# Finding Value of Closing Stock from Sales

 We may be able to ascertain what is left out if we know what has been sold. This logic may be applied in finding the value of closing stock. However, to know this, we need to ascertain the value of cost of goods sold. Gross Profit = Sales − Cost of Goods Sold Cost of Goods Sold = Opening Stock + Purchases + Direct Expenses − Closing Stock Gross Profit = Sales − (Opening Stock + Purchases + Direct Expenses − Closing Stock) [From (i) and (ii)] = Sales − Opening Stock − Purchases − Direct Expenses + Closing Stock Closing Stock = Opening Stock + Purchases + Direct Expenses + Gross Profit − Sales [From (iii)] To use this relation to obtain the value of closing stock, we need the information relating to Gross Profit. All other information in this relation is readily available from the accounting records.

# • Ratio : Percentage

Ratio is a comparison between two numerical quantities of the same kind.

Ratio between two quantities is expressed in the form a : b or
 a b
, where "a" and "b" do not have a common factor.

Percentage = Ratio × 100

# • Gross Profit Ratio

Gross Profit Ratio is the ratio of Gross Profit to Net Sales Value or Cost of Goods Sold.

## » To Sales

Gross Profit Ratio =
 Gross Profit Net Sales

Gross Profit as a % of Sales =
 Gross Profit Net Sales
× 100
(Or) = Gross Profit Ratio (to Sales) × 100

## » To Cost of Goods Sold

Gross Profit Ratio =
 Gross Profit Cost of Goods Sold

Gross Profit as a % of Cost of Goods Sold =
 Gross Profit Cost of Goods Sold
× 100
(Or) = Gross Profit Ratio (to Cost) × 100

# • Inter-Relationship between the two Ratios

The Gross Profit Ratio (to Sales) and Gross Profit Ratio (to Cost of Goods Sold) are interrelated and one can be obtained if the other is known.

## » Finding GP Ratio (to Cost) when GP Ratio (to Sales) is known Show/Hide

The data relating to the Gross Profit as a % of Sales given can be considered in three different forms. The formula used for conversion (expressing the interrelationship) varies depending on the form of the data considered.

# • Data on 1 Scale

Expressing the data on 1 scale, amounts to expressing the value either in decimals or as a fraction.

Consider the following data:

• Sales = x
• Gross Profit Ratio (to Sales) = y (one scale)

 Gross Profit = Sales × Gross Profit Ratio (to Sales) = x × y = xy

 Cost of Goods Sold = Sales − Gross Profit = x − xy = x (1 − y)

Gross Profit Ratio (to Cost) =
 Gross Profit Cost of Goods Sold
=
 xy x (1 − y)
=
 y (1 − y)

## » Example

 Given » Gross Profit Ratio (to Sales) is 0.25 ⇒ y = 0.25

Therefore, Gross Profit Ratio (to Cost) =
 y (1 − y)
=
 0.25 (1 − 0.25)
=
 0.25 0.75
=
 1 3
= 0.33

Gross Profit (as a % to Cost) = Gross Profit Ratio (to Cost) × 100
= 0.33 × 100
=
33
 1 3
%

# • Data on 100 Scale

Expressing the data on 100 scale implies expressing the % without using the denominator 100.
[42% is taken as 42 for calculation purposes if it is taken on a 100 scale.]

Let the data on 100 scale be represented by 'm'. ⇒ y =
 m 100

Substituting this value for 'y' in the above formula we get,
Gross Profit Ratio (as a % of Cost) =
 y (1 − y)
× 100
=
 m 100
(1 −
 m 100
)
× 100
=
 m 100
 100 − m 100
× 100
=
 m 100
×
 100 100 − m
× 100
=
 m 100 − m
× 100

## » Example

Given » Gross Profit is 25% of Sales ⇒ m =25

Therefore, Gross Profit as a % of Cost =
 m 100 − m
× 100
=
 25 100 − 25
× 100
=
 25 75
× 100
=
 100 3
=
33
 1 3

# • Data as a ratio with numerator 1

In some cases, for some common values that we use in problem solving, we use a formula based on the Gross Profit Ratio expressed as a ratio with a numerator 1.

