Chapter 7 Cost Volume Profit (CVP) Analysis
1. Objectives
1.1 Explain the nature of CVP analysis.
1.2 Calculate and interpret breakeven point and margin of safety.
1.3 Calculate the contribution to sales ratio, in single and multiproduct situations, and demonstrate an understanding of its use.
1.4 Calculate target profit or revenue in single and multiproduct situations, and demonstrate an understanding of its use.
1.5 Prepare break even charts and profit volume charts and interpret the information contained within each, including multiproduct situations
1.6 Discuss the limitations of CVP analysis for planning and decision making.
2. A Recap of Basic CVP Analysis for Single Product
2.1 Breakeven analysis
2.1.1 
Key Terms 


(a) Contribution per unit = unit selling price – unit variable costs (b) Breakeven point = activity level at which there is neither profit nor loss (c) Contribution/sales (C/S) ratio = profit/volume (P/V) ratio (d) Sales revenue at breakeven point = fixed costs ÷ C/S ratio (e) Margin of safety (in units) = budgeted sales units – breakeven sales units

The Graphical Approach for Single Product
2.2.1 The second way to find the breakeven is to use the graphical method. The graphical method is based on the breakeven chart, a graphical representation of costvolumeprofit relationships and the breakeven point. It is an attempt to help management in their understanding of these relationships and so enable them to decide on the optimum level of output.
2.2.2 
Example 1 


A new product has the following sales and cost data.
Forecast sales 1,800 units per month Required: Solution: 
3. Breakeven Analysis for Multiple Products
3.1 A major assumption
3.1.1 Organisations typically produce and sell a variety of products and services. To perform breakeven analysis in a multiproduct organisation, however, a constant product sales mix must be assumed. In other words, we have to assume that whenever x units of product A are sold, y units of product B and z units of product C are also sold.
3.1.2 
Example 2 


PL produces and sells two products. The M sells for $7 per unit and has a total variable cost of $2.94 per unit, while the N sells for $15 per unit and has a total variable cost of $4.5 per unit. The marketing department has estimated that for every five units of M sold, one unit of N will be sold. The organization’s fixed costs total $36,000. Required: Calculate the breakeven point for PL. Solution:
2. Calculate contribution per mix 3. Calculate the breakeven point in terms of the number of mixes 4. Calculate the breakeven point in terms of the number of units of products 5. Calculate the breakeven point in terms of revenue 
3.1.3 
Exercise 2 


Alpha manufactures and sells three products, the beta, the gamma and the delta. Relevant information is as follows.
Total fixed costs are $950,000. An analysis of past trading patterns indicates that the products are sold in the ratio 3:4:5 Required: Calculate the breakeven point for Alpha. 
3.2 Contribution to sales (C/S) ratio for multiple products
3.2.1 The breakeven point in terms of sales revenue can be calculated as fixed costs / average C/S ratio.
3.2.2 Any change in the proportions of products in the mix will change the contribution per mix and the average C/S ratio and hence the breakeven point.
3.2.3 You should know that the C/S ratio is sometimes called the profit/volume ratio or P/V ratio.
3.2.4 
Example 3 

As example 2 above, we can calculate the breakeven point of PL as follows. Solution: 2. Calculate contribution per mix (see example 2) 3. Calculate average C/S ratio 4. Calculate the breakeven point 5. Calculate revenue ratio of mix 6. Calculate breakeven sales 
3.2.5 
Exercise 3 

Calculate the breakeven sales revenue of product Beta, Gamma and Delta (see Exercise 2 above) using the approach shown in Example 3. 
Solution:

3.2.6 
Points to Bear in Mind 

Any change in the proportions of products in the mix will change the contribution per mix and the average C/S ratio and hence the breakeven point. 
3.3 Margin of safety for multiple products
3.3.1 The margin of safety for a multiproduct organisation is equal to the budgeted sales in the standard mix less the breakeven sales in the standard mix. It may be expressed as a percentage of the budgeted sales.
3.3.2 
Example 4 


BA produces and sells two products. The W sells for $8 per unit and has a total variable cost of $3.80 per unit, while the R sells for $14 per unit and has a total variable cost of $4.20. For every five units of W sold, six units of R are sold. BA's fixed costs are $43,890 per period. Budgeted sales revenue for next period is $74,400, in the standard mix. Required: Calculate the margin of safety in terms of sales revenue and also as a percentage of budgeted sales revenues. Solution:
1. Calculate contribution per unit
2. Calculate contribution per mix 3. Calculate the breakeven point in terms of the number of mixes 4. Calculate the breakeven point in terms of the number of units of products 5. Calculate the breakeven point in terms of revenue 6. Calculate the margin of safety 
3.4 Target profits for multiple products
3.4.1 The number of mixes of products required to be sold to achieve a target profit is calculated as:
(fixed costs + required profit)/contribution per mix. 
3.4.2 
Example 5 


