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**Cost – Volume – Profit Analysis**

Chapter Three Cost – Volume – Profit Analysis In Chapter Three we will learn how company’s 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.

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Jeff Jamail is evaluating a business opportunity to sell cookware at trade shows. Mr. Jamail can buy the cookware at a wholesale cost of $210 per set. He plans to sell the cookware for $350 per set. He estimates fixed costs such as plane fare, booth rental cost, and lodging to be $5,600 per trade show. How many cookware sets must Mr. Jamail sell in order to breakeven?

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**Cost-Volume-Profit Relationship**

There are 3 methods to analyze: (1.) Contribution Margin per Unit (2.) Contribution Ratio (3.) Equation Method NOTE: Each method yields the same results.

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**Cost-Plus Pricing Strategy**

It sets prices at cost plus a mark-up For example: Product cost $20 to make Mgmt decides to mark-up 30% Selling Price = $20 + ($20 * 30%) = $26

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**Break-Even Point Fixed Costs / Contribution Margin per Unit**

Point where Total Revenue = Total Costs Break-even Volume in Units = Fixed Costs / Contribution Margin per Unit Once fixed costs have been covered, net income will increase per unit contribution margin for each additional unit sold

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**Determining the Break-even Point**

Bright Day produces one produce 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 markup 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 can sell enough bottles of Delatine to cover it fixed costs and make a profit!

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**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 I 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 computer the break-even point is sales volume. Part II 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 III I our cash 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

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**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). The produces a contribution margin of sixty thousand dollars which is exactly equal to the fixed advertising costs, so the profit is zero.

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**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. $12 Part I Once Bright Day sells five thousand bottles of Delatine, each additional bottle in produce twelve dollars in profit. Part II This table shows the unit sales around the break-even point of five thousand bottles. Notice that if Bright Day sells five thousand and one bottles, it will produce profit of twelve dollar, 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 III 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. What will be the increase in net income if units sold increase from 5,000 units to $5,600 units?

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**Determining the Break-even Point**

What will be the increase in net income if units sold increase from 5,000 units to $5,600 units? Part I At five thousand six hundred bottles, Bright Day would be six hundred bottles above the break-even point. Net operating income would be seven thousand two hundred dollars given the contribution margin per unit of twelve dollars. Part II Here is a reconstruction of the contribution margin income statement at both five thousand and five thousand six hundred bottles. As you can see, net income increases from zero to seven thousand two hundred dollars.

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**Reaching a Target Profit Level**

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

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**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.

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Check Yourself Matrix, Inc. manufactures one model of lawnmower the 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 I 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 II 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

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**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 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.

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**Effects of Changes in Sales Price**

Step 1 Break-even volume in units = Fixed costs + Desired profit Contribution margin per unit Step 2 Part I The new contribution margin is four dollars per bottle. There has been no change in the variable production costs per bottle. Part II 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 III 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

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**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.

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**Target Costing Determine the market price at which product will sell**

This is the Target Price Must develop the product at a cost that will enable company to be profitable selling the product at the target price This is known as TARGET COSTING

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**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 she 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.

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**Changes in Variable Costs**

Step 1 Break-even volume in units = Fixed costs + Desired profit Contribution margin per unit Step 2 Part I Our new contribution margin per bottle is sixteen dollars based on the new selling price and new variable costs per bottle. Part II We will still use of basic equation to solve the problem. Part III 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

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**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.

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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 Break-even volume (units) Part I The market 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 II Bright Day must sell four thousand three hundred seventy five units. Part III Here is the proof.

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**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 Break-even volume (units) Part I The margin of safety is the cushion that exists between budgeted, or actual, sales and the break-even sales. Part II With the information give the unit sales that produce a profit of forty thousand dollars are four thousand three hundred seventy five. The break-even units 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)

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**Calculating the Margin of Safety**

Part I The units selling price is twenty eight dollars, so the margin of safety is two thousand five hundred units or seventy thousand dollars. Part II We can express the margin of safety as a percent with this equation. Part III In our fact situation, the margin of safety is fifty seven point one four percent.

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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 want to earn a $40,000 profit on Delatine. The sales volume to achieve this profit level is 8,334 bottles sold. Part I 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 breakeven. Part II Next, we interjected the notion of desired profit levels. Management wanted to each 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. Next, we decided to drop the selling price per bottle and discovered that we must sell twenty five thousand bottles to each 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.

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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 I 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 II 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 II 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.

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**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 I 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 II Under the new proposal the contribution market would drop from sixteen dollars to thirteen dollars, but the units sold will jump from four thousand three hundred seventy five to five thousand.

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**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 I In our current situation we are earning a profit of forty thousand dollars, which meets the desired goal of the company’s president. Part II Under the marketing managers proposal, profits would drop by five thousand dollars to thirty five thousand dollars. Part III We should reject the proposal because of its adverse impact on income.

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**Increased in Fixed Costs and Increase in Sales Volume**

After the previous project was rejects, 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 I 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 II 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 II Here are the two contribution margin income statements comparing the current situation with the new proposal.

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**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 reengineering 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.

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**Change in Several Variables**

Profit = Contribution margin – Fixed cost Profit = (4,200 × $17) – $22,000 = $49,400 Current Situation Proposed Situation Part I Here is our statement that profit is equal to contribution margin less fixed costs. Part II 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 III Here are the contribution income statements for our current situation and under the new proposal.

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**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.

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**Contribution Margin Ratio Approach**

= Contribution Margin / Sales 1st – Identify Contribution Margin $60,000 2nd – Identify Sales $180,000 = $60,000 / $180,000 = 0.33

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**What does this Ratio mean?**

Ratio means that every dollar of sales provides $0.33 to cover Fixed Costs After Fixed Costs are covered – Each $1 provides $0.33 of profit

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**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.

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**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 I 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 II 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.

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**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 I 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 II We follow an identical procedures for break-even dollars, except we divide the total by the contribution margin ratio. If Bright Day wants to each 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 III 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

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**The Equation Method At the break-even point:**

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

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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 I 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 II 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 each a profit of eight thousand dollars.

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Check Yourself Matrix, Inc. manufactures one model of lawnmower the 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 I Read through the information carefully and see if you can determine the number of units that Matrix must sell. Part II The correct answer is three thousand five hundred units. How did you do?

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**Weighted-Average Contribution Margin per Unit**

In the real world, a company is selling more than one product Product A Product B Unit Selling Price $ 100 $ 200 Unit Variable Cost Unit Fixed Cost Total Units Sold 10, ,000

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**Step 1: Find the CM for each**

Product A = 100 – 40 = 60/unit Product B = 200 – 60 = 140/unit Step 2: Find the total # of units sold 10, ,000 = 30,000 Step 3: Find the % sold of each product Product A = 10,000 / 30,000 = 33% Product B = 20,000 / 30,000 = 67% Step 4: Find the Weighted CM Product A = $ 60 * 33% = $19.80 / unit Product B = $ 140 * 67% = $93.80 / unit Total CM = $ $93.80 = $ / unit

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