1. Analysis of Cost, Volume, and Pricing to Increase Profitability
Chapter Nineteen
Analysis of Cost, Volume, and Pricing to Increase Profitability
In Chapter Nineteen 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.

2. Learning Objective 1
Determine the sales price of a product using a cost-plus pricing approach.
Learning Objective One:
Determine the sales price of a product using a cost-plus pricing approach.

3. Determining Contribution Margin per Unit
Bright Day produces one product called Delatine. The company uses a cost-plus-pricing strategy; it sets prices at cost plus a markup of 50% of cost. Delatine cost $24 per bottle to manufacture, so a bottle sells for $36 ($24 + [50% × $24]). The contribution margin per bottle is:
Bright Day is considering adding a new product to its current product line. The new product is call Delatine and cost twenty-four dollars per bottle to manufacture. It is the company’s policy to mark up all products fifty percent above cost, so Delatine will have a selling price of thirty-six dollars per bottle. When we subtract the variable cost of production from the sales revenue per unit, we get the contribution margin per bottle of twelve dollars. This is a critical value for management’s decision process. The first question the CEO of Bright Day has is, “Can the company sell enough bottles to make a profit?” Let’s see if we can help him answer this question.
The company’s first concern is if it can sell enough bottles of Delatine to cover its fixed costs and make a profit!

4. Learning Objective 2
Use the contribution per unit approach to calculate the break-even point.
Learning Objective Two:
Use the contribution per unit approach to calculate the break-even point.

5. Determining the Break-even Point
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.
Break-even volume in units =
Fixed costs Contribution margin per unit
Part One The break-even point is where total revenue is equal to total costs, both variable and fixed. In other words, we generate just enough revenue to cover our costs. There is no profit at the break-even point. Bright Day is going to undertake an advertising campaign that will cost sixty thousand dollars. The purpose of the advertising is to get the word out about Delatine. We now have enough information to compute the break-even point in sales volume.
Part Two
The break-even point in sales volume (bottles of Delatine) is equal to the total fixed costs divided by the contribution margin per unit.
Part Three
The break-even number of units that must be sold is five thousand. We arrive at this value by dividing the sixty thousand dollars of fixed cost by the twelve dollar per unit contribution market. At sales of five thousand units, Bright Day will just cover all its costs. =
$60,000 $12
= 5,000 units

6. Determining the Break-even Point
For Delatine, the break-even point in sales dollars is $180,000 (5,000 bottles × $36 selling price).
Here is the proof about break-even. At thirty-six dollars per bottle sales revenue, Bright Day will produce total revenue of one hundred eighty thousand dollars. The total variable costs are one hundred twenty thousand dollars (five thousand units times twenty-four dollars per bottle variable cost). This produces a contribution margin of sixty thousand dollars which is exactly equal to the fixed advertising costs, so the profit is zero.

7. Determining the Break-even Point
Once all fixed costs have been covered (5,000 bottles sold), net income will increase by $12 per unit contribution margin.
Part One
Once Bright Day sells five thousand bottles of Delatine, each additional bottle sold produces twelve dollars in profit.
Part Two This table shows the unit sales around the break-even point of five thousand bottles. Notice that if Bright Day sells five thousand one bottles, it will produce profit of twelve dollars, the amount of the contribution margin per bottle. See how profits increase by an additional twelve dollars for each additional unit sold. You can also see that this works when sales are below the break-even.
Part Three Take a few minutes and see if you can calculate the net income that Bright Day would earn if it sold five thousand six hundred bottles.
$12
What will be the increase in net income if units sold increase from 5,400 units to $5,600 units?

8. Determining the Break-even Point
What will be the increase in net income if units sold increase from 5,400 units to $5,600 units?
Part One At five thousand six hundred bottles, Bright Day would be two hundred bottles above the previous sales level. This increase will affect profitability by two thousand four hundred dollars (two hundred additional bottles times twelve dollar contribution margin per unit).
Part Two Here is a reconstruction of the contribution margin income statement at both five thousand four hundred and five thousand six hundred bottles. As you can see, net income increases from four thousand eight hundred to seven thousand two hundred dollars.

9. Learning Objective 3
Use the contribution per unit approach to calculate the sales volume required to realize a target profit.
Learning Objective Three:
Use the contribution per unit approach to calculate the sales volume required to realize a target profit.

