Closing Stock, Opening Stock - Ascertainment and Valuation

Finding Value of Closing Stock from Sales

We will 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.

Cost of Goods Sold

Opening Stock
+ Purchases
+ Direct Expenses
− Closing Stock
− Stock Used for Non Trading purposes

⇒ Closing Stock

Opening Stock
+ Purchases
+ Direct Expenses
− Stock Used for Non Trading purposes
− Cost of Goods Sold

To use this relation to find the value of closing stock, we need to be in the know of the ascertained value of cost of goods sold. All other information can be obtained from the accounting records.

From Trading account, we can write

Opening Stock

+ Purchases
+ Direct Expenses
+ Gross Profit

Sales
+ Closing Stock
+ Stock Used for Non Trading purposes

⇒ Closing Stock

Opening Stock
+ Purchases
+ Direct Expenses
+ Gross Profit
− Sales
− Stock Used for Non Trading purposes

To use this relation to find the value of closing stock, we need to be in the know of gross profit. All other information can be obtained from the accounting records.

Since reflecting the value of cost of goods sold and thereby finding gross profit is the objective of preparation of the Trading a/c, we can say that this route for finding the value of closing stock is not a feasible idea unless there is a possibility of finding gross profit.

Can Gross Profit be calculated based on Sales Value

Fixed value for Gross Profit

The organisation may consider Gross profit at a fixed value for each item it sells.

Sale price = Cost of goods sold + Fixed Gross Profit

Requirement : Cost of goods sold should be known for each sale.

Using a fixed value for Gross Profit is possible only if the organisation is in the know of the cost of goods sold for every sale.

If sale price is fixed

If the sale price is also a fixed value for each sale, then it amounts to the cost of goods sold also being a fixed value for each sale.

Gross Profit = Cost of goods sold × Gross Profit as a % of cost

Fixed % for Gross Profit

The organisation may consider Gross profit at a fixed % of cost or sales.

Gross Profit = Cost of goods sold × Gross Profit as a % of cost

Sale price = Cost of goods sold + Gross Profit

Requirement : Cost of goods sold should be known for each sale.

Using a fixed % (on cost/sale) for Gross Profit is also possible only if the organisation is in the know of the cost of goods sold for every sale.

Gross Profit may be ascertained without having to know the value of closing stock only if there is some way to ascertain the value of cost of goods sold and the gross profit is taken at fixed value or a fixed percentage of cost or sales.

Knowing the cost of goods sold for each sale is a possibility in organisations which maintain cost accounting records or inventory records with values for all products they deal with.

Where such records are being maintained the value of closing stock will also be available readyhand in the same records and as such the need to calculate gross profit this way does not arise.

if a fixed amount is being added up to cost as gross profit and that amount is known for each and every sale that has been made during the accounting period.
For this to be happening, apart from the fixed gross profit that the organisation intends to make from each sale, it should also be in the know of the cost of goods sold for each sale so as to add the gross profit to it and arrive at a selling price.
if a fixed amount is being added up to cost as gross profit and that amount is known for each and every sale that has been made during the accounting period.

calculated based on Sales value, if it is known as a fixed percentage of sales or cost of goods sold.

Gross Profit = Sales × Gross Profit as a % of Sales
Gross Profit = Cost of goods sold × Gross Profit as a % of Cost of Goods sold

Gross profit as a % of cost of goods sold can always be converted to Gross Profit as a % of sales. As such the first relation can be used even when Gross Profit is given as a % of cost of goods sold.

Limitations

Calculating gross profit from sales and Gross profit as a % of sales is theoretically possible if the Gross profit % is known for every single sale made, which is rarely the case.

Gross profit percentages are generally fixed based on historical cost data or based on policy decisions and are maintained for a substantial period of time. Just knowing the gross profit percentage that the organisation intends to make To be able to ascertain gross profit for every single sale, the data Gross Profit = Sales - Cost of Goods Sold
For Gross Profit to be consistent

Gross Profit is generally Non-Uniform

The gross profit earned by an organisation 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.

Gross Profit Ratios - Math

Ratio : Percentage

Ratio is the relationship between two quantities of the same units expressed in the form a : b or

\frac{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 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

The data relating to the Gross Profit as a % of Sales (or Cost of Goods sold) may be given in any of the three different forms and can be converted from one form to another.