Let the data be represented by
 1 a
⇒ y =
 1 a

Substituting this value for 'y' in the formula in (1) we get,
Gross Profit Ratio (to Cost) =
 y (1 − y)
=
 1 a
(1 −
 1 a
)
=
 1 a
 a − 1 a
=
 1 a
×
 a a − 1
=
 1 a − 1

## » Example

Given » Gross Profit Ratio (to Sales) =
 1 4
⇒ a = 4

Gross Profit Ratio (to Cost) =
 1 a − 1
=
 1 4 − 1
=
 1 3

Gross Profit (as a % to Cost) = Gross Profit Ratio (to Cost) × 100
=
 1 3
× 100
=
33
 1 3
%

## » Finding GP Ratio (to Sales) when GP Ratio (to Cost) is known Show/Hide

The data relating to the Gross Profit as a % of Cost of Goods Sold given can be considered in three different forms. The formula used for conversion (expressing the interrelationship) varies depending on the form of the data considered.

# • Data on 1 Scale

Expressing the data on 1 scale, amounts to expressing the value either in decimals or as a fraction.

Consider the following data:

• Cost of Goods Sold = p
• Gross Profit (to Cost of Goods Sold) = q (one scale)

 Gross Profit = Cost of Goods Sold × Gross Profit (to Cost of Goods Sold) = p × q = pq

 Sales = Cost of Goods Sold + Gross Profit = p + pq = p (1 + q)

Gross Profit Ratio (to Sales) =
 Gross Profit Net Sales
=
 pq p (1 + q)
=
 q (1 + q)

## » Example

Given » Gross Profit Ratio (to Cost) is 0.2 ⇒ p = 0.2

Therefore, Gross Profit Ratio (to Sales) =
 q (1 + q)
=
 0.2 (1 + 0.2)
=
 0.2 1.2
=
 1 6

Gross Profit (as a % to Sales) = Gross Profit Ratio (to Cost) × 100
=
 1 6
× 100
=
16
 2 3
%

# • Data on 100 Scale

Expressing the data on 100 scale implies expressing the % without using the denominator 100.
[35% is taken as 35 for calculation purposes if it is taken on a 100 scale.]

Let the data on 100 scale be represented by 'n'. ⇒ q =
 n 100

Substituting this value for 'q' in the above formula we get,
Gross Profit as a % of Sales =
 q (1 + q)
× 100
=
 n 100
(1 +
 n 100
)
× 100
=
 n 100
 100 + n 100
× 100
=
 n 100
×
 100 100 + n
× 100
=
 n 100 + n
× 100

## » Example

Given » Gross Profit is 20% of Cost ⇒ n =20

Therefore, Gross Profit as a percentage of Saes =
 n 100 + n
× 100
=
 20 100 + 20
× 100
=
 20 120
× 100
=
 1 6
× 100
= 16 2/3%

# • Data as a ratio with numerator 1

In some cases, for some common values that we use in problem solving, we use a formula based on the Gross Profit Ratio expressed as a ratio with a numerator 1.

Let the data be represented by
 1 b
⇒ q =
 1 b

Substituting this value for 'q' in the formula in (1) we get,
Gross Profit Ratio (to Sales) =
 q (1 + q)
=
 1 b
(1 +
 1 b
)
=
 1 b
 b + 1 b
=
 1 b
×
 b b + 1
=
 1 b + 1

## » Example

Given » Gross Profit Ratio (to Sales) is
 1 5
⇒ b = 5

Gross Profit Ratio (to Sales) =
 1 b + 1
=
 1 5 + 1
=
 1 6

Gross Profit Ratio (as a % to Sales) = Ratio × 100
=
 1 6
× 100
=
16
 2 3
%

# • Hundred Scale

As a % of Cost 20 25
33
 1 3
50
66
 2 3
100
As a % of Sales
16
 2 3
20 25
33
 1 3
40 50

# • One Scale

 As a % of Cost 0.2 0.25 0.333 0.5 0.666 1 As a % of Sales 0.166 0.2 0.25 0.333 0.4 0.5

As a % of Cost
 1 5
 1 4
 1 3
 1 2
 2 3
 1 1
As a % of Sales
 1 6
 1 5
 1 4
 1 3
 2 5
 1 2

# Gross Profit is generally Non-Uniform

The gross profit earned by an organsation is in almost all cases not a figure that can be easily derived (without the availability of the value of closing stock). Deriving the value of closing stock would be far easier than deriving the value of gross profit made (based on sales).

# • Variety of Products being Sold

The organisation may be selling a number of products with different selling prices and different rates of gross profits.

In such cases, if the gross profit figure is to be ascertained from the sales figure, sales records should be maintained so as to give the sales details relating to each product with a distinct Gross Profit %. This would involve a lot of work and would be impractical, more so where there are a large number of products being dealt with.

