost at the highest level of output and the lowest IS linear because any two points represent a linear relationship. We’ll see that on a graph in a minute.
A bigger assumption is that the linear relationship between the high and the low is representative of the relationship at other levels of output.
We also must assume that the change in cost from the highest to the lowest level is entirely due to the change in units. This is true if there is, indeed, a fixed component to the cost. The elements of cost that are truly fixed will not change as level of output changes.

6. High-Low Calculation Step 1: Calculate Variable Cost $/unit:
Change in cost / change in units or:
$ at high output – $ at low output
# Units at high output – # Units at low output
Step 2 Calculate Fixed Cost :
Total Cost – Variable Cost or:
$ high output – VC $/unit * # Units high output
Activity step 1 Describe High-low method
[Students will have the blank slide]

7. High-Low Calculation Step 1: Calculate Variable Cost $/unit:
Change in cost / change in units or:
$ at high output – $ at low output
# Units at high output – # Units at low output
Step 2 Calculate Fixed Cost :
Total Cost – Variable Cost or:
$ high output – VC $/unit * # Units high output
Activity step 1 Describe High-low method
Step 1: Calculate Variable Cost $/unit:
Change in cost / change in units or:
$ at high output – $ at low output
# Units at high output – # Units at low output
The change in cost between the highest and lowest levels of output is due to change in number of units of output.
$ at high output – $ at low output = the change in cost from highest output to lowest output
# Units at high output – # Units at low output = the change in units from highest output to lowest output

8. High-Low Calculation Step 1: Calculate Variable Cost $/unit:
Change in cost / change in units or:
$ at high output – $ at low output
# Units at high output – # Units at low output
Step 2 Calculate Fixed Cost :
Total Cost – Variable Cost or:
Total $ high output – (VC $/unit * # Units high output)
Activity step 1 Describe High-low method
Step 2 Calculate Fixed Cost :
Total Cost – Variable Cost or:
Total $ high output – (VC $/unit * # Units high output)
Once we know the variable cost per unit, we can work backward to calculate the fixed cost. We know that:
Total cost = Fixed cost + variable cost
So, Total cost – variable cost = fixed cost

9. High-Low Calculation
Step 3: Develop the cost expression for total cost:
Total cost = VC $/unit * # units + Fixed cost
This equation can be used for:
Planning for various levels of output
Break even analysis (Day 9)
Activity step 1 Describe High-low method
Step 3: Develop the mixed cost expression
VC $/unit * # units + Fixed cost

10. Check on Learning
In the High-Low method, the change in cost from the high level of output to the low level of output is assumed to be caused by…?
How is fixed cost calculated using the High-Low method?
In the High-Low method, the change in cost from the high level of output to the low level of output is assumed to be caused by…? The change in number of units
How is fixed cost calculated using the High-Low method? Total cost at high level minus variable cost at high level.

11. High-Low Example
The purchasing department shows the following activity for the last four months:
Month POs Processed Total Costs
Jan $2500
Feb
Mar
April
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The purchasing department shows the following activity for the last four months:
Month POs Processed Total Costs
Jan
Feb
Mar
April
Look at the pattern. As purchase orders processed increases, total costs increase. When purchase orders are 80, cost is $ At an output level of 100 purchase orders, cost is $ At 120 purchase orders, total cost is $3000.

12. High-Low Example
The manager of the purchasing department sees that total costs increase as Purchase Orders increase
However, he knows that the cost is not strictly variable
He would like to segregate the variable component of the cost from the fixed cost
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The manager of the purchasing department sees that total costs increase as Purchase Orders increase
However, he knows that the cost is not strictly variable
He would like to segregate the variable component of the cost from the fixed cost

13. Graph of Actual Costs Cost at 120 POs = $3000 Cost at 80 POs = $2200
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
This graph plots number of purchase orders against total cost. The X axis represents number of purchase orders. The range is from 80 to 100 purchase orders. Cost at 80 POs = $2200. Cost at 120 POs = $3000
Cost at 80 POs
= $2200
X-Axis represents number of Purchase Orders

14. Multiple Linear Relationships Exist
Essentially any two points on the graph represent a linear relationship
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
Multiple linear relationships are possible – essentially a line between any two points on the graph could be chosen. The dotted lines represent all of these options. Or, using regression analysis, the “least error” method, the line may not actually intersect any of the points. The solid gray line represents the regression line. It touches the highest level, but doesn’t intersect any of the other points on the graph.
X-Axis represents number of Purchase Orders

