Business Studies: Break even analysis the graphical method example

• As has been pointed out there are two approaches to break even analysis
• In this post we will look at the graphical method
• To help make matters clear we will make extensive use of an example below

Shona runs a take-away pizza business. She has estimated that she can produce as many as
1000 pizzas per week although she is only selling 700 on average at present. Shona recently
looked again at her costs and prices. These are shown in Table 1.

Required:

1. Give an example of Shona’s:
   1. Variable Cost
   2. Fixed Cost
2. Draw a weekly break even chart for Shona’s Pizzaria

Solution:

1. If this were an example you would only be required to give an example but we have provided a definition and multiple examples for your benefit:
   1. Variable costs are costs which vary according to the level of production all direct costs are variable costs. For Shona variable costs can come in the form of flour/dough, salt, sugar, toppings etc
   2. Fixed costs are costs that do not vary with the level of production in the short run for example rent for the Pizzaria, lighting expenses etc
2. We will now draw the chart:
   • When drawing a break even chart you need to plot the following lines:
   • The Total Variable Cost line (VC)
   • The Total Fixed Cost line (FC)
   • The Total Cost line (TC)
   • The Sales Revenue line (SR)
   • First you need to determine an appropriate scale for both the x and y axis of your graph
   • Drawing graphs/charts is part science part art but there is a logic to it
   • Your graph should be as large as possible and cover the alloted space
   • To determine the scale for the x (horizontal axis):
     1. Determine the minimum and maximum values to be shown
     2. The minimum value is 0 pizzas(units)
     3. The maximum value is 1000 pizzas(units) this is the maximum level of activity Shona cannot produce more pizzas than this
     4. Count the number of bold border-lined squares on the graph paper from the left to the right
     5. Now the scale would be:
     6. \mathrm{\dfrac{(Maximum \quad Value-Minimum\quad Value)}{Number \quad of\quad Squares}}
     7. In our example there were 5 squares counting horizontally now in that instance the scale was:
     8. \mathrm{\dfrac{1000-0}{5}}
     9. 200
     10. This means each large square will represent 200 pizzas (units) horizontally
   • For the y-axis:
     1. Obtain the maximum possible value using the formula:
     2. \mathrm{Selling\quad Price\quad Per\quad Unit\quad x\quad Maximum\quad Activity\quad Level}
     3. \mathrm{7 x 1000}
     4. $7000
     5. If you count the squares in above grid from the bottom to the top you will get 5 and using the above formula you will get
     6. 1400 i.e each large square would represent $1400
     7. You could go ahead and use this scale but things will be a bit unkempt on the y axis
     8. A more neat solution would be to use $1000 as the maximum value
     9. This would yield:
     10. 1000 i.e. each large square would represent $1000
   • The next step is to create a table of values:

• • If you are wondering how we came up with the output levels to put in the table here is how we did it:
  • The fixed costs are fixed so the value does not change
  • \mathrm{Total\quad Variable\quad Costs (VC)=4 x Level\quad of\quad Activity}
  • \mathrm{Sales\quad Revenue (SR)= 7 x Level\quad of\quad Activity}
  • Now that we have a table draw the x-axis and the y-axis
  • Plot each line onto the graph
  • Join each point using a ruler
  • Below is the result

Simple BEP in darker colors

• • To avoid clutter we have avoided showing the margin of safety
  • It would be shown by drawing a vertical line down through the break even point
  • Another line would be drawn down the maximum level of output
  • The result is depicted as below:
• 

  Simple break even chart

  NB The last graph is for illustration only the solution is shown in the graph above it:

• 

  Shona’s BEP in light color

  NB An alternative depiction using lighter colors

To learn about Break Even Analysis using formulae instead click here

To access more topics go to the O Level Business Notes