1. Analysis of Cost, Volume, and Pricing to Increase Profitability
CHAPTER 3
Analysis of Cost, Volume, and Pricing to Increase Profitability
Chapter 3: Analysis of Cost, Volume, and Pricing to Increase Profitability
In Chapter Three we will learn how companies analyze costs, sales volume, and pricing to improve overall profitability. Soon after graduation you will be in a management position and understanding the relationships in this chapter will help you become a more effective manager.
PowerPoint Author:
LuAnn Bean, Ph.D., CPA, CIA, CFE
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. The Equation Method At the break-even point:
Sales = Variable cost + Fixed cost
We can look at the above equation like this:
Part I We can look at this relationship in a different way by breaking down sales into the number of units sold times the selling price per unit. We can do the same for our variable costs. The point at which a company covers its variable and fixed costs and has a profit of zero is called the break-even point. The break-even point can be calculated using the equation method, the contribution margin per unit method, or the contribution margin ratio method. We will examine each of these three methods.
Part II At the break-even point sales are equal to variable costs plus fixed costs because profit is zero.

3. Determining the Break-Even Point Using the Equation Method
The break-even point is the point where total revenue equals total costs (both variable and fixed). For Bright Day, the cost of advertising is estimated to be $60,000. Advertising costs are the fixed costs of the company. We use the following formula to determine the break-even point in units.
The equation method begins by expressing the income statement as follows. At the break-even point, profit is equal to zero.
Sales – Total variable cost – Total fixed cost = Profit
$36N - $24N - $60,000 = 0
$12N = $60,000
N = $60,000/$12 = 5,000 Units
Part l
Bright Day Distributors sells one product called Delatine, a nonprescription herb mixture. Delatine costs $24 per bottle, and Bright Day plans to sell the product for $36.
Part ll
The company is considering a $60,000 advertising campaign, and the president is concerned about whether they can sell at least enough bottles of Delatine to cover the cost of the advertising.
The equation method begins by expressing the income statement as sales minus total variable cost, minus total fixed cost equals a profit of zero. For Delatine, sales can be expressed as $36, the selling price, times X, the number of bottles sold. Total variable cost can be expressed as $24, the variable cost per unit, times X, the number of bottles sold, and the total fixed cost is $60,000, the cost of the advertising campaign.
Using the equation method, we can determine that Bright Day would need to sell five thousand bottles of Delatine to earn a profit of zero, or to break even.

4. Determining the Contribution Margin per Unit
The contribution margin per bottle of Delatine is:
Break-even volume in units =
Fixed costs Contribution margin per unit
Part l
We can also determine the break-even point by using contribution margin per unit. Recall that contribution margin is the difference between sales revenue and variable costs. Contribution margin per unit is equal to the selling price for one unit minus the variable cost per unit. The contribution margin per bottle of Delatine is $12. This means that for every bottle of Delatine it sells, Bright Day earns $12 in contribution margin to help pay fixed costs. Therefore, Bright Day will reach the break-even point when it sells enough bottles of Delatine to cover its fixed cost.
Part ll
Break-even point can be determined by dividing fixed cost by the contribution margin per unit. Note that both the equation method and the contribution margin per unit method yield the amount of break-even sales measured in units.
Part lll
To determine the break-even point in dollars, we can multiply the number of unit, five thousand, by the sales price per unit, thirty six. The break-even point for Delatine, therefore, is $180,000. =
$60,000 $12
= 5,000 units

5. Determining the Break-even Point
The break-even sales volume expressed in dollars can also be determined by dividing the fixed cost by the contribution margin ratio (which is contribution margin divided by sales) computed using either total or per unit figures.
Contribution margin ratio = Contribution margin ÷ Sales
Break-even volume in dollars =
Fixed costs Contribution margin ratio
Part l
The break-even point in dollars can also be determined using the contribution margin ratio method.
Part ll
The contribution margin ratio can be calculated by dividing contribution margin by sales, either on a total or a per unit basis.
Part lll
For Delatine, the contribution margin ratio is , or twelve divided by thirty six. The break-even volume in dollars is computed by dividing fixed cost, $60,000, by You see that again, the break-even point is $180,000. All three methods yield the same results because all three are merely different derivations of the income statement formula. =
$60,
= $180,000
$60,000 $60,000 / $180,000

