Cost-Volume-Profit analysis considers, individually and in combination, the effect(s) on profit of
Sales volume (activity)
Variable cost per unit
Total fixed cost
The contribution margin income statement (introduced in Chapter 3 if you need to refer back) can be expressed in total dollars, in dollars per unit (for sales and variable costs only), and also, as we’ll see a little further on, as a percent of sales (usually, but not always, for variable costs, but also, when total sales are used, for fixed costs for some purposes).
Contribution margin = sales – variable costs
Fixed costs profits
When all fixed costs are covered, company is said to break even, no profit, no loss.
QUOTES TO NOTE: Page 115: “Once the break-even point has been reached, net operating income will increase by the amount of the unit contribution margin for each additional unit sold.”
Profit = (Su – VCu)*Q – TFC S = selling price
VC = variable cost
TFC = total fixed costs
Q = sales volume
Since S – VC = CM (contribution margin),
Profit = Contribution Margin Units * Q – TFC
CVP (cost-volume-profit) graph:
Volume on X-axis (line F – G)
Dollars (of cost or revenue) on Y-axis (line A – F)
Note that revenue line (line F – B) begins at the origin, but total cost line (line D – C) begins where fixed cost line (line D – E) intersects Y-axis, because even at “0” volume, there will still be fixed cost, so TC = FC * VCu * Q
Break-even point (point H): where total cost line crosses the revenue (sales) line (line F – B))
If revenue in units changes, it won’t change the SLOPE of the revenue line, it will only change the POINT on the revenue line where current revenues have reached.
The slope of the revenue line (F – B) is selling price per unit.
The slope of the total cost line (D – C) is variable cost per unit.
If fixed costs increase, the FC line e (D – E) will “move up,” that is, intersect the dollar (Y) axis at a higher point. That means the total cost line (D – C) will also “move up.”
Contribution margin ratio: CM / sales (Can be calculated in total, or per unit – should yield the same ratio. Can you explain why this is true?)
This is the third way of expressing the CM income statement, mentioned above: variable costs and CM as a percentage of sales.
CM % (CM ratio) * change in sales dollars = dollar change in net operating income
Variable expense ratio = Variable Cost / Selling Price
Incremental analysis: consider only those elements of revenue, cost, volume that will change based on the decision you are considering.
NOTE that any time sales volume changes, the change in income can be measured using contribution margin because variable costs always change directly and proportionately with sales
A change in cost structure involves exchanging fixed costs for variable costs, or, in the other direction, variable cost for fixed costs.
Break-even point: where S*Q – VC*Q – FC = 0
Fixed Cost / Contribution Margin Unit
Fixed Cost / Contribution Margin Ratio
Target profit analysis is a modification of break even: calculate the amount of sales needed to earn a specific profit, rather than zero profit (break even).
Q for target (desired) profit = CMuQ – FC
(Fixed Cost + Target Profit) / Contribution Margin Unit
Sales for target profit: $ sales = (Target Profit + Fixed Cost) / Contribution Margin %
Margin of safety: how far beyond break-even have you progressed? Conversely: by how much can sales drop before we’re “in the red?”
Margin of Safety $ = current sales $ - break-even sales $
Margin of Safety % = (Current S$ - Break-even S$) / current Selling Price
Margin of Safety Units = current sales units – break-even sales units
Cost structure: proportion of fixed costs and variable costs employed
Fixed costs increase volatility, risk
However lower variable costs = higher CM = more rapid profit growth
See the graph below
Operating leverage, related to cost structure, measures the