10. Reaching a Target Profit Level
Bright Day’s president wants the advertising campaign to produce profits of $40,000 for the company.
Break-even volume in units =
Fixed costs + Desired profit Contribution margin per unit =
$60,000 + $40,000 $12
= 8, units
Part One We treat the desired profit just like another fixed cost.
Part Two The break-even units are eight thousand three hundred thirty-four whole units. We combine the sixty thousand dollars fixed costs with the desired profit of forty thousand dollars and divide by the contribution margin per unit of twelve dollars.

11. Reaching a Target Profit Level
At $36 per unit selling price, the sales dollars are equal to $300,000, as shown below:
Here is the proof of the math we did on the last screen. As you can see, if unit sales reach the desired level, profits will be forty thousand dollars.

12. Check Yourself
Matrix, Inc. manufactures one model of lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per month, and management wants to earn a profit in the coming month of $37,500. Matrix must sell the following number of lawnmowers:
3,000.
3,500.
4,000.
4,500.
Part One Read through the information carefully and see if you can determine how many lawnmowers Matrix must sell to earn a monthly profit of thirty-seven thousand five hundred dollars.
Part Two
How did you do? The correct answer is three thousand five hundred lawnmowers. You can review the computations on your screen.
$225,000 + $37,500 $75
= 3,500

13. Learning Objective 4
Use the contribution per unit approach to conduct cost-volume-profit analysis.
Learning Objective Four:
Use the contribution per unit approach to conduct cost-volume-profit analysis.

14. Effects of Changes in Sales Price
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. See if you can provide an answer to the president before going to the next screen!
Here is a proposal to drop the selling price of Delatine by eight dollars per bottle to make it a more attractive product in the market. The president still wants to earn a profit of forty thousand dollars from the sale of this new product. Calculate the number of units that must be sold at the new selling price to meet the president’s profit objective. After you have done your calculations, go to the next screen.

15. Effects of Changes in Sales Price
Step 1
Sales volume in units =
Fixed costs + Desired profit Contribution margin per unit
Step 2
Part One The new contribution margin is four dollars per bottle. There has been no change in the variable production costs per bottle.
Part Two
We need to combine the fixed advertising costs with the desired profit and divide by the new contribution margin to determine the number of units that must be sold.
Part Three
As you can see, Bright Day must sell twenty-five thousand bottles to Delatine to earn the desired profit of forty thousand dollars. =
$60,000 + $40,000 $4
= 25,000 units
Step3

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

17. Changes in Variable Costs
Bright Day is considering an alternative mixture for Delatine along with new packaging. This new product would sell for $28 per bottle and have a variable cost per bottle of $12. The president is not in favor of the new product but wants to know how many units must be sold to produce the desired profit of $40,000. You have been asked to determine the units that must be sold and the total sales revenue that will be produced!
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 twelve dollars per bottle and the marketing department believes the company should sell the product for twenty-eight dollars. The president is not in favor of the change because he feels the chemists are diluting the product and the consumer may not be aware of the change. The president still demands a forty thousand dollar profit on the product. Why don’t you see if you can tell the president just how many bottles of the new formula must be sold to meet the stated profit goals? When you are done, go to the next screen.

18. Changes in Variable Costs
Step 1
Sales volume in units =
Fixed costs + Desired profit Contribution margin per unit
Step 2
Part One Our new contribution margin per bottle is sixteen dollars based on the new selling price and new variable costs per bottle.
Part Two We will still use the basic equation to solve the problem.
Part Three The company must sell six thousand two hundred fifty bottles of the newly formulated Delatine to meet the forty thousand dollar profit goal. =
$60,000 + $40,000 $16
= 6,250 units
Step3

19. Changes in Variable Costs
At $28 per unit selling price, the sales dollars are equal to $175,000 as shown below:
Review this contribution margin income statement and see that our math was correct.

20. 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. =
$30,000 + $40,000 $16
= 4,375 units
Sales
volume (units)
Part One 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 thirty thousand dollars. 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 Two
Bright Day must sell four thousand three hundred seventy-five units.
Part Three Here is the proof.

21. Learning Objective 5 Use target pricing to re-engineer a product.
Learning Objective Five:
Use target pricing to re-engineer a product.

22. Target Pricing
Target pricing begins by determining the market price at which a product will sell. The focus of target pricing is on producing the product at a cost that will provide an adequate profit at the established target price. Target pricing focuses on the design stage of product development.
When we target price we begin by looking in the market and seeing what our product could see for, given the competition. The focus of target pricing is on product design and controlling product costs.

23. Learning Objective 6 Draw and interpret a cost-volume-profit graph.
Learning Objective Six:
Draw and interpret a cost-volume-profit graph.

