Cost-Volume-Profit Models Tutorial
Summary
The cost-volume-profit model models the behavior of costs, revenues and profits
over a range of volume levels. The model's basic structure is depicted above in
the cost-volume-profit graph. The point where the total revenue and total cost
lines intersect is referred to as the breakeven point or breakeven volume.
Volumes to the right of the breakeven volume generate profits. Volumes to the
left of the breakeven volume lead to losses.
The cost-volume-profit model's revenue equation volume is:
Rt = Ru x Q
Where:
Rt = Total revenue
Ru = Revenue per unit
Q = Quantity
The total cost is the sum of three types of cost. Namely:
•
•
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Variable costs - Costs that in total vary directly and proportionally to
changes in volume
Fixed costs - Costs that in total remain unchanged with changes in volume
Semivariable costs - Costs that in total include both a variable and a fixed
cost component
The model's general equation for total cost is:
Ct = FCt + (VCu x Q)
Where:
Ct = Total cost
FCt = Total fixed cost
VCu = Variable cost per unit
Q = Quantity
VCu x Q = Total variable cost
The general equation for total profit is:
Pt = (Rt - Ct)
Where:
Pt = Total profit
Rt = Total revenue
Ct = Total cost
Unit contribution is the difference between a unit's revenue per unit and its
variable cost per unit. The general equation for the calculation of contribution per
unit is:
CONu = (Ru - VCu)
Where:
CONu = Contribution per unit
Ru = Revenue per unit
VCu = Variable cost per unit
The total contribution equation is:
CONt = (Ru x Q) - (VCu x Q)
or
CONt = (Ru - VCu)Q
Where:
CONt = Total contribution
Ru = Revenue per unit
VCu = Variable cost per unit
Q = Quantity
Ru - VCu = Contribution per unit
Breakeven Volume
Breakeven volume is the sales volume at which total revenues equal total costs.
On the cost-volume-profit graph, it is the volume level corresponding to the
intersection of the total revenue and total cost lines. At this volume profit is zero.
The general equation for determining breakeven volume is:
BEV = FCt / CONu
Where:
BEV = Breakeven volume
FCt = Total fixed costs
CONu = Contribution per unit
Caveats
There are a number of caveats that should be kept in mind when using the costvolume-profit graph and its variations.
They are:
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The cost-volume relationship diagrammed is unlikely to be true for the
entire range of volume presented
•
Costs are not solely volume driven
•
The classification of costs as being either fixed or variable changes as the
time horizon being considered expands or contracts
•
Variable costs can be sticky
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Not all costs change in a linear relationship to volume
Expectations
Now that you have completed the Cost-Volume-Profit Models tutorial, you
should have an understanding of:
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How to identify variable, fixed and semivariable costs and their role in the
cost-volume-profit model
•
How to use the cost-volume-profit model to determine profits at various
levels of unit volume
•
How to use the contribution-volume-profit model, which is a variation of
the basic cost-volume-profit model
•
How to calculate the volume needed to breakeven.
We hope this tutorial was helpful.