Why is it important to understand cost behaviour?
> It helps in decision making, If there is excess capacity accept any price greater than variable cost
> Helps in planning and control.
> Helps in performance evaluation . Segmented reporting based on cost behaviour and whether cost is controllable or not
We say normally that fixed cost is more controllable than non variable cost
The more debt you have the more leverage you have, fixed cost vs variable cost.
High fixed cost companies > Cell phone companies, utilities , they are really capital intensive companies.
Low fixed cost companies > Retailers , online web based companies
Variable cost behaviour
Examples
Type of organization Variable costs
Merchandising firm Cost of goods sold
Manufacturing firm DM DL
Both Merc and manufacturing Commisions and the delivery of goods ( selling costs
Service organizations Pharmaceuticals , Laundry , Food , Cleaning.
Variable cost patterns
Variable cost changes in total in direct proportion to changes in level of activity
Variable cost is constant on a per unit basis
Activity base
For a cost to be variable it must be variable with something
Usual cost drivers are production and sales activities.
True variable costs are amount not used can be stored and carried forward next period , for example direct materials
Step variable > cant be stored , increases in small steps , available in chunks
For example 2 hours or 4 hours chunks
Strategy of management would be to obtain the fullest use of services
Relevant range is the range of activity management expect to operate. Fc will remain fixed at certain amount within relevant range and VC will be constant per unit within relevant range.
Fixed cost behabiour
Commited fixed behaviour
– Investment in plant , equipment , basic organizational structure of a firm
These costs are : 1 ) Long term in nature
1) Usually continue even in times of economic difficulty
Control of commited costs comes through utilization ( used as effectively and efficiently achieving firms objectives and goals
Discretionary fixed costs
Cost arising from annual decisions that management tend to spend the fixed cost in certain specific areas
These costs are short term in nature
Period of economic difficulty , possible to cut back for short periods of time with minimal damage to long run goals of organization.
Examples are labour , advertising , travel and training and R & D
Trend toward Fixed costs
The Trend today is toward greater fixed cost relative to variable costs
Reasons are > Guaranteed contracts , Automation
Is there a trend toward variable costs too ? outsourcing , JIT
Fixed cost pattern remains constant in total throughout wide ranges of activity
Unitary fixed cost varies inversely with activity if expressed per unit based
Always think of fixed cost in total ,
Step fixed cost are a bit the same as step variable costs except that
1) It cannot be changed as easily as step variable
2) Width of steps is much greater than step variable..
Mixed cost
Is a combination of a fixed cost element and a variable cost element
Example would be home phone bill and salary + commission
Analysis of mixed cost
Fixed cost represents the basic minimum charge for having ready and available service for use
Variable cost represents the actual consumption of the service
Analysis of mixed cost is done on an aggregate basis by looking at past behaviour of a costs at a various levels of activity in order to predict future costs
The results obtained are good approximations of fixed and variable cost
Chapter 7
CVP concepts
Cost Volume Profit
For management accounting as its is a decision making focus we have to understand concepts before coming to a solution
We are going to understand a few concepts and then we will solve problems to see if you understand the topic or not
A)
Sales
-Variable costs ( dm, dl , vmoh, Vselling&A)
= Contribution margin
– All fixed cost ( FMOH, Fs&A)
= Net income before tax ( NIBT)
– Taxes
= Net income ( AFTER Tax)
Where sales – VC = CM and CM % = CM/ Sales
B) Sales per unit – VC per Unit = CM per unit
$ CM per unit is the incremental profit of selling one more unit
IF current NIBT = 10000 and cm per unit = 12 what if we sell 10 more units then NIBT would increase by 120.
