Profit & Loss are part and parcel of every commercial transaction. In fact, the entire economy and the concept of capitalism is based on the so called “Profit Motive”.
Profit & Loss in Case of Individual Transactions
We will first investigate the concept of Profit & Loss in the case of individual transactions. Certain concepts are important in such transactions. They are:
The price at which a person buys a product is the cost price of the product for that person. In other words, the amount paid or expended in either purchasing or pro- ducing an object is known as its Cost Price (also written as CP).
The price at which a person sells a product is the sales price of the product for that person. In other words, the amount got when an object is sold is called as the Selling Price (SP) of the object from the
seller’s point of view.
When a person is able to sell a product at a price higher than its cost price, we say that he has earned a profit. That is,
If SP > CP, the difference, SP – CP is known as the profit or gain.
Similarly, if a person sells an item for a price lower than its cost price, we say that a loss has been
incurred.
The basic concept of profit and loss is as simple as this.
If, however, SP < CP, then the difference, CP – SP is called the loss.
It must be noted here that the Selling Price of the seller is the Cost Price of the buyer.
Thus we can say that in the case of profit the following formulae hold true:
We will first investigate the concept of Profit & Loss in the case of individual transactions. Certain concepts are important in such transactions. They are:
The price at which a person buys a product is the cost price of the product for that person. In other words, the amount paid or expended in either purchasing or pro- ducing an object is known as its Cost Price (also written as CP).
The price at which a person sells a product is the sales price of the product for that person. In other words, the amount got when an object is sold is called as the Selling Price (SP) of the object from the
seller’s point of view.
When a person is able to sell a product at a price higher than its cost price, we say that he has earned a profit. That is,
If SP > CP, the difference, SP – CP is known as the profit or gain.
Similarly, if a person sells an item for a price lower than its cost price, we say that a loss has been
incurred.
The basic concept of profit and loss is as simple as this.
If, however, SP < CP, then the difference, CP – SP is called the loss.
It must be noted here that the Selling Price of the seller is the Cost Price of the buyer.
Thus we can say that in the case of profit the following formulae hold true:
1. Profit = SP – CP
2. SP = Profit + CP
3. CP = SP – Profit
4. Percentage Profit = (Profit x 100) / CP
Percentage Profit is always calculated on CP unless otherwise stated.
2. SP = Profit + CP
3. CP = SP – Profit
4. Percentage Profit = (Profit x 100) / CP
Percentage Profit is always calculated on CP unless otherwise stated.
Notice that
SP = CP + Gain
= CP + (Gain on Re 1) × CP
= CP + (Gain%/100) × CP
SP = CP + Gain
= CP + (Gain on Re 1) × CP
= CP + (Gain%/100) × CP
Example: A man purchases an item for ` 120. If he sells it at a 20 per cent profit find his selling price.
Solution: The selling price is given by 120 + 120 × 0.2 = 144
= CP + (Gain%/100) × CP = CP[1 + (%Gain/100)]
For the above problem, the selling price is given by this method as: Selling Price = 1.2 × 120 = 144.
Hence, we also have the following:
In case of loss
1. Loss = CP – SP2. SP = CP – Loss
3. CP = SP + Loss
4. Loss% = Loss on ` 100 = (Loss x 100) / CP
Percentage Loss is always calculated on CP unless otherwise stated.
The above situation (although it is the basic building block of Profit and Loss) is not the normal situation where we face Profit and Loss problems. In fact, there is a wide application of profit and loss in day-today business and economic transactions. It is in these situations that we normally have to work out profit and loss problems.
Having investigated the basic concept of profit and loss for an individual transaction of selling and buying one unit of a product, let us now look at the concept of profit and loss applied to day-to-day business and commercial transactions.
Having investigated the basic concept of profit and loss for an individual transaction of selling and buying one unit of a product, let us now look at the concept of profit and loss applied to day-to-day business and commercial transactions.
Profit & Loss as Applied to Business and Commercial Transactions
Profit & Loss when Multiple Units of a Product are Being Bought and Sold The basic concept of profit and loss remains unchanged for this situation. However, a common mistake in this type of problem can be avoided if the following basic principle is adopted:
Profit or Loss in terms of money can only be calculated when the number of items bought and sold are equal.