24. Cost-Volume-Profit Graph
We have developed income statements for zero sales, break-even sales, and six thousand units.
Part One Some managers prefer to look at a cost-volume-profit graph rather than all the numbers. We can use Excel to build a cost-volume-profit graph. We have developed a contribution margin income statement of zero units sold, one thousand eight hundred seventy-five units sold, and six thousand units sold.
Part Two From these income statements we have extracted key information that will make the development of the Excel graph easier. We need the units sold, total sales, total cost, and fixed cost. In addition, the descriptions in the far left column will serve as the legend for the graph.
Information to prepare a break-even Excel graph.

25. Cost-Volume-Profit Graph
Here is our graph. The break-even units are one thousand eight hundred seventy-five and break-even sales dollars are fifty-two thousand five hundred. Our fixed costs plot as a straight-line parallel to the X axis. Total sales starts at the zero zero coordinate, and total cost slopes upward beginning where the fixed costs intercept the Y axis.
Every unit we sell to the right of the break-even point results in profit to the company, and sales to the left of the break-even point produce losses.

26. Learning Objective 7
Calculate the margin of safety in units, dollars, and percentage.
Learning Objective Seven:
Calculate the margin of safety in units, dollars, and percentage.

27. 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. With a selling price of $28 per unit and variable costs of $12 per unit, and a desired profit of $40,000, budgeted sales were: =
$30,000 + $40,000 $16
= 4,375 units
Sales
volume (units)
Part One The margin of safety is the cushion that exists between budgeted, or actual, sales and the break-even sales.
Part Two
With the information given, the unit sales that produce a profit of forty thousand dollars are four thousand three hundred seventy-five. The break-even unit sales are one thousand eight hundred seventy-five.
Break-even unit sales assuming no profit would be: =
= 1,875 units
$30,000 $16
Break-even
volume (units)

28. Calculating the Margin of Safety=
Budgeted sales – Break-even sales Budgeted sales
Part One
The unit’s selling price is twenty-eight dollars, so the margin of safety is two thousand five hundred units or seventy thousand dollars.
Part Two We can express the margin of safety as a percent with this equation.
Part Three In our fact situation, the margin of safety is fifty-seven point one four percent.
Margin of
safety =
$122,500 – $52,500 $122,500
= 57.14%

29. Management considers a new product, Delatine that has a sales price of $36 and variable costs of $24 per bottle. Fixed costs are $60,000. Break- even is 5,000 units.
Management wants to earn a $40,000 profit on Delatine. The sales volume to achieve this profit level is 8,334 bottles sold.
Part One Let’s look at the ground we have covered to this point. Remember that we started with our new product Delatine and determined that we must sell five thousand bottles to break even.
Part Two
Next, we interjected the notion of desired profit levels. Management wanted to reach a profit of forty thousand dollars on the sale of Delatine, and we determined that to do so would mean that the company must sell eight thousand three hundred thirty-four bottles.
Part Three
Next, we decided to drop the selling price per bottle and discovered that we must sell twenty-five thousand bottles to reach a profit of forty thousand dollars.
Marketing advocates a target price of $28 per bottle. The sales volume required to earn a $40,000 profit increases to 25,000 bottles.

30. Target costing is employed to reengineer the product and reduces variable cost per unit to $12. To earn the desired profit of $40,000, sales volume decreases to 6,250 units.
Target costing is applied and fixed costs are reduced to $30,000. The sales volume to earn the desired $40,000 profit is 4,375 units.
Part One We turned to target pricing and reduced our variable costs to twelve dollars per bottle. To meet the profit goal we must sell six thousand two hundred fifty bottles.
Part Two With target pricing in place, we decided it was a good idea to reduce our fixed advertising budget. Now, to meet our profit goals, we had to sell only four thousand three hundred seventy-five bottles.
Part Three Finally, we looked at the margin of safety associated with our new product and determined that it was two thousand five hundred bottles or seventy thousand dollars in sales revenue. We have covered a great deal of territory.
In view of the 57.14% margin of safety, management decides to add Delatine to its product line.

31. Learning Objective 8
Explain how spreadsheet software can be used to conduct sensitivity analysis for cost-volume-profit relationships.
Learning Objective Eight:
Explain how spreadsheet software can be used to conduct sensitivity analysis for cost-volume-profit relationships.

32. Sensitivity Analysis & Spreadsheets
Profitability is affected by multidimensional forces. Fixed costs, variable costs, and sales volume can all differ from expectations.
Profitability is affected by multidimensional forces. Fixed costs, variable costs, and sales volume can all differ from expectations.
Spreadsheet software can show the sensitivity of profits to simultaneous changes in fixed costs, variable costs, and sales volume.
Spreadsheet software can show the sensitivity of profits to simultaneous changes in fixed costs, variable costs, and sales volume.