CM % on the other hand is the incremental profit of selling one more dollar
For example if NIBT= 10000 and CM % = 40 % then assuming if we sell 1000 $ more NIBT would increase by $400
C) Taxes
NIBT- TAX = NIAT
Therfore NIBT = NIAT / ( 1- Tax rate)
Or NIAT= NIBT ( 1- Tax rate)
D) Break even points in units
Given is sales per unit = $ 500 , VC per unit = 300 $ and Fc = 80 000
There fore let x be the amount of units sold
500 x- 300 x – 80 000 = 0 ( BEP nibt=o)
X=400 units
BEP in dollars
Let x be $ 1 of sales
Therefore 300/500 = 0.6 and CM = 0.4
x- 0.6x – 80 000 = 0
x= 200 000 BEP dollars = Units sold at break even and Sales per unit
E ) High degree of operating leverage ( DOL ) = Higher fixed cost , lower variable cost and higher Contribution margin which is more sensible to degree of change in sales
LOW degree of Operating leverage means a lower fixed cost , higher variable cost and lower Contribution margin.
E) Indifference analysis would be where the level of sales where profit under bothe alternative would be the same
Alternative one VS Alternative 2
S – VC – FC S- VC- FC
F) Don’t forget opportunity costs ( for example salary forgone to open a business)
You are willing to quit your job and open a coffee shop. If you currently get an amount of 50 000 and benefits ( 20 % of salary ) at your present job what would be the break even point for the coffee shop?
At break even point the NIBT should be 50 000 * 1.2 = 60 000 $
G) When dealing with sales mix situations always think of weighted average when calculating the selling price , the variable cost and the variable CM
1st example : UBC COMPANY
| Sales total | Per unit | Percent | |
| Sales – 500 unit | $250000 | 500 $ | 100 % |
| Less vc – Same 500 | 150000 | 300 | 60 |
| Cm | 100 000 | 200 | 40 |
| Less fc | 80 000 | 200 | |
| Net income before tax | 20000 |
Contribution margin per unit = 500 – 300 = 200
This amount would be covering first toward fixed cost and then toward profit
Cm per unit means incremental profit from selling one more unit
CM Ratio ( CM % ) = Contribution margin / sales = 200 / 500 = 40 %
Cm ratio means the incremental profit from selling one more dollar. The Cm ratio is very important in a way that it shows the manager how the CM and the NIBT would be affected by a given change in sales
VC ratio would be the VC / sales or SALES – CM
Therefore here for example VC for ABC = 300 / 500 = 60 % or 100- 40 = 60 %
Assume that UBC company sales increase by 15 0 000 next month . What would be the effect on the CM ? And what about the NIBT?
Effect on CM ?
Increase in sales $ 150 000
Therefore the increase in CM would be the 0.40 * 150 000 = 60 000 $
On the other hand the NIBT would increase by 60 000 as FC doesn’t change
The effect on NIBT of any dollar change in sales can be computed by multiplying the change by the cm ratio assuming the fixed cost doesn’t change
Management pont is that with everything equal , the manager would search out and promote sales that have highest cm ratio..
Example A- sp of 100 and cm = 30 percent
B- sp = 100 and CM= 40 percent.
The sale of which product will result in a higher NIBT?
Sales of A would increase NIBT by 30 $
B would increase by 40 $
Therefore there is a change of 10 $ that could be spent on advertising and we would accept product B considering the fact of a higher NIBT
At the break even point ( BEP ) can be defined as where the amount of total sales revenue = total costs or even the point where the total CM = total fixed cost.
For example
UBC food club manufactures pies and the cost and revenue data is as follows :
Selling price 500 $, 100 percent
Variable cost 300$, 60 percent
Contribution M 200 $ , 40 percent
Fixed cost are 80 000 per month
Calculate : Sales in units :
500 x – 300 x- 80 000 =0
X= 400 units
Sales in dollars
x-0.6 x – 80 000 = 0
x= 200 000 $ or also we can do 400 units * selling price = 200 000 $
Other useful formulas to use can be BEP units = fixed costs + nibt ( 0 ) / cm unit
BEP ( $) = Fixed cost + nibt (0) / cm %
Targeted profit
Sales= vc + fc +target profit before tax ( nibt)
Target after tax profit
Niat= Nibt ( 1- tax rate) , therefore NIBT= NIAT/ ( 1- T)
Applications of CVP concepts
1 ) Compare incremental CM to incremental fixed cost to derive incremental NIBT
3) Understand the equations and use them as necessary
Example
UBC bookstore is currently selling 500 books per month. The sales manager believes that a $10 000 increase in the monthly advertising budjet would increase sales by 15 % ( 500 *15 =75 more bikes ) Should the advertising budjet be increased?
