Cost Volume Profit Analysis (CVP Analysis)
This is a very powerful tool in management accounting. Its main purpose is to help management understand the relationship among cost, volume and profit, and management uses the information derived from the analysis to make sound business decisions regarding products to be produced and sold, prices to be charged for the product, cost structure to maintain, marketing strategy to adapt and so much more.
Cost volume profit analysis provides answers to questions about the consequences of following particular courses of action. Questions cost volume profit analysis seek to provide answers to include:
 How many units of a product must be sold to break even
 What would be the effect on profit if our selling price is reduced in a bid to sell more of our products
 Should we pay our sales people on the basis of commission per sale only, or fixed salary only, or a combination of both?
 How many additional units must we sell to meet up with additional fixed expenses arising as a result of an advertising campaign
 What is the maximum amount to be spent on an advertising campaing, assuming it would contribute X number of goods sold.
CVP analysis seeks to analyze the firm’s relationship between the activity level and changes in sales, revenue, expenses and net profit. With this information, the firm can make decisions on production levels or pricing model for the product.
To summarize, a CVP analysis seeks to establish the financial effect or result of a change in activity level of a firm in order to enable management make informed decisions, ascertain critical output level and determine break even points of new or existing products.
Cost Volume Profit analysis is based on certain assumptions, without these assumptions, it would be impossible to use the CVP analysis. These assumptions are:]
 All costs can be accurately classified as either fixed costs or variable costs.
 Costs are linear within the relevant range
 Units sold equals units produced
 Selling price remains constant no matter the volume sold
 CVP analysis applies only to a short time horizon
Explanation of assumptions
a) All costs can be accurately classified as either fixed costs or variable costs: CVP analysis uses contribution margin to ascertain break even points and the effect of selling price change (Don’t worry, contribution margin would be discussed later on). As a result of the use of the concept of contribution which is (selling price – Variable cost), we need to be able to accurately differentiate variable costs from fixed costs.
b) Costs are linear within the relevant range: We assume that variable cost is constant per unit within the relevant range. The term relevant range refers to the output range at which the firm expects to be operating within a short term planning horizon. Within this range, we assume that the variable cost per unit is the same throughout the entire range of output. We also assume that fixed cost is constant for a specific range of output (i.e relevant range). It should be noted that outside the relevant range, fixed costs can rise and this would result into a step fixed cost. A step fixed cost occurs when a specified activity level is passed, and the new activity level requires an additional fixed cost. For example, the production of Product B between 0 – 40,000 units incurs a fixed cost of $20,000 and if the production rises above 40,000 units in any given year, to a point less than or equal to 50,000 units, then an additional $5,000 of fixed cost is incurred. For production levels between 50,001 – 60,000 units, total fixed cost would amount to $30,000
Analysis

From the above, production between 40,001 – 50,000 incurs a step fixed cost, and this raises total fixed cost to $25,000. If production cost is between 50,001 – 60,000 units, then another step fixed cost is incurred, thereby raising the total fixed cost to $30,000.
C) Units sold equals units produced. Cost volume analysis makes use of contribution margin, and to derive our contribution, we need to use marginal costing technique. This is because under marginal costing, we can easily classify costs as variable or fixed costs. Marginal costing assumes that units sold equals units produced, and fixed costs are charged as period costs (i.e charged in full during each period), unlike absorption costing, another costing technique which divides fixed costs into variable manufacturing overhead and fixed manufacturing overhead. Absorption costing treats fixed costs as product costs, and apportions them based on the units produced within the period.
d) Selling price remains constant no matter the volume sold: In cost volume profit analysis, we assume that selling price is fixed, except management decides to reduce prices in order to increase sales volume. We do not take Into consideration discounts allowed on large volumes of sale which might be applicable in real life situations.
e) Cvp analysis applies only to short term horizons. From the previously mentioned points it is evident that the CVP analysis can be used for only short term planning. We discussed step fixed costs in point 2, and this would be inevitable as the company expands and increases capacity. Step fixed costs might come in the form of additional supervision and machinery, appointment of additional sales person and the expansion of the firm’s distribution facilities.
Concept of Contribution
As discussed earlier, contribution is “Bae” in cost volume profit analysis. In this section we would be taking a brief look at the concept of contribution. Are you ready? Sure you are! Let’s fire on then.
Remember under the assumptions of CVP analysis, we talked about it being easier to classify fixed costs into fixed costs or variable costs under marginal costing than absorption costing. For this reason, our preferred costing technique under cost volume profit analysis is marginal costing. For further explanation, the reason is that if we can identify the variable costs associated with producing and selling a product or service, then we can highlight a very important measure which is contribution. As mentioned earlier, contribution is “bae” in cost volume analysis, that is why we pick marginal costing over absorption costing.
Contribution may be defined as the value of sales or revenue contributed towards fixed costs and profits after variable costs has been removed. Once the contribution of a product or service has been calculated, the fixed costs associated with the product or service can be deducted to determine the profit for the period.
How then do we find contribution? We simply say:
Contribution = Sales Value – Variable Costs
Calculating the breakeven point (BEP) in units
Breakeven point is the sales revenue or units of goods sold that would be just enough to cover variable costs and fixed costs, without leaving any profit, i.e zero profit is made. We can say that it is a point of sale where neither profit nor losses are made.