6. Reaching a Target Profit
Bright Day’s president wants the advertising campaign to produce profits of $40,000 to the company.
Sales – Total variable cost – Total fixed cost = Profit
$36N - $24N - $60,000 = $40,000
N = $100,000/$12 = 8, Units
Sales volume in units =
Fixed costs + Desired profit Contribution margin per unit
Part I Bright Day’s president decides the ad campaign should produce a $40,000 profit. Using the equation method, we set the desired profit at $40,000, and determine that Bright Day must sell 8, units, rounded to 8,334.
Part II We can also use any of the other break-even methods by simply adding desired profit to fixed costs. After all, the company must achieve the contribution margin needed to cover its fixed costs and the desired profit. =
$60,000 + $40,000 $12
= 8,334 units

7. Effects of Changes in Sales Price
Using the equation method, the units required to yield a $40,000 profit are:
Sales – Total variable cost – Total fixed cost = Profit
$28N - $24N - $60,000 = $40,000
$4N = $100,000
N = $100,000/$4 = 25,000 Units
Using the contribution margin per unit method:
Part I
The Marketing Department at Bright Day suggests that a price drop from $36 per bottle to $28 per bottle will make Delatine a more attractive product to sell. The president wants to know what effect such a price drop would have on the company’s stated goal of producing a $40,000 profit. You have been asked to determine the number of bottles that must be sold to earn the $40,000 profit at the new $28 selling price per bottle.
Part II Lowering the contribution margin per unit will dramatically increase the sales volume necessary to attain the desired profit when the sales price per unit is reduced to $28. We can use the equation model to see the effect of lowering the price.
Part III
Using the contribution margin per unit method, we need to combine the fixed advertising costs with the desired profit and divide by the new contribution margin. As you can see, Bright Day must sell 25,000 bottles of Delatine to earn the desired profit of $40,000. =
$60,000 + $40,000 $4
= 25,000 units

8. Effects of Changes in Sales Price
The required sales volume in dollars is $700,000 (25,000 units × $28 per bottle) as shown below:
Here is the contribution margin income statement to prove that the math from our last screen was correct.

9. Assessing the Effects of Changes in Variable Costs
Sales – Total variable cost – Total fixed cost = Profit
$28N - $12N - $60,000 = $40,000
$16N = $100,000
N = $100,000/$16 = 6,250 Units
Break-even volume in units =
Fixed costs + Desired profit Contribution margin per unit
Part I
The chemists at Bright Day have found an alternative mixture for Delatine that will meet all laws and regulations concerning the product. The new mixture lowers the variable production costs to $12 per bottle and the marketing department believes the company should sell the product for $28. The president still demands a $40,000 profit on the product. How many bottles of the new formula must be sold to meet the stated profit goals?
Part II
Using the equation method, we set variable costs to the new $12 per bottle.
Part III We can also use the contribution margin per unit method, with a new contribution margin per unit of $16.
Part IV The company must sell 6,250 bottles of the newly formulated Delatine to meet the $40,000 profit goal. =
$60,000 + $40,000 $16
= 6,250 units

10. Assessing the Effects of Changes in Fixed Costs
Bright Day’s president has asked you to determine the required sales volume if advertising costs were reduced to $30,000, from the planned level of $60,000.
Sales – Total variable cost – Total fixed cost = Profit
$28N - $12N - $30,000 = $40,000
$16N = $70,000
N = $70,000/$16 = 4,375 Units
Part I The marketing manager tells the president that with the new formulation, lower selling price, and sixteen dollar contribution margin, he believes that the advertising budget can be cut in half to $30,000. The president asks you to determine the number of units that must be sold to meet the profit goal. See if you can calculate the number of units before going to the next screen.
Part II
Bright Day must sell 4,375 units.
Part III Here is the proof. =
= 4,375 units
$30,000 + $40,000 $16
Break-even
volume (units)

11. Cost-Volume-Profit Graph
Here is the graph for Delatine with fixed costs of $30,000, a selling price of $28 and variable expenses of $12. Our fixed costs plot as a straight-line parallel to the X axis that intercepts the Y axis at $30,000. Total cost slopes upward beginning where fixed cost intercepts the Y axis and has a slope equal to the variable cost per unit. The sales line starts at the origin and has a slope equal to the selling price per unit.
The point at which the total cost line crosses the sales line is the break-even point, $52,500 or 1,875 units. Any level of sales to the left of the break even point is in the area of loss and any level to the right is in the area of profitability.

