cvp analysis
DESCRIPTION
cost volume profit analysisTRANSCRIPT
Cost Behavior and Cost-Volume Relationships
Cost Behavior and Cost-Volume Relationships
Product and Period Costs• Product costs: Costs related to getting a product or service
ready for sale.– Appear “above the line” for gross margin in income statements– These costs can be inventoried
• They flow through the inventory account in the balance sheet • Sometime called “Inventoriable costs.”
• Period costs: Costs that are not product costs. Related to marketing and administration – Appear “below the line” for gross margin– These costs are expensed in the period they are incurred.– These costs do not flow through inventory accounts
Period Costs
Product Costs
A Traditional Income Statement
Usefulness for Internal Decisions
• The statement only considers expenses– Cost versus expense
• An expense is a cost recognized in the income statement
• The gross margin income statement mingles– Relevant & non relevant costs– Variable and fixed costs– Direct and indirect costs
Service Firms
• Products are not tangible or storable– Hotels, restaurants, consulting, airlines, gyms,
universities, museums,…
• Generally, there is no inventory of their final product– Exceptions exist
• We can inventory costs of software projects that go across accounting periods
Flow of Costs: Service Settings
Merchandising Firms
• Examples include Wal Mart, Big Bazaar etc.• These firms
– Sell substantively the same product they purchase.– Carry inventory to make goods available in the
quantities, varieties and delivery schedules demanded by customers.
Inventory Equation
• Need to flow costs via inventory account– Cost of purchase is NOT the cost of goods sold
• We can capture flow as:Cost of beginning inventory
+ Cost of goods purchased during the period– Cost of ending inventory= Cost of goods sold (COGS) during the period
• Make inventory cost flow assumption– First In First Out (FIFO)– Last In First Out (LIFO)
Cost of beginning inventory $3,450,200+ Cost of goods purchased + 24,795,740- Cost of ending inventory - 3,745,600= Cost of goods sold = $24,500,340
Solution
Flow of Costs in Merchandising
Transportation in, stocking
Transportation in, stocking
Manufacturing Firms
• Use labor and equipment to transform raw materials into finished goods– Have work-in-process– Need inventory accounts for all three kinds of
stages in the production process
• Much variation in– Nature of production process– Relative amounts of different costs
Cost Terms in Manufacturing
Names for Groups of Costs
Cost Terms in Manufacturing Prime Costs
Prime Costs
Conversion Costs
Conversion Costs
To verify the amounts specified above, THREE calculations need to be made:To verify the amounts specified above, THREE calculations need to be made:
Calculate Raw Materials UsedCalculate Raw Materials Used11Procedure Result
22 Calculate Cost of Goods ManufacturedCalculate Cost of Goods Manufactured
33 Calculate Cost of Goods SoldCalculate Cost of Goods Sold
Beginning materials inventory $240,000+ Purchases + 1,200,000- Ending materials inventory - 320,000= Raw materials used = $1,120,000
Beginning WIP inventory $50,000+ Materials used + 1,120,000+ Labor cost + 845,000+ Manufacturing overhead + 760,500- Ending WIP inventory - 100,000= Cost of goods manufactured = 2,675,500
Beginning FG inventory $375,000+ COGM + 2,675,500- Ending FG inventory - 294,500= Cost of goods sold = $2,765,000
Calculation
Cost Hierarchy• The cost hierarchy broadens the principle of
variability– Allows us to consider multiple activities
• The cost hierarchy recognizes four types of costs – Unit-level costs– Batch-level costs – Product-level costs– Facility-level costs
Why the Cost Hierarchy?
• Allows us to compute a more accurate estimate of costs– Can extend concept to other “levels”
• Customer level costs, channel level costs,…
• However,– Difficult to assign many costs to hierarchy categories
• Need finer data on operations
– Wrong classification of levels introduces errors in cost estimation
Example: Deluxe Checks
Variable and Fixed Cost
BehaviorA variable cost changes in direct proportion to changes in the cost-driver level.
A variable cost changes in direct proportion to changes in the cost-driver level.
A fixed cost is not immediately affected by changes in the cost-driver.
A fixed cost is not immediately affected by changes in the cost-driver.
Think of variable costs on a per-unit basis.Think of variable costs on a per-unit basis.
The per-unit variable cost remains unchanged regardless of changes in the cost-driver.
The per-unit variable cost remains unchanged regardless of changes in the cost-driver.
