3.3+Break+Even+Analysis

[used to be 5.3 - part of Operations Management - under the old syllabus, last Exams June 2015]
 * Unit 3.3 Break Even Analysis**



__KEY WORDS__: BREAK EVEN POINT CONTRIBUTION [TOTAL V PER UNIT] // this latter part needs developing // MARGIN OF SAFETY TARGETS : TARGET PROFIT, TARGET PRICE

Key Issues we looked at : This section actually covers the core question " HOW MUCH SHOULD WE PRODUCE " - which is why it used to fall under Unit 5. However as it involves calculations - and of course the Finance in terms of how to get Production started - we now file it under Unit 3. .................................... __DEFINITION__ : The number of units a firm needs to make (and sell) in order to cover all of its costs. It is the survival point, in which profit is not yet made, but loss is avoided. Total Revenue = Total Costs .................................... We will need these key formuales looked at previously:


 * TOTAL PROFIT** = TOTAL SALES REVENUE - TOTAL COSTS


 * TOTAL COSTS** = (TOTAL) FIXED COSTS + TOTAL VARIABLE COSTS
 * TOTAL VARIABLE COSTS** = VARIABLE COST PER UNIT x # OF UNITS


 * (TOTAL) SALES REVENUE** = PRICE PER UNIT x # OF UNITS

....................................... Practical idea is based on the fact that there is a TIME LINE in reality.

Production Managers need 50 bags of cement. They are more likely to get a discount (and other JIC benefits) if they ..... [1] Purchase all 50 on 1st March, than if they [2] Purchase 20 on the 1st March, 15 on the 17th March and 15 on the 30th March So a decision about HOW MUCH stock to buy - directly influenced by HOW MUCH output we plan to make - needs to be made // in advance //.

Equally with Payment issues .. A Firm may pay $100 for 50 bags of cement - and use them to create a product for which they charge $500. A good profit - however.. [*] the bags of cement need to be paid for //some time before// the customer pays for your service : $100 needs to go out __before__ the $500 comes in. So you can imagine there might be some concerns regarding HOW MUCH to buy.

As with 'lag times' - time passes between taking a decision and completing it - i.e. * the time taken between deciding to make a product - and having it made. * the time taken between deciding to buy a product and actually buying it

If the customer says on the 1st March they want a product - but you cant get it ready until the 4th March, then there is a real likelihood that the customer will go somewhere else. Some firms need to start Production //before// demand is established.

There is plenty of uncertainty involved in production and a key number for a lot of firms is : WHAT IS THE AMOUNT I NEED TO MAKE (AND SELL) TO AT LEAST ENSURE I AVOID A LOSS. This gives them a focus, a number to work towards, and then breath a sigh of relief after its achieved.

Break Even Analysis is a //decision-making tool!//

So Break Even Analysis is a tool to help us decide HOW MUCH we should produce.

............................................ It can be established via a [1] Formula,or a [2] Graph

[1] FORMULA:

Is based around 3 simple figures that we got familiar with in Unit 2.3 : (1) Sales price per unit (ii) variable cost per unit (iii) fixed costs


 * Break Even = Fixed Costs / **** Contribution **
 * Contribution**** = Sales price - variable cost **

If we have been looking at TOTAL COSTS previously why is the numerator only FIXED Costs? So when we establish the contribution for a unit of output we have already accounted for Variable Costs - leaving only Fixed Costs to cover.
 * A/ Contribution = Price per unit - Variable Cost per unit **

