Week 8 Breakeven Chart

Breakeven Chart

In analyses like this, questions invariably arise, such as:

• Well, how little can we charge and still make a profit? or
• If Fixed Costs go up by 10% how will that affect profit?

Questions like this are most easily analyzed with a breakeven chart on which the results of the breakeven formula can be displayed.

Making a Breakeven Chart
A breakeven chart plots total revenue (TR) against total cost (TC). So, to make a breakeven chart we first need a Revenue Function.

In our case that would be TR = P x Q

We can graph this function on a chart by filling in numbers in the equation. We will want to do this more than once so we can produce more than one data point to plot on the chart. We know the Price (P) is $75, and that doesn’t change, so we choose a number of different values for Q. For this example, let’s let Q = 0 and 3,000

For Q =	0	TR =	$75 x 0	=	0
For Q =	3,000	TR =	$75 x 3,000	=	$225,000

Plotting this on a breakeven chart where TR is on the vertical, or Y axis, and Q is on the horizontal, or X axis, looks like this:

Now let’s add costs to our chart. To do that, we need a Cost Function. This will be:

TC = FC + (VC x Q)

Just like Revenue, we can graph this function on a chart by filling in numbers in the equation. Again we will want to do this more than once so we can produce more than one data point to plot on the chart. We know the Fixed Cost (FC) is $100,000 and we know Variable Cost (VC) is $22, so all we have to do is choose a number of different values for Q. For this example, let’s let Q = 0 and 3,000 again:

For Q =	0	TC =	$100,000 + ($22 x 0)	=	$100,000
For Q =	3,000	TC =	$100,000 + ($22 x 3,000)	=	$166,000

Adding this data to the breakeven chart produces the following results:

Now the breakeven chart is complete. Notice the two lines cross at just under the point where Q = 2,000 (from the breakeven formula we know the exact point is 1,887 units).

By changing the input numbers and watching how the two lines adjust, we can answer “what if” , questions about the chart. For example lowering FC will move the breakeven point to the left. Raising P will move it to the right, and so on.

Problems with Breakeven Analysis
The biggest problem with breakeven analysis is that in the real world revenues and cost may not behave linearly as they are shown to do on the breakeven chart we just developed. For example, on the chart we show Amalgamated’s total cost beginning at $100,000 for zero units produced. Each unit produced adds $22 to this total, resulting in a linear increase in total costs to $166,000 for 3,000 units produced. In the real world, however, the average variable cost per unit would probably not remain constant. The variable cost to produce the first unit would be very high, the cost of the second would still be high, but quite as high as the first, and so on until by the time the 1,000 units were produced it would cost very little to add the 1,001st (this is called economies of scale). Eventually, however, the capacity of the production process becomes strained, so the cost to produce one more begins to rise again until a point is reached where the cost to produce one more would be prohibitive. The total cost curve in this kind of environment would look something like this:

Similar arguments can be made that show the revenue line would behave non-linearly as well. As a result, breakeven calculations made with the equation we have been using would be inaccurate.

Important Note: Breakeven analysis can be conducted without assuming linear curves, but the equations involved are beyond the scope of this course.