Tuesday, March 8, 2011

What is break even analysis? How you can use the concept in analysing share trades

What does "break even" mean?

For a company -> When total revenue or sales equals total expenses
In general -> When you haven't made a profit and you haven't made a loss

If you haven't got any overheads, fixed costs or transactional costs then break even is very simple - if you sell the item at whatever it cost you to buy that item in the first place then that's considered as breaking even. If you sell the item at a price more than what it cost you then that's a profit.

Once you have overheads, fixed or transactional costs, then it gets a bit more complex to calculate the price that you need to sell your items or goods at to break even and not incur losses.

Examples to illustrate

1) If you buy an iphone for $800 and then sell it to someone else for $900, then you've made a profit of $100. To break even, you need to sell the iphone for at least $800

2) What if you rented a market stall for $30, bought the iphone for $800? Then you need to sell the iphone for at least $830 to breakeven

3) What if you rented a market stall for $30, bought 45 iphones at $800 each then what is your break even? You would need to sell the iphones for at least $800.67 each to break even. The maths: [(45* $800)+30]/45 = $800.67 per unit to break even. If you can sell the iphones at a price greater than $800.67 then you'll be making a profit.

It's so simple, not widely understood but yet so relevant in all applications - whether you run a business, whether you invest or trade in stocks or anything that involves buying and selling to earn a profit.

How do I apply the concept of break even in share trading as a practical scenario?

To buy or sell my stocks, it costs me $19.95 each time. So if I were trading in stocks, it would cost me $39.90 (the maths: $19.95*2=$39.90) to buy and sell. $39.90 is what I consider my fixed costs and what I use to calculate for my break even analysis.

Break even formula for trading stocks:

Break even price to sell each stock at = (quantity bought * buy price per unit) + total buy and sell costs
                                                                 quantity bought

Example 1:
i) I buy 2000 units of Coca Cola Amatil Ltd (ASX:CCL) at $11.83/unit = $23,660
ii) My transactional costs to buy and sell is $19.95 each way, therefore a total of $39.90
iii) Calculating my break even costs:
($23,660+$39.90)/2000 = $11.85/unit
iv) Therefore I MUST sell my CCL stocks for at least $11.85/unit to break even.
If I sell for anything greater than $11.85/unit then I've made a profit, which is known as capital gains.

Although if you're going to engage in trading stocks, then you also need to work out the opportunity costs and weigh whether trading gains will exceed the other uses of your funds - this concept however will not be explored in this post because it deserves a post of its own.

Before I invest or trade in any stocks, I ALWAYS use the above calculation to see what potential profits or returns are there. With fixed transaction costs, such as $39.90 used in the example above, then the more stocks you buy, the lower your break even costs. Let me illustrate using the above example to compare. This next example will see me buying 1000 CCL stocks instead of 2000 CCL stocks.

Example 2:
i) I buy 1000 units of Coca Cola Amatil Ltd (ASX:CCL) at $11.83/unit = $11,830
ii) My transactional costs to buy and sell is $19.95 each way, therefore a total of $39.90
iii) Calculating my break even costs: ($11,830+$39.90)/1000 = $11.87/unit
iv) Therefore I MUST sell my CCL stocks for at least $11.87/unit to break even.

Comparing the above two examples with the only variable being the quantity of stock purchased:

i) Assuming buy and sell costs are the same at $19.95 each way, and $39.90 in total
ii) In example 1, if I  bought 2000 stocks @ $11.83/unit, break even would require me to sell my stocks at $11.85/unit
iii) In example 2, if I bought 1000 stocks @ $11.83/unit, break even would require me to sell my stocks at $11.87/unit

In example 1, it only requires an upward price movement of 2 cents/unit to break even whereas if I bought less as illustrated in example 2, then I would need an upward price movement of 4 cents/unit to breakeven.

You would need larger price volatility if your transaction costs is flat but you buy a smaller quantity of stock for trading. Larger price volatility always implies larger risks.

For those keen on the maths behind the typical break even analysis (screenshot from Wikipedia):

Using the official BE formula:
X =  TFC
     (P - V)

Where X= unit sales, TFC= total fixed costs, P=unit sale price, V=unit variable costs
Using the numbers from my example 2, from above: X=1000 units, TFC=$39.90 to buy and sell, P=unknown unit sell price, V=$11.83/unit of CCL stocks

Because our CCL (Coca Cola share price) break even sell price (P) is unknown the formula becomes:
i) 1000=   $39.90
ii) 1000(P-$11.83) = $39.90
iii) (P-$11.83) = $39.90
iv) P = $39.90  + $11.83
v) P = 0.399 + $11.83
vi) P = $11.87 to break even

The break even analysis applied in a business context:

The break even formula or concept is commonly applied in a business context, although it can be used in any situation that requires you to work out the point at which you incur no loss. Let's apply this break even formula to the iphone example from above, where P is the break even price that you need to sell each iphone at:
i) X =  TFC
         (P - V)
ii) 45 iphones = $30 market stall rental
                       (P - $800 cost per unit)
iii) P =       $30         + $800
            45 iphones
iv) Break even selling price per iphone would have to be $800.67 minimum

Thefore you must sell each iphone @ $800.67 each minimum if you want to break even, and more than that price if you want to make a profit.
Anyway, you can also apply that same concept to any of your investment calculations.


  1. i didnt know there would be so much math to it -.-

  2. The concept itself is rather simple :) Add up your costs and divide it by the quantity that you bought, and that result to the cost price.

    It gets tricky in the business environment because there are so many variable costs(wages/supplies/fuel etc) and fixed costs(rent/insurance etc) that needs to be calculated so that products could be sold at a margin that is profitable.

  3. sorry, 'and that to the cost price' should have read as 'add that result to the cost price'

  4. Now that is all good, but it is simplified.
    I would like you to show the same example with Capital Gain tax included in the calculation.
    That way you will have a complete overview of your P&L.
    The example you are showing is incomplete

    1. Thig blog post and my example demonstrates how to calculate break even prices, so it IS complete.

      I have been too busy and finally getting around to moderating and replying to comments. Don't know if you're still hanging the blog but I'll respond to this comment for anyone else with capital gain queries.

      Calculating capital gains tax(CGT) is not the same thing as calculating break even. I provided an example on how to calculate BE price. You, as the investor or trader will be paying CGT at your marginal rate of tax(MRT). There are several tax brackets depending on what you earn in the financial year so everyone will have different amount of tax applicable to their profits.

      In Oz, a few tax rules apply.

      1. If you hold an investment asset(eg house or stock) for over 1 year, you are applicable for a 50% CGT discount
      2. If you buy and sell shares frequently and meet the ATO's description of share trading, then gains/taxable profits are added to your taxable income and taxed at your MRT without any CGT discounts