class 06 -- optional cost-volume-profit analyis
DESCRIPTION
CVP analysisTRANSCRIPT
Importanceof
C-V-P Analysismyaccountingteacher.c
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C-V-P Analysis
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C = CostV= VolumeP = Profit
Cost-Volume-Profit AnalysisHow much does our profit (or loss) vary depending on our level of sales?
BasicCost Behavior
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Cost Behavior?
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“Behavior” with respect to changes in the volume of activity
If sales go up 40%, what happens to each one of my costs?• Up or down?• By more or less than 40%?• Do any of my costs stay the same whether I sell
anything or not?
C-V-P Analysis
Basic Cost Behavior
Variable CostsCosts that INCREASE the more you make or sell.
Fixed CostsCosts that STAY THE SAME the more you make or sell.
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VARIABLE COST
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Consider a small restaurant that sells ONLY hamburgers. The cost of the meat for each hamburger is $0.50.• What is the meat cost if the restaurant sells 0 hamburgers?
• 0 hamburgers × $0.50 per hamburger = $0 meat cost• What is the meat cost if the restaurant sells 1,000 hamburgers?
• 1,000 hamburgers × $0.50 per hamburger = $500 meat cost
This is a variable cost.• Variable cost per unit is constant.• Total variable cost increases proportionately as the
number of units increases.
VARIABLE COST
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Other examples of variable costs• Wood cost in a company that makes wooden tables.• Metal cost in a company that makes automobiles.• Direct labor cost in a company with a strict schedule
in which workers are paid only for the actual number of units they produce
• Salespersons’ salary cost in a company that pays strictly on commissions.
VARIABLE COST
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Variable Cost
RELEVANT RANGE
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0 40 80 120
160
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
$7,000
Number of Units
COST
FIXED COST
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Consider a small restaurant that sells ONLY hamburgers. The amount of rent on the restaurant location is $2,300 per month.• What is the rent cost if the restaurant sells 1 hamburger?
• $2,300• What is the rent cost if the restaurant sells 1,000 hamburgers?
• $2,300
This is a fixed cost.• Total fixed cost is constant as the number of units increases or
decreases. -- $2,300 • Fixed cost per unit decreases as the number of units increases.
• Sell 1 hamburger: $2,300 / 1 = $2,300 fixed cost per hamburger• Sell 1,000 hamburgers: $2,300 / 1,000 = $2.30 fixed cost per
hamburger
Fixed Cost = $2,300
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0 500 1,000 1,500 2,000$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
$7,000
Number of Units
COST
Fixed Cost
RELEVANT RANGE
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Fixed Cost
STEPPED FIXED COST
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MIXED COST
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Consider an automobile dealership. The rent is $4,000 per month PLUS 1% of sales.
• This is a common rental arrangement for store locations in a mall.• What is the rent cost if the dealership has sales of $0?
• $4,000 + ($0 × 0.01) = $4,000 rent cost• What is the rent cost if the dealership has sales of $500,000?
• $4,000 + ($500,000 × 0.01) = $9,000 rent cost
This is a mixed cost.
MIXED COST
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MIXED COST
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Other examples of mixed costs• Electricity cost in a factory. – There is some cost of electricity
even if you don’t make anything.• Salespersons’ salary cost in a company that pays both
a base salary PLUS commissions.• Some cell phone bills. – Fixed monthly charge plus additional
charges if you go over some minute limit or text limit.
Analysisof
Mixed Costsmyaccountingteacher.c
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MIXED COST
Why Do We Care?
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In order to perform an accurate C-V-P analysis, you have to know which costs will change as the level of activity changes.• Variable costs change.• Fixed costs do not change.Mixed costs must be separated into their variable and fixed components.
Mixed Cost Analysis
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3 Approaches• Detailed, invoice-by-invoice categorization• Scattergraph method, a visual approach• High-low method, a computational approach
Example
Graph of Electricity Cost
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Graph of Electricity Cost
Scattergraph Method
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• Regression line: The straight line that best fits among all of the data points.• In this case, the regression line gives an estimate
of the total electricity cost at any number of direct labor hours.
• Variable cost per hour: The slope of the total cost line
• Fixed cost: The y-intercept of the total cost line
Graph of Electricity Cost
Slope = Variable Cost per Unit
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S
Rise (increase in costs)Run (increase in level of activity)
Choose 7,000 hours (because it falls exactly on the line; any other point on the line would give the same answer)
$70,000 - $40,0007,000 hours – 0 hours
$30,0007,000 hours
$4.29 per hour
Graph of Electricity Cost
Total Cost Equation
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Fixed costy-intercept = $40,000SlopeVariable cost per unit
= $4.29 per direct labor hour
Total cost = $40,000 + ($4.29 × Hours)
Practice withTotal Cost Equation
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Total cost = $40,000 + ($4.29 × Hours)
Direct ||| TotalLabor ||| Variable Fixed ElectricityHours ||| Cost Cost Cost
1. 4,000 ||| $17,160 + $40,000 = $57,160
2. 10,000 ||| 42,900 + 40,000 = 82,900
3. 15,000 ||| 64,350 + 40,000 = 104,350
4. 20,000 ||| 85,800 + 40,000 = 125,800
Total Cost Estimate
Steps in the
Scattergraph Method
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1. Draw the empty graph with the costs on the y-axis and the level of activity on the x-axis.
