2. CVP Relationships : A Graphical Analysis
Costs and Revenue
Break-even Profit
Point
in Dollars
Loss
Volume in Units 20-8
2
3. Fixed Costs: The cost when there is no
production.
Variable cost: The cost of producing one
additional unit at any given production level.
3
4. Price does not change with quantity.
Variable cost per unit does not change with
quantity.
Fixed costs are known.
4
5. Total Cost = Fixed Cost + (Variable Cost * Q)
TC = FC + (VC x Q)
5
6. Contribution margin per unit equals price per
unit minus variable cost per unit:
CM = (P – VC)
Total contribution margin equals total revenue
minus total variable costs:
(CM * Q) = (P*Q) – (VC*Q)
6
7. Breakeven point: The number of units that must be sold at
price P such that total revenues (TR) equal total costs (TC).
TR = TC
(P * QBE) = FC + (VC * QBE)
(P - VC) * QBE = FC
QBE = FC / (P – VC)
QBE = (FC / CM)
At breakeven, the total contribution margin equals fixed
costs.
CM = FC
7
8. Computing Break-Even Point
Total Unit
Sales Revenue (2,000 units) $ 100,000 $ 50
Less: Variable costs 60,000 30
Contribution margin $ 40,000 $ 20
Less: Fixed costs 30,000
Operating income $ 10,000
How many units must this company which company
How many units must is margin mustsell torevenue
How much contribution amount must this revenue
How much contribution margin by which company
Contribution margin this company sell to cover its
Contribution margin is amount by this cover its
exceeds the variable costs of producing the revenue.
exceeds the variable costs of producing even)?
have to cover costs (break even)? the revenue.
have to cover its fixed costs (break even)?
fixed costs (break even)?
fixed its fixed costs (break
Answer: $30,000 ÷ $20 $30,000 = 1,500 units
Answer: per unit
Answer: $30,000 ÷ $20 $30,000 = 1,500 units
Answer: per unit
20-13
8
9. How Many Dollars in Sales at
Break-even point?
The break-even formula can be expressed
in sales dollars.
Break-even Fixed costs
=
point in dollars Contribution margin ratio
Unit sales price
Unit variable cost
20-15
9
11. Total Revenue - Total Costs = Profit
{(P * Q ) - [(VC * Q ) – FC]} = Profit
{[(P - VC) * Q] - FC} = Profit
[(CM * Q) - FC] = Profit
(CM * Q) = (Profit + FC)
Q = [(Profit + FC )/CM]
The number of units that must be sold to earn a
target profit is equal to the target profit plus the
fixed cost divided by the contribution margin.
11
12. Computing Sales Needed to
Achieve Target Operating Income
Fixed costs + Target income
Unit sales =
Contribution margin per unit
Fixed costs + Target income
Dollar sales =
Contribution margin ratio
20-18
12
13. Computing Sales Needed to
Achieve Target Operating Income
ABC Co. sells product XYZ at $5.00 per unit.
If fixed costs are $200,000 and variable
costs are $3.00 per unit, how many units
must be sold to earn operating income of
$40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
20-19
13
15. Applications of CVP
Should Speedo spend $12,000 on
advertising to increase sales by 10 percent?
T o ta l P e r Un it P e rc e n t
S a l e s (5 0 0 b i k e s) $ 250,000 $ 500 100%
L e ss: v a ri a b l e e x p e n se s 150,000 300 60%
C o n tri b u ti o n m a rg i n $ 100,000 $ 200 40%
L e ss: fi x e d e x p e n se s 80,000
O p e ra ti n g i n c o m e $ 20,000
20-24
15
16. Business Applications of CVP
Should Speedo spend $12,000 on
advertising to increase sales by 10 percent?
500 550
550 × $500
Bikes Bikes
Sales $ 250,000 $ 275,000
Less: variable expenses 150,000 550 × $300 165,000
Contribution margin $ 100,000 $ 110,000
Less: fixed expenses 80,000 $80K + $12K 92,000
Operating income $ 20,000 $ 18,000
No, income is decreased.
20-25
16
17. Applications of CVP
Now, in combination with advertising and a price cut, Speedo
will replace $50,000 in sales salaries with a $25 per bike
commission, increasing sales by 50 percent above the
original 500 bikes. What is the effect on income?
500 1.5 × 500 750
Bike s Bike s
750 × $450
S a le s $ 250,000 $ 337,500
L e ss: v a ri a b l e e x p e n se s 150,000 243,750
750 × $325
C o n tri b u ti o n m a rg i n $ 100,000 $ 93,750
L e ss: fi x e d e x p e n se s 80,000 42,000
$92K - $50K
O p e ra ti n g i n c o m e $ 20,000 $ 51,750
The combination of advertising, a price cut,
and change in compensation increases income.
20-27
17