EXAMPLE

$50 price $500 fixed cost

This cool shirt has VARIABLE costs of $10 (that include cotton, colour, etc), To produce it they also had to buy Sewing machine as a fixed cost of $500. They set a price of $50 for the shirt. Every new shirt they get an additional **sales revenue** of $50. Sell 2 shirts get $100, sell 10 get $500 BUt each new shirt also generates variable costs. Make 2 shirts, generate variable costs of $20, make 10 and pay $200. So each shirt generates $50 sales, and $10 variable costs. Leaving a sum of $40. This $40 is NOT profit because we haven't covered the Sewing Machine cost of $500. If we consider each shirt to contribute $40 and not $50 then we have covered the variable costs but not the Fixed costs. Make and sell 1 shirt and your Fixed Cost //debt// falls to $460, Make and sell 2 and the Fixed Cost debt falls to ($460 - $40) = $420. The more you sell the more your debt falls, until you make and sell 12.5* shirts. At 13 shirts (rounded up, because you cant sell half a shirt), each shirt is contributing $40 to cover the Fixed Cost and you have (13 x $40) = $520! You have covered your Fixed Costs : ** 13 shirts is the minimum amount of units you have to make to avoid a loss **

//Can you see why it would (usually) be a terrible pricing policy to have Price below Variable Cost per unit?// A/ with every product you make you would be failing further and further into loss, because the price doesn't even cover the cost directly associated with making the product, let alone the other indirect costs. In this scenario the best decision would just be to stop. Stop producing, then at least you don't generate Variable Costs.

Let's spend a bit of time consolidating our knowledge on this important idea of a products CONTRIBUTION before we move onto the Graph method. A ppt is attached to help you out, if you need it - take a look..

[2] GRAPH METHOD

The idea is this :
 * we will plot the two key variables (Total Costs & Total Revenue)
 * find the point at which those two lines have exactly the same value (the point at which they cross, because at this point Total Costs = Total Revenue).
 * Having found this point (which we can see visually) we will determine its value on the X axis - which is Output.
 * That value will be the break even point - because at that value : Total Costs = Total Revenue..

It will give us the exact same result as using the Formulae method.

STEPS [1] Give the graph a title. : typically with a label in this simple format : "Break Even Graph for Firm X" [2] Draw the Axis (i) X is in $, as it will be used to plot both Costs and Revenue (ii) Y is in output. //i will assume you already have the skills to draw sensible scales on each axis.// [3] Plot the **Total Costs** line starting when output is zero. //Remember Fixed Costs will exist when output is zero, so Total Costs will __not__ start at 'point of origin'.// As output goes up your Total Costs will go up. Plot the points and join them up. You will find it is a straight line because assumptions are made about consistent Variable cost, which actually is seldom that realistic as Economies of Scale do occur - but that's a limitation that we accept. [4] Plot the **Total Revenue** line, also starting when output is zero. //Now normally if you haven't made anything you can't sell anything so Total Revenue will start at the 'point of origin'.// As you produce & sell more your Total Revenue will climb. Plot the points at join them up. - TR line starts at the bottom of the Y axis, TC starts above it. - TR line should climb faster provided Price > Variable Cost .. Which it really always should be. How much faster it climbs will depend on how much bigger Price is than Variable Cost - so at some point TR will cross and overtake TC - at that overtake point TR = TC, which is your Break Even [5] Create a line to one of the axis (usually a line down to the X axis) starting at the TR=TC point. Where this line hits the X axis is your Break Even point. Label it as such.

Done! So lets show you how to draw the Steps outlined above.

STEP 1,2&3



STEP 4

STEP 5



That's what your Basic BREAK EVEN GRAPH looks like ! .................................................

a moment to re-enforce an idea. If Price is not 'greater than Variable Cost' eg its $0.55 then we sell one pen we make a loss of $0.10, we sell 2 pens we make a loss of $0.20, we sell 3 pens we make a loss of $0.30 - in fact the more we sell the more loss we make !! - __before__ even considering the Fixed Costs of rent, salaries etc. !!!

Price must be '< Variable Cost' : and it is this fact that makes the TR line climb faster than the TC.

.......................................................................

There are some key ideas with the graph we need to look at (1) Area of Profit (2) Area of Loss (3) Margin of Safety
 * The first two are directly tied into our Cost/Revue formuales



X = Break Even point Y = Planned Output (//because very few firms want to stop production at break even : they want PROFIT//)

In the graph above this would be = Y - X
 * MARGIN OF SAFETY** IS DEFINED AS "The difference between a firms Planned level of output, and its Break Even level of output"

Margin Of Safety gives us an idea of the extent to which our Plan can fail - and we can still be alright. If X, the break even point, is 55, and our Y is 85, our Margin of Safety would be 30. We could fail* on our Plan by 30 units and still be OK. Fail by 31 and we are now to the left of X and in the Loss zone.