Think of fixed costs on a total-cost basis.Think of fixed costs on a total-cost basis.
Total fixed costs remain unchanged regardless of changes in the cost-driver.
Total fixed costs remain unchanged regardless of changes in the cost-driver.
Examples of Variable Costs
Direct material consumed.Direct LabourDirect Expenses/overheadsSelling commission based on number of units sold
Direct material consumed.Direct LabourDirect Expenses/overheadsSelling commission based on number of units sold
Examples of Fixed Cost
Salary of factory managerFactory RentDepreciation on machineryOffice & administrative costsSelling & distribution costs if fixed
Salary of factory managerFactory RentDepreciation on machineryOffice & administrative costsSelling & distribution costs if fixed
Committed Fixed Costs:Those fixed costs which cannot be reduced withoutcurtailing the organisation’s operations substantially
Committed Fixed Costs:Those fixed costs which cannot be reduced withoutcurtailing the organisation’s operations substantially
Discretionary Fixed Costs:Those fixed costs which can be reduced in difficult times
Discretionary Fixed Costs:Those fixed costs which can be reduced in difficult times
Relevant Range
The relevant range is the limitof cost-driver activity level within which aspecific relationship between costsand the cost driver is valid.
The relevant range is the limitof cost-driver activity level within which aspecific relationship between costsand the cost driver is valid.
Even within the relevant range, a fixed cost remains fixed only over a given period of time Usually the budget period.
Even within the relevant range, a fixed cost remains fixed only over a given period of time Usually the budget period.
Fixed Costs and Relevant Range
20 40 60 80 100 20 40 60 80 100
$115,000$115,000 100,000 100,000
60,000 60,000
Total Cost-Driver Activity in Thousands of Cases per Month
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Fix
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Costs
Relevant range$115,000$115,000 100,000 100,000
60,000 60,000
20 40 60 80 100
CVP Scenario
Per Unit Percentage of Sales Selling price $3.00 100%Variable cost of each item 2.10 70Selling price less variable cost $ .90 30%
Monthly fixed expenses: Rent $10,000 Depreciation 20,000 Other fixed expenses 15,000Total fixed expenses per month $ 45,000
Per Unit Percentage of Sales Selling price $3.00 100%Variable cost of each item 2.10 70Selling price less variable cost $ .90 30%
Monthly fixed expenses: Rent $10,000 Depreciation 20,000 Other fixed expenses 15,000Total fixed expenses per month $ 45,000
Cost-volume-profit (CVP) analysis is the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit).Cost-volume-profit (CVP) analysis is the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit).
Break-Even Point
The break-even point is the level of sales at which revenue equals expenses and net income is zero.The break-even point is the level of sales at which revenue equals expenses and net income is zero.
Sales - Variable expenses- Fixed expensesZero net income (break-even point)
Sales - Variable expenses- Fixed expensesZero net income (break-even point)
Contribution Margin Method
$45,000 fixed costs ÷ $.90= 50,000 units (break even)$45,000 fixed costs ÷ $.90= 50,000 units (break even)
Contribution margin Per UnitSelling price $3.00 Variable costs 2.10Contribution margin $ .90
Contribution margin Per UnitSelling price $3.00 Variable costs 2.10Contribution margin $ .90
Contribution margin ratioPer Unit %Selling price 100 Variable costs 70 Contribution margin 30
Contribution margin ratioPer Unit %Selling price 100 Variable costs 70 Contribution margin 30
Contribution Margin Method
$45,000 fixed costs÷ 30% (contribution-margin percentage)= $150,000 of sales to break even
$45,000 fixed costs÷ 30% (contribution-margin percentage)= $150,000 of sales to break even
50,000 units × $3.00 = $150,000in sales to break even50,000 units × $3.00 = $150,000in sales to break even
Equation Method
Sales – variable expenses – fixed expenses = net income$3.00N – $2.10N – $45,000 = 0$.90N = $45,000N = $45,000 ÷ $.90N = 50,000 Units
Sales – variable expenses – fixed expenses = net income$3.00N – $2.10N – $45,000 = 0$.90N = $45,000N = $45,000 ÷ $.90N = 50,000 Units
Let N = number of unitsto be sold to break even.Let N = number of unitsto be sold to break even.
Equation Method
S – .70S – $45,000 = 0.30S = $45,000S = $45,000 ÷ .30S = $150,000
S – .70S – $45,000 = 0.30S = $45,000S = $45,000 ÷ .30S = $150,000
Let S = sales in dollarsneeded to break even.Let S = sales in dollarsneeded to break even.
