{"id":49,"date":"2015-06-03T19:17:36","date_gmt":"2015-06-03T19:17:36","guid":{"rendered":"https:\/\/courses.candelalearning.com\/managacct2x10xmaster\/?post_type=chapter&p=49"},"modified":"2015-12-27T15:21:16","modified_gmt":"2015-12-27T15:21:16","slug":"break-even-point","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-managacct\/chapter\/break-even-point\/","title":{"raw":"5.6 Break - Even Point for a single product","rendered":"5.6 Break – Even Point for a single product"},"content":{"raw":"
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Finding the break-even point<\/strong><\/h4>\r\nA company breaks even for a given period when sales revenue and costs charged to that period are equal. Thus, the break-even point<\/strong> is that level of operations at which a company realizes no net income or loss.\r\n\r\nA company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss. To illustrate the calculation of a break-even point watch the following video and then we will work with the previous company, Video Productions.\r\n\r\nhttps:\/\/youtu.be\/94lrvPlG9P4\r\n\r\nBefore we can begin, we need two things from the previous page:\u00a0 Contribution Margin per unit and Contribution Margin RATIO.\u00a0 These formulas are:\r\n\r\n\r\n\r\n
Contribution Margin per unit =<\/strong><\/td>\r\n\u00a0 Sales Price - Variable Cost per Unit<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n \r\n\r\n\r\n\r\n\r\n
Contribution Margin Ratio =<\/strong><\/td>\r\nContribution margin (Sales - Variable Cost)<\/strong><\/span><\/td>\r\n<\/tr>\r\n
Sales<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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\r\n\r\nBreak-even in units<\/strong>\r\n\r\nRecall that Video Productions produces DVDs selling for $20 per unit. Fixed costs per period total $40,000, while variable cost is $12 per unit.\u00a0 We compute the break-even point in units as:\r\n\r\n\r\n\r\n\r\n
BE Units =\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>\r\n<\/strong><\/td>\r\nFixed Costs<\/strong><\/span><\/td>\r\n<\/tr>\r\n
Contribution Margin per unit<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nVideo Productions contribution margin per unit is $ 8 ($ 20 selling price per unit - $ 12 variable cost per unit). The break even point in units would be calculated as:\r\n\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n\r\n
BE Units =<\/strong><\/td>\r\nFixed Costs<\/span><\/td>\r\n$40,000<\/span><\/td>\r\n= 5,000 units<\/td>\r\n<\/tr>\r\n
Contribution Margin per unit<\/td>\r\n$8<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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<\/div>\r\n
\r\n\r\nThe result tells us that Video Productions breaks even at a volume of 5,000 units per month. We can prove that to be true by computing the revenue and total costs at a volume of 5,000 units. Revenue = (5,000 units X\u00a0 $20 sales price per unit) $100,000. Total costs = $100,000 ($40,000 fixed costs + $60,000 variable costs\u00a0 calculated as $12 per unit X 5,000 units).\r\n\r\nLook at the cost-volume-profit chart and note that the revenue and total cost lines cross at 5,000 units\u2014the break-even point. Video Productions has net income at volumes greater than 5,000, but it has losses at volumes less than 5,000 units.\r\n\r\n\"cvp<\/a>\r\n\r\nBreak-even in sales dollars<\/strong> Companies frequently think of volume in sales dollars instead of units. For a company such as GM that makes Cadillacs and certain small components, it makes no sense to think of a break-even point in units. GM breaks even in sales dollars.\r\n\r\nThe formula to compute the break-even point in sales dollars looks a lot like the formula to compute the break-even in units, except we divide fixed costs by the contribution margin ratio<\/strong> instead of the contribution margin per unit.\r\n\r\nThe contribution margin ratio expresses the contribution margin as a percentage of sales. To calculate this ratio, divide the contribution margin per unit by the selling price per unit, or total contribution margin by total revenues. Video Production's contribution margin ratio is:\r\n\r\n\r\n\r\n\r\n