Increase in Cm = 75 * 200 = 15 000 Increase in fixed cost = 10000 therefore the total
Increase in NIBT would be 5000 $ , Thus we should increase advertising budjet as profits would increase.
Management point
1) The size of the unit CM figure ( and the CM ratio ) should have a heavy influence on which the steps the company is willing to take to improve profits . The greater the CM/ Unit for a product , the greater the amount the company will be willing to spend for advertising to increase the sales for that particular product
2 ) some firms should base sales persons commissions on CM generated rather than sales generated
Assume that a firm should base sales persons commissions on CM rather than sales generated
| Product a | Product b
|
|
| Sales price | 100 | 150 |
| Vc | 75 | 132 |
| Cm | 25 | 18 |
| Greater | lower |
What product will salespeople push if they are paid a commission of 10 % of sales
Commission 10 $ A
Commissions 15 $ B
From a standpoint of copany which product would company like to push
Product A as higher contribution margin
How can the company achieve its objective
Base commissions on CM rather than sales ( goal congruence), or provide greater commission for sales of product A
Indifference analysis
Sometime the company has to choose between alternatives that involves Higher fc / lower Vc or lower VC and higher VC
Examples Automation vs labour and salary vs commission etc
| Alternative one labour intensive | Alternative 2 Automation |
| Sales – vc- fc | = Sales –vc –fc |
| 600 x -320x -900 000 | =600 x-240x-1200 000 |
| X | =3750 units |
| Cm of 280 | Cm of 360 |
If expected sales are greater than 3750 units i would push option two as it yields a greater Cm per unit of sales which makes an increase in 80 $ more in NIBT
If expected sales are less than 3750 Units i would push option one more as it yields a lower cm per unit of sales and which makes NIBT 80 $ less
Dont ignore qualitative factors when changing compensation from commission to salary , consider the effects on employees motivation
Operating leverage
A measure of fixed cost in an organization
Firms with high leverage are considered to be more risky in the terms that the company has to pay the same amount of loan payments and fixed costs
If the company has a high operating leverage which means a greater proportion of fixed costs in relation to variable costs, its profits are really more sensitive when we compare it to changes in sales. Higher operating leverage results in a larger change in NIBT with only a smaller change in sales. NIBT change more is cm % is higher
Degree of operating leverage is calculated when CM/ NIBT
Assume NIBT company x and company y is both 60 000
The cm for company x is 15 0 000 and CM for company Y is 400 000
Sales for company x is 500 000 and Sales for company Y is 500 000
Therefore DOL for x is 150 000/60 000 = 2.5 and Company Y is 400 000/60000 = 6.67
Therefore assuming Companies experiences a 10 Percent increase in sales what will be the new NIBT be :
1) Using DOL
Company x NIBT increase by 2.5 *10 % = 25 % therefore new nibt would be 60 000 * 1.25 = 75 k
Company y would be 6.67 *10 % = 66.67 %
Therefore New NIBT would be old NIBT * 66.67 *60000=100k
Therefore we can conclude that the greater the change in DOL ther greater the fluctuation in NIBT
Or we can use cm %
If sales increase by $1 then NIBT increase by 30 cents for company x , Therefore the sales in Company x would be 500 k * 10 percent= 50 000 wwhich would implement a change in the sales of 50 000 * 30 percent to give an additional nibt of 15 k
Therefore the new nibt for company x would be 60 k + 15 k= 75 k
Margin of safety is the excess of sales( actual/ budgeted over the break even level of sales ( actual/ budjeted )
Total sales- Break even sales = MS in $
MS in $/ Total sales= MS in percent
What does it means in words
MS means that it shows the amount where sales can drop before losses begin to be incurred
| Company x | Company y | |||
| Amount | Percent | Amount | Percent | |
| Sales | 500 000 | 100 | 500 000 | 100 |
| Vc | 350000 | 70 | 100 000 | 20 |
| CM | 150000 | 30 | 400 000 | 80 |
| FC | 90 000 | 340000 | ||
| NIBT | 60 000 | 60000 | ||
BEP ( in dollar ) = 90 000 +0 / 0.3= 300 000 company x , company y = 425000
MS in $ = 500-300= $ 200 k where for company Y it would be 75 000 $
MS in %= 40 % where 200/500 whereas for company Y it would be 15 %
Why is the Ms of Company Y smaller than that of company X
For every dollar of sales Y Nibt would decrease 80 – 30 =50 cents more than x NIBT
Company x , to eliminate the 60 000 $ , 200 000* 30%= 60 000
Company Y , to eliminate the 60 000 $ , we take 75000 *80 percent which gives 60 000.