Shortcut formulas:Break-even volume in units = fixed expenses unit contribution margin
Break-even volume in sales = fixed expenses contribution margin ratio
Shortcut formulas:Break-even volume in units = fixed expenses unit contribution margin
Break-even volume in sales = fixed expenses contribution margin ratio
Target Net Profit
Managers use CVP analysis to determine the total sales, in units and dollars, needed To reach a target net profit.
Managers use CVP analysis to determine the total sales, in units and dollars, needed To reach a target net profit.
Target sales – variable expenses – fixed expenses target net income
Target sales – variable expenses – fixed expenses target net income
$9,000 per month is the minimumacceptable net income.
$9,000 per month is the minimumacceptable net income.
Target sales volume in units =(Fixed expenses + Target net income)÷ Contribution margin per unit
Target sales volume in units =(Fixed expenses + Target net income)÷ Contribution margin per unit
($45,000 + $9,000) ÷ $.90 = 60,000 units($45,000 + $9,000) ÷ $.90 = 60,000 units
Target Net Profit
Selling price $3.00 Variable costs 2.10 Contribution margin per unit $ .90
Selling price $3.00 Variable costs 2.10 Contribution margin per unit $ .90
Target sales dollars = sales price X sales volume in unitsTarget sales dollars = $3.00 X 60,000 units = $180,000.Target sales dollars = sales price X sales volume in unitsTarget sales dollars = $3.00 X 60,000 units = $180,000.
Sales volume in dollars = 45,000 + $9,000 = $180,000 .30
Sales volume in dollars = 45,000 + $9,000 = $180,000 .30
Target Net Profit
Target sales volume in dollars = Fixed expenses + target net incomecontribution margin ratio
Target sales volume in dollars = Fixed expenses + target net incomecontribution margin ratio
Contribution margin ratioPer Unit %Selling price 100 Variable costs 70 Contribution margin 30
Contribution margin ratioPer Unit %Selling price 100 Variable costs 70 Contribution margin 30
Margin of Safety
The excess of actual sales revenue over the break even sales revenue.The excess of actual sales revenue over the break even sales revenue.
Margin of safety divided by actual sales revenue gives the Margin of Safety Ratio.Higher the Margin of Safety Ratio, better it is.
Margin of safety divided by actual sales revenue gives the Margin of Safety Ratio.Higher the Margin of Safety Ratio, better it is.
Example
A company had incurred fixed expenses of Rs.4,50,000 with sales of Rs.15,00,000 and earned a profit of Rs.3,00,000 during the first halfof the year. In the Second half, it suffered a loss of Rs.1,50,000.
Compute:i. The profit volume ratio, break even point and margin of safety
for the first half.ii. Sales volume of second half assuming that the selling price and
fixed expenses remained unchanged.iii. The margin of safety and breakeven point for the whole year.
A company had incurred fixed expenses of Rs.4,50,000 with sales of Rs.15,00,000 and earned a profit of Rs.3,00,000 during the first halfof the year. In the Second half, it suffered a loss of Rs.1,50,000.
Compute:i. The profit volume ratio, break even point and margin of safety
for the first half.ii. Sales volume of second half assuming that the selling price and
fixed expenses remained unchanged.iii. The margin of safety and breakeven point for the whole year.
Assumptions of CVP Analysis
• Costs can be classified between Variable and Fixed costcomponents.
• The relationship of revenues and variable costs with output is linear.
• No changes in efficiency or productivity.
• Sales mix remains constant.
• Inventory level does not change significantly.
• Costs can be classified between Variable and Fixed costcomponents.
• The relationship of revenues and variable costs with output is linear.
• No changes in efficiency or productivity.
• Sales mix remains constant.
• Inventory level does not change significantly.
Operating Leverage
Operating leverage: a firm’s ratio of fixed costs to variable costs. Operating leverage: a firm’s ratio of fixed costs to variable costs.
Margin of safety = planned unit sales – break-even sales How far can sales fall below the planned level before losses occur?Margin of safety = planned unit sales – break-even sales How far can sales fall below the planned level before losses occur?
Highly leveraged firms have high fixed costs and low variable costs. A small change in sales volume = a large change in net income.Highly leveraged firms have high fixed costs and low variable costs. A small change in sales volume = a large change in net income.