Contribution Margin Ratio =<\/strong><\/td>\r\nContribution margin<\/span><\/td>\r\n$8<\/span><\/td>\r\n\u00a0 = 0.4 or 40%<\/td>\r\n<\/tr>\r\n
Sales<\/td>\r\n\u00a0 $20<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nOr, referring to the income statement in which Video Productions had a total contribution margin of $48,000 on revenues of $ 120,000, we compute the contribution margin ratio as contribution margin $48,000 \/ Revenues $120,000 = 0.40 or 40%.\r\n\r\nThat is, for each dollar of sales, there is a $ 0.40 left over after variable costs to\u00a0 contribute to covering fixed costs and generating net income.\r\n\r\nUsing this contribution margin ratio, we calculate Video Production's break-even point in sales dollars as:\r\n\r\n\r\n\r\n\r\n
BE in Sales Dollars =<\/strong><\/td>\r\nFixed Costs<\/span><\/td>\r\n$40,000<\/span><\/td>\r\n= $100,000<\/td>\r\n<\/tr>\r\n
Contribution Margin RATIO<\/td>\r\n0.40<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe break-even volume of sales is $ 100,000 (can also be calculated as break even point in units 5,000 units x sales price $ 20 per unit). At this level of sales, fixed costs plus variable costs equal sales revenue, as shown here:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Revenue<\/td>\r\n\u00a0$ 100,000<\/td>\r\n(5,000 units x $20 per unit)<\/em><\/td>\r\n<\/tr>\r\n
Less: variable costs<\/td>\r\n60,000<\/span><\/td>\r\n(5,000 units x $12 per unit)<\/em><\/td>\r\n<\/tr>\r\n
Contribution margin<\/td>\r\n40,000<\/td>\r\n(100,000 - 60,000)<\/em><\/td>\r\n<\/tr>\r\n
Less: Fixed costs<\/td>\r\n40,000<\/span><\/td>\r\n<\/tr>\r\n
\u00a0Net Income<\/td>\r\n$\u00a0 0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nMargin of Safety<\/strong>\r\n\r\nIf a company's current sales are more than its break-even point, it has a margin of safety equal to current sales minus break-even sales. The margin of safety<\/strong> is the amount by which sales can decrease before the company incurs a loss. For example, assume Video Productions currently has sales of $120,000 and its break-even sales are $ 100,000. The margin of safety is $ 20,000, computed as follows:\r\n\r\nMargin of safety = Current sales \u2013 Break even sales<\/strong>\r\n\r\nMargin of safety = $ 120,000 - $ 100,000 = $ 20,000\r\n\r\nSometimes people express the margin of safety as a percentage, called the margin of safety rate or just margin of safety percentage. The margin of safety rate <\/strong>is equal to\r\n\r\n\r\n\r\n\r\n
Margin of Safety Percent =<\/td>\r\nCurrent Sales - Break even Sales<\/span><\/td>\r\n<\/tr>\r\n
Current Sales<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nUsing the data just presented, we compute the margin of safety rate is $20,000 \/ 120,000 = 16.67 %\r\n\r\nThis means that sales volume could drop by 16.67 percent before the company would incur a loss.\r\n\r\nTargeted Profit or Income\r\n<\/strong>\r\n\r\nYou can also use this same type of analysis to determine how many sales units or sales dollars you would need to make a specific profit (very helpful!).\u00a0 The good news is you have already learned the basic formula, we are just changing it slightly.\u00a0 The formulas we will need are:\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n\r\n\r\n\r\n\r\n
Units at Target Profit<\/strong> =<\/td>\r\nFixed Costs + Target Income<\/span><\/td>\r\n<\/tr>\r\n
Contribution Margin per unit<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n\r\n\r\n\r\n
Sales Dollars for Target Profit =<\/strong>\u00a0<\/strong><\/td>\r\nFixed Costs + Target Income<\/span><\/td>\r\n<\/tr>\r\n
Contribution Margin RATIO<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThese look familiar (or they should!).\u00a0 These are the same formulas we used for break even analysis but this time we have added target income.\u00a0 If you think about it, it IS the same formula because at break even our target income is ZERO.\r\n\r\nhttps:\/\/youtu.be\/4U60Ya5ysMU\r\n