//__ * __// __ **notice** __ that we are talking about "make-and-sell" here : if you plan to make-and-sell 85 and //make// 85 but only //sell// 55 (ie have 30 unsold) you will __not__ break even. if you plan to make-and-sell 85 but plans later change and you only make-and-sell 55 (ie 30 unmade), // you will // break even. if you plan to make-and-sell 85 but plans later change and you only make-and-sell 54 (ie 31 unmade), you will not break even

This is an often-quoted __**limitation**__ of the Break Even model : it often assumes we will sell everything we make. .............................................. A TABLE ....

If you are working out the Break Even via the Graph method, you will clearly need points to plot, right! Below is the typical way the details are set out - all based on the same formulaes and data we've used throughout : those associated with 'Costs' and 'Revenue'

I hope you would be able to work out what the abbreviation stand for - the two key ones are ...
 * TC = Total Costs
 * SR = Sales Revenue

Notice the green instructions at the bottom of each row. A completed table would look like this..
 * Output ||  (T)FC  ||  VC /pu  ||  TVC  ||  TC  ||  Price  ||  SR  ||  Profit  ||
 * 0 ||  650  ||  10  ||  0  ||  650  ||  15  ||  0  ||  -650  ||
 * 25 ||   ||   ||   ||   ||   ||   ||   ||
 * 50 ||   ||   ||   ||   ||   ||   ||   ||
 * 75 ||   ||   ||   ||   ||   ||   ||   ||
 * 100 ||   ||   ||   ||   ||   ||   ||   ||
 * 125 ||   ||   ||   ||   ||   ||   ||   ||
 * 150 ||   ||   ||   ||   ||   ||   ||   ||
 * 175 ||   ||   ||   ||   ||   ||   ||   ||
 * This you make up and vary as you want. Start with zero, go up in equal portions ||  does not change with output  ||  might actually change with Economies of Scale - but we will presume it does NOT  ||  =VC x output  ||  =TFC + TVC  ||  =SR/Output … usually given to you though  ||  =P x output .. If you are not given Price then you will be given this  ||  =SR-TC  ||
 * Output ||  (T)FC  ||  VC /pu  ||  TVC  ||  TC  ||  Price  ||  SR  ||  Profit  ||
 * 0 ||  650  ||  10  ||  0  ||  650  ||  15  ||  0  ||  -650  ||
 * 25 ||  650  ||  10  ||  250  ||  900  ||  15  ||  375  ||  -525  ||
 * 50 ||  650  ||  10  ||  500  ||  1150  ||  15  ||  750  ||  -400  ||
 * 75 ||  650  ||  10  ||  750  ||  1400  ||  15  ||  1125  ||  -275  ||
 * 100 ||  650  ||  10  ||  1000  ||  1650  ||  15  ||  1500  ||  -150  ||
 * 125 ||  650  ||  10  ||  1250  ||  1900  ||  15  ||  1875  ||  -25  ||
 * 150 ||  650  ||  10  ||  1500  ||  2150  ||  15  ||  2250  ||  100  ||
 * 175 ||  650  ||  10  ||  1750  ||  2400  ||  15  ||  2625  ||  225  ||
 * This you make up and vary as you want. Start with zero, go up in equal portions ||  does not change with output  ||  per unit (might actually change with Economies of Scale - but we will presume it doesn’t)  ||  =VC x output  ||  =TFC + TVC  ||  =SR/Output … usually given to you though  ||  =P x output .. If you are not given Price then you will be given this  ||  =SR-TC  ||


 * As a visual check point, we can immediately see that ....
 * at **125** units we still have a [small] loss, Break Even point has not yet been reached
 * at **150** units we have a profit, the Break Even point has been exceeded

so somewhere between 125 and 150 is our BreakEven point.