Low leveraged firms have lower fixed costs and higher variable costs. Changes in sales volume will have a smaller effect on net income.Low leveraged firms have lower fixed costs and higher variable costs. Changes in sales volume will have a smaller effect on net income.
Sales Mix Analysis
Sales mix is the relative proportions orcombinations of quantities of productsthat comprise total sales.
Sales mix is the relative proportions orcombinations of quantities of productsthat comprise total sales.
Sales Mix AnalysisRamos Company Example
Sales in units 300,000 75,000 375,000Sales @ $8 and $5 $2,400,000 $375,000 $2,775,000Variable expenses @ $7 and $3 2,100,000 225,000 2,325,000 Contribution margins @ $1 and $2 $ 300,000 $150,000 $ 450,000Fixed expenses 180,000 Net income $ 270,000
Sales in units 300,000 75,000 375,000Sales @ $8 and $5 $2,400,000 $375,000 $2,775,000Variable expenses @ $7 and $3 2,100,000 225,000 2,325,000 Contribution margins @ $1 and $2 $ 300,000 $150,000 $ 450,000Fixed expenses 180,000 Net income $ 270,000
Wallets(W)
Key Cases(K) Total
How much units of Wallets and Key Cases should the company sell to break even?
Sales Mix Analysis
Break-even point for a constant sales mix of 4 units of W for every unit of K.sales – variable expenses - fixed expenses = zero net income[$8(4K) + $5(K)] – [$7(4K) + $3(K)] – $180,000 = 0 32K + 5K - 28K - 3K - 180,000 = 06K = 180,000 K = 30,000W = 4K = 120,000
Break-even point for a constant sales mix of 4 units of W for every unit of K.sales – variable expenses - fixed expenses = zero net income[$8(4K) + $5(K)] – [$7(4K) + $3(K)] – $180,000 = 0 32K + 5K - 28K - 3K - 180,000 = 06K = 180,000 K = 30,000W = 4K = 120,000
Let K = number of units of K to break even, and4K = number of units of W to break even.Let K = number of units of K to break even, and4K = number of units of W to break even.
Sales Mix Analysis
If the company sells only key cases:break-even point = fixed expenses
contribution margin per unit = $180,000
$2 = 90,000 key cases
If the company sells only key cases:break-even point = fixed expenses
contribution margin per unit = $180,000
$2 = 90,000 key cases
If the company sells only wallets:break-even point = fixed expenses
contribution margin per unit = $180,000
$1 = 180,000 wallets
If the company sells only wallets:break-even point = fixed expenses
contribution margin per unit = $180,000
$1 = 180,000 wallets
Sales Mix Analysis
Suppose total sales were equal to the budget of 375,000 units.Suppose total sales were equal to the budget of 375,000 units.
However, Ramos sold only 50,000 key casesAnd 325,000 wallets.What is net income?
However, Ramos sold only 50,000 key casesAnd 325,000 wallets.What is net income?
Sales Mix Analysis
Ramos Company Example
Sales in units 325,000 50,000 375,000 Sales @ $8 and $5 $2,600,000 $250,000 $2,850,000 Variable expenses @ $7 and $3 2,275,000 150,000 2,425,000 Contribution margins @ $1 and $2 $ 325,000 $100,000 $ 425,000 Fixed expenses 180,000 Net income $ 245,000
Sales in units 325,000 50,000 375,000 Sales @ $8 and $5 $2,600,000 $250,000 $2,850,000 Variable expenses @ $7 and $3 2,275,000 150,000 2,425,000 Contribution margins @ $1 and $2 $ 325,000 $100,000 $ 425,000 Fixed expenses 180,000 Net income $ 245,000
Wallets(W)
Key Cases(K) Total
Example
The Garware Paints Ltd. presents you the following income statement for the first quarter
Product Total X Y Z Sales 100,000 60,000 40,000 200,000 Variable Costs 80,000 42,000 24,000 146,000 Contribution 20,000 18,000 16,000 54,000 Fixed costs 27,000 Net Income 27,000 P/V ratio 0.27Break Even sales 100,000 Sales mix percent 0.50 0.30 0.20 1.00
If Rs.40,000 of the sales shown for the product X could be shifted to product Y and Z equally, how would the net income, P/V ratio and BEP change.
Impact of Income Taxes
Suppose that a company earns $480 before taxes and pays income tax at a rate of 40%.Suppose that a company earns $480 before taxes and pays income tax at a rate of 40%.
