COST-VOLUME-PROFIT ANALYSIS: D8
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Key ratios/formulae:
Breakeven Units = FC/Contribution per unit
Breakeven Value
Target Profit (F and V)
Profit/Volume Ratio
% Margin of Safety
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Key assumptions:
All other variables remain constant
Single product or constant sales mix
TC & TR are linear functions of output
Profits calculated on a VC basis
Analysis applied to relevant range only
Costs can be accurately divided in F and V elements
S/T horizon only
The relevant range of activity
Accountant’s fixed cost function
1. Within the short term the firm anticipates that it will operate
between output levels Q2 and Q3 and commits itself to fixed
costs of 0A.
2. Costs are fixed in the short term, but can be changed in the
longer term.
CVP analysis: non-graphical computations
Example 8.1
Fixed costs per annum
R60 000
Unit selling price
R20
Unit variable cost
R10
Relevant range
4 000 - 12 000 tickets
1. Break-even point
Net profit =
Total revenue – total costs
NP
=
px – (a + bx)
BEP 0
=
or
1. Break-even point
=
Fixed costs
Contribution per unit
=
or
1. What if units unknown?
R60 000/R10 = 6 000 units
CVP analysis: non-graphical computations cont
If unit fixed costs and revenues are not given, the breakeven point (expressed in sales values) can be calculated
as follows:
Total fixed costs
x Total sales
Total contribution
Profit volume ratio = Contribution x 100
Sales revenue
Percentage margin of safety =
Expected sales - Break-even sales
Expected sales
CVP analysis: non-graphical computations cont
2a. Units to be sold to obtain a R30 000 profit:
Fixed costs + desired profit = R90 000/R10 = 9 000 units
Contribution per unit
2b. Units to be sold to obtain a profit = 20% of sales
Fixed costs_______________ = R60 000/R6 = 10 000 units
Contribution per unit – desired profit
CVP analysis: non-graphical computations cont
3.
NP if 8000 tickets are sold
Breakeven =
Incremental units =
x contribution per unit =
6000 units
Proof:
R20 x 8000 units – (R10 x 8000 units + R60K)
What if a further 1000 units are sold?
CVP analysis: non-graphical computations cont
4.
SP to get NP of R30K on x = 8000 units
R30K
=
8000P – (R10 x 8000+ R60K)
5.
Advertising increases by R8K, what increase in sales volume is
required?
Other key ratios/formulae:
Percentage margin of safety =
Expected sales - Break-even sales
Expected sales
How far above BE am I?
Interpretation?
The Profit-Volume Ratio
FC / Contribution per unit
=
What proportion of sales = contribution
If sales increases by R10K, R20K from BE how much will NP
change?
R60K x
=
R60K =
R70K x
=
R60K =
R80K x
=
R60K =
R200K x
=
R60K =
The variable cost ratio
What proportion of sales = variable costs
Sensitivity analysis
Assume directors unhappy with forecast performance. Two
alternatives proposed:
(a)
Reduce selling price by 10%
Increase advertising by R2 000
Sales tickets expected to increase to 9000 from 7000
(b)
No change to selling price
Increase advertising by R2 000
Offer ticket agents a 5% commission per ticket sold
Sales tickets expected to increase to 10000 from 7000
• For each alternative, calculate net profit, break-even point and
MOS %.
Break-even chart for 8.1
Contribution chart for 8.1
Profit volume graph for 8.1
Multi-product breakeven analysis
Example
Unit contribution
Product D
R150
Product S
R90
Budgeted sales mix
2/3
1/3
Actual sales mix
1/2
1/2
Fixed costs are R117 000 + 39 000 = R156 000
Budgeted BEP = R156 000 /R130 (a) = 1 200 units
Actual BEP = R156 000 /R120 (b) = 1 300 units
a: (2/3xR150)+(1/3xR90) = R130
b: (1/2xR150)+(1/2%x90) = R120
Multi-product breakeven
D
S
Sales/unit
R300
R200
Less: VC/unit
R150
R110
= Contribution/unit
R150
R90
Specific FC
R90K
R27K
= Product breakeven 600 units 300 units
If we sell exactly these units, our loss =
Any units sold above product breakeven, offset the loss
incurred by common (unavoidable FC)
Having sold 600 D and 600 S, our loss = R12K
In a sales mix, BEP is a unique number. If the mix changes,
the BEP changes!