When calculating the breakeven point in units, we need to know how many units of a product must be sold to just cover its variable cost and its share of fixed costs. To be able to do this, we need to know the contribution per unit of the product and also its fixed costs. After getting the contribution, we use this formula to derive our breakeven point in units:
Breakeven point in units =
Let us take an example:
A company manufactures product Enigma, incurring variable costs of $20 per unit and Fixed costs of $60,000 per year. If the product sells for $60 per unit, what is the breakeven point in units?
Possible Solution
Recall that
Break even point in units =
To calculate the contribution per unit, we say: Selling price per unit – Variable cost per unit
So we have our contribution per unit to be = $50 – $20
= $30
Now that we have the contribution per unit and the fixed cost, we can go ahead to find the reak even point in units.
BEP _{(Units) }=
Where fixed cost = $60,000
Contribution per unit = $30
Bep _{(units) }=
Bep _{(units) }= 2,000 units
This means we need to sell 2,000 units of product enigma per year to be able to cover both variable and fixed costs without leaving any profit behind for the period concerned.
Margin of Safety
Margin of safety represents the amount by which expected sales can fall, while the company still covers the variable and fixed costs. It is the difference between the expected level of sales and the breakeven point. The larger the margin of safety, the more likely it is that profit would be made. For there to be any margin of safety, we assume that projected sales volume are higher than the breakeven point in units.
From the previous example, let us assume that projected sales volume is 2,500 units. To calculate our margin of safety, we simply say:
Margin of safety = Projected sales – Breakeven point.
Recall that
Projected sales = 2500 units
Breakeven point = 2000 units
Our margin of safety = 2500 units – 2000 units
= 500 units
Breakeven point in sales value:
Breakeven point in sales value is the value total sales must be in order to cover total costs (variable costs + fixed costs). To be able to calculate the breakeven point in sales value, we need to know the contribution to sales ratio. As the name implies, the contribution to sales ratio is simply the ratio of contribution to sales. It is usually expressed as a percentage, and a higher contribution to sales ratio means that contribution grows more quickly as sales levels increase. The formula for finding the contribution to sales ratio is:
From the previous example where our selling price was $50 per unit and variable cost $20 per unit, we calculated our contribution per unit to be $30 per unit. Our contribution to sales ratio (c/s ratio) would then be
=
= 60 %
Now that we have learnt how ot calculate the c/s ratio, we can go ahead to calculate the breakeven point in sales value. The formula for finding the breakeven point in sales value =
Recall that our fixed cost is $60,000 and we know our c/s ratio to be 60% or 0.60. Our breakeven point in sales value would then be :
= $100,000
This means we must make total sales revenue of $100,000 if we want to cover fixed costs and variable costs only.
Calculating units to be sold in order to obtain a target profit
Assuming we want to make a target profit of $51,000 in the previous example, we can derive the total units that must be sold inorder to obtain this target profit. To do this, we use this formula:
Recall that our fixed cost = $60,000
Target profit = $51,000
Contribution per unit = $30
Units to be sold =
=
= 3,700 units
That means that we need to sell a total of 3700 units to make a profit of $51,000.
Calculating the maximum amount to spend on an advertising campaign
Remember I saw that cost volume profit analysis seeks to provide answers to some questions. I went on further to list some of the questions, and one of the questions mentioned was that CVP analysis seeks to provide answers to ascertaining the maximum amount to be spent on an advertising campaign assuming it would contribute x number of goods sold.
In this section, I am going to demonstrate how we can use cost volume profit analysis to determine this. Let’s assume that we seek to launch an advertising campaign which has a projected result of increasing total units sold by 3000 units. Our selling price is $100 and our variable cost is $60. What is the maximum amount we can spend on this advertising campaign?
Simple right? Yup! You guessed right. All we need to do is to determine the contribution per unit and then multiply it with the additional units the advertisements would bring in.
So we say: Contribution = Selling price – Variable cost
= $100 – 60
= $ 40
The maximum amount that can be spent on the advertisement
= Contribution per unit X additional sales from advertising
= $40 X 3000
= $12,000
This means that the maximum amount we can spend on the advertising campaign is $12,000
Limitations of cost volume profit analysis
 Selling price is assumed to be constant for every unit sold. This may be unrealistic because some situations may require a reduction of the selling price. For example, if the company wants to achieve higher sales volume, it may need to reduce its selling price. Also, the company may need to give discounts on large volume purchases in order to retain valuable customers and promote customer loyalty.
 It doesn’t take into cognizance other factors that might affect costs. Cost volume profit analysis assumes that only activity level drives cost. Factors such as inflation are ignored. This is essentially the reason why it CVP analysis is limited to a short term horizon
 The analysis suggests that as long as the activity level is above the breakeven point, profit would be made. Whereas, in real life situations, certain changes in cost and revenue patterns may create a second breakeven point after which losses are made.
Recommended Readings
Colin Drury., Management Accounting for Business
Jae sim., Joel siegel., Schaum’s outline of managerial accounting
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