Chapter 18 - Cost Behavior and Cost-Volume-Profit Analysis

cost-volume profit analysis

looks at how income (profit) is affected by these factors:

• sales price per unit

• variables costs per unit

• volume (# units)

• fixed costs (total)

managers use it to predict how changes in costs and sales levels affect profit

fixed costs

don’t change when volume of activity changes

ex: monthly rent for a factory is the same for the month even if they increase production

when volume increases, total fixed costs stay the same but fixed cost per unit decreases as volume increases

variable costs

change in proportion to changes in volume of activity

ex: if each unit uses $2 of direct materials, then when 10 units are made, total direct materials = $20

when volume increases, total variable costs increase but variable costs per unit remain the same **OPPOSITE of fixed costs

mixed costs

include both fixed and variable cost components

ex: compensation for sales reps has fixed salary + sales commission (variable)
ex: utilities - typically there’s a base rate and then variable rate w usage

like a fixed cost, mixed cost is greater than 0 when production is at 0 but it also increases proportionately w increases in volume

step-wise cost

has a step pattern in costs

ex: adding another shift in the schedule, you can’t do this gradually, it’s just a whole extra step that increases by a lump sum

relevant range of operations

normal operating range for a business

ex: one production shift can produce up to 2000 units

examples of each kind of cost

fixed = rent, insurance, deprecitaion, properyty taxes, office salaries

variable = direct materials, direct labor, packaging, shipping, indirect materials

mixed costs = sales reps, utilies, natural gas, maintenance, etc.

step-wise costs = add or drop shift of workers, add or drop production line, add or drop warehouse

three methods commonly used to estimate fixed and variable cost components

scatter diagram

high low method

least suqares regression

scatter diagram

graph of unit volume and cost data

• each point reflects total costs and units produced during each of last 12 months

**estimated line of cost behavior is drawn to shown relation between cost and unit volume

high-low method

uses only two points to estimate cost equation: highest and lowest VOLUME levels which doesn’t necesarily follow highest and lowest cost levels

3 steps:

(1) identify highest and lowest volume

(2) compute slope (variable cost per unit) using high and low volume

(3) compute total fixed costs by computing total variable cost at either high or low volume, then subtract that amonut from total cost at that volume

regression

statistical method for identifying cost behavior

comparing cost estimation methods

diff cost estimation methods usually result in diff estimates of fixed and variable costs

**regression uses more data nad is typically more accurate than high-low but high-low is easier for quick estimates

contribution marhin

goes to cover fixed costs and any excess is income

= sales - variable costs

contribution margin per unit

amount by which a product’s unit selling price exceeds its variable costs per unit

= selling price per unit - variable costs per unit

contribution margin ratio

% of each sales dollar that remains after deducting unit variable cost

= contribution marhin per unit / selling price per unit

= contribution margin / sales

break even point

sales level at which total sales = total costs —> zero income

can be stated in uints of product or dollars of sales

3 methods for break even point

formula method

contribution margin income statement

cost-volum profit chart

formula method (untis and dollars)

ubreak even (units) = fixed costs / contribution margin per unit

break even (dollars) = fixed costs / contribution margin ratio

contribution margin income statement

important tool for internal decision making but does not replace GAAP income statement for financial accounting

separately classifies costs as variable or fixed, and reports contribution margin

whereas GAAP income statement separately classifies costs as product or period and reports gross profit

contribution margin income statement format

sales

(variable costs)

= contribution margin

(fixed costs)

= income margin

cost-volume-profit chart 

has a line for total costs and line for total sales

**where they intersect = break even

to the left of it shows loss

to the right of it shows profit area

total sales line - total costs line = income

effects of changes in CVP inputs on break even

if sales price per unit inrceases, break even decreases

if sales price per unit decreases, break even increases

if variable cost per unit inrceases, break even increases

if variable cost per unit decreases, break even decreases

if total fixed costs increase, break even increases

if total fixed costs decrease, break even decreases

margin of safety

amount that sales can decline before the company incurs a loss

**expressed in dollars or % sales

= expected (or actual) sales - break even sales

(%) = (expected - break even) / expected

computing sales for a target income

dollar sales at target income = (fixed costs + target income) / CMR

unit sales at target income = (fixed costs + target income) / contribution margin per uint

evaluating business strategies

we can do this using CVP, by using initial break even and then finding revised break even

revised break even ($) = revised fixed costs / revised contribution margin raito

sales mix

the proportion of sales volume for each production if a company sells more than one product

ex: company sells 6 footballs and 4 baseballs —> sales mix: 60% for footballs and 40% for baseballs ;

weighted average contribution margin per unit

used for sales mix, this is how we do break even

measure combines per unit contribution margin of each product by their weights in the sales mix

ex: if baseball CMPU = $4 and football CMPU = $5 and salex mix: B=40%, F=60%,

weighted average contribution margin per unit = $4(40%) + $5(60%)

then break even = fixed costs / weighted avg contr margin per unit

assumptions in cost-volume-profit analysis

• costs can be classified as variable or fixed

• costs are linear w/in relevant range

• units produced are sold (inventory is constant)

• sales mix is constant

**if costs and sales are different, CVP not as useful

big data

refers to mssive complex data sets, differs from other data due to 3 Vs:

(1) volume: refers to vast amount of data being generated and stored

(2) velocity: rapid speeds at which data are created and processed, companies monitor inventory levels in real time using RIFD tags and machines w/ sensors

(3) variety: refers to type of data generated (structured comes from sales and other transactions), (unstructured comes from customer reviews, social media, etc.)

machine learning

subset of artificial intelligence that enables computers to learn and make choices using algorithms and statistical models

applying it to structured data helps understand cost behavior and sales mix and prepare CVP analysis

large language models

type of AI that can generate and summarize text

helpful when applied to unstructured data —> can put them into sales forecasts

CVP analysis for service businesses

break even points computed not using units of product

ex: for a sports team maybe tickets sold per season

ex: for an online education, students per course

river cruis: passengers per cruise

degree of operating leverage

= contribution margin / income

useful measure to assess effect of changes in level of sales on income

ex: if DOL = 30%, that means if its sales increase by 10%, income will increases by 30%

company w dol of 3 will expect a higher increase in income from a 10% increase in sales than a company with dol of 2

**higher is better

variable costing

only ariable costs relating to production are included in product costs

**includes direct materials, direct labor and variable overhead costs

excludes fixed overhead costs —> they’re expensed in period incurred instead

**not allowed under GAAP for external reporting - GAAP requires absorption costing

absorption costing

product costs include direct materials, direct labor, fixed and variable overhead

**fixed overhead costs expensed when goods are sold

what is the main difference between variable and absorption costing??

variable costing excludes fixed overhead from product costs

income statement for absorption costing

sales

(cogs)

= gross profit

(selling and administrative)

= income

income statement for variable costing

sales

(variable costs)

• variable costs of goods sold

• variable selling and administrative expenses

= contribution margin

(fixed expenses)

• fixed overhead

• fixed selling and administrative

= income

relationship between units produced and absorportion and variable costing

when untis produced are:

• equal to units sold, income under absorption = variable

• > units sold, income under absorption > income under variable

• < units sold, income under absorption < income under variable

converting income under variable costing to income under absorption costing

income under absorption costing = income under variable costing + fixed overhead cost in ending inventory - fixed overhead cost in beg inventory