### MANAGEMENT ACCOUNTING LECTURE 2 COST

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MANAGEMENT ACCOUNTING
LECTURE 2 COST-VOLUME PROFIT (CVP) ANALYSIS
RECOMMENDED QUESTIONS
Drury, 7th & CTA1 & CTA2: 8.11 – 8.15; 8.17; 8.21; 8.22; IM8.5(a), IM8.5(d); IM8.6;
8th edition
IM8.7; IM8.10; IM8.11
CTA2: IM8.8; IM8.9
Acknowledgment: Management and cost accounting, Colin Drury, 8th edition
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CVP
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This section focuses on what will happen to the financial results if a specific level of activity
or volume fluctuates. The information is required for making optional short-term output
decisions.
The CVP analysis examines the relationship between changes in activity (i.e. output) and
changes in total sales revenue, costs and net profit.
This information is vital to management, since one of the most important variables
influencing total sales revenue, total costs and total profits is output or volume.
Therefore, knowledge of this relationship enables management to identify critical output
levels, such as the level at which neither profit nor a loss will occur.
Often costs and prices of a firm’s products or services will already have been determined
over a short-run period, and the major area of uncertainty will be the sales volumes.
Cost relationships
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Cost relationships can be linear (accountant’s view) or curvilinear (economists’ view). For
our purpose, we are going to focus on linear relationship.
Linear relationship assumes that the variable cost per unit always remain constant (think
matric maths: y = mx + c)
Linear relationship is not intended to provide an accurate representation of total costs and
total revenue throughout all ranges of output.
It only represents the cost behaviour for the range of output at which a firm expects to be
operating within a short term planning horizon. This range is referred to as a relevant
range.
The relevant range also broadly represents the output levels that the firm has had
experience of operating in the past and for which cost information is available.
CVP analysis should therefore only be applied within the relevant range, i.e. it can be used
for decisions that results in outcomes within the relevant range.
Example 1: Relevant range
The total manufacturing costs of a company are R330,000 at an output level of 30,000 units
and R390,000 at an output level of 40,000 units. The total costs increase to R560,000 when
output increases to 60,000 units. Based on past experience, it is estimated that the fixed cost
component of the total costs increase by R50,000 beyond output level of 50,000 units while
the variable cost per unit is constant throughout.
You are required to calculate the total manufacturing costs for producing (i) 45,000 units (i)
70,000 units
Key to solution:
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Note that the total manufacturing costs are provided. The cost appears to be a mixed cost,
i.e. comprises a variable and fixed component, and therefore the use of a methodology
such as hi-low would be appropriate.
The hi-low method is a simplistic non-mathematical technique which consists of examining
past costs and activity, selecting the highest and the lowest activity levels and comparing
the changes in costs which results from the two levels. There appears to be two ranges of
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output where a cost relationship is defined, (i) the range whereby output level is below
50,000 units and (ii) range whereby output level is greater than 50,000 units.
The hi-low method cannot be applied on costs analysis within different relevant ranges.
Costs (R)
Activity (units)
Low
330,000
30,000
Hi
390,000
40,000
Change
60,000
10,000
Variable cost per unit (R)
Activity level
Total manufacturing costs (R)
Total variable cost at R6 per unit
Fixed costs (R)
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6
45,000
60,000
70,000
390,000 420,000
240,000 270,000
150,000 150,000
560,000
360,000
200,000
620,000
420,000
200,000
30,000
330,000
180,000
150,000
40,000
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Numerical approach to CVP
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The most common application of CVP is the determination of break-even point.
A break-even point refers to a point where the company makes neither a profit nor a loss.
Example 2: Single product break-even analysis
Neo Ltd is a telecommunication company that sells telephone handsets. The variable cost of
manufacturing each handset is R500 while the selling price is R800 per unit. The total fixed
manufacturing costs are R900,000.
The non-manufacturing costs comprise a mixture of variable costs and fixed costs. The
variable cost per unit is R50 while the fixed costs amount to R150,000.