15. High-Low Relationship
High-Low Method assumes the relationship between highest point and lowest point is representative of the whole
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The High-Low method uses the simplifying assumption that the line between the highest and lowest point approximates variable cost. It gives a standardized protocol for segregating the fixed and variable components of cost, and it brings the calculation down to simple math. It seems to be a reasonable assumption in this particular case. It is actually very close to the regression trend line. And, it falls in between the other two data points, so that it is reasonable to accept this relationship as representative of the whole.
X-Axis represents number of Purchase Orders

16. Calculate Unit Variable Cost
Change in Cost / Change in Units = Total $ at high output – Total $ at low output # Units at high output – # Units at low output ($3000 – $2200) / (120 units – 80 units) $800/40 units $20/unit
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The first step in the process is to calculate the variable cost per unit. Again, the assumption is that the change in cost is due to the change in number of units. [Let the students set up the equation before moving on to the next slide. Or, complete the calculation on the board or overhead projector and use the next slide to confirm your calculation]
Change in Cost / Change in Units =
Total $ at high output – Total $ at low output
# Units at high output – # Units at low output

17. Calculate Unit Variable Cost
Change in Cost / Change in Units = Total $ at high output – Total $ at low output # Units at high output – # Units at low output ($3000 – $2200) / (120 units – 80 units) $800/40 units $20/unit
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The equation should be:
($3000 – $2200) / (120 units – 80 units)

18. Calculate Unit Variable Cost
Change in Cost / Change in Units = Total $ at high output – Total $ at low output # Units at high output – # Units at low output ($3000 – $2200) / (120 units – 80 units) $800/40 units $20/unit
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The solution is:
$800/40 units =
$20/unit
The average variable cost per unit between the highest level of output and the lowest is $20/unit
Now we can use this information to complete step 2.

19. Calculate Fixed Cost Total Cost – Variable Cost =
Total $ high output – VC $/unit * # Units high output
$3000 – ($20/unit * 120 units)
$3000 – ($20 * 120 )
$3000 – $2400
= $600
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
Step 2 of the process is to calculate fixed cost. Fixed cost is the difference between total cost at the high output and variable cost at the high output.
Total Cost – Variable Cost =
Total $ high output – VC $/unit * # Units high output
[Let the students set up the equation before proceeding to the next slide]

20. Calculate Fixed Cost Total Cost – Variable Cost =
Total $ high output – VC $/unit * # Units high output
$3000 – ($20/unit * 120 units)
$3000 – ($20 * 120 )
$3000 – $2400
= $600
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The equation is:
$3000 – ($20/unit * 120 units)

21. Calculate Fixed Cost Total Cost – Variable Cost =
Total $ high output – VC $/unit * # Units high output
$3000 – ($20/unit * 120 units)
$3000 – ($20 * 120 )
$3000 – $2400
= $600
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
To solve:
$3000 – ($20/unit * 120 units)
Using algebraic rules on our units of measure, we cancel out “units”.
The equation becomes:
$3000 – ($20 * 120 )

22. Calculate Fixed Cost Total Cost – Variable Cost =
Total $ high output – VC $/unit * # Units high output
$3000 – ($20/unit * 120 units)
$3000 – ($20 * 120 )
$3000 – $2400
= $600
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
From this point the calculation is simple arithmetic:
$3000 – $2400
= $600

23. Express the Mixed Cost Relationship
Total Cost = VC $/Unit * # Units + Fixed Cost
Total Cost = $20/Unit * # Units + $600
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The third step is to develop the cost expression. The generic equation is:
Total Cost = VC $/Unit * # Units + Fixed Cost
[Let the students develop the cost expression before continuing to the next slide]

24. Express the Mixed Cost Relationship
Total Cost = VC $/Unit * # Units + Fixed Cost
Total Cost = $20/Unit * # Units + $600
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
The cost expression is:
Total Cost = $20/Unit * # Units + $600

25. Using the Cost Expression
For planning:
If planned output in May is 60 purchase orders, what is our expected cost?
$20/PO * 60 POs + $600 = $1800
If planned output in June is 130 purchase orders?
$20/PO * 130 POs + $600 = $3200
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
[Students will have the blank slide]
For planning:
If planned output in May is 60 purchase orders, what is our expected cost?
If planned output in June is 130 purchase orders?