Let's look at another example. The management of a major airline wishes to know how many seats must be sold on Flight 529 to make $8,000 in profit. To solve this problem, management must identify and separate costs into fixed and variable categories.<\/p>\r\n

The fixed costs of Flight 529 are the same regardless of the number of seats filled. Fixed costs include the fuel required to fly the plane and crew (with no passengers) to its destination; depreciation on the plane used on the flight; and salaries of required crew members, gate attendants, and maintenance and refueling personnel.\u00a0 Fixed costs are $12,000.<\/p>\r\n

The variable costs vary directly with the number of passengers. Variable costs include snacks and beverages provided to passengers, baggage handling costs, and the cost of the additional fuel required to fly the plane with passengers to its destination. Management would express each variable cost on a per passenger basis.\u00a0 Variable costs are $25 per passenger.<\/p>\r\n

Tickets are sold for $125 each. The contribution margin is $100 ($125 sales - $25 variable) and the contribution margin ratio is 80% ($100 contribution margin \/$125 sales).\u00a0 We can calculate the units and sales dollar required to make $8,000 in profit by:<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
Units at Target Profit =<\/strong><\/td>\r\nFixed Costs + Target Income<\/span><\/td>\r\n= 12,000 + 8,000<\/span><\/td>\r\n\u00a0= $20,000<\/span><\/td>\r\n= 200 tickets<\/td>\r\n<\/tr>\r\n
Contribution Margin per unit<\/td>\r\n$100<\/td>\r\n$100<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

The sales dollars required could be calculated as break even units of 200 tickets x $125 sales price per ticket = $25,000 or by using the following formula:<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
Sales Dollars for Target Profit =<\/strong>\u00a0<\/strong><\/td>\r\nFixed Costs + Target Income =\r\n<\/span><\/td>\r\n12,000 + 8,000 =\r\n<\/span><\/td>\r\n$20,000<\/span><\/td>\r\n\u00a0= $25,000<\/td>\r\n<\/tr>\r\n
Contribution Margin RATIO<\/td>\r\n0.80<\/td>\r\n0.80<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nManagement can also use its knowledge of cost-volume-profit relationships to determine whether to increase sales promotion costs in an effort to increase sales volume or to accept an order at a lower-than-usual price. In general, the careful study of cost behavior helps management plan future courses of action.","rendered":"
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Finding the break-even point<\/strong><\/h4>\n

A company breaks even for a given period when sales revenue and costs charged to that period are equal. Thus, the break-even point<\/strong> is that level of operations at which a company realizes no net income or loss.<\/p>\n

A company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss. To illustrate the calculation of a break-even point watch the following video and then we will work with the previous company, Video Productions.<\/p>\n

https:\/\/youtu.be\/94lrvPlG9P4<\/p>\n

Before we can begin, we need two things from the previous page:\u00a0 Contribution Margin per unit and Contribution Margin RATIO.\u00a0 These formulas are:<\/p>\n\n\n\n
Contribution Margin per unit =<\/strong><\/td>\n\u00a0 Sales Price – Variable Cost per Unit<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

 <\/p>\n\n\n\n\n
Contribution Margin Ratio =<\/strong><\/td>\nContribution margin (Sales – Variable Cost)<\/strong><\/span><\/td>\n<\/tr>\n
Sales<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Break-even in units<\/strong><\/p>\n

Recall that Video Productions produces DVDs selling for $20 per unit. Fixed costs per period total $40,000, while variable cost is $12 per unit.\u00a0 We compute the break-even point in units as:<\/p>\n\n\n\n\n
BE Units =\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>
\n<\/strong><\/td>\n		Fixed Costs<\/strong><\/span><\/td>\n<\/tr>\n
Contribution Margin per unit<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Video Productions contribution margin per unit is $ 8 ($ 20 selling price per unit – $ 12 variable cost per unit). The break even point in units would be calculated as:<\/p>\n<\/div>\n<\/div>\n\n\n\n\n
BE Units =<\/strong><\/td>\nFixed Costs<\/span><\/td>\n$40,000<\/span><\/td>\n= 5,000 units<\/td>\n<\/tr>\n
Contribution Margin per unit<\/td>\n$8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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<\/div>\n
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The result tells us that Video Productions breaks even at a volume of 5,000 units per month. We can prove that to be true by computing the revenue and total costs at a volume of 5,000 units. Revenue = (5,000 units X\u00a0 $20 sales price per unit) $100,000. Total costs = $100,000 ($40,000 fixed costs + $60,000 variable costs\u00a0 calculated as $12 per unit X 5,000 units).<\/p>\n

Look at the cost-volume-profit chart and note that the revenue and total cost lines cross at 5,000 units\u2014the break-even point. Video Productions has net income at volumes greater than 5,000, but it has losses at volumes less than 5,000 units.<\/p>\n

\"cvp<\/a><\/p>\n

Break-even in sales dollars<\/strong> Companies frequently think of volume in sales dollars instead of units. For a company such as GM that makes Cadillacs and certain small components, it makes no sense to think of a break-even point in units. GM breaks even in sales dollars.<\/p>\n