Sales mix ( multi product firm )
The relative combination in which companys products are sold. The managers try to achieve the combination of sales mix that yield the greatest amount of profits. Profits are greater if high margin items make up a relatively large proportion of total sales than if sales consist mostly of low margin items
Changes in the sales mix can have a heavy impact on both profits and the BEP. A significant shift in the sales mix from the high margin items to low margin items can cause total profits to decrease the even though total sales may increase
| Product a | Product b | |
| Sales Price | 100 | 75 |
| VC | 50 | 55 |
| Cm | 50 | 20 ( low margin ) |
The company sells a total of 300 units ( sales mix 2a :1 B ) and sales increase to 400 units. ( sales mix changes 1 A : 3 B) . What will be the effect on sales & CM?
A = 2/3 B=1/3
Sales ( Current sales mix)
Product A : 2/3*300= 200 units
Product B : 1/3* 300= 100 units
Total sales : ( 200*100 + 100*75)= $27500
Total Cm= ( 200*50+100*200)=12000
Sales new mix = Product A ( 400* 1/ 4) = 100
Product B (units ) = 400* ¾= 300
Total sales ( 100 * 100+ 300 *75)= 32500, Total CM = ( 100*50+300*20)= 11000
If Cm decrease and Fc remain the same , NIBT would decrease by the same amount
Multiproduct break even analysis
The BEP depends on the mix in which the products are sold. Why ? because of different selling variable costs and everything and most likely different contribution margins
The break even point is calculated by dividing the FC by the company weighted average CM/ Unit sales mix . IF sales mix change then BEP also changes
Cm % of A * ( DOLLAR SALES A/ TOTAL DOLLAR SALES ) + CM % OF B * ( DOLLAR SALES B / TOTAL DOLLAR SALES )
Weighted average Cm %
Examples
Weighter cm : 30 % * 100/400 + 60% * 300/400 = 52.5
NiBT quick way = 52.5 % * 400 000= -141750
Break even point total sales = 141750 +0 / 0.525 = 270 000
Break even point sales A = 270 000 * ¼= 67500
Break even point sales B= 270 000 * ¾ =202 500
Proof of correctness would be that if sold 67500, therefore this me that every dollar i sold made me 30 cents whereas if i sold 202500 each dollar i sold made me 60 cents
Break even point therefore would be 67500 ( 0.3)+ 202500 ( 0.6 )= 141 750
Different example
| Contribution Margin per unit | Total units sold
2010 2009 |
Total cm
2010 2009 |
|||
| Product M | $5 | 1000 2000 | 5000 10000 | ||
| Product N | $3 | 3000 2000 | 9000 6000 | ||
| 4000 4000 | 14000 1600 | ||||
Weighted CM per unit when sales mix is given in units ie 1000 Units of M and 3000 Units of N
Weighted average Cm per unit
Cm/unit for M * ( Units of X/ total units ) + CM/unit of N * ( Units of Y/total Units )
2009 : Weighted average CM Unit ( 16000/ 4000 units ) = $ 4
Using formula : 5 * 2/4 + 3*3/4
2010 : Weighted average CM unit ( 14000/4000)= $3.50
Using formula = 5 *1/4 + 3*3/4= $3.50
Assuming Fc are $210 000 what is the BEP in unit sales of M and N for 2010 ?