What is the after-tax income?What is the after-tax income?
Impact of Income Taxes
Target income before taxes = Target after-tax net income 1 – tax rate
Target income before taxes = $ 288 = $480 1 – 0.40
Suppose the target net incomeafter taxes was $288.
Impact of Income Taxes
Target sales – Variable expenses – Fixed expenses= Target after-tax net income ÷ (1 – tax rate)Target sales – Variable expenses – Fixed expenses= Target after-tax net income ÷ (1 – tax rate)
$.50N – $.40N – $6,000 = $288 ÷ (1 – 0.40)$.10N = $6,000 + ($288/.6)$.06N = $3,600 + $288 = $3,888 N = $3,888/$.06 N = 64,800 units
$.50N – $.40N – $6,000 = $288 ÷ (1 – 0.40)$.10N = $6,000 + ($288/.6)$.06N = $3,600 + $288 = $3,888 N = $3,888/$.06 N = 64,800 units
Impact of Income Taxes
Suppose target net income after taxes was $480Suppose target net income after taxes was $480
$.50N – $.40N – $6,000 = $480 ÷ (1 – 0.40)$.10N = $6,000 + ($480/.6) $.06N = $3,600 + $480 = $4080N = $4,080 ÷ $.06 N = 68,000 units
$.50N – $.40N – $6,000 = $480 ÷ (1 – 0.40)$.10N = $6,000 + ($480/.6) $.06N = $3,600 + $480 = $4080N = $4,080 ÷ $.06 N = 68,000 units
Q. State whether P/V ratio will increase or decrease or remain unchanged in the following situations (Consider all situations independently keeping other things constant):
An increase in physical sales volumeNo Change
An increase in fixed costsNo Change
A decrease in variable cost per unitIncrease.
A decrease in contribution margin per unitDecrease
An increase in Selling priceIncrease
A decrease in fixed costsNo change
A 10% increase in both variable costs and selling priceNo Change
A 10% increase in selling price and 10% decrease in physical sales volumeIncrease
A 50% increase in variable cost and 50% decrease in fixed costsDecrease
An increase in angle of incidenceIncrease
Example
S Ltd. furnishes the following data relating to the year 2012:
Ist Half of the yearIInd Half of the year
Sales 45,000 50,000 Total Cost 40,000 43,000
Assuming that there is no change in prices and variable costs per unit and that the fixed expenses are incurred equally in the two half year periods, calculate for the entire year:
i. The profit volume ratioii. Fixed expensesiii. Break even salesiv. Margin of safety ratio
ExampleM Ltd. manufactures three products P, Q and R. The unit selling price of these products are Rs.100, Rs.80 and Rs.50 respectively. The corresponding unit variable costs are Rs.50, Rs.40 and Rs.20. The proportions (quantity wise) in which these products are manufactured and sold are 20%, 30% and 50% respectively. The total fixed costs are Rs.14,80,000.
Given the above information you are required to work out overall break even quantity and product wise break up of such quantity.
Example
Two competing companies HERO Ltd. and ZERO Ltd. sell same type of product in the same market. Their forecasted Profit and Loss A/c for the year ending Mar 2011 are as follows:
HERO ZERO
Sales 500,000 500,000
Less: Variable Costs 400,000 300,000
Fixed costs 50,000 150,000
Forecasted net profit 50,000 50,000
You are required to state which company is likely greater profits in the conditions of:a. Low demandb. High Demand.
Example
A Japanese soft drink is planning to establish a subsidiary company in India to produce mineral water.Based on the estimated annual sales of 40,000 bottles of mineral water, cost studies produced the following estimates for Indian Subsidiary:
Total Annual CostsPercent of total annual cost which is variable
Material 210,000 100%Labour 150,000 80%Factory overheads 92,000 60%Administration expenses 40,000 35%
The Indian production will be sold by the manufacturer's representatives who will receive a commission of 8% of the sale price.i. What should be the selling price per bottle to earn a net profit of 10% on sales.ii. What will be the break even point in units and in Rupee sales at the above
computed selling price.
ExampleSuppose a Holiday Inn Hotel has annual fixed costs applicable to its rooms of $1.2 million for its 300-room hotel, average daily room rents of $50, and average variable costs of $10 for each room rented. It operates 365 days per year.
What is the amount of net income on rooms that will be generated if the hotel is half full throughout the entire year?
What is the break even point in number of room days?
