MANAGEMENT ACCOUNTING MODULE 4 - CMA-AP

432 Pages·2010·2.55 MB·English

CMA Accelerated Program

MANAGEMENT ACCOUNTING
MODULE 4
Management Accounting

Table of Contents

9. Cost-Volume-Profit Analysis 3
10. Relevant Costs 33
11. Linear Programming 75
12. Uncertainty 117
13. Pricing 148
14. Budgeting 177
15. Capital Budgeting 217
16. The Lease or Buy Decision 240
17. Cost Variances 250
18. Revenue Variances 280
19. Variable and Absorption Costing 309
20. Transfer Pricing 344
21. Performance Evaluation 399
22. Strategic Cost Management Techniques(cid:1) 419
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Management Accounting

9. Cost-Volume-Profit Analysis

Learning Objectives
After completing this chapter, you will:
1. Understand the role of cost volume profit analysis
2. Be able to apply cost volume profit analysis in both single product and multi-product
settings
3. Be able to adapt and use cost volume profit analysis to evaluate the profit effect of
management initiatives such as advertising and re-engineering
4. Understand and be able to adapt cost volume profit tools to more complex, spreadsheet-
based models
The Cost Volume Profit Model
The basic cost volume profit (CVP) model makes the
CVP Analysis in the News
following important assumptions:
The automaker (Chrysler) can break
1. The volume of sales does not affect product price.
even by selling one million cars
annually in the US and make $1 2. The volume of product does not affect variable
billion for every additional 100,000 cost per unit.
vehicles, two people familiar with its
finances have said. 3. All costs are either variable or fixed.
Source: 4. All production is sold.
http://www.bloomberg.com/apps/news?pid=
20601087&sid=alTdWHyet7II&pos=1 With these assumptions, we can use the profit
equation to develop the CVP relationship.

Let:
• P = price per unit
• V = variable cost per unit
• F = total fixed cost
• x = number of units produced and sold
• OI = operating income

Revenues - costs = operating income
Px - Vx - F = OI
x (P - V) - F = OI
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Management Accounting

Accountants call price per unit minus variable cost per unit (P – V) the contribution margin per
unit. The contribution margin per unit is the dollar amount that each unit made and sold
contributes to covering fixed costs and provides a profit. We can now write the above equation
as:
xCM - F = OI
x = (fixed costs + operating income) / contribution margin per unit
For convenience, we will refer to this equation as the units CVP equation. What the units CVP
equation does is it allows the decision maker to identify the number of units (x) that must be
made and sold to cover fixed costs and provide a target profit. Or, put another way, it predicts
the profit (or loss) resulting from a given level of unit sales.
Using the Units Cost Volume Profit Model
The following is an example illustrating the use of the units CVP model. Russell Company sells
a product that has a price of $4 per unit, variable manufacturing costs of $2 per unit and selling
costs of $.50 per unit. Russell Company has fixed manufacturing costs of $125,000 and fixed
general, selling and administrative expenses of $25,000. Assume management has two
questions:
1. How many units does Russell Company have to sell to breakeven?
2. How many units does Russell Company have to sell to earn a pre-tax profit of $100,000?
The total variable cost of the company’s product is $2.50 ($2 + $.50). Therefore, the
contribution margin per unit is $1.50 ($4 - $2.50). The company’s total fixed cost is $150,000.
Breakeven means zero profit, so putting this data in the units CVP equation we have:
x = 150,000 / 1.50 = 100,000 units
The following equation computes the unit sales needed to generate a target profit of $100,000
X = (100,000 + 150,000) / 1.50 = 166,667 units
We will follow the convention in these notes that when a target quantity is computed, it will be
rounded up, when necessary, to calculate the solution.
A measure that management accountants often find useful as a means of expressing financial risk
is the margin of safety measure. The margin of safety is computed as follows:
Margin of safety = expected units - breakeven units
Or as the margin of safety percentage:
Margin of safety percentage = (expected units - breakeven units) / expected units
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Management Accounting

