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Chapter Four
Lecture Notes
Understanding Costs
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What Does It Cost?
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It depends! How a manager or policy maker looks at and
measures cost depends on why the cost analysis is being
done. What question are we trying to answer?
Cost Objective is term used for the focus of the cost analysis.
It may be a unit of service, a program, or a department.
Relevant costs are those that have an impact on, or are
impacted by, the decision being considered. Determining
what costs are relevant depends on
- the cost objective.
- the time frame for the analysis.
- the expected range of volume.
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Cost Definitions
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Full or Total Cost is the sum of all costs associated with
the cost objective.
Direct Costs
costs incurred within an organizational unit.
cost of resources used to produce a good or service.
Indirect Costs (Overhead)
costs that are assigned to a unit from outside.
costs of resources not used directly to provide service.
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Full cost = direct cost + indirect cost.
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Is a maintenance worker direct or indirect?
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More Cost Definitions
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Average Cost is the full cost of a cost object divided by the
number of units of service provided.
Fixed Costs are those costs which remain (relatively)
unchanged in total for some time period as the volume of
services changes over a relevant range of activity.
Variable Costs are those costs that vary directly with changes
in the volume of service units over a relevant range of activity.
Relevant Range is the normal range of expected activity.
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Fixed and Variable Costs
Fixed Costs do not
vary with volume
over the relevant
range.
Variable Costs vary
proportionately with
volume.
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Total Cost
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Average Cost
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Fixed Cost
Variable Cost
Direct
Indirect
What is an example of an expense for each of the four boxes?
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And More Cost Definitions
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Marginal Costs are the "additional" costs incurred as the
result of providing one more unit of service (incremental costs).
Mixed Costs are costs that contain both fixed and variable
costs.
Step-Fixed or Semi-Variable Cost are costs that are fixed
over ranges of activity that are less than the relevant range.
Marginal costs are equal to Variable costs unless there are
changes in Step-Fixed costs.
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Step-Fixed Costs
Cost
Volume
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Relevant Cost Analysis
The urban planner for Millbridge is working on a housing project. The
Fixed Costs are $300,000 for the project, and Variable Costs are $250
each time a family moves into an apartment. The cost structure of the
housing project would be:
Volume
Fixed
Cost
Variable
Cost
Total Cost
Full Cost
Average
Cost
100
$300,000
$25,000
$325,000
$3,250
500
$300,000
$125,000
$425,000
$850
1,500
$300,000
$375,000
$675,000
$450
2,500
$300,000
$625,000
$925,000
$370
3,000
$300,000
$750,000
$1,050,000
$350
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What is the Right Decision?
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The housing project now has 2,500 move-ins per year. To
encourage the town to expand the program, the state offers
to pay $300 for each of 500 move-ins if they expand to 3,000
per year. Should the town expand the housing project?
The average cost per move-in at 2,500 per year is $370.
The average cost per move-in at 3,000 per year is $350.
The variable cost per move-in is $250.
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What is your decision?
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New Revenue
New Cost
Apparent Loss
$300 x 500 move-ins
$350 x 500 move-ins
However, what is the Total Cost
for 3,000 move-ins (slide 11)?
What is the Total Cost for
2,500 move-ins (slide 11)?
How much did costs increase?
Extra revenue from extra move-ins
Extra cost from extra move-ins
Extra profit
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$ 150,000
175,000
$ (25,000)
$1,050,000
925,000
$ 125,000
$ 150,000
125,000
$ 25,000
Why did we first see a $25,000 loss, then see a $25,000 profit?
Average cost assigns some FC to new move-ins.
Average Cost = $350 per move-in.
Marginal cost looks at only additional costs of new move-ins.
Marginal Cost = $250 per move-in
Consider the difference:
Average Cost
Marginal Cost
Difference
$350
-250
$100
x 500 move-ins = $50,000
That $50,000 is the difference between thinking of this as a
$25,000 loss versus as a $25,000 profit. So the key question
is, will FC go up or not?
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Deriving the Break-Even Formula
Total Revenue = price * quantity = P * Q
Total Expense = variable cost + fixed cost = (VC * Q) + FC
Break even occurs when Total Revenue = Total Expense
P * Q = (VC * Q) + FC subtracting (VC * Q) from both sides
(P * Q) - (VC * Q) = FC factor out Q
Q * (P - VC) = FC
divide both sides by (P - VC)
BEQ =
FC
----------P – VC
BEQ is the Break-Even Quantity.
(P - VC) is often called the Contribution Margin.
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Break-Even Analysis
Break Even
Profit
Loss
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A Break-Even Example
Feed-A-Child Foundation wants to start a new program which
will have $30 in variable costs per child and fixed costs of
soliciting donations to fund the program of $10,000. If each
donor were to give FAC $50, and each donor feeds one child,
how many donors would be needed for FAC to break even?
Contribution Margin = (P - VC) = ($50 - $30) = $20
Fixed Costs = $10,000
BEQ = FC/CM = $10,000/$20 = 500 donors to break even
FC
FC
$10,000
$10,000
BEQ = ----------- = ------ = ------------ = ----------- = 500
P - VC
CM
$50 - $30
$20
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Suppose that Feed-A-Child ran three regional programs
with $100,000 of fixed costs and the average donations,
variable costs, and mix of contributions shown below.
What would the break-even volume be?
Mix of
Contributions
Program
Average
Donation
Average
Variable Cost
Contribution
Margin
Africa
70%
$36
$32
$ 4.00
Asia
25%
40
29
11.00
5%
50
30
20.00
South
America
Total
100%
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To solve the problem, we first find the weighted
average Contribution Margin and then apply the
normal Break-Even formula!
Percent of
Donations
Program
Africa
Asia
South
America
Total
Contribution
Margin
Weighted Average
CM
70%
$4
$2.80
25%
11
2.75
5%
20
1.00
$6.55
BEQ = FC/CM = $100,000/$6.55 per donation = 15,267 donations
Note that this cannot be done as separate break-even calculations for each program!
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Other Uses of
Break-Even / Profit Analysis
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Organizations with limited capacity can find the price that
they must charge to break even.
Where an organization knows both the price it can charge
and the units of service it will deliver, break-even analysis
can be used to determine the maximum level of costs
(fixed, variable, or total) that the organization can bear.
In short, you can determine the appropriate Price, FC, VC if you
know how many units you are going to sell.
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Managerial
Implications and Cautions
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Suppose the organization finds that it cannot reach
the break-even volume, what can the managers do
to preserve the service?
Some cautions
- managers must rationally assess their ability to
reach the break-even volume.
- managers must be aware that prices and costs
are not constant over time.
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