# • Variations in Sale Prices

The prices charged to customers are dependent on a number of factors like the market conditions, the immediate competition existing in the market, the loyalty of the customers etc.

Depending on the market conditions, some times the prices may be varied instantaneously.

Depending on the customer to whom the product is being sold, the prices may be varied (a discount may be given to loyal customers) etc.

In such a situations there would not be uniformity in the Gross profit percentage and it would be near to impossible to ascertain the gross profit made using the sales figures.

Since using the figure of gross profit to ascertain the value of closing stock available in the organisation is not a feasible idea, we look at other methods for finding out the value of closing stock.

# • Physical Stock

Closing stock is the stock/goods unsold at the end of the accounting period.

The details relating to the physical stock would be readily available with the organisation only if the inventory records are being maintained by the organisation. In other cases the physical stock would have to be ascertained by stock taking.

# • Stock Value

There is no specific ledger account in financial accounting that would give us the information relating to the value of closing stock ready hand.

The value of closing stock is available ready hand only if inventory records are being maintained that too from the inventory records.

 The value of Closing Stock is ascertained by Physical Verification of Stock on the last day of the accounting period and its valuation at Cost or Market Price (Net Realisable Value) whichever is lesser

This is the most common method for valuing the closing stock.

The information relating to the value of closing stock is not regularly required by the organisation. It is however required at the end of the accounting period for the purpose of evaluation of the Cost of Goods Sold.

# • Net Realisable Value of Stock

For the purpose of Valuation of closing Stock, Market Price implies Net Realisable Value/Rate and not the Selling Price.

Net Realisable Value of stock is the net sale realisation excluding all the expenses directly and exclusively relatable to the sale (Sale commission, Brokerage etc) from the Sale Realisation.

Therefore, in trying to ascertain the Market Price to be used for valuation, care should be taken to ensure that such expenses are deducted from the sales price to ascertain the net realisable value of stock.

# • Convention of Conservatism

 By the Convention of Conservatism we take into consideration all those expenses and losses of which we are aware, even if they relate to the subsequent accounting periods.

The act of valuing closing stock at cost or market price is based on the "Convention of Conservatism".

# Convention of Conservatism : Valuation of Closing Stock : Illustration

Following is the "Trading a/c" relating to an organisation, wherein the Closing Stock has been recorded at cost.

Particulars Amount
(in Rs)
Particulars Amount
(in Rs)
To Opening Stock
To Purchases
To Direct Expenses
To Gross Profit
20,000
2,48,000
54,000
94,000
By Sales
By Closing Stock
3,80,000
36,000
4,16,000   4,16,000

## » Closing Stock details

The closing stock is made up of
• Batch N :: 600 units valued at Rs. 36/unit with a total value of Rs. 21,600
• Batch M :: 600 units valued at Rs. 24/unit with a total value of Rs. 14,400
• Total 1,200 units with a total value of Rs. 36,000

Value here implies cost + direct expenses

The selling prices and the related expenses are

• Batch N :: Rs. 50/unit
• Batch M :: Rs. 50/unit [Regular price]
Batch M :: Rs. 25/unit [Current price]

This stock represents an outdated model of the product and the present market conditions would enable the stock to be sold only at a price of Rs. 25 per unit.

• The sales of all stocks are made through a dealer who would charge a commission of 10% of the sale proceeds.

## » Cost and Net Realisable Values of Closing Stock

From the available data, Closing stock can be valued at two different rates. Cost and Market Price (Net Realisable Rate).
• ## 600 units [Batch N]

1. Cost = Rs. 36/unit.
2. Market Price = Rs. 50/unit.
3. Expenses directly relatable to sale = Rs. 5/unit
(10% of selling price = Rs. 50/unit × 10%).
4. Net Realisable Value = Rs. 45/unit
[Market Price (Rs. 50/unit) − Expenses relatable to sale (Rs. 5/unit)]
• ## 600 units [Batch M]

1. Cost = Rs. 24/unit.
2. Market Price = Rs. 25/unit.
3. Expenses directly relatable to sale = Rs. 2.50/unit
(10% of selling price = Rs. 25/unit × 10%).
4. Net Realisable Value = Rs. 22.50/unit
[Market Price (Rs. 25/unit) − Expenses relatable to sale (Rs. 2.50/unit)].

• ## 600 units [Batch N]

Cost = Rs. 36/unit. Net Realisable Rate = Rs. 45/unit.