The formula to compute the break-even point in sales dollars looks a lot like the formula to compute the break-even in units, except we divide fixed costs by the contribution margin ratio<\/strong> instead of the contribution margin per unit.<\/p>\n

The contribution margin ratio expresses the contribution margin as a percentage of sales. To calculate this ratio, divide the contribution margin per unit by the selling price per unit, or total contribution margin by total revenues. Video Production’s contribution margin ratio is:<\/p>\n\n\n\n\n
Contribution Margin Ratio =<\/strong><\/td>\nContribution margin<\/span><\/td>\n$8<\/span><\/td>\n\u00a0 = 0.4 or 40%<\/td>\n<\/tr>\n
Sales<\/td>\n\u00a0 $20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Or, referring to the income statement in which Video Productions had a total contribution margin of $48,000 on revenues of $ 120,000, we compute the contribution margin ratio as contribution margin $48,000 \/ Revenues $120,000 = 0.40 or 40%.<\/p>\n

That is, for each dollar of sales, there is a $ 0.40 left over after variable costs to\u00a0 contribute to covering fixed costs and generating net income.<\/p>\n

Using this contribution margin ratio, we calculate Video Production’s break-even point in sales dollars as:<\/p>\n\n\n\n\n
BE in Sales Dollars =<\/strong><\/td>\nFixed Costs<\/span><\/td>\n$40,000<\/span><\/td>\n= $100,000<\/td>\n<\/tr>\n
Contribution Margin RATIO<\/td>\n0.40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The break-even volume of sales is $ 100,000 (can also be calculated as break even point in units 5,000 units x sales price $ 20 per unit). At this level of sales, fixed costs plus variable costs equal sales revenue, as shown here:<\/p>\n\n\n\n\n\n\n\n
Revenue<\/td>\n\u00a0$ 100,000<\/td>\n(5,000 units x $20 per unit)<\/em><\/td>\n<\/tr>\n
Less: variable costs<\/td>\n60,000<\/span><\/td>\n(5,000 units x $12 per unit)<\/em><\/td>\n<\/tr>\n
Contribution margin<\/td>\n40,000<\/td>\n(100,000 – 60,000)<\/em><\/td>\n<\/tr>\n
Less: Fixed costs<\/td>\n40,000<\/span><\/td>\n<\/tr>\n
\u00a0Net Income<\/td>\n$\u00a0 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Margin of Safety<\/strong><\/p>\n

If a company’s current sales are more than its break-even point, it has a margin of safety equal to current sales minus break-even sales. The margin of safety<\/strong> is the amount by which sales can decrease before the company incurs a loss. For example, assume Video Productions currently has sales of $120,000 and its break-even sales are $ 100,000. The margin of safety is $ 20,000, computed as follows:<\/p>\n

Margin of safety = Current sales \u2013 Break even sales<\/strong><\/p>\n

Margin of safety = $ 120,000 – $ 100,000 = $ 20,000<\/p>\n

Sometimes people express the margin of safety as a percentage, called the margin of safety rate or just margin of safety percentage. The margin of safety rate <\/strong>is equal to<\/p>\n\n\n\n\n
Margin of Safety Percent =<\/td>\nCurrent Sales – Break even Sales<\/span><\/td>\n<\/tr>\n
Current Sales<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Using the data just presented, we compute the margin of safety rate is $20,000 \/ 120,000 = 16.67 %<\/p>\n

This means that sales volume could drop by 16.67 percent before the company would incur a loss.<\/p>\n

Targeted Profit or Income
\n<\/strong><\/p>\n

You can also use this same type of analysis to determine how many sales units or sales dollars you would need to make a specific profit (very helpful!).\u00a0 The good news is you have already learned the basic formula, we are just changing it slightly.\u00a0 The formulas we will need are:<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n\n
Units at Target Profit<\/strong> =<\/td>\nFixed Costs + Target Income<\/span><\/td>\n<\/tr>\n
Contribution Margin per unit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n
Sales Dollars for Target Profit =<\/strong>\u00a0<\/strong><\/td>\nFixed Costs + Target Income<\/span><\/td>\n<\/tr>\n
Contribution Margin RATIO<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

These look familiar (or they should!).\u00a0 These are the same formulas we used for break even analysis but this time we have added target income.\u00a0 If you think about it, it IS the same formula because at break even our target income is ZERO.<\/p>\n