Assume in the above example management believes the company will sell 150,000 units, the
margin of safety is 150,000 - 100,000 = 50,000 units. The margin of safety percentage is 33%
[(150,000 - 100,000) / 150,000]. The margin of safety percentage measure says that sales would
have to drop at least 33% from expected levels before losses would occur.
Developing and Using the Revenue Cost Volume Profit Model
Often decision makers prefer that the required levels to achieve breakeven or a target profit be
stated in revenue terms. We can easily adapt the units CVP model to adopt the revenue
perspective.
Return to the units CVP equation. Note that we can convert this equation to a revenue equation
by multiplying both sides of the equation by price per unit. We now have:
Revenue = Px = P(operating income + fixed costs)
CM per unit
Dividing the top and the bottom of the right hand side of the equation, we have:
Revenue = (operating income + fixed costs) / (CM/unit / P)
Management accountants call the ratio of contribution margin per unit divided by price per unit
the contribution margin ratio. The contribution margin ratio reflects the proportion of each sales
dollar that goes toward covering fixed costs and providing a profit.
So, we have the following equation, which we will call the revenue CVP equation:
Revenue = (operating income + fixed costs) / CM ratio
Returning to the Russell Company example, we can compute the product’s contribution margin
ratio as follows:
$1.50 / 4 = 37.5%
We can now answer the following questions expressed in revenue terms for the above product:
1. What sales revenue must Russell Company achieve to breakeven?
2. What sales revenue must Russell Company achieve to earn a profit of $100,000?
Question one can be answered with the following calculation:
$150,000 / .375 = $400,000
Question two can be answered with the following calculation:
($150,000 + 100,000) / .375 = $666,667
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Management Accounting

The Cost Volume Profit Chart
Often, management accountants find it useful to express the CVP relationship in a CVP chart.
The CVP chart for the product described above would look as follows:

The advantage of the CVP chart is it provides a visual representation of units, revenues, costs
and profits, which often help communicate these relationships more effectively.
Taxes and the CVP Equations
Returning to the basic profit equation, we have:
After tax profit = (revenue – variable cost – fixed cost) * (1 – tax rate)
or, using the notation, we developed above:
After tax profit = ((P – V)x – f) * (1 – tax rate))
rearranging, and recalling that (p – v) is the unit contribution margin, we get the following unit
CFP equation adapted for taxes:
x = [(after tax profit / 1 - t)] + fixed costs / CM per unit
and following the same procedure we used above, we can develop the following sales CVP
equation:
Revenue = [(after tax profit / 1 - t)] + fixed costs / CM ratio

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Management Accounting

Returning to Russell Company, assume the company faces a tax rate of 30%, how many units
must Russell Company sell to earn a post-tax profit of $100,000?
We have, in units:
[(100,000 / .7) + 150,000] / 1.5 = 195,339 units
or, in revenue:
[(100,000 / .7) + 150,000] / .375 = $780,953
Exploiting the Profit Equation
The profit equation provides, in effect, a financial model of the organization. Manipulating the
profit equation allows management to undertake analyses to predict the effect of proposed
decisions, a process called what-if analysis.
Assume, given the data noted above, Russell Company management expects unit sales of
160,000 for the upcoming period. The marketing manager believes that a 5% price decrease and
a $25,000 advertising budget will increase sales to 175,000 units. Are these changes desirable?
We use incremental analysis to calculate the incremental income of the proposed change as
follows:
Total contribution margin
Before: 160,000 units x $1.50 $240,000
After: 175,000 x $1.30* 227,500
Incremental contribution margin 12,500
Advertising costs 25,000
Incremental income ($12,500)

* Sales price decrease = decrease in CM/Unit = $4 x 5% = $.20
New CM/unit = $1.50 - .20 = $1.30

Modelling Uncertainty
Even with limited computational power, decision makers were able to incorporate probabilistic
concepts into CVP analysis. Again, the applications required considerable simplification.
For example, return to the original Russell Company example and assume demand in the
forthcoming period is uncertain and has been estimated at between 80,000 and 180,000, with all
units on this interval equally likely. In effect, sales have been estimated as following a uniform
distribution.
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Management Accounting

Recall that breakeven sales were computed as 100,000 units. The probability of at least breaking
even given this uniform distribution is computed as follows:
Probability = upper limit - breakeven quantity = 180,000 - 100,000 = 80%
upper limit - lower limit 180,000 - 80,000

As an exercise you should verify that the probability that Russell Company will earn $100,000 or
more is 13.3%.