2. Plot the data.3. Draw the “regression line.”4. Compute the slope of the regression line
which is the variable cost per unit.5. Identify the y-intercept which is the fixed
cost.
LIMITATIONS of the
Scattergraph Method
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• It isn’t exact.• Two different people won’t get EXACTLY the same
numbers for fixed cost and variable cost per unit.=====================================Yes, but …• It is a quick and useful tool.• It can be made mathematically precise, if
desired. (This statistically precise regression analysis is outside the scope of this course.)
Steps in the
High-Low Method
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1. Identify the highest and the lowest levels of activity.2. Compute the increase in cost from the lowest level of
activity to the highest. Also compute the increase in activity level from the low to the high.
3. Compute the slope (rise over run).4. Compute Fixed Cost using
Total Cost = Variable + Fixed
High-Low Method
Step 1: Identify High and Low
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Month Direct Labor Hours Worked Total Electricity Cost
January 7,000 $70,000 February 6,000 60,000
March 12,000 100,000April 6,600 80,000May 18,000 120,000June 14,000 110,000
High-Low MethodSteps 2 and 3: Compute RISE, RUN, and SLOPE
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Rise (increase in costs)Run (increase in level of activity
$120,000 - $60,00018,000 hours – 6,000 hours
$60,00012,000 hours
$5.00 per hour
High-Low Method
Step 4: Compute FIXED Cost
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Total Cost = Variable + FixedFixed = Total Cost - Variable
HighFixed = $120,000 – (18,000 × $5)Fixed = $120,000 - $90,000 = $30,000LowFixed = $60,000 – (6,000 × $5)Fixed = $60,000 - $30,000 = $30,000
High-Low Method
Total Cost Equation
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Fixed costy-intercept = $30,000SlopeVariable cost per unit
= $5.00 per direct labor hourTotal cost = $30,000 + ($5.00 × Hours)
Scattergraph and High-Low
Numerical Comparison
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Scattergraph High-LowFixed cost: y-intercept $40,000 $30,000Slope: Variable cost per unit $4.29/hour $5.00/hour
Example: 10,000 hours$40,000 + $30,000 +
($4.29 × 10,000) = ($5.00 × 10,000) =$82,900 $80,000
Scattergraph and High-Low
Comparison
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Scattergraph• Uses all of the data• NOT mathematically precise
High-Low• Mathematically precise• Only uses two data points
Remember that the PURPOSE of these two methods is to separate a mixed cost into its FIXED and VARIABLE components.
These are only ESTIMATES!!!
Methodsof
C-V-P Analysismyaccountingteacher.c
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Contribution Margin
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Sales- Variable Costs= Contribution Margin
When you sell a hamburger, how much of the selling price is left after you pay for the meat, bun, pickles, onions, tomatoes, lettuce, ketchup, and cook’s labor cost?
CONTRIBUTION MARGINToward what is the “contribution margin” contributing?
Toward paying for the Fixed Costs!!
RegularIncome Statement
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Question: If sales increase by 20% (to 1,200 gloves), what will the PROFIT be?
TotalSales revenue (1,000 gloves) $200,000Less operating costs (173,000)Profit $27,000
Jewels CorporationRegular Income Statement
For the Month
Contribution MarginIncome Statement
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Question: If sales increase by 20% (to 1,200 gloves), what will the PROFIT be?
Total Per UnitSales revenue (1,000 gloves) $200,000 $200Less variable costs (110,000) (110)Contribution margin $90,000 $90
Less fixed costs (63,000)Profit $27,000
Jewels CorporationContribution Margin Income Statement
For the Month
Contribution MarginIncome Statement
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What if sales increase by 20% (to 1,200 gloves)?
Total Per UnitSales revenue (1,200 gloves) $240,000 $200Less variable costs (132,000) (110)Contribution margin $108,000 $90
Less fixed costs (63,000)Profit $45,000
Jewels CorporationContribution Margin Income Statement
For the Month
Contribution MarginIncome Statement
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Comparison of 1,000 gloves sold and 1,200 gloves sold.