What is the percentage of occupancy needed to break even?
Ans: $990,000, 30,000 room days27.4%
ExampleGeneral Hospital has total variable costs of 90% of total revenues and fixed costs of $5 million per year. There are 50,000 patient-days estimated for next year. What is the average daily revenue per patient necessary to breakeven?
Ans: $1,000 average daily revenue per patient necessary to breakeven
ExampleBerea Company currently sells 19,000 units. Total fixed costs are $84,000, and the contribution margin per unit is $6.00. Berea’s tax rate is 40%. What is the margin of safety in units?
Ans: 5,000 units
EaxmpleMuy Mal Company, a producer of salsa, has the following information:
Income tax rate 30%Selling price per unit $5.00 Variable cost per unit $3.00 Total fixed costs $90,000.00
How many number of units must be sold to obtain a targeted after-tax income of $14,000?
Ans: 55,000 units
ExampleBonnie and Clyde started the BC Restaurant in 20X0. They rented a building, bought equipment, and hired two employees to work full time at a fixed monthly salary. Utilities and other operating charges remain fairly constant during each month. During the past two years, the business has grown with average sales increasing 1% a month. This situation pleases both Bonnie and Clyde, but they do not understand how sales can grow by one percent a month while profits are increasing at an even faster pace. They are afraid that one day they will wake up to increasing sales but decreasing profits. Required: Explain why the profits have increased at a faster rate than sales.
Linear-cost Behavior
Costs are assumed to be fixed or variable within the relevant range of activity
Step Cost Behavior Patterns
Step costs change abruptly at intervalsof activity because the resources andtheir costs come in indivisible chunks.
Step Cost Behavior Patterns
Mixed-Cost Behavior Patterns
Mixed costs contain elements of bothfixed- and variable-cost behavior.
The fixed-cost element is unchangedover a range of cost-driver activity.
The variable-cost element variesproportionately with cost-driver activity.
Mixed-Cost Behavior PatternsParkview Medical Center Predicted costs = fixed + variable
costs (patient-days) Predicted costs = $10,000 + $5(4,000)
Predicted costs = $30,000
Distribution channels
Choice of process and product design
Quality levels
Product features
Management’s Influence on Cost Behavior
Capacity Decisions
They are the fixed costs of being ableto achieve a desired level of production orto provide a desired level of service whilemaintaining product or service attributes.
Committed Fixed Costs
Salaries of key personnel
Committed fixed costs arisefrom the possession of facilities,
equipment, and a basic organization.
Lease payments
Property taxes
Discretionary Fixed Costs
Discretionary fixed costs are costs fixed at certain levels only because management decided that these levels of cost
should be incurred to meet the organization’s goals.
These discretionary fixed costs have no obvious relationship to levels of output activity but
are determined as part of the periodic planning process.
Each planning period, management will determine how much to spend on discretionary items. These costs
then become fixed until the next planning period.
Examples of DiscretionaryFixed Costs
Advertising and promotion
Research and development
Management salaries
Employee training
Technology Decisions
Choice of technology (e-commerce versusin-store or mail-order sales) positions theorganization to meet its current goals andto respond to changes in the environment.
Cost Functions
Planning and controlling the activitiesof an organization require accurate
and useful estimates of futurefixed and variable costs.
Cost Functions
Understanding relationships between costsand their cost drivers allows managers to...
Make better operating, marketing, And production decisions
Plan and evaluate actions
Determine appropriate costs for short-run and long-run decisions.
Cost Functions
The first step in estimating or predictingcosts is measuring cost behavior as afunction of appropriate cost drivers.
The second step is to use these costmeasures to estimate future costs atexpected levels of cost-driver activity.
Cost Function EquationLet:Y = Total cost F = Fixed costV = Variable cost per unitX = Cost-driver activity in number of units
Mixed-cost function:Y = F + VX
Y = $10,000 + $5.00X
The mixed-cost function is called a linear-cost function.
Developing Cost Functions
A cost function’s estimates of costsat actual levels of activity must reliablyconform with actually observed costs.
The cost function must be believable.
Choice of Cost Drivers: Activity Analysis
Choosing a cost function startswith choosing cost drivers.
Managers use activity analysis toidentify appropriate cost drivers.
Activity analysis directs managementaccountants to the appropriate
cost drivers for each cost.