To be more precise we would plot all the points - see a start below

as we continued to plot the 3rd-8th sets of data (ie output 50 - 175) we would end up with a standard Break Even Chart like those above. Drop a line down to the X axis to get the precise Break Even point!


 * Want to try it?**

//(BE point should be 130 units)//

//..............................................// CHANGES // - IN PRICE OR COSTS //

As IB students we need to have an understanding of the impact on the Break Even Point should there be change in price or costs from one production batch to the next..

The above graph shows the impact of an __//**increase in price**//__ : the TR line shifts to the left* and the break even point decreases // * we say 'shift' though it maintains the same point of origin - so really its becoming steeper rather than shifting, but either verb will do //

Here's the //explanation// if you want to understand it - The **contribution** of each product becomes greater ( contribution = price - variable cost : and now price has gone up!). Therefore you need less products to cover the Fixed Costs. You used to need 14 - now you only need 8 because each product is making a greater contribution. The graph above shows the impact of an __//**increase in costs**//__ : the TC line shifts to the left* and the break even point increases.

Here's the //explanation// if you want to understand it - The contribution of each product falls ( contribution = price - variable cost : and now variable costs has gone up!). Therefore you need more products to cover the Fixed Costs. You used to only need 7, when each was contributing more - now you need 11 because each product is making a lesser contribution.

Remember : Total Costs = Fixed Costs + Total Variable Costs.

Want to be more precise, and understand why the reminder is relevant? check the ppt below. If you think you only just understand this and don't want any more info - then do NOT check the ppt/



............................................... TARGET PROFIT

Business Managers may decide to address the 'How much..?" question by referring to their objectives and establishing **how much profit** they want to make. This would be called their TARGET PROFIT - and they would make the quantity of units required to achieve this Target Profit.

This 'Target Profit' could be determined by //various factors// - which could include [1] investment/purchasing plans ie they need to buy a $5000 machine, [2] promises to shareholders ie they have promised a dividend pay-out of $4000.

Can you work out what the formula for // Target Profit __Quantity__ // might be?

Clue : consider 'Target Profit' to be an additional cost that the revenue needs to cover.

Answer on the PPT attached below



- and thats kind of all there is to it. How many units they produce is determined by How much profit they want to make. !

.............................................. TARGET PROFIT PRICE

Now it might be that sometimes a Producer already knows how much [a] she wants to make-and-sell and [b] profit she wants to make. This could be due to predicted demand, it could be due to restrictions on Productive Capacity - it could be due to Objectives of the owner - she only wants to spend 30 hours a week working, she has other priorities..... Whatever. The starting point then is not 'How much should I produce?' - this is known, the starting point is **What Price Do I Charge**??.

There is a formulae for this ... but to work out the price you would have to ask the business lady for these two pieces of information.. [1] how many units she wants to make -- ie //Output Level X//. Let's say she answers **"100"** [2] how much profit she wants to make -- ie //Target Profit Y//. Let's say she answers **"$5000"**

Can you work out what the formula for Target Profit Price might be?

Answer on the PPT attached below.



............................................. LIMITATIONS

The analysis __falsely__ assumes a static business environment, it assume that as time goes on price of supplies will NOT change, costs like salaries will NOT change etc : of course the reality is, firms operate in a dynamic environment where demand, costs etc could change at any point in time. These change could occur **within** a production cycle rather than //between// one cycle and the next - as the graphs in 3 paragraph above indicate.

Similar but slightly different from above : is the price. Price of raw materials (which translates as 'costs') and the price offered to customers. Again there is the false assumptions these stay static. If you look at the table above
 * // Variable Cots per unit (VC p/u) // stay at $10 all the way through, there is NO Economies of Scale evident?!
 * //Price// remains at $15 all the way through - no promotional pricing - no reduced prices to increase demand ?!

............................................. If you prefer listening to reading, here is a video from evideolearner that goes over the interpretation of a BE Graph (though they call it a Cost Volume Profit Graph). media type="file" key="Lesson FA-20-050 - Clip 12 - CVP Graph - Part 2 - Breakeven,.mp4" width="300" height="300"

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