Similar statements could be developed for any other standard distribution whose properties are
well known such as the normal distribution.
Multi-Product
Most of what we have discussed in this chapter was well known to, and practiced by, both
managers and accountants in the early 1900s. In fact, there is evidence to suggest that CVP
analysis was originally developed by managers and not accountants. This approach was,
therefore, developed at a time when there were no calculators, let alone computers. For this
reason assumptions needed to be made to make the analysis tractable. This is why assumptions
like constant prices, variable costs and fixed costs were so important.
So, when decision makers decided they wanted to adapt the CVP models described above to
multi-product organizations, they needed to make another assumption to make the CVP model
work. The assumption made was as total sales levels increased or decreased, each product’s
proportion of total sales would remain constant.
An example best illustrates the approach and the insights of multi-product CVP analysis.
Brant Consulting design costing and transfer pricing systems for its clients. The following is a
summary of volume, revenue and cost expectations for the upcoming year:

Costing Projects Transfer Pricing Projects
Item Number 50 Number 75 Firm Total
Per Job Total Per Job Total
Revenue $10,000 $500,000 $15,000 $1,125,000 $1,650,000
Variable cost 4,500 225,000 11,500 862,500 1,103,500
Contribution margin $5,500 $275,000 $3,500 $262,500 $537,500
Fixed cost 475,000
Profit $62,500
The solution to the problem comprises of combining units in a 'bundle' based on their sales mix.
In this case, the sales mix is 50 costing projects (CP) and 75 transfer pricing projects (TPP). At
its lowest common denominator, we can say the sales mix is 2:3 (CP:TPP).

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Management Accounting

We then create a product bundle containing two CP and three TPP and calculate the contribution
margin generated by that bundle:

(2 x $5,500) + (3 x $3,500) = 21,500

The number of bundles needed to be sold to breakeven are:

$475,000 / 21,500 = 22.1

We then break out the bundles into the individual products:

Costing projects: 22.1 bundles x 2 = 45
Transfer pricing projects: 22.1 bundles x 3 = 67

The unit sales Brant Consulting needs to achieve an operating income of $60,000 is:

($475,000 + 60,000) / 21,500 = 24.88

Breaking out the bundles into the individual products:

Costing projects: 24.88 bundles x 2 = 50
Transfer pricing projects: 24.88 bundles x 3 = 75

Spreadsheets
Today, with powerful computers and electronic spreadsheets, business modelling is done on
computers. However, the basic modelling insights developed in CVP analysis underlies the
financial models implemented on computers.
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Management Accounting

Problems with Solutions

Multiple Choice Questions

1.
  Spencer Company expects to sell 60,000 units of Product B next year. Variable
production costs are $4 per unit and variable selling costs are 10% of the selling
price. Fixed costs are $115,000 per year and the company desires an after-tax profit
of $30,000 next year. The company's tax rate is 40%. Based on this information, the
unit selling price next year should be:

  a)
  $7.00

  b)
  $10.75

  c)
  $7.50

  d)
  $6.75

  e)
  None of the above

2.
  Operating income is shown on a cost-volume-profit chart where the:

  a)
  Total variable cost line exceeds the total fixed cost line

  b)
  Total cost line exceeds the total sales revenue line

  c)
  Total sales revenue line exceeds the total fixed cost line

  d)
  Total sales revenue line exceeds the total cost line

  e)
  Total cost line intersects the total sales revenue line

3.
  The following information relates to a new product an organization plans to
introduce:

  Selling price
 $80 per unit

  Variable selling cost $ 5
 per unit

  Direct materials $
 25 per unit

  Direct labour $
 10 per unit

  Variable overhead $ 2 0
  per unit

  Fixed overhead
  $140,000 per year

  Fixed selling expense $
 60,000 per year

  How many units of this product must be sold each year to breakeven?

  a)
  2,500

  b)
  10,000

  c)
  7,000

  d)
  8,000

  e)
  4,444

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 2011