Considering each part independently, you are required to:
i) Determine the point at which Neo Ltd will make neither a profit nor a loss (‘break-even’) –
express the answer in units and also sales value.
ii) If it is the desire of Neo Ltd to generate a profit of R200,000, calculate the number of units
to be sold and the amount of revenue to be generated.
iii) If 5,000 units are budgeted to be sold, what is Neo Ltd’s margin of safety in units and sales
iv) Calculate the impact on break-even units if the fixed manufacturing costs increase by
R100,000.
Key to solution:
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The break-even calculation requires that the company generates sufficient contribution
margin to cover the total fixed cost (i.e. manufacturing and non-manufacturing fixed costs).
The contribution margin per unit is the selling price per unit less all variable costs per unit
(manufacturing and non-manufacturing costs)
The break-even point determines the number of units to be sold or the sales value required
in order to generate neither a profit nor a loss (recall our earlier point: “Often costs and
prices of a firm’s products or services will already have been determined over a short-run
period, and the major area of uncertainty will be the sales volumes.”)
If the company has a target profit then the total contribution margin generated should be
sufficient to cover the total fixed costs and the required profit.
Pay attention to the required – does it require break-even units or sales value?
Understanding of the technical term ‘margin of safety’
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i) Determine the point at which Neo Ltd will make neither a profit nor a loss (‘break-even’) –
express the answer in units and also sales value.
Manufacturing costs
Non-manufacturing costs
Total fixed costs
R900,000
R150,000
R1,050,000
Selling price per unit
Manufacturing variable costs per unit
Non-manufacturing variable costs per unit
Contribution margin per unit
R800
(R500)
(R50)
R250
Break-even units (total fixed costs / contribution margin)
Selling price per unit
Break-even sales revenue
4,200
R800
R3,360,000
ii) If it is the desire of Neo Ltd to generate a profit of R200,000, calculate the number of units
to be sold and the amount of revenue to be generated.
Total fixed costs (see part (i))
Target profit
R1,050,000
R200,000
R1,250,000
Contribution margin (see part (i))
R250
Break-even units
Selling price
Break-even sales revenue
5,000
R800
R4,000,000
iii) If 5,000 units are budgeted to be sold, what is Neo Ltd’s margin of safety in units and sales
Note: Management might be interested in understanding how much comfort does the
budgeted level of output provide in relation to the point where the company will neither
generate a profit nor a loss
Break-even units (see part (i))
Budgeted sales
Margin of safety in units
Selling price
Margin of safety in revenue terms
4,200
5,000
800
R800
R640,000
Margin of safety (%) (margin of safety revenue / expected revenue)
Margin of safely
Total sales (5,000 * 800)
16%
R640,000
R4,000,000
In this this example, revenue and consequently the contribution margin can decrease by 16%
before the company can start making a loss.
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iv)
Calculate the impact on break-even units if the fixed manufacturing costs increase by
R100,000.
Total fixed costs (see part (i))
Additional fixed costs to be covered
R1,050,000
R100,000
R1,150,000
Contribution margin
R250
Break-even units
Selling price
Break-even sales revenue
January 2014
4,600
R800
R3,680,000
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Example 3: Multi-product break-even analysis
Orange Ltd is a technology company that manufactures and sells smartphones and tablets.
Details relating to the smartphones and tablets are provided below:
Budgeted sales
Selling price unit (R)
Variable costs (R)
Attributable fixed costs
Smartphones
150,000
1,000
600
Tablets
50,000
2,000
600
250,000
300,000
Common fixed costs for the budgeted period amounted to R347,000.
You are required to:
i) Determine the point at which Orange Ltd will make neither a profit nor a loss (‘break-even’)
– express the answer in units and also sales value for each product type (smartphones
and tablets).
Key to solution:
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The principles in Example 3 are applicable but require additional consideration in order to
The multi-product break-even approach is often applicable when there are common fixed
manufacturing costs.
It is normally not applicable for circumstances whereby there are only attributable fixed
costs (i.e. fixed costs that are avoidable should a product line be discontinued) as each
product line will be expected to cover its attributable fixed costs
Alternatively, the common fixed costs may be allocated to product lines – However, the
issue then becomes the determination of an allocation that is not arbitrary as these costs
are only avoidable if production for both products cease.