1 Scale
The value is either in decimals or as a fraction.
- Ratio of Gross Profit to sales is 0.4.
  To convert to 100 scale, multiply with 100.
  Gross Profit as a % of sales = Gross Profit Ratio × 100.
  = 0.4 × 100
  = 40%
- Gross Profit is 0.4 of sales.
- Gross Profit is ${\frac{3}{8}}^{t h}$ of cost.
  To convert to 100 scale, multiply with 100.
  Gross Profit as a % of cost = Gross Profit Ratio × 100.
  = $\frac{3}{8}$ × 100
  = 27.5%
100 Scale
The % value without considering the % (denominator 100).
Gross Profit is 15% of sales. It is taken as 15 in calculations.
To convert to 1 scale, divide with 100.
Gross Profit Ratio = $\frac{Gross Profit as a % of Sales}{100}$
= $\frac{15}{100}$
= $\frac{3}{20}$
or = 0.15
a ratio with numerator 1
The value is also a fraction and can be considered to be on 1 scale. Specific methodology can be adopted in calculations if the numerator is 1, so this is identified as another data type.
Gross Profit is ${\frac{1}{6}}^{t h}$ of Cost

Gross Profit Ratio to Sales ⇔ Gross Profit Ratio to Cost of Goods Sold

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.

The formula used for conversion depends on the form of the data considered.

Notations used

Gross Profit Ratio as a % of Sales ⇒ GP(S)
Gross Profit Ratio as a % of Cost ⇒ GP(C)

GP Ratio (to Cost) from GP Ratio (to Sales)

Data on 1 Scale
Ratio has to be taken in the decimal form.
GP(C) = $\frac{GP(S)}{1 − GP(S)}$
Example
Gross Profit Ratio (to Sales) is 0.2 ⇒ GP(S) = 0.2
GP(C) = $\frac{GP(S)}{1 − GP(S)}$
= $\frac{0.2}{1 − 0.2}$
= $\frac{0.2}{0.8}$
= $\frac{1}{4}$
or = 0.25
Proof
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)
Data on 100 Scale
Data has to be expressed as a % without the denominator.
GP(C) = $\frac{GP(S)}{100 − GP(S)} \times 100$
Example
Gross Profit is 50% of Sales ⇒ GP(S) = 50
GP(C) = $\frac{GP(S)}{100 − GP(S)} \times 100$
= $\frac{50}{100 − 50} \times 100$
= $\frac{50}{50} \times 100$
= 100%
Proof
Let the data on 100 scale be represented by 'm'. ⇒ y =
m
100
Substituting this value for 'y' in the formula for fractional data we get,
Gross Profit Ratio (as a % of Cost) =
y
(1 − y)
× 100
= $\frac{\frac{m}{100}}{(1 - \frac{m}{100})} \times 100$
= $\frac{\frac{m}{100}}{\frac{100 - m}{100}} \times 100$
=
m
100
×
100
100 − m
× 100
=
m
100 − m
× 100
Data as a ratio with numerator 1
Where 'a' represents the denominator of the fraction representing the ratio.
GP(C) =
1
a − 1
Example
Gross Profit is ${\frac{1}{5}}^{t h}$ of Sales ⇒ a = 5
GP(C) =
1
a − 1
=
1
5 − 1
=
1
4
Proof
Let the ratio be
1
a
⇒ y =
1
a
Substituting this value for 'y' in the formula for fractional data we get,
Gross Profit Ratio (to Cost) =
y
(1 − y)
= $\frac{\frac{1}{a}}{(1 - \frac{1}{a})}$
= $\frac{\frac{1}{a}}{\frac{a - 1}{a}}$
=
1
a
×
a
a − 1
=
1
a − 1

GP Ratio (to Sales) from GP Ratio (to Cost)