33. Sensitivity Analysis & Spreadsheets
Study this exhibit to see how profits are affected by changes in more than one variable.

34. Decrease in Sales Price with an Increase in Sales Volume
The marketing manager believes reducing the sales price per bottle to $25 will increase sales volume by 625 units. Previous sales volume was: =
$30,000 + $40,000 $16
= 4,375 units
Break-even
volume (units)
Anticipated changes:
Part One Now, let’s look at another proposal from the marketing manager. He suggests that the company drop the selling price to twenty-five dollars per bottle and strongly believes that this move will lead to an increase sale of six hundred twenty-five bottles. In our current situation the break-even to meet our profit goal is four thousand three hundred seventy-five bottles.
Part Two Under the new proposal the contribution margin would drop from sixteen dollars to thirteen dollars, but the units sold will jump from four thousand three hundred seventy-five to five thousand.

35. Decrease in Sales Price with an Increase in Sales Volume
Current Situation
Because budgeted income will fall by $5,000, the proposal should be rejected!
Proposed Situation
Part One In our current situation we are earning a profit of forty thousand dollars, which meets the desired goal of the company’s president.
Part Two Under the marketing manager’s proposal, profits would drop by five thousand dollars to thirty-five thousand dollars.
Part Three
We should reject the proposal because of its adverse impact on income.

36. Increase in Fixed Costs and Increase in Sales Volume
After the previous project was rejected, the advertising manager believes that buying an additional $12,000 in advertising can increase sales volume to 6,000 units. The contribution margin will remain at $16. Should the company buy the additional advertising?
Profit = Contribution margin – Fixed cost
Profit = (6,000 × $16) – $42,000 = $54,000
Current Situation
Proposed Situation
Part One After rejecting the previous proposal, the advertising manager suggests that if we spend an additional twelve thousand dollars on advertising, unit sales should increase to six thousand. We know that profit is equal to contribution margin less fixed costs.
Part Two In this new proposal, we will earn sixteen dollars on each of the six thousand bottles sold. However, our fixed advertising costs will jump from thirty thousand dollars to forty-two thousand dollars. This new proposal will produce income of fifty-four thousand dollars for the company, an amount well in excess of the current forty thousand dollars.
Part Three Here are the two contribution margin income statements comparing the current situation with the new proposal.

37. Change in Several Variables
Management has been able to reduce variable costs to $8 per bottle and decides to reduce the selling price per bottle to $25 (so the contribution margin is now $17). Further, management believes that if advertising is cut to $22,000, the company can still expect sales volume to be 4,200 units.
Should management adopt this plan?
Because of product re-engineering, Bright Day has been able to reduce its variable production costs to eight dollars per bottle. As a result, the president decides she will reduce the selling price to twenty-five dollars per bottle and cut advertising from thirty thousand dollars to twenty-two thousand dollars. Do you think management should accept this plan? Make sure you attempt to do the math before going to the next screen.

38. Change in Several Variables
Profit = Contribution margin – Fixed cost
Profit = (4,200 × $17) – $22,000 = $49,400
Current Situation
Proposed Situation
Part One Here is our statement that profit is equal to contribution margin less fixed costs.
Part Two If we adopt the proposal we will earn contribution of seventeen dollars on each of the four thousand two hundred bottles sold. From this amount we must subtract our fixed costs of twenty-two thousand dollars. The new proposal will generate income of forty-nine thousand four hundred dollars, and should be accepted.
Part Three Here are the contribution income statements for our current situation and under the new proposal.

39. Learning Objective 9
Use the contribution margin ratio and the equation method to conduct cost-volume-profit analysis.
Learning Objective Nine:
Use the contribution margin ratio and the equation method to conduct cost-volume-profit analysis.

40. Contribution Margin Ratio
The contribution margin ratio is the contribution margin divided by sales, computed using either total figures or per unit figures. Here is the total dollar, per unit and contribution margin (CM) ratio for Bright Day when sales volume is 5,000 bottles.
The contribution margin ratio is the contribution margin, in total or per unit, divided by the revenue. In the case of Bright Day, we can see that the contribution margin ratio is thirty-three point three three percent.