An organisation makes and sells three products, F, G and H. The products are sold in the proportions F:G:H = 2:1:3. The organisation's fixed costs are $80,000 per month and details of the products are as follows.
The organisation wishes to earn a profit of $52,000 next month. Calculate the required sales value of each product in order to achieve this target profit. Solution:
2. Calculate contribution per mix
3. Calculate the required number of mixes 4. Calculate the required sales in terms of the number of units of the products and sales revenue of each product
The sales revenue of $464,000 will generate a profit of $52,000 if the products are sold in the mix 2:1:3. Alternatively the C/S ratio could be used to determine the required sales revenue for a profit of $52,000. The method is again similar to that demonstrated earlier when calculating the breakeven point. 
3.4.3 
Example 6 

Using the information as Example 5, calculate the required sales of each products by using the C/S ratio. Solution: Which, allowing for roundings, is the same answer as calculated in the first example. 
3.5 Multiproduct breakeven charts
(A) Breakeven charts
3.5.1 Breakeven charts for multiple products can be drawn if a constant product sales mix is assumed.
3.5.2 Here, there are three approaches to draw the multiproduct breakeven charts.
3.5.3 
Example 7 – Approach 1: Output in $ Sales and a Constant Product Mix 


Assume that budgeted sales are 2,000 units of X, 4,000 units of Y and 3,000 units of Z. A breakeven chart would make the assumption that output and sales of X, Y and Z are in the proportions 2,000: 4,000: 3,000 at all levels of activity, in other words that the sales mix is 'fixed' in these proportions. We begin by carrying out some calculations.
The breakeven chart can now be drawn. The breakeven point is approximately $27,500 of sales revenue. This may either be read from the chart or computed mathematically. The margin of safety is approximately $(58,000 – 27,500) = $30,500. 
3.5.4 
Example 8 – Approach 2: Products in Sequence 


The products could be plotted in a particular sequence (say X first, then Y, then Z). Using the data from Approach 1, we can calculate cumulative costs and revenues as follows.
The breakeven chart can now be drawn. In this case the breakeven point occurs at 2,000 units of sales (2,000 units of product X). The margin of safety is roughly 4,000 units of Y and 3,000 units of Z. 
3.5.5 
Example 9 – Approach 3: Output in Terms of % of Forecast Sales and a Constant Product Mix 

The breakeven point can be read from the graph as approximately 48% of forecast sales ($30,000 of revenue). Alternatively, with contribution of $(58,000 – 37,000) = $21,000, one percent of forecast sales is associated with $21,000/100 = $210 contribution. Breakeven point (%) = fixed costs/contribution per 1% 
(B) Multiproduct P/V charts
3.5.6 The same information could be shown on a P/V chart.
3.5.8 
Exercise 4 


A company sells three products, X, Y and Z. Cost and sales data for one period are as follows.
Required: Construct a multiproduct P/V chart based on the above information on the axes below. 
4. Further Aspects of CVP Analysis
4.1 The usefulness of CVP analysis is restricted by its unrealistic assumptions, such as constant sales price at all levels of activity. However CVP has the advantage of being more easily understood by nonfinancial managers due to its graphical depiction of cost and revenue data.
4.2 Limitations:
(a) It is assumed that fixed costs are the same in total and variable costs are the same per unit at all levels of output. This assumption is a great simplification.
(i) Fixed costs will change if output falls or increases substantially (most fixed costs are step costs).
(ii) The variable cost per unit will decrease where economies of scale are made at higher output volumes, but the variable cost per unit will also eventually rise when diseconomies of scale begin to appear at even higher volumes of output (for example the extra cost of labour in overtime working).
(b) The assumption is only correct within a normal range or relevant range of output. It is generally assumed that both the budgeted output and the breakeven point lie within this relevant range.
(c) It is assumed that sales prices will be constant at all levels of activity. This may not be true, especially at higher volumes of output, where the price may have to be reduced to win the extra sales.
(d) Production and sales are assumed to be the same, so that the consequences of any increase in inventory levels or of 'destocking' are ignored.
(e) Uncertainty in the estimates of fixed costs and unit variable costs is often ignored.
4.3 Advantages:
(a) Graphical representation of cost and revenue data (breakeven charts) can be more easily understood by nonfinancial managers.
(b) A breakeven model enables profit or loss at any level of activity within the range for which the model is valid to be determined, and the C/S ratio can indicate the relative profitability of different products.
(c) Highlighting the breakeven point and the margin of safety gives managers some indication of the level of risk involved.
Examination Style Questions
Question 1 – Breakeven Chart with Increases in Fixed Costs
(a) Identify and discuss briefly five assumptions underlying costvolumeprofit analysis.
(10 marks)
(b) A local authority, whose area include a holiday resort situated on the east coast, operates, for 30 weeks each year, a holiday home which is let to visiting parties of children in care from other authorities. The children are accompanied by their own house mothers who supervise them throughout their holiday. From six to fifteen guests are accepted on terms of £100 per person per week. No differential charges exist for adults and children.
Weekly costs incurred by the host authority are:

