Target Profit analysis

Very often businesses face situation where they are required not only to recover their fixed production, marketing and administrative overheads but also some profits after tax to provide return to shareholders and build retained earnings. Such retained earnings can be used to finance future projects.

We have already studied the formula of break but for the sake of ease of understanding, the formula is reproduced below.

Break-even units = Fixed costs / contribution margin per unit

Targeted Profit without tax effects

When company is required to earn the targeted profit, the above formula must be modified to include effects of such profit. Contribution margin will now need to cover not only fixed costs but also the targeted profit.Therefore, the simple break-even formula will now look like this.

Units to sell to earn desired profit = (Fixed costs + Targeted Profit) / contribution margin per unit

I would again resort to the same example as used in Simple Break-Even Analysis to explain the application of this concept.

Q # Mr. A manufactures a machine AS-1000. AS-1000 sells for Rs. 1,000. It's variable cost of production is Rs. 700. Variable selling and distribution costs is Rs.75 per unit. Fixed cost is Rs. 10,000,000. Fixed cost covers shop rental and depreciation of plant used to manufacture machines. Determine the break-even units and sales value if the Mr. A desires to earn targeted profit of Rs. 800,000 ?

contribution margin per unit = 1,000-700-75 => 225

Units to sell to earn desired profit = (10,000,000+800,000)/225

Units to sell to earn desired profit = 48000 units

Required sales value to earn desired profit = (10,000,000+800,000)/22.5%

Required sales value to earn desired profit = 48,000,000

Let's check answer.

Targeted Profit with tax effects

When tax is given in question, our above desired profit formula needs a little modification i.e. the amount of desired profit is required to be grossed up by tax percentage. For example if tax rate is 35%, then the profit will be as follows.

Profit = 800,000 x 1/(1-tax%)
Profit = 800,000 x 1/(1-0.65)

Profit = 1,230,769.23

Our targeted profit will now be Rs.1,230,769.23 instead of Rs.800,000. This is because after deduction of 35% tax, we will have 65% profit after tax which is Rs.800,000. Now desired units to sell to earn Rs. 800,000 profit after tax are:

Units to sell to earn profit after tax of Rs.800,000 = (10,000,000 + 1,230,769.23)/225

Units to sell to earn profit after tax of Rs.800,000 = 49914.5 units

Sales value to earn desired profit of Rs.800,000 = (10,000,000 + 1,230,769.23)/0.225

Sales value to earn desired profit of Rs.800,000 = 49,914,529.9

Let's check our answer.

Friends, please let me know if you have any questions regarding the topic.

Break-Even Analysis

Break-even Analysis is one of the most examined topic in academic and professional qualifications. students often face problems in grasping the underlying assumptions and concepts due to lack of knowledge of relevant costing and practice. In my discussion on the topic, I will explain all concepts that will help you to develop strong grip on break even questions.

Break-even simply helps a business determine when it will be able to cover its its total costs (variable + fixed cost) with its revenue. this is better explained with this equation.

Total revenue = Variable costs + Fixed costs

Simple Break-Even

 Break-even analysis encompasses three main components as follows :

1. Sale Price 
2. Variable Cost
3. Contribution Margin
4. Fixed Cost

Sale price is what company earns by selling each unit of its product. Variable cost is the cost of producing and selling a single unit and varies with each unit. Fixed cost is cost constant upto certain level of production. Fixed does not change within given volume.

Contribution margin is sale price per unit less variable cost of producing that unit. It indicates what is left after covering all types of variable costs. Contribution margin covers fixed costs. After covering all types of fixed cost, the whole of the contribution margin is profit.

It is important to note that variable costs not only include variable production cost per unit but also variable marketing, distribution and administrative cost per unit, if given. Next  time when you are given contribution margin per unit or contribution margin percentage in question, you don't need to deduct marketing and selling overheads again as the figure would have taken into account effects of variable cost therein. We can now check the formula of contribution margin.

Contribution margin( Rs. per unit) = Sales price per unit - variable cost per unit

Contribution margin (%) = (Sales price per unit - variable cost per unit)/Sale price per unit 

Contribution margin per unit is always used to calculate break even units whereas contribution margin percentage is always used to calculate break even sales value.

Now let's take a question for making you understand the concept.

Q # Mr. A manufactures a machine AS-1000. AS-1000 sells for Rs. 1,000. It's variable cost of production is Rs. 700. Variable selling and distribution costs is Rs.75 per unit. Fixed cost is Rs. 10,000,000. Fixed cost covers shop rental and depreciation of plant used to manufacture machines. Tax rate is 30%. Determine the break-even units and sales value?

Now we see how many units Mr. A needs to sell to cover fixed costs of Rs.10 million but first we need to calculate contribution margin as follows 

contribution margin per unit = 1,000-700-75 => 225

contribution margin percentage = (1,000-700-75)/1000 => 22.5 %

Break-even units = Fixed costs / contribution margin per unit

Break-even units = 10,000,000/ 225

Break-even units = 44444.44 units

Mr. A needs to sell 44444.44 units to cover fixed costs of Rs.10 million. After covering Rs.10 million whole contribution margin will be profit of the company.

Break-even sales value = Fixed Costs / contribution margin percentage

Break-even sales value = 10,000,000/ 22.5%

Break-even sales value = 44,444,444.44 

let's check the validity of our answer.

As you can see that, there is no profit when 44444.44 units are sold at sale price of Rs.1,000. One last but very important thing in calculating break-even is that tax has nothing to do with break-even calculation. As the purpose of break-even is to determine no loss no profit situation, tax cannot be involved in such scenario. 

Tax involvement becomes necessary when we have desired profit to achieve in addition to covering fixed costs.

we can also prove our earlier equation i.e. total revenue = total costs

Revenue 44,444,444 = Total costs (31,111,111+3,333,333+10,000,000) 44,444,444