26. Using the Cost Expression
For planning:
If planned output in May is 60 purchase orders, what is our expected cost?
$20/PO * 60 POs + $600 = $1800
If planned output in June is 130 purchase orders?
$20/PO * 130 POs + $600 = $3200
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
[Students will have the blank slide]
For planning:
If planned output in May is 60 purchase orders, what is our expected cost?
If planned output in June is 130 purchase orders?

27. Using the Cost Expression
For planning:
If planned output in May is 60 purchase orders, what is our expected cost?
$20/PO * 60 POs + $600 = $1800
If planned output in June is 130 purchase orders?
$20/PO * 130 POs + $600 = $3200
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
[Students will have the blank slide]
For planning:
If planned output in May is 60 purchase orders, what is our expected cost?
If planned output in June is 130 purchase orders?

28. Using the Cost Expression
For comparison and learning
April’s cost of $2750 for 105 POs was higher than expected. Why?
Expected cost = $20/PO * 105 POs + $600 = $2700
January’s cost of $2500 for 100 POs was lower than expected. Why?
Expected cost = $20/PO * 100 POs + $600 = $2600
What did we do differently? What can we learn?
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
For comparison and learning
April’s cost of $2750 for 105 POs was higher than expected. Why?
January’s cost of $2500 for 100 POs was lower than expected. Why?
The variable cost and fixed cost calculated using the high-low method only represents an average between the two levels of output. It may be useful to understand why there are differences in the months when the actual cost differs from the average.

29. Using the Cost Expression
For comparison and learning
April’s cost of $2750 for 105 POs was higher than expected. Why?
Expected cost = $20/PO * 105 POs + $600 = $2700
January’s cost of $2500 for 100 POs was lower than expected. Why?
Expected cost = $20/PO * 100 POs + $600 = $2600
What did we do differently? What can we learn?
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
For comparison and learning
April’s cost of $2750 for 105 POs was higher than expected. Why?
Expected cost = $20/PO * 105 POs + $600 = $2700
Using the cost expression developed with the high-low method, our cost is expected to be $2700 for 105 POs. In April it was different. If the difference is significant, we should attempt to understand why.

30. Using the Cost Expression
For comparison and learning
April’s cost of $2750 for 105 POs was higher than expected. Why?
Expected cost = $20/PO * 105 POs + $600 = $2700
January’s cost of $2500 for 100 POs was lower than expected. Why?
Expected cost = $20/PO * 100 POs + $600 = $2600
What did we do differently? What can we learn?
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
January’s cost of $2500 for 100 POs was lower than expected. Why?
Expected cost = $20/PO * 100 POs + $600 = $2600
Using the cost expression, we would have expected the cost for 100 POs to be $ It would be useful to understand what caused the difference.

31. Using the Cost Expression
For comparison and learning
April’s cost of $2750 for 105 POs was higher than expected. Why?
Expected cost = $20/PO * 105 POs + $600 = $2700
January’s cost of $2500 for 100 POs was lower than expected. Why?
Expected cost = $20/PO * 100 POs + $600 = $2600
What did we do differently? What can we learn?
Activity step 2 Demonstration problem Calculate fixed and variable cost components from mixed cost data
What did we do differently? What can we learn?
Were we somehow more efficient in January? Why? Or, was there a difference in the type of purchase orders processed in January? Were they simpler? Was more documentation provided by the requisitioning organization? Can we incorporate this efficiency into our regular operations?
Were we less efficient in April? Or was there a difference in the type of output? Was it more complex? Was the information provided by the requisitioning organization incomplete? Can we incorporate this knowledge into our operations?

32. Check on Learning
What might cause a difference between the expected cost using High-Low and the actual cost?
What might cause a difference between the expected cost using High-Low and the actual cost?
High-Low is just an average, assuming the relationship between the highest output and the lowest are representative of the whole. This may not be the case. Sometimes the differences are due to actual cost overruns or savings from efficiencies.

33. Practical Exercise

34. Enter and Filter Data to identify if relationship is reasonably linear
The spreadsheet calculates the Variable and Fixed portions of the cost

35. Practical Exercise