12. Calculating the Margin of Safety
The margin of safety measures the cushion between budgeted sales and the break-even point. It quantifies the amount by which actual sales can fall short of expectations before the company will begin to incur losses.
Break-even
volume (units) =
$30,000 ÷ $16 = 1,875 units
Part l
Recall that Bright Day’s budgeted sales are 4,375 units, or $122,500.
Part II The margin of safety measures the cushion between budgeted sales and the break-even point. It quantifies the amount by which actual sales can fall short of expectations before the company will begin to incur losses.
Part III
With the information given the unit sales that produce a profit of $40,000 are 4,375. The break-even unit sales are 1,875.
Part IV
The unit selling price is $28, so break-even sales are $52,500. The margin of safety is 2,500 units or $70,000.
Part V We can express the margin of safety as a percent with this equation.
Part VI In our fact situation, the margin of safety is percent.
Margin of
safety =
Budgeted sales – Break-even sales Budgeted sales
Margin of
safety =
$122,500 – $52,500 $122,500
= 57.14%

13. Break-Even Analysis for Multiple Products
Synthetic C
Organic C
Sales Price $7 $9
Variable Cost 5 6
Contribution Margin $2 $3
The first step in determining the break-even point is to
compute the
weighted average contribution margin per unit.
Up to this point, our discussion of CVP assumed that a company sells only one product. However, in the real world, most companies sell many products, with each having an independent impact on the profitability of the company.
Assume that Bright Day’s management team is examining its annual Vitamin C Sales Days event. The sales event focuses on two products. One product is labeled Synthetic C; the other is called Organic C. The sales price, variable cost, and contribution margin for each bottle of each product is shown here. Due to its lower cost, Synthetic C has consistently outsold the Organic C.
Indeed, Synthetic C historically accounts for approximately 80 percent of the total sales; with Organic C making up the remaining 20 percent. The fixed costs for the annual sales event are expected to be $2,112. These fixed costs are largely composed of advertising and training expenses. The management team begins its examination by determining the break-even point.
The first step in determining the break-even point is to compute the weighted average contribution margin per unit.

14. Break-Even Analysis for Multiple Products
Using the per unit contribution margin approach,
the break-even point in total units can be determined by
dividing the fixed cost by the weighted average contribution
margin as follows.
Break-even
sales =
Fixed costs Weighted average per unit cont. margin
Part l
Break-even sales for multiple products can be determined using a weighted-average contribution margin. In this example, we set the relative quantity of Synthetic Vitamin C and Organic Vitamin C sold at 80% and 20% respectively. The contribution margin per unit of each product is multiplied by the percentage of that product in the product mix, and then that amount is totaled for all products to determine the weighted average per unit contribution margin.
Part ll
The break-even point in total units for an 80/20 sales mix is computed by dividing total fixed costs for all products, $2,112 by the weighted average per unit contribution margin, $2.20, giving 960 total units for break-even sales.
Part III
By multiplying the total sales of 960 times the respective 80/20 sales mix, we find that 768 bottles of Synthetic Vitamin C and 192 bottles of Organic Vitamin C must be sold to breakeven.
Part IV
It is also possible to figure a target profit for multiple products, as well as experiment with what-if scenarios for shifting the sales mix and changing sales price and contribution margins for multiple products.
Break-even
sales =
$2,112/$2.20 = 960 total units

15. Cost-Volume-Profit Limitations
CVP is limited by a number of underlying assumptions. 1
The selling price is constant. 2
Costs are linear. 3
The multiproduct sales mix is constant. 4
Inventory levels in manufacturing companies are constant. 5
All CVP variables are within the relevant range.
CVP is limited by a number of underlying assumptions. These assumptions include:
1. The selling price is constant. It does not increase or decrease regardless of changes in sales volume.
2. Costs are linear. More specifically, three conditions exist; they are (a) The variable cost per unit is constant and moves in direct proportion with changes in sales volume; (b)Total fixed costs do not change with changes in sales volume; and (c) Efficiency and productivity are constant.
3. The sales mix in multiproduct companies is constant.
4. Inventory levels in manufacturing companies are constant.
5. All CVP variables are within the relevant range.
Violating these assumptions will produce inaccuracies in CVP analysis.

16. End of Chapter 3
End of Chapter 3.