Methods of Measuring Cost Functions
1. Engineering analysis 2. Account analysis 3. High-low analysis 4. Visual-fit analysis 5. Least-squares regression analysis
Engineering Analysis
Engineering analysis measures cost behavior according to what costs should be,
not by what costs have been.
Engineering analysis entails a systematicreview of materials, supplies, labor,
support services, and facilitiesneeded for products and services.
Account Analysis
The simplest method of account analysis selects a plausiblecost driver and classifies each account as a variable or fixed cost.
Supervisor’s salary and benefits $ 3,800 $3,800 Hourly workers’ wages and benefits 14,674 $14,674Equipment depreciation and rentals 5,873 5,873 Equipment repairs 5,604 5,604 Cleaning supplies 7,472 7,472 Total maintenance costs $37,423 $9,673 $27,750
Monthly cost Amount Fixed Variable
Parkview Medical Center
Account Analysis Example
Fixed cost per month = $9,673
Variable cost per patient-day= $27,750 ÷ 3,700
= $7.50 per patient-day
3,700 patient-days
Y = $9,673 + ($7.50 × patient-days)
High-Low Method
Focus on the highest- and lowest-activity points.
Plot historical data points on a graph.
High month: AprilMaintenance cost: $47,000
Number of patient-days: 4,900
Low month: SeptemberMaintenance cost: $17,000
Number of patient-days: 1,200
High-Low Method Example
The point at which the line intersects the Y axis is the intercept, F, or estimate of Fixed Costs, and the slope of the line measures the variable cost.
High-Low Method Example
Variable costs = Change in costs change in activity
V = ($47,000 – $17,000) ÷ (4,900 – 1,200) = $30,000 ÷ 3,700 = $8.1081
What is the variable cost (V)?Using algebra to solve for variable and fixed costs.
High-Low Method Example
F = Total mixed cost – total variable costAt X (high) F = $47,000 - ($8.1081× 4,900 patient days)
= $47,000 – $39,730 = $7,270 a month
At X (low) F = $17,000 = ($8.1081× 1,200 patient days)= $17,000 – $9,730 = $7,270 a month
Cost function measured by high-low method: Y = $7,270
per month + ($8.1081 × patient-days)
What is the fixed cost (F)?
Visual-Fit Method
In the visual-fit method, the cost analystvisually fits a straight line through a plot
of all of the available data, not justbetween the high point and the
low point, making it more reliablethan the high-low method.
Least-Squares Regression Method
Regression analysis measuresa cost function more objectivelyby using statistics to fit a cost
function to all the data.
Regression analysis measurescost behavior more reliably than
other cost measurement methods.
Coefficient of Determination
One measure of reliability,or goodness of fit, is the
coefficient of determination,R² (or R-squared).
The coefficient of determinationmeasures how much of the
fluctuation of a cost is explainedby changes in the cost driver.
ExamplePresented below is the production data for the first six months of the year showing the mixed costs incurred by Euclid Company.
Month Cost Units
January $7,500 4,000February 13,000 7,500March 11,500 9,000April 11,700 11,500May 13,500 12,000June 11,850 6,000
Euclid Company uses the high low method to analyze mixed costs. ‑
What shall be cost function?
ExampleThe Reynolds Company used regression analysis to predict the annual cost of utilities. The results were as follows:
Utilities CostExplained by Direct Labor Hours
Constant $7,650 Standard error of Y estimate $245.20 R squared ‑ 0.8650 No. of observations 30 Degrees of freedom 28
X coefficient(s) 8.437 Standard error of coefficient(s) 0.917
What shall be the estimated total cost for 1,000 units?
Example:The cost of the maintenance department at Forest Manufacturing has always been charged to the production departments based upon number of employees. Recently, an activity analysis of possible cost drivers was performed which indicated that the square feet of space may also be a predictor of costs to be assigned to each department. Given the following data, compare the different amounts of maintenance department cost that would be allocated to each of the production departments if the cost driver used is (a) number of employees, and (b) the square feet of space.
Dept. X Dept. Y Dept. ZNumber of employees 300 250 50Square feet of space 15,000 25,000 10,000
Total production department cost: $ 1,000,000
Example
Two manufacturing companies which have the following operating details decided to merge:
Company 1 Company 2Capacity Utiliation (%) 90 60Sales (Rs. Lakhs) 540 300
Variable Costs (Rs.Lakhs) 396 225Fixed Costs 80 50
Assuming that the proposal is implemented, calculate:
i. Break even sales for the merged plant and the capacity utilization at that stage.ii. Profitability of the merged plant at 80% capacity utilization.iii. Sales turnover of the merged plant to earn a profit of Rs.75 Lakhiv. When the merged plant is working at a capacity to earn a profit of Rs.75 lakhs, what
percentage increase in selling price is required to sustain an increase of 5% in fixed overheads.