Data on 1 Scale
Ratio has to be taken in the decimal form.
GP(S) = $\frac{GP(C)}{1 − GP(C)}$
Example
Gross Profit Ratio (to Cost) is 0.25 ⇒ GP(C) = 0.25
GP(S) = $\frac{GP(C)}{1 + GP(C)}$
= $\frac{0.25}{1 + 0.25}$
= $\frac{0.25}{1.25}$
= $\frac{1}{5}$
or = 0.2
Proof
Consider the following data:
- Cost of Goods Sold = p
- Gross Profit Ratio (to Cost) = q (one scale)
Gross Profit = Cost of Goods Sold × Gross Profit Ratio (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)
Data on 100 Scale
Data has to be expressed as a % without the denominator.
GP(S) = $\frac{GP(C)}{100 + GP(C)} \times 100$
Example
Gross Profit is 100% of Cost ⇒ GP(C) = 100
GP(S) = $\frac{GP(C)}{100 + GP(C)} \times 100$
= $\frac{100}{100 + 100} \times 100$
= $\frac{100}{200} \times 100$
= 50%
Proof
Let the data on 100 scale be represented by 'n'. ⇒ q =
n
100
Substituting this value for 'q' in the formula for fractional data we get,
Gross Profit Ratio (as a % of Sales) =
q
(1 + q)
× 100
= $\frac{\frac{n}{100}}{(1 + \frac{n}{100})} \times 100$
= $\frac{\frac{n}{100}}{\frac{100 + n}{100}} \times 100$
=
n
100
×
100
100 + n
× 100
=
n
100 + n
× 100
Data as a ratio with numerator 1
Where 'b' represents the denominator of the fraction representing the ratio.
GP(S) =
1
b + 1
Example
Gross Profit is ${\frac{1}{4}}^{t h}$ of Cost ⇒ b = 4
GP(S) =
1
b + 1
=
1
4 + 1
=
1
5
Proof
Let the ratio be
1
b
⇒ q =
1
b
Substituting this value for 'q' in the formula for fractional data we get,
Gross Profit Ratio (to Sales) =
q
(1 + q)
= $\frac{\frac{1}{b}}{(1 + \frac{1}{b})}$
= $\frac{\frac{1}{b}}{\frac{b + 1}{b}}$
=
1
b
×
b
b + 1
=
1
b + 1

Frequently used conversions

As a % of Cost

1 scale

0.2

0.25

0.333

0.5

0.666

100 scale

100

Inverse

As a % of Sales

Inverse

100 scale

1 scale

0.166

0.20

0.25

0.333

0.4

0.5

How is the Quantity and value of Closing Stock ascertained?

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

Quantity of Stock

The quantitative details of stock would be readily available with the organisation only if the inventory records are being maintained by the organisation, like in the case of an organisation maintaining cost accounting records or specific inventory records. In other cases the quantity of stock would have to be ascertained by physical stock taking.

Value of stock

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 along with the value details. This may be possible if the organisation maintains cost accounting 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

The information relating to the value of closing stock is not regularly required by the organisation. It is required at the end of the accounting period for preparation of final accounts, both in ascertaining gross profit (or cost of goods sold) and for being included in the assets in the balance sheet.

Net Realisable Value of Stock

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).

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

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

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

Convention of Conservatism : Valuation of Closing Stock : Illustration

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

Trading a/c
DrCr
Particulars	Amount	Particulars	Amount
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

	Batch M			Batch N			Total
	Qty Units	Rate/unit	Value	Qty Units	Rate/unit	Value	Value
Stock (at cost)	600	36	21,600	600	24	14,400	36,000

Value of stock includes cost and direct expenses

Batch M and N are regularly sold at 50 and 40 per unit respectively. The current stock of Batch M is an outdated model of the product and the market conditions would enable the stock to be sold only at a price of 30 per unit.

All sales are made through a dealer who would charge a commission of 10% of the sale proceeds.

Selling Price and Net Realisable Rate
	Batch M	Batch N
	Rate/unit	Rate/unit
a) Regular Selling Price b) Selling Commission @10% of Sale Price	50 5	40 4
1) Net Realisable Price (Regular) (a) − (b)	45	36
p) Current Selling Price q) Selling Commission @10% of Sale Price	30 3
2) Net Realisable Price (Current) (p) − (q)	27

Net Realisable Price

Selling Price − Expenses directly relatable to sales

Selling commission is the expense directly relatable to sales here.

Net Realisable values of Closing Stock

	Batch M			Batch N
	Qty Units	Rate/unit	Value	Qty Units	Rate/unit	Value
@ Regular Price @ Current Price	600 600	45 27	27,000 16,200	600	36	21,600

Closing stock is valued at cost or Market (Net realisable) value whichever is lesser.

	Batch M	Batch N
	Value	Value
@ Cost @ Net Realisable (Regular) Price @ Net Realisable (Current) Price	21,600 ~~27,000~~ ✔ 16,200	✔ 14,400 21,600

In following the convention of conservatism, each kind of stock is to be assessed distinctly.