1,000 1,200Gloves Gloves
Sales revenue $200,000 $240,000Less variable costs (110,000) (132,000)Contribution margin $90,000 $108,000Less fixed costs (63,000) (63,000)Profit $27,000 $45,000
Jewels CorporationContribution Margin Income Statement
For the Month
Contribution MarginRATIO
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Variable cost ratio = 55% • The percentage of the selling price paid for variable costsContribution margin ratio = 45%• The percentage of the selling price you get to KEEP
RatioTotal Per Unit (Percentage)
Sales revenue (1,000 gloves) $200,000 $200 100%Less variable costs (110,000) (110) -55%Contribution margin $90,000 $90 45%
Less fixed costs (63,000)Profit $27,000
Jewels CorporationContribution Margin Income Statement
For the Month
C-V-PEquation
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Contribution MarginIncome Statement
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Total Per UnitSales revenue (1,200 gloves) $240,000 $200Less variable costs (132,000) (110)Contribution margin $108,000 $90
Less fixed costs (63,000)Profit $45,000
Jewels CorporationContribution Margin Income Statement
For the Month
C-V-PEquation
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Sales Revenue – Variable Costs – Fixed Costs = Profit
$240,000 – $132,000 – $63,000 = $45,000
C-V-PEquation
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Sales Revenue – Variable Costs – Fixed Costs = Profit$240,000 – $132,000 – $63,000 = $45,000
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,200) – ($110 × 1,200) – $63,000 = $45,000
C-V-PEquation
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Sales Revenue – Variable Costs – Fixed Costs = Profit$240,000 – $132,000 – $63,000 = $45,000
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,200) – ($110 × 1,200) – $63,000 = $45,000
Sales Revenue – (Variable Cost Ratio × Sales Revenue) – Fixed Costs = Profit
$240,000 – (0.55 × $240,000) – $63,000 = $45,000
C-V-PEquation
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Sales Revenue – Variable Costs – Fixed Costs = Profit
Sales Revenue = Sales Price per unit × UnitsTotal Variable Costs = Variable Cost per unit × UnitsTotal Variable Costs = Sales Revenue × VC Ratio
C-V-P Equation
Break-Even Point
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Break-Even PointLevel of sales such that profit is exactly equal to $0
Sales Revenue – Variable Costs – Fixed Costs = $0
C-V-P Equation
Break-Even Point
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(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,200) – ($110 × 1,200) – $63,000 = $45,000-------------------------------------------------------------------------Define “X” as the break-even number of units.(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit
($200 × X) – ($110 × X) – $63,000 = $0 ($90 × X) – $63,000 = $0
($90 × X) = $63,000 X = 700 units
C-V-P Equation
Break-Even Point
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Our Claim: With sales of 700 units, the company will break even, meaning that profit will be $0.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 700) – ($110 × 700) – $63,000 = ?????$140,000 – $77,000 – $63,000 = ?????$140,000 – $77,000 – $63,000 = $0 !!!!!!!
C-V-P Equation
Target Income
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How many sales units will result in a profit of $36,000?Define “X” as the number of units yielding profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × X) – ($110 × X) – $63,000 = $36,000 ($90 × X) – $63,000 = $36,000 ($90 × X) = $99,000
X = 1,100 units
C-V-P Equation
Target Income
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Our Claim: With sales of 1,100 units, the company will have a profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,100) – ($110 × 1,100) – $63,000 = ?????$220,000 – $121,000 – $63,000 = ?????$220,000 – $184,000 = $36,000 !!!!!!!
Remember This!!!
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Sales 100% of sales- Variable Costs - 55% of sales= Contribution Margin = 45% of sales
Variable Cost Ratio + Contribution Margin Ratio = 100%
ALWAYS!!
C-V-P EquationPractice
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C-V-PEquation
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Sales Revenue – Variable Costs – Fixed Costs = Profit
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit
Sales Revenue – (Variable Cost Ratio × Sales Revenue) – Fixed Costs = Profit
Jewels Baseball Gloves
Initial Data
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Sales Price per unit = $200 per unitVariable Cost per unit = $110 per unitTotal Fixed Cost = $63,000
C-V-P Equation
Change in Fixed Costs
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Increase Fixed Costs from $63,000 to $81,000Target Income is $36,000What is the necessary number of units sold?-------------------------------------------------------------------------Define “X” as the number of units yielding profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × X) – ($110 × X) – $81,000 = $36,000 ($90 × X) – $81,000 = $36,000 ($90 × X) = $117,000
X = 1,300 units
C-V-P Equation
Change in Fixed Costs
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Our Claim: With sales of 1,300 units and fixed costs of $81,000, the company will have a profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,300) – ($110 × 1,300) – $81,000 = ?????$260,000 – $143,000 – $81,000 = ?????$260,000 – $143,000 – $81,000 = $36,000
C-V-P Equation
Change in Variable Costs
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Increase Variable Cost per unit from $110 to $130Target Income is $36,000What is the necessary number of units sold?-------------------------------------------------------------------------Define “X” as the number of units yielding profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × X) – ($130 × X) – $63,000 = $36,000 ($70 × X) – $63,000 = $36,000 ($70 × X) = $99,000
X = 1,415 units
C-V-P Equation
Change in Variable Costs
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Our Claim: With sales of 1,415 units and fixed costs of $63,000 and variable cost per unit of $130, the company will have a profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,415) – ($130 × 1,415) – $63,000 = ?????$283,000 – $183,950 – $63,000 = ?????$283,000 – $183,950 – $63,000 = $36,050OK, the exact answer is 1,414.285714… units. We round up.
