Class 06 -- OPTIONAL Cost-Volume-Profit Analyis

Importanceof

C-V-P Analysismyaccountingteacher.c

om

C-V-P Analysis

myaccountingteacher.com

C = CostV= VolumeP = Profit

Cost-Volume-Profit AnalysisHow much does our profit (or loss) vary depending on our level of sales?

BasicCost Behavior


Cost Behavior?


“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.


VARIABLE COST


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


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


Variable Cost

RELEVANT RANGE


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


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


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


Fixed Cost

STEPPED FIXED COST


MIXED COST


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


MIXED COST


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?


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


3 Approaches• Detailed, invoice-by-invoice categorization• Scattergraph method, a visual approach• High-low method, a computational approach

Example

Graph of Electricity Cost



Scattergraph Method


• 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


Slope = Variable Cost per Unit


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


Total Cost Equation


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


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


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


• 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


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


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


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


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


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


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


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


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


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


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



What if sales increase by 20% (to 1,200 gloves)?




For the Month



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


For the Month

Contribution MarginRATIO


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%



For the Month

C-V-PEquation







For the Month

C-V-PEquation


Sales Revenue – Variable Costs – Fixed Costs = Profit

$240,000 – $132,000 – $63,000 = $45,000

C-V-PEquation


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


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



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


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


(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


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


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


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!!!


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


C-V-PEquation



(Sales Price × Units) – (Variable Cost × Units) – Fixed Costs = Profit

Sales Revenue – (Variable Cost Ratio × Sales Revenue) – Fixed Costs = Profit

Jewels Baseball Gloves

Initial Data


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


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.


X = 1,300 units

C-V-P Equation

Change in Fixed Costs


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


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.


X = 1,415 units

C-V-P Equation



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


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.


X = 825 units

C-V-P Equation



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)


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


(II)


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


(III)


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


(III)


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


• Get comfortable with the C-V-P Equation.

• Check your work!!!

C-V-PGraphs


C-V-P Graph


C-V-P Graphy-INTERCEPT of Total Cost

Line


y-Interceptof Total Cost Line:

The cost whenthere are0 units.

FIXED COST =

$63,000

C-V-P Graph

Slope of the Revenue Line


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



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


• 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


C-V-P Graph

Slope of the Profit Line



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


Class 06 -- OPTIONAL Cost-Volume-Profit Analyis

Documents

metal cost

hamburgerfixed cost

cost of electricity

total fixed cost

profit costvolume

total variable cost

direct labor cost

fixed coststepped fixed