The total value of stock at cost would be 36,000 and following the convention of conservatism it would be 30,600 (16,200 + 14,400)

Trading a/c

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

Trading a/c
DrCr
Particulars	Amount	Particulars	Amount
To Opening Stock To Purchases To Direct Expenses To Gross Profit	20,000 2,48,000 54,000 88,600	By Sales By Closing Stock	3,80,000 30,600
	4,10,600		4,10,600

Lower valuation of closing stock ⇒ Loss

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.

Reducing a credit will have the same effect as increasing a debit. Thus reduction in value of closing stock can also be interpreted as taking up an additional debit which will result in a lower profit.

The Gross profit has gone down by 5,400 (94,000 − 88,600) as closing stock is considered at a value lesser by 5,400 (36,000 − 30,600).

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 5,400 [ 21,600 (cost) − 16,200 (net realisable value)] as and when it sells the stock of Batch M at the net realisable rate.

When?

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 30 per unit (which gives a net realisation of 27 per unit).

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 may not have to be incurred.

Future Loss Absorbed now

The loss that may have to be incurred in the subsequent accounting periods as and when the stock is disposed at the net realisable price is absorbed in the current accounting period by reducing the value of closing stock.

Closing Stock of a period is 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 subsequent accounting periods through the closing entry.

Opening Stock a/c

The Closing Stock a/c is renamed Opening Stock a/c at the beginning of the subsequent accounting period into which it is carried forward, while bringing the values of assets and liabilities into the books of accounts through the Opening Entry.

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 : The Edifier

Page 12

Gross Profit as a % of sales	=	Gross Profit Ratio × 100.
	=	0.4 × 100
	=	40%

Gross Profit as a % of cost	=	Gross Profit Ratio × 100.
	=	$\frac{3}{8}$ × 100
	=	27.5%

Gross Profit Ratio	=	$\frac{Gross Profit as a % of Sales}{100}$
	=	$\frac{15}{100}$
	=	$\frac{3}{20}$
or	=	0.15

GP(C)	=	$\frac{GP(S)}{1 − GP(S)}$
	=	$\frac{0.2}{1 − 0.2}$
	=	$\frac{0.2}{0.8}$
	=	$\frac{1}{4}$
or	=	0.25

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

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

GP(C)	=	$\frac{GP(S)}{100 − GP(S)} \times 100$
	=	$\frac{50}{100 − 50} \times 100$
	=	$\frac{50}{50} \times 100$
	=	100%

GP(S)	=	$\frac{GP(C)}{1 + GP(C)}$
	=	$\frac{0.25}{1 + 0.25}$
	=	$\frac{0.25}{1.25}$
	=	$\frac{1}{5}$
or	=	0.2

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

GP(S)	=	$\frac{GP(C)}{100 + GP(C)} \times 100$
	=	$\frac{100}{100 + 100} \times 100$
	=	$\frac{100}{200} \times 100$
	=	50%

Closing Stock, Opening Stock - Ascertainment and Valuation

Finding Value of Closing Stock from Sales

Can Gross Profit be calculated based on Sales Value

Fixed value for Gross Profit

If sale price is fixed

Fixed % for Gross Profit

Limitations

Gross Profit is generally Non-Uniform

Variety of Products being Sold

Variations in Sale Prices

Gross Profit Ratios - Math

Ratio : Percentage

Gross Profit Ratio

to Sales

to Cost of Goods Sold

1 Scale

100 Scale

a ratio with numerator 1

Gross Profit Ratio to Sales ⇔ Gross Profit Ratio to Cost of Goods Sold

GP Ratio (to Cost) from GP Ratio (to Sales)

Data on 1 Scale

Example

Proof

Data on 100 Scale

Example

Proof

Data as a ratio with numerator 1

Example

Proof

GP Ratio (to Sales) from GP Ratio (to Cost)

Data on 1 Scale

Example

Proof

Data on 100 Scale

Example

Proof

Data as a ratio with numerator 1

Example

Proof

Frequently used conversions

How is the Quantity and value of Closing Stock ascertained?

Quantity of Stock

Value of stock

Net Realisable Value of Stock

Convention of Conservatism

Convention of Conservatism : Valuation of Closing Stock : Illustration

Closing Stock

Net Realisable values of Closing Stock

Trading a/c

Lower valuation of closing stock ⇒ Loss

Role of Convention of Conservatism

Future Losses

When?

Is the loss for sure?

Future Loss Absorbed now

Closing Stock of a period is Opening Stock of the Subsequent Period

Closing Stock a/c

Opening Stock a/c

Note