BEP ( total units)= 210 000/ 3.50 = 60 000 units
Note that each unit is ¼ M and ¾ N
BEP ( total Units for 2010 )= 210 000 / 3.50 = 60 000 Units
Therefore for unit sales we would have M : ¼ * 60 000 units = 15000
N: ¾ *60 000 units = 45000
Proof of correctness
15000* ( 5) + 45000* (3)=210 000 which is equal to the fixed cost
Linear assumptions in cvp analysis :
1) Assume a linear revenue function and a linear cost function
2) Assume that price ( total fixed cost and Unit variable cost can be accurately identified and remain constant over the relevant range)
3) Assume what is produced and what is sold – ie no change in inventories during the period.
4) For Multiple product analysis , the sales mix is assumed to be known.
5) The selling prices and cost are assumed to be known with certainty
Summary of equations
1) Operating income ( NIBT) = ( price* units )- ( Unit variable cost * units ) – Fixed cost.
2) Break even point in units= Fixed cost/ Cm per unit
3) Break even in sales dollars= Fixed cost / contribution margin ratio
= Fixed cost / ( 1- variable cost ratio)
= Break even point in units * selling price per unit
4) Variable cost ratio = total variable cost / sales
= Unit variable cost / Price
5) Contribution margin ratio = contribution margin / sales
6) Margin of safety= sales- Break even sales
7) Degree of operating leverage= total contribution margin / NIBT
8) % change in NIBT= Degree of operating leverage* % change in sales
9) After Tax income= Operating income ( or NIBT)- ( Tax rate * operating income)
10) Income taxes= Tax rate * Operating income
11) Before tax income= After tax income / ( 1- tax rate)
UBC manufactures and sells compact discs ( CDS) . Price and costs are as follows
Forecasted annual sales ( 120 000 units ) @ 25 $ $ 3000 000
Variable costs per unit
Direct material $ 10.50
Direct labour $ 5.00
Manufacturing overhead $ 3.00
Selling expenses $ 1.30
Total variable costs 19.80
Annual fixed costs 468000
1) What is ubc break even point in units?
= fixed cost / cm unit = 468000/ ( 25-19.8) =90000 units to break even
2) What is UBC break even point in Sales dollars ?
468000/ cm ratio= 468000/ 0.208=2.25 M
Cm % = cm / Sales= 5.2/25= 0.208
3) How many units would sfi have to sell in order to earn 260 000 $?
(468000 + 260 000) / 5.20 = 140 000 units
4) How many units UBC have to sell in order to earn a profit of 10 % of sales ?
Therefore UBC has to sell :
5.20 x- 468000 = 2.5 x
X= 173334
5) If SFI expects to sell 120 000 units what selling price would result in a 20 % of sales ?
120000 x – 19.8 ( 120000 x)- 468000= 0.20 ( 120000 x)
X= 29.63
6) What is the firm margin of safety?
Total sales – break even sales = margin of safety
Break even sales = fc + nibt / cm %
= 3 M- 2.25 M = 0.75 M
0.75 m/3= 25 % margin of safety
7) Management estimates that direct labour cost would increase by 8 percent next year ? How many units does ubc has to sell to break even ?
New cm per unit = 5.20 – ( 5* 0.08) = 4.80
Break even point = 468000 +0 / 4.8= 97 500 units
All other things equal as cm per unit increase break even point decrease
There is an inverse relationship that happens and it is the same case for the other scenario.
8) If UBC direct labour cost do increase by 8 percent next year, What price must it charge to maintain the same contribution margin ratio?
Contribution margin ratio = cm / sales =
x-(20.2) / x = 0.208