41. Contribution Margin Ratio
Bright Day is considering the introduction of a new product called Multi Minerals. Here is some per unit information about Multi Minerals:
Bright Day is considering the introduction of a second new product, Multi Minerals. The product has a budgeted contribution margin of eight dollars, and a contribution margin ratio of forty percent. Let’s do some break-even analysis.
Bright Day expects to incur $24,000 in fixed marketing costs in connection with Multi Minerals.
Let’s look at the calculation of the break-even point in units and dollars.

42. Contribution Margin Ratio
Break-even in Units
Fixed costs CM per unit
$24,000 $8
= 3,000 units
Break-even in Dollars
Fixed costs CM ratio
$24,000 40%
= $60,000
Part One To determine the break-even in units, we divide the fixed costs by the contribution margin per unit. In the case of Multi Minerals, Bright Day must sell three thousand units to break even.
Part Two To determine the break-even sales dollars, we divide the fixed costs by the contribution margin ratio. In our case, the break-even dollars are sixty thousand.

43. Contribution Margin Ratio
Break-even in Units
Fixed costs + Desired profit CM per unit
Break-even in Dollars
Fixed costs + Desired profit CM ratio
Bright Day desires to earn a profit of $8,000 on the sale of Multi Minerals
Part One We already know that we add desired profit to the fixed cost and divide the total by the contribution margin per unit to get break-even units.
Part Two
We follow an identical procedure for break-even dollars, except we divide the total by the contribution margin ratio. If Bright Day wants to reach a profit of eight thousand dollars from the sales of Multi Minerals, how many units must it sell and what are the dollar sales at the break-even point?
Part Three
Bright Day would have to sell four thousand units or eighty thousand dollars to break even on Multi Minerals.
= 4,000 units
$24,000 + $8,000 $8
$24,000 + $8,000 40%
= $80,000

44. The Equation Method At the break-even point:
Sales = Variable cost + Fixed cost
We can look at the above equation like this:
Part One At the break-even point sales are equal to variable costs plus fixed costs because profit is zero.
Part Two 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.

45. The Equation Method
Let’s use our information from Multi Minerals to solve the equation for the number of units sold.
If we want to consider the desired profit of $8,000 the solution would be:
Part One We can use this expanded equation to compute unit sales at the break-even point. The unknown is units, so we solve for that variable.
Part Two We can use the expanded equation to solve for unit sales to achieve a desired profit level by merely adding the desired profit to the fixed costs. In this case Bright Day would have to sell four thousand units to reach a profit of eight thousand dollars.

46. Check Yourself
Matrix, Inc. manufactures one model of lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per month, and management wants to earn a profit in the coming month of $37,500. Use the equation method to determine how many lawnmowers Matrix must sell next month:
3,000.
3,500.
4,000.
4,500.
Part One
Read through the information carefully and see if you can determine the number of units that Matrix must sell.
Part Two The correct answer is three thousand five hundred units. How did you do?

47. Learning Objective 10
Identify the limitations of cost-volume-profit analysis.
Learning Objective Ten:
Identify the limitations of cost-volume-profit analysis.

48. Cost-Volume-Profit Limitations
The accuracy of cost-volume-profit analysis (CVP) is affected by the following:
Assumption of strict linear behavior among the variables.
Assumption that inventory levels remain constant during the period.
i.e., Sales and production are assumed to be equal.
The accuracy of cost-volume-profit analysis (CVP) is affected by:
Assumption of strict linear behavior among the variables.
Assumption that inventory levels remain constant during the period.
i.e., Sales and production are assumed to be equal.
Limitations

49. Learning Objective 11
Perform multiple-product break-even analysis. (Appendix)
Learning Objective Eleven:
Perform multiple-product break-even analysis. (Appendix)

50. Multiple-product break-even analysis
Companies must consider sales mix when conducting break-even analysis for multi-product business ventures. The multiple product break-even point can be determined using the per unit contribution margin approach.
Break-even point = Fixed costs + Weighted average per unit
contribution margin
Companies must consider sales mix when conducting break-even analysis for multi-product business ventures. The multiple product break-even point can be determined using the per unit contribution margin approach.
Break-even point = Fixed costs + Weighted average per unit contribution margin
It is necessary to use a weighted average to determine the per unit contribution margin. The contribution margin of each product must be weighted by its proportionate share of units sold.
It is necessary to use a weighted average to determine the per unit contribution margin. The contribution margin of each product must be weighted by its proportionate share of units sold.

51. End of Chapter Nineteen
As a manager you will be faced with many proposals concerning units to be sold, costs incurred, and profit to be earned. We hope this chapter has provided you with insights into how an effective manager uses available information to reach an informed decision.