MANAGERIAL ACCOUNTING

3rd Topic

FIXED AND VARIABLE COSTS, FIXED AND VARIABLE COSTS,

COST-VOLUME-PROFIT ANALYSIS

3.1 Identifying cost behaviour

3.2 CVP terminology

3.3 CVP formulas

3.4 Break-Even Analysis

Structure of the lecture 3

3.4 Break-Even Analysis

3.5 Profit-volume chart

3.6 Weakness of break-even analysis

3.7 CVP analysis – example (computation, grafical solution)

3.1 Identifying Cost Behaviour

Successful management = planning a company′s

future activities, prediction of:

- Volume of the activity

- Cost to be incurred- Cost to be incurred

- Sales to be made

- Profit to be received.

3.1 Identifying Cost BehaviourCost-volume-profit (CVP) analysis

helps predict how changes in costs and sales levels

affect income,

examines the behaviour of total revenues, total costs,

and operating income as changes occur in the output

level, selling price, variable costs, or fixed costs.level, selling price, variable costs, or fixed costs.

Tool used to help answer managerial questions such:

How will revenues and costs be affected

- if sale will be increased?

- if selling prices will be raised or lowered?

- if business will be expanded into overseas markets?

3.2 CVP terminologyRevenues

are inflows of assets received in exchange for products or services provided to customers.

Revenue driver

Is a factor that affects revenues (e.g. Units of output sold, selling prices, and levels of marketing costs).

(Cost driver

Any factor that affects cost, change in the cost driver will cause a Any factor that affects cost, change in the cost driver will cause a change in the total cost of a related cost object

(e.g. Units of output manufactured, number of sales visits made, and number of packages shipped)).

The most detailed way of prediction: multiple revenue drivers and multiple cost drivers (general case) – extensive analysis, time-consuming.

Special case of CVP: single revenue driver and single cost driver, is helpful in decisions relating to overall strategies ad long-range plans; widely used.

3.2 CVP terminologyCVP analysis (special case) is based on the following

assumptions:

• total costs can be divided into a fixed components and a component that is variable with respect to the level of output of single product or constant sale mix.

• The behaviour of total revenues and total costs is • The behaviour of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range for short time horizont.

Measure of output = number of units manufactured or units sold (e.g. Airlines – passenger-miles; automobiles – vehicles manufactured; hospitals –patient-days; hotels – room occupied; universities –student credit-hours, …)

3.2 CVP terminologyFixed costs (FC)

Remain unchanged in amount when the volume of activity varies from period to period within a relevant range - fixed cost remains constant

(e.g. monthly rent paid for a factory building, property taxes, office salaries, depreciation, property taxes, office salaries, depreciation, service department costs…).

While total fixed cost does not change as the volume of the production changes (increases), the fixed cost per unit of output decreases.

If the relevant range changes, the amount of fixed cost will likely change (step-wise costs).

3.2 CVP terminologyFixed costs as to the volume of activity

3.2 CVP terminologyFixed costs if relevatnt range changes (step-wise costs)

3.2 CVP terminologyVariable costs (VC)

Change in proportion to changes in volume of

activity, total amount of variable cost changes with

the level of production.

(e.g. Direct material, direct labour, sales (e.g. Direct material, direct labour, sales

commissions, shipping costs, and some overhead

costs.)

Variable cost per unit remains constant,

total amount of variable cost changes with the level

of production.

3.2 CVP terminologyVariable costs as to the volume of activity

3.2 CVP terminologyTotal costs (TC) = Fixed costs (FC) + Variable costs (VC)

3.2 CVP terminologyMixed (semi-variable; semi-fixed) costs

Includes both fixed and variable cost components.

(salary of sale representatives includes fixed monthly

salary and variable commission based on sales).

In CVP analysis, mixed costs are often separated into In CVP analysis, mixed costs are often separated into

fixed and variable components.

Curvilinear (nonlinear) costs

Increases at a non-constant rate as volume increases.

(total direct labour costs when workers are paid by

the hour)

3.2 CVP terminologyCurvilinear (nonlinear) costs

the shape of the total cost function:

• initial steep rise, levels off, followed by a further steep rise.

3.2 CVP terminology

Curvilinear variable cost function

3.3 CVP formulas I.

Total costs = fixed costs + variable costs

TC = VC + FC

TC = vu*Q + FC

Average unit cost = total cost / quantity

c = TC / Qcu = TC / Q

cu = FC / Q + vu

Income = Total revenues (sales) – total costs

= total revenue – variable costs – fixed costs

I = S – TC

I = S – VC - FC

3.4 Break-Even Analysis, formulas II.

Break-even analysis is a special case of CVP analysis

Break-even point (BEP) is the sales level at which a

company neither earns a profit nor incurs a loss. It

is the moment when sales cover total costs.is the moment when sales cover total costs.