£ per guest 
Food 
25 
Electricity for heating and cooking 
3 
Domestic (laundry, cleaning, etc.) expenses 
5 
Use of minibus 
10 
Seasonal staff supervise and carry out the necessary duties at the home at a cost of £11,000 for the 30week period. This provides staffing sufficient for six to ten guests per week but if eleven or more guests are to be accommodated, additional staff at a total cost of £200 per week are engaged for the whole of the 30week period.
Rent, including rates for the property, is £4,000 per annum and the garden of the home is maintained by the council’s recreation department which charges a nominal fee of £1,000 per annum.
Required:
(i) Tabulate the appropriate figures in such a way as to show the breakeven point(s) and to comment on your figures. (8 marks)
(ii) Draw, on the graph paper provided, a chart to illustrate your answer to (b)(i) above. (7 marks)
(Total 25 marks)
Question 2 – Multiproduct Profitvolume Graph
JK Limited has prepared a budget for the next 12 months when it intends to make and sell four products, details of which are shown below:
Product 
Sales in units 
Selling price per unit 
Variable cost per unit 

(000) 
£ 
£ 
J 
10 
20 
14.00 
K 
10 
40 
8.00 
L 
50 
4 
4.20 
M 
20 
10 
7.00 
Budgeted fixed costs are £240,000 per annum and total assets employed are £570,000.
Required:
(a) Calculate the total contribution earned by each product and their combined total contributions. (2 marks)
(b) Plot the data of your answer to (a) above in the form of a contribution to sales graph (or P/V graph) on the graph paper provided. (6 marks)
(c) Explain your graph to management, to comment on the results shown and to state the breakeven point. (4 marks)
(d) Describe briefly three ways in which the overall contribution to sales ratio could be improved. (3 marks)
(Total 15 marks)
Question 3
You are the assistant management accountant of QXY plc, a food manufacturer. The Board of Directors is concerned that its operational managers may not be fully aware of the importance of understanding the costs incurred by the business and the effect that this has on their operational decision making. In addition, the operational managers need to be aware of the implications of their pricing policy when trying to increase the volume of sales.
You are scheduled to make a presentation to the operational managers tomorrow to explain to them the different costs that are incurred by the business, the results of some research that has been conducted into the implications for pricing and the importance of understanding these issues for their decision making. The diagram on the next page has already been prepared for the presentation.
Required:
You are required to interpret the diagram and explain how it illustrates issues that the operational managers should consider when making decisions. (Note: your answer must include explanations of the Sales Revenue, Total Cost and Fixed Cost lines, and the significance of each of the activity levels labelled A, B, C, D.) (10 marks)
Question 4
RDF Ltd offers four services to television companies The number of services provided is measured in service units and details of RDF Ltd's draft budget for its year ending 30 June 2005 are as follows.

Service K 
Service L 
Service M 
Service N 
No. of service units 
1,000 
2,300 
1,450 
1,970 
Selling price per unit ($) 
18 
16 
12 
20 
Variable cost per unit ($) 
8 
10 
13 
13 
Fixed cost per unit ($) 
2 
3 
2 
4 
The budgeted level of activity shown in the table above has been based on fully meeting the forecasted market demand for each type of service.
The following chart has been prepared based on the draft budget above.
Required:
(a) Explain the meaning of the values shown as points A and B on the chart. (Note. Calculations are not required.) (4 marks)
(b) Further investigation into the nature of the fixed costs has shown that some of those shown in the original budget are incurred as a direct result of providing specific services as follows.

$ 
Service K 
4,400 
Service L 
3,700 
Service M 
Nil 
Service N 
2,650 
The remaining budgeted fixed costs are general fixed costs that will be incurred regardless of the type and number of services provided.
RDF Ltd entered into a threeyear contract in June 2002 which requires it to provide 500 units of service M per year or suffer significant financial penalties. These services are included in the budgeted demand.
Required:
(i) Evaluate the financial viability of each of the four services currently provided.
(6 marks)
(ii) Recommend the operating plan that will maximise profit for the year ended 30 June 2005 and state the resulting profit. Explain the assumptions that led to your decision and other factors that should be considered. (5 marks)
(iii) Calculate the overall breakeven sales value for the operating plan you have recommended in answer to (b)(ii), stating clearly the assumptions made in your calculations. (5 marks)
(iv) Comment on any limitations of using breakeven analysis for decision making purposes. (5 marks)
(Total = 25 marks)
3.5.7 
Example 10 


Same information as Example 7,
By convention, the products are shown individually on a P/V chart from left to right, in order of the size of their C/S ratio. In this example, product X will be plotted first, then product Y and finally product Z. A dotted line is used to show the cumulative profit/loss and the cumulative sales as each product's sales and contribution in turn are added to the sales mix.
You will see on the graph which follows that these three pairs of data are used to plot the dotted line, to indicate the contribution from each product. The solid line which joins the two ends of this dotted line indicates the average profit which will be earned from sales of the three products in this mix. The diagram highlights the following points. The multiproduct P/V chart therefore helps to identify the following. 
2.1.2 
Exercise 1 


A company manufactures a single product which has the following cost structure based on a production budget of 10,000 units.
Variable production overheads are recovered at the rate of $8 per direct labour hour. Other costs incurred by the company are:
The selling and distribution overheads include a variable element due to a distribution cost of $2 per unit. The fixed selling price of the unit is $129. Required: 
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