Since Cost < Net Realisable Value, the goods are to be valued at cost.
⇒ Value of 600 units is Rs. 21,600 (600 units × Rs. 36/unit)

• ## 600 units [Batch M]

Cost = Rs. 24/unit. Net Realisable Rate = Rs. 22.50/unit.

Since Net Realisable Value < Cost, the goods are to be valued at the net realisable value.
⇒ Value of 600 units is Rs. 13,500 (600 units × Rs. 22.50/unit)

Value of Closing stock if valued at cost = Rs. 14,400 (600 units × Rs. 24/unit)

The Closing Stock should be valued therefore at Rs. 35,100 (Rs. 21,600 + 13,500).

If value of Closing Stock is taken based on the Convention of Conservatism, the Trading a/c would be

Particulars Amount
(in Rs)
Particulars Amount
(in Rs)
To Opening Stock
To Purchases
To Direct Expenses
To Gross Profit
20,000
2,48,000
54,000
93,100
By Sales
By Closing Stock
3,80,000
35,100
4,15,100   4,15,100

The Gross profit has gone down by Rs. 900 since closing stock is considered at a lesser value.

# Role of Convention of Conservatism

The convention of conservatism asks us to take into consideration all those expenses and losses relating to the subsequent periods of which we are aware.

## » Future Losses

Where the Net realisable value of stock is less than its cost, the organisation may incur a loss.

In the above case, the organisation may have to incur a loss of Rs. 900 [Rs. 14,400 (cost) − Rs. 13,500 (net realisable value)].

## • When?

This loss would have to be borne by the organisation if it sells the stock at the net realisable rate.

Since it is the end of the accounting period, such a sale at such a price, if at all it takes place, would be in the subsequent accounting period.

Thus, the organisation may have to incur this loss in the future.

## • Is the loss for sure?

The loss may have to be incurred in the future only if the stock has to be sold at Rs. 25 per unit (which gives a net realisation of Rs. 22.50).

We may consider such a loss a certainty in cases where the stock is required to be sold at the lower price on account of it becoming obsolete, losing demand etc.

Bu where the lower market rate is on account of normal market fluctuation and if the rates go up in the subsequent period and the product can be sold at a higher price, this loss need not be incurred.

# How is the loss absorbed?

Based on the Convention of Conservatism, the loss though it may have to be incurred in the future period, is absorbed in the current period itself, since its information is known.

This will be the case where the lower valuation is on account of conditions which are certain (obsolete goods, demand going down etc).

## » Crediting a Nominal a/c implies gain

The value of closing stock is credited to the "Trading a/c". By the principle of credit in relation to nominal accounts (Credit all Incomes and Gains), we can assume the value to indicate a gain.

Reducing the value of closing stock would therefore amount to reducing the credit made to the Trading a/c, which would be reducing the gain. Debiting an amount is an equivalent of deducting the amount from the opposite side i.e. the credit side. Therefore, reducing the gain is the same as taking in additional loss.

Therefore, the loss is absorbed by considering the value of closing stock at a lesser value i.e. the net realisable value. [In the above example, by considering the closing stock at the lower value, the estimated loss of Rs. 900 relating to the subsequent accounting periods has been absorbed in the current period itself.]

# Value of Closing Stock = Value of Opening Stock of the Subsequent Period

The Closing Stock a/c relating to an accounting period and the Opening Stock a/c relating to the subsequent accounting period represent the same account. Therefore, the value of the closing stock at the end of the accounting period and the opening stock at the beginning of the subsequent accounting period are the same.

# • Closing Stock a/c

The "Closing Stock a/c" is a real account and is created at the last moment of the accounting period.

It represents Stock as an asset. The balance in the "Closing Stock a/c" is carried forward to the next accounting periods.

# • Opening Stock a/c

The account that we name "Closing Stock a/c" is renamed "Opening Stock a/c" at the beginning of the next accounting period while bringing the values of assets and liabilities into the books of accounts with the help of an "Opening Entry".

This "Opening Stock a/c" is treated as an equivalent of a Nominal account.

Like other nominal accounts it is closed at the end of the accounting period. It is closed by transfer to the "Trading a/c" since it goes into the value of cost of goods sold.

## » Note

The value of Opening and Closing stocks relating to a particular accounting period do not mean the same. They are two indicated by distinct ledger accounts - Opening stock by "Opening Stock a/c" which is a nominal account and Closing stock by "Closing Stock a/c" which is a Real account.

They may or may not have the same values.

 Author Credit : The Edifier ... Continued Page 12