C-V-P Equation
Change in Selling Price
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Increase Selling Price per unit from $200 to $230Target Income is $36,000What is the necessary number of units sold?-------------------------------------------------------------------------Define “X” as the number of units yielding profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($230 × X) – ($110 × X) – $63,000 = $36,000 ($120 × X) – $63,000 = $36,000 ($120 × X) = $99,000
X = 825 units
C-V-P Equation
Change in Variable Costs
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Our Claim: With sales of 825 units and fixed costs of $63,000 and variable cost per unit of $110 and selling price per unit of $230, the company will have a profit of $36,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($230 × 825) – ($110 × 825) – $63,000 = ?????$189,750 – $90,750 – $63,000 = ?????$189,750 – $90,750 – $63,000 = $36,000
C-V-P EquationChange Several Things
(I)
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Decrease Selling Price per unit from $200 to $180Increase sales volume to 1,600 unitsIncrease Fixed Costs from $63,000 to $83,000
What is the new profit?-------------------------------------------------------------------------(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($180 × 1,600) – ($110 × 1,600) – $83,000 = ?????? ($70 × 1,600) – $83,000 = ??????
$112,000 – $83,000 = ??????New Profit = $29,000
C-V-P EquationChange Several Things
(II)
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Decrease Variable Cost per unit from $110 to $100Sales volume is 1,100 unitsIncrease Fixed Costs from $63,000 to $68,000
What is the new profit?-------------------------------------------------------------------------(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($200 × 1,100) – ($100 × 1,100) – $68,000 = ?????? ($100 × 1,100) – $68,000 = ??????
$110,000 – $68,000 = ??????New Profit = $42,000
C-V-P EquationChange Several Things
(III)
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Sell bats with a selling price per unit of $90Variable cost per unit of the bats is $45Fixed cost of bat production is $40,000Target net income is $25,000
How many bats must be sold?-------------------------------------------------------------------------(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($90 × X) – ($45 × X) – $40,000 = $25,000 ($45 × X) = $65,000
X = $65,000/$45X = 1,445 units
C-V-P EquationChange Several Things
(III)
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Our Claim: With sales of 1,445 units and fixed costs of $40,000 and variable cost per unit of $45 and selling price per unit of $90, the company will have a profit on bats of $25,000.
(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit($90 × 1,445) – ($45 × 1,445) – $40,000 = ?????$130,050 – $65,025 – $40,000 = ?????$130,050 – $65,025 – $40,000 = $25,025
OK, the exact answer is 1,444.444444… units. We round up.
Key Points
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• Get comfortable with the C-V-P Equation.
• Check your work!!!
C-V-PGraphs
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C-V-P Graph
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C-V-P Graphy-INTERCEPT of Total Cost
Line
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y-Interceptof Total Cost Line:
The cost whenthere are0 units.
FIXED COST =
$63,000
C-V-P Graph
Slope of the Revenue Line
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Slope = Rise / RunLet’s use thechange from 0 unitsTo 700 units.
Rise = $140,000 - $0 = $140,000Run = 700 units – 0 units = 700 units$140,000 / 700 units
Price per unit:$200 per unit
C-V-P Graph
Slope of the Total Cost Line
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Slope = Rise / RunLet’s use thechange from 0 unitsTo 700 units.
Rise = $140,000 - $63,000 = $77,000Run = 700 units – 0 units = 700 units$77,000 / 700 units
Variable Cost per unit:$110 per unit
Profit Graph
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• Instead of showing total revenue and total cost, a profit graph shows TOTAL PROFIT for each level of activity.
• y-axis is for TOTAL PROFIT.• x-axis is for level of activity• Plot the PROFIT at two points.
• Activity = 0. “Profit” is a loss equal to the fixed cost.• Activity = Breakeven. Profit = $0
• Connect the two points.
Profit Graph
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C-V-P Graph
Slope of the Profit Line
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Slope = Rise / RunLet’s use thechange from 0 unitsTo 700 units.
Rise = $0 – (-$63,000) = $63,000Run = 700 units – 0 units = 700 units$63,000 / 700 units
Cont. Margin per unit:$90 per unit
Compare Graphs:
C-V-P and Profit
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