The break-even point (or the sales volumes required to achieve a target profit) varies
depending upon the composition of the sales mix. In other words, it is only valid for the
planned sales mix. (another underlying assumption of CVP analysis)
Approach:
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Convert the sales volume measure of the individual products into standard batches of
products based on the planned sales mix (think of it this way, if a customer is walking out
from Orange Ltd with a standard bag, how many smartphones are included in that bag
and how many tablets are included in the same bag?).
Determine the contribution margin per batch (i.e. what is the total contribution margin
received by Orange Ltd when it sells a standard bag?) – this is calculated as the weighted
average of the contribution margin of both products, i.e. (number of smartphones in one
batch * contribution margin per smartphone) + (number of tablets in one batch *
contribution margin per tablet)
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Determine the total fixed costs (manufacturing, non-manufacturing and common fixed
costs)
Determine the break-even number of batches (note that this is not the actual sales volume
for both products)
Determine the number of each product type within a single batch and multiply this by the
number of total break-even batches to determine the number of individual products
required to break-even
Note that there are two ways to undertake the break-even analysis for a multi-product
scenario. There are subtle differences between the two approaches and candidates need
to be aware of these as to avoid using both approaches in determining the break-even
point.
Selling price per unit
Variable costs per unit
Contribution margin per unit
Smartphones
1,000
(600)
400
Tablets
2,000
(600)
1,400
Smartphones
150,000
3
Tablets
50,000
1
1,200
1,400
Fixed costs
250,000
300,000
347,000
897,000
Contribution
1,200
1,400
2,600
ALTERNATIVE 1
Number of units
Ratio (number of units in a single batch)
Contribution per standard bag
Smartphones
Tablets
Common fixed costs
Break-even batches
345
Smartphones
345
3
1,035
1,000
1,035,000
Batches
Numbers of units in 1 batch
Total units
Selling price unit
Total sales revenue
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Tablets
345
1
345
2,000
690,000
Endunamoo CTA – Costing CVP
ALTERNATIVE 2
Number of units
Ratio
Contribution per standard bag
Smartphones
Tablets
Common fixed costs
Smartphones
150,000
0.75
Tablets
50,000
0.25
300
350
Fixed costs
250,000
300,000
347,000
897,000
Contribution
300
350
650
Break-even batches
1,380
Smartphones
1,380
0.75
1,035
1,000
1,035,000
Batches
Numbers of units in 1 batch
Total units
Selling price unit
Total sales revenue
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Tablets
1,380
0.25
345
2,000
690,000
Endunamoo CTA – Costing CVP
Operating leverage
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Operating leverage is used as a measure of the sensitivity of profits to changes in sales.
The greater the degree of operating leverage, the more that changes in sales activity will
affect profits.
The degree of operating leverage (DoL) can be measured for a given level of sales by the
following formula:
DoL = Contribution margin / Profit
Example 4: Operating leverage
Labour intensive
1,000,000
(800,000)
200,000
(100,000)
100,000
Sales revenue
Variable expenses
Contribution margin
Fixed expenses
Profit
Capital intensive
1,000,000
(200,000)
800,000
(700,000)
100,000
You are required to determine the total profit if there is a (i) 10% decline in sales revenue, (ii)
20% increase in sales revenue for each case.
Approach:
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Calculate the DoL
Multiply the change in sales revenue by DoL
Recognise that the question requires the total revised profit and not the impact on profit
Labour intensive
200,000
100,000
2
Capital intensive
800,000
100,000
8
(i) 10% decline in sales revenue
Change in profit (DoL * change in sales revenue)
Impact on profit (profit * change in profit)
Total profit
(20%)
(20,000)
80,000
(80%)
(80,000)
20,000
(ii) 20% increase in sales revenue
Change in profit (DoL * change in sales revenue)
Impact on profit (profit * change in profit)
Total profit
40%
40,000
140,000
160%
160,000
260,000
Contribution margin
Profit
DoL
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CVP ANALYSIS ASSUMPTIONS
1. All other variables remain constant
2. Single product or constant sales mix
3. Total costs and total revenue are linear functions of output
4. Profits are calculated on a variable costing basis
5. Costs can be accurately divided into their fixed and variable elements
6. Analysis applies only to the relevant range
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