That is, Profit or Loss in money terms cannot be calculated unless we equate the number of products bought and sold.
This is normally achieved by equating the number of items bought and sold at 1 or 100 or some other convenient figure as per the problem asked.
Profit & Loss when Multiple Units of a Product are Being Bought and Sold The basic concept of profit and loss remains unchanged for this situation. However, a common mistake in this type of problem can be avoided if the following basic principle is adopted:
Profit or Loss in terms of money can only be calculated when the number of items bought and sold are equal.
That is, Profit or Loss in money terms cannot be calculated unless we equate the number of products bought and sold.
This is normally achieved by equating the number of items bought and sold at 1 or 100 or some other convenient figure as per the problem asked.
Types of Costs In any business dealing, there is a situation of selling and buying of products and services. From the sellers point of view, his principle interest, apart from maximizing the sales price of a product/service, is to minimize the costs associated with the selling of that product/service. The costs that a businessman/trader faces in the process of day-to-day business transaction can be subdivided into three basic categories:
1. Direct Costs or Variable Costs This is the cost associated with direct selling of product/service.
In other words, this is the cost that varies with every unit of the product sold. Hence, if the variable cost in selling a pen for ` 20 is ` 5, then the variable cost for selling 10 units of the same pen is 10 × 5 = ` 50.
As is clear from the above example, that part of the cost that varies directly for every additional unit of the product sold is called as direct or variable cost.
Typical examples of direct costs are: Raw material used in producing one unit of the product, wages to labour in producing one unit of the product when the wages are given on a piece rate basis, and so on. In the case of traders, the cost price per unit bought is also a direct cost (i.e. every such expense that can be tied down to every additional unit of the product sold is a direct cost).
2. Indirect Costs (Overhead Costs) or Fixed Costs There are some types of costs that have to be incurred irrespective of the number of items sold and are called as fixed or indirect costs. For example, irrespective of the number of units of a product sold, the rent of the corporate office is fixed. Now, whether the company sells 10 units or 100 units, this rent is fixed and is hence a fixed cost.
Other examples of indirect or fixed costs: Salary to executives and managers, rent for office, office telephone charges, office electricity charges.
Apportionment of indirect (or fixed) costs: Fixed Costs are apportioned equally among each unit
of the product sold. Thus, if n units of a product is sold, then the fixed cost to be apportioned to
each unit sold is given by Fixed Costs/n.
of the product sold. Thus, if n units of a product is sold, then the fixed cost to be apportioned to
each unit sold is given by Fixed Costs/n.
3. Semi-Variable Costs Some costs are such that they behave as fixed costs under normal circumstances but have to be increased when a certain level of sales figure is reached. For instance, if the sales increase to such an extent that the company needs to take up additional office space to accommodate the increase in work due to the increase in sales then the rent for the office space becomes a part of the semi-variable cost.
The Concept of Margin or Contribution per unit The difference between the value of the selling price and the variable cost for a product is known as the margin or the contribution of the product. This margin goes towards the recovery of the fixed costs incurred in selling the product/service.
The Concept of the Break-even Point The break-even point is defined as the volume of sale at which there is no profit or no loss. In other words, the sales value in terms of the number of units sold at which the company breaks even is called the break-even point. This point is also called the break-even sales.
Since for every unit of the product the contribution goes towards recovering the fixed costs, as soon as a company sells more than the break-even sales, the company starts earning a profit. Conversely, when the sales value in terms of the number of units is below the break-even sales, the company makes losses.
The entire scenario is best described through the following example.
Let us suppose that a paan shop has to pay a rent of ` 1000 per month and salaries of ` 4000 to the
assistants. Also suppose that this paan shop sells only one variety of paan for ` 5 each. Further, the direct cost (variable cost) in making one paan is ` 2.50 per paan, then the margin is ` (5 – 2.50) = ` 2.50 per paan. Now, break-even sales will be given by:
Break-even-sales = Fixed costs/Margin per unit = 5000/2.5 = 2000 paans.
Hence, the paan shop breaks-even on a monthly basis by selling 2000 paans.
Selling every additional paan after the 2000th paan goes towards increasing the profit of the shop. Also, in the case of the shop incurring a loss, the number of paans that are left to be sold to break-even will determine the quantum of the loss.