Sales = fixed costs + variable costs

S = FC + VC

su*Q = FC + vu*Q

QBEP = FC / (su – vu)

3.4 Break-Even Analysis

Linear CVP relationships (special case of CVP)

1. Constant variable cost and selling price is assumed.

2. Only one break-even point, and profit increases as volume increases.

2. Only one break-even point, and profit increases as volume increases.

3. The diagram is not intended to provide an accurate representation for all levels of output. The objective is to provide an accurate representation of cost and revenue behaviour only within the relevant range of output.

3.4 Break-Even Analysis

Break-even chart (linear CVP)

3.4 Break-Even Analysis, formulas III.

Contribution margin per unit is the difference between selling price per unit and variable cost per unit. Usedfor decision on optimal structure of the production.

cmu = su – vu

then

BEP in output units = fixed costs divided by contribution margin per unit

BEP in output units = fixed costs divided by contribution margin per unit

QBEP = FC / cmu

QBEP = FC / (su – vu)

Total contribution margin:

CM = S – VC

CM = cmu*Q

3.4 Break-Even Analysis, formulas IV.Contribution margin ratio (contribution to sales; profit-volume ratio)

is the proportion of sales available to cover fixed costs and provide for profit, which is defined as contribution margin per unit divided by unit selling price.

cmru = cmu/su

- using either unit or total figures.

- Usage: when given estimate of total sales revenue, it is possible toestimate total contribution.

- Usage: when given estimate of total sales revenue, it is possible toestimate total contribution.

BEP in monetary units = fixed costs divided by contribution

margin ratio BEP = FC / cmru

Margin of safety

is the amount by which sales may decrease before a loss occurs.

MoS = (Expected sales – BEP) / Expected sales

3.4 Break-Even Analysis, formulas V.

Quantification of the income

I = S – VC – FC

I = su*Q – vu*Q – FC

I = cmu*Q – FC ,

Also:Also:

I = S – VC – FC

I = cmru*S – FC

I + FC = cmru*S

and, when I = 0, then BEP = FC / cmru

3.5 Profit-volume chartsProfit-volume chart

variant of break-even chart, shows the impact on

income of changes in the output level.

PV chart is obtained by plotting loss or profit against

volume of activity.volume of activity.

The slope of the graph is equal to the contribution

per unit – each additional unit sold decreases the

loss, or increases the profit.

At zero activity there are no contributions, so there

will be a loss equal to the total fixed costs.

3.5 Profit-volume chart

3.6 Weakness of break-even analysis1. Non-straight-line relationships

We assumes strictly straight-line relationships between sales revenues, variable costs and volume of activity what usually is not in real life.

2. Stepped fixed costs

Most fixed costs are not fixed over all volumes of activity, they tend to be „stepped“.

3. Multi-product businesses.

We assume effect of additional sales of one product (or service); problem of identifying the fixed costs of one particular activity

3. 7 CVP analysis:

non-graphical computations

Example 1

– Fixed costs per annum £60,000

– Unit selling price £20

– Unit variable cost £10

– Relevant range 4,000 – 12,000 units

Question 1: Break even point?

Question 2: How many units to be sold to obtain £30,000

profit?

Question 3: How much is total contribution when we

estimate total sales £200,000?

3. 7 CVP analysis:

non-graphical computationsExample 1

• Question 1: Break-even point (in units; £)

_ Fixed costs = £60,000/£10 = 6,000 units Contribution per unit

6,000 units * £20 = £120,000

• Question 2: Units to be sold to obtain a £30,000 profit:• Question 2: Units to be sold to obtain a £30,000 profit:

Fixed costs + desired profit = £90,000/£10 = 9,000 units

Contribution per unit

• Question 3: Total contribution by sales £200,000

Cmru = cmu/Su = £10 / £20 = 0.5

CM = S * cmru = £200,000 * 0.5 = £100,000

(I = CM– FC = £100,000 – £60,000 = £40,000;

when I = 0, then BEP = FC / cmru = £60,000 / 0.5 = £120,000)

3. 7 CVP analysis: break-even chart

3. 7 CVP analysis: contribution chart

3. 7 CVP analysis: profit-volume chart

Break-even chart for exerise 3.1Decision making: purchase of new machine?

Break-even chart for exerise 3.1Decision making