ExampleABC Ltd. has installed capacity of 1,20,000 units per annum. The cost structure of the product manufactured is as under:
Variable Cost:Materials Rs.8Labour Rs.8Overheads Rs.3
Fixed overheads Rs.168750 per annumSemi variable overheads Rs.48,000 at 60% capacity and Rs.60,000 at 80% capacity.
The capacity utilization for next year is estimated at 60% for first two months , 70% for next six months and 80% for rest of the year. Company is planning to have a profit of 25% on sales.
Compute the selling price per unit and break even point in units at the computed selling price.
Example:XYZ School has a total of 150 students. The school plans a picnic to places like Zoo, Planetarium etc. A private bus operator has come forward to lease out the bus(es). Each bus will have 50 seats for students besides 2 seats reserved for teachers. There will be two teachers per bus and each teacher will be paid an allowance of Rs.50. The following are other cost estimates:
Cost per StudentBreak fast Rs.5Lunch Rs.10Tea Rs.3Entrance at Zoo Rs.2
Rent per bus is Rs.650. Special permit of Rs.50 per bus is also required to be paid. Block entrance fees at planetarium is Rs.250. Prizes to students for games Rs.250.
School charges Rs.45 per student. Compute the break even point.
Example
6000 pen drives of 2GB to be sold in a perfectly competitive market to earn Rs.1,06,000 of profit, whereas in monopoly only 1200 units are required to be sold to earn the same profit. The fixed costs for the period are Rs.74,000. The contribution per unit in monopoly market is as high as three fourth of it variable costs. Determine the target selling price per unit under each market condition.
Example
Paints Ltd. manufactures 2,00,000 tins of paints annually at normal capacity. It incurs the following manufacturing cost per unit:
Direct material Rs.7.80Direct Labour Rs.2.10Variable overhead Rs.2.50Fixed overhead Rs.4.00
Each unit is sold for Rs.21 with an additional variable selling overhead incurred at Rs.0.60 per unit. During the next quarter only 10,000 units can be produced and sold. Management plans to shut down the plant estimating that the fixed manufacturing costs can be reduced to Rs.74,000 for the quarter. When the plant is operating, the fixed overheads are incurred at uniform rate through out the year. Additional costs plant shut down for the quarter are estimated at Rs.14,000.
You are required to advise whether it is more economical to shut down the plant during the quarter rather than operate the plant.
ExampleEntertain U Ltd hires an air conditioned theatre to stage plays on weekend evenings. One play is staged per evening. The following are the seating arrangements:VIP Rows – First 3 rows of 10 seats per row, priced at Rs 320 per seat.Middle Level – The next 18 rows of 20 seats per row, priced at Rs 220 per seat.Last Level – 6 rows of 30 seats per row, priced at Rs 120 per seat.For each evening, a drama troupe has to be hired at Rs 71,000, rent has to be paid to theatre at Rs 14,000 per evening and air conditioning and other stage arrangement charges work out to Rs 7,400 per evening. Every time a play is staged, the drama troupe’s friends and guests occupy the first row of the VIP class, free of charge by virtue of passes granted to these guests. The troupe ensures that 50% of the remaining seats in the VIP class and 50% of the seats of the other two classes are sold to outsiders in advance and the money is passed on to Entertain U. The troupe also finds for every evening, a sponsor who puts up his advertisement banner near the stage and pays Entertain U a sum of Rs 9,000 per evening. Entertain U supplies snacks during the interval, free of charge to all guests in the hall, including the VIP free guests. The snacks cost Entertain U Rs 20 per person. Entertain U sells the remaining tickets and observes that for every one seat demanded from the last level, there are 3 seats demanded from middle level and 1 seat demanded from the VIP level. You may assume that in case any level is filled, the visitor buys the next higher or lower level, subject to availability.You are required to calculate the number of seats that Entertain U has to sell in order to break-even and give the category wise total seat occupancy at BEP.
CVP Analysis and Environmental Factors:
Economy-Industry relationship
Industry-Company relationship
Controllable factors affecting Sales-Profit Analysis:Advertising outlays
Market research expenditures
New product development
Extension of marketing territories