Note the following formulae:
Profit = (Actual sales – Break-even sales) × Contribution per unit
Also in the case of a loss:
Loss = (Break-even sales – Actual sales) × Contribution per unit
Also, if the break-even sales equals the actual sales, then we reach the point of no profit no loss, which is also the technical definition of the break-even point.
Note that the break-even point can be calculated on the basis of any time period (but is normally done
annually or monthly).
Profit Calculation on the Basis of Equating the Amount Spent and the Amount Earned
We have already seen that profit can only be calculated in the case of the number of items being bought and sold being equal. In such a case, we take the difference of the money got and the money given to get the calculation of the profit or the loss in the transaction.
There is another possibility, however, of calculating the profit. This is done by equating the money got and the money spent. In such a case, the profit can be represented by the amount of goods left. This is so because in terms of money the person going through the transaction has got back all the money that he has spent, but has ended up with some amount of goods left over after the transaction. These left over items can then be viewed as the profit or gain for the individual in consideration.
Hence, profit when money is equated is given by Goods left. Also, cost in this case is represented by
Goods sold and hence percentage profit = (Goods Left / Goods Sold) × 100.
Example: A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his percentage profit.
Solution: Since the money spent is equal to the money earned the percentage profit is given by:
% Profit = (Goods Left / Goods Sold) × 100 = 5 × 100/20 = 25%
We have already seen that profit can only be calculated in the case of the number of items being bought and sold being equal. In such a case, we take the difference of the money got and the money given to get the calculation of the profit or the loss in the transaction.
There is another possibility, however, of calculating the profit. This is done by equating the money got and the money spent. In such a case, the profit can be represented by the amount of goods left. This is so because in terms of money the person going through the transaction has got back all the money that he has spent, but has ended up with some amount of goods left over after the transaction. These left over items can then be viewed as the profit or gain for the individual in consideration.
Hence, profit when money is equated is given by Goods left. Also, cost in this case is represented by
Goods sold and hence percentage profit = (Goods Left / Goods Sold) × 100.
Example: A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his percentage profit.
Solution: Since the money spent is equal to the money earned the percentage profit is given by:
% Profit = (Goods Left / Goods Sold) × 100 = 5 × 100/20 = 25%
Concept of Mark Up
Traders/businessmen, while selling goods, add a certain percentage on the cost price. This addition is called percentage mark up (if it is in money terms), and the price thus obtained is called as the marked price (this is also the price printed on the product in the shop).
The operative relationship is
CP + Mark up = Marked price
or CP + % Mark up on CP = Marked Price
The product is normally sold at the marked price in which case the marked price = the selling price
CP + Mark up = Marked price
or CP + % Mark up on CP = Marked Price
The product is normally sold at the marked price in which case the marked price = the selling price
If the trader/shopkeeper gives a discount, he does so on the marked price and after the discount the product is sold at its discounted price.
Hence, the following relationship operates:
CP + % Mark up (Calculated on CP) = Marked Price
Marked price – % Discount = Selling price
Use of PCG in Profit and Loss
1. The relationship between CP and SP is typically defined through a percentage relationship. As we have seen earlier, this percentage value is called as the percentage mark up. (And is also equal to the percentage profit if there is no discount).
Consider the following situation ––
Suppose the SP is 25% greater than the CP. This relationship can be seen in the following diagram.
Hence, the following relationship operates:
CP + % Mark up (Calculated on CP) = Marked Price
Marked price – % Discount = Selling price
Use of PCG in Profit and Loss
1. The relationship between CP and SP is typically defined through a percentage relationship. As we have seen earlier, this percentage value is called as the percentage mark up. (And is also equal to the percentage profit if there is no discount).
Consider the following situation ––
Suppose the SP is 25% greater than the CP. This relationship can be seen in the following diagram.
In such a case the reverse relationship will be got by the AÆBÆA application of PCG and will be seen as follows:
If the profit is 25% :
Example:
Suppose you know that by selling an item at 25%, profit the Sales price of a bottle of wine is `
1600. With this information, you can easily calculate the cost price by reducing the sales price by
20%. Thus, the CP is
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