Mark-up and Margins

CIMA-BA3 · Chapter 19

Mark-up and Margins

A mark-up is gross profit as a percentage of cost; a gross profit margin is gross profit as a percentage of selling price. If you know one of cost, gross profit or sales and the percentage, you can find the other two — working forwards or backwards. The same idea is one of the tools for incomplete records: when a business has not kept full books, the missing figures are found from the accounting equation, the mark-up or margin, the receivables and payables ledgers, and the cash and bank accounts.

1 Introduction

Occasionally it is the case that all selling prices are calculated so as to give a fixed percentage profit.

This information means that if we know the cost of sales we are able to calculate the sales (and vice versa). Make sure that you can do the arithmetic, but that also you learn the terminology and remember the difference between a mark-up and a gross profit margin.

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2 Mark-up

A mark-up is the gross profit expressed as a percentage of the cost.

If the mark-up is 25%, then for every $100 of cost the business adds $25 of gross profit and sells for $125. Put the other way round, cost is always 100/125 of the selling price.

	Cost	Gross profit	Sales
Mark-up of 25% (per $100 of cost)	100	25	125

Jelena has cost of goods sold of $20,000 and applies a mark-up of 20%.
What are the sales?
Karen has sales of $50,000 and applies a mark-up of 25%.
What is her cost of goods sold?

(a) Sales = 20,000 + (20% × 20,000) = $24,000

(b) If cost of goods sold is x, the mark-up is 0.25x, so 50,000 = x + 0.25x = 1.25x.

Cost of goods sold: x = 50,000 ÷ 1.25 = $40,000

Without algebra: for every $125 of sales the cost is $100, so cost = 50,000 × 100/125 = $40,000. Check: 25% of 40,000 is 10,000, and 40,000 + 10,000 = 50,000.

3 Gross profit margin

The gross profit margin is the gross profit expressed as a percentage of the selling price.

If the margin is 25%, then for every $100 of sales the gross profit is $25 and the cost is $75. Cost is always 75/100 of the selling price.

	Cost	Gross profit	Sales
Margin of 25% (per $100 of sales)	75	25	100

Peter has sales of $120,000. His gross profit margin is 20%.
What is his cost of goods sold?
Paul has a cost of goods sold of $45,000 and a gross profit margin of 25%.
What are his sales?

(a) Cost of goods sold = 120,000 − (20% × 120,000) = $96,000

(b) If sales are x, the margin is 0.25x, so 45,000 = x − 0.25x = 0.75x.

Sales: x = 45,000 ÷ 0.75 = $60,000

Without algebra: for every $75 of cost the sales are $100, so sales = 45,000 × 100/75 = $60,000. Check: 25% of 60,000 is 15,000, and 60,000 − 15,000 = 45,000.

3.1 Mark-up and margin compared

The same sale gives a different percentage depending on the base. A mark-up is always the larger of the two, because cost is smaller than selling price. Questions often give one and expect you to use the other:

To convert	Formula	Example
Mark-up to margin	margin = mark-up ÷ (1 + mark-up)	25% mark-up: 0.25 ÷ 1.25 = 20% margin
Margin to mark-up	mark-up = margin ÷ (1 − margin)	20% margin: 0.20 ÷ 0.80 = 25% mark-up

If you find formulae hard to remember, build the ‘per $100’ line instead. A mark-up of 50% means cost 100, profit 50, sales 150, so the margin is 50/150 = 33⅓%. A margin of 25% means sales 100, profit 25, cost 75, so the mark-up is 25/75 = 33⅓%.

Mark-up on cost	Cost	Gross profit	Sales	Margin on sales
25%	100	25	125	20%
33⅓%	100	33⅓	133⅓	25%
50%	100	50	150	33⅓%
100%	100	100	200	50%

4 More complicated questions

Questions in the exam can test you on mark-ups and margins in a slightly more interesting way, as in the following example.

These questions use the cost of sales calculation from Chapter 2:

Cost of sales = opening inventory + purchases − closing inventory

If any three of these four figures are known, the fourth can be found. When cost of sales itself is unknown, find it from the sales and the mark-up or margin first.

A business made purchases during the year of $90,000, and sales during the year of $120,000.

The opening inventory was $30,000.

There had been a fire that had destroyed much of the inventory, and the inventory remaining at the end of the year was $12,000.

If the business always has a mark-up of 20% of cost, then what was the cost of the inventory that had been destroyed?

Start with a trading account and leave closing inventory as the unknown. With a mark-up of 20%, for every $120 of sales the cost is $100, so cost of sales = 120,000 × 100/120 = $100,000 and gross profit = $20,000.

	$	$
Sales		120,000
Opening inventory	30,000
Purchases	90,000
	120,000
Less: Closing inventory (balancing figure)	(20,000)
Cost of sales (120,000 × 100/120)		(100,000)
Gross profit (20% × 100,000)		20,000

Without the fire, closing inventory would have been $20,000. Only $12,000 remained, so the cost of the inventory destroyed was 20,000 − 12,000 = $8,000.

In the statement of profit or loss the trading account stays as above, so that gross profit shows the profit on what was actually sold. The $8,000 is shown separately as an expense (‘loss from fire’), and the statement of financial position shows the inventory actually held, $12,000.

5 Incomplete records

Some businesses, usually small sole traders, do not keep a full double-entry system. They may have only a bank statement, a list of amounts owed by customers and to suppliers, and the owner’s memory. To prepare financial statements from incomplete records, you rebuild the missing figures with four tools:

Tool	What it finds
The accounting equation (Chapter 2, section 6)	Opening and closing capital; profit, when only the net assets at each end of the year are known
Mark-up and margin (sections 2–4 above)	Sales from cost of sales, or cost of sales (and so a missing inventory or purchases figure) from sales
Receivables and payables ledgers (Chapter 15, section 6)	Credit sales and credit purchases, as the balancing figure in a total receivables or total payables account
Cash and bank ledgers	A missing receipt or payment — most often drawings, or cash takings that were never banked

5.1 The accounting equation

Capital = assets − liabilities, at any date. So the opening capital of a business with no records is found by listing its assets and liabilities at the start of the year. Over the year:

Increase in net assets = capital introduced + profit − drawings

so profit = increase in net assets − capital introduced + drawings.

Grace Mensah does not keep books. At 1 January her business assets were $30,000 and its liabilities $8,000. At 31 December the assets were $41,000 and the liabilities $9,500. During the year she paid in $2,000 of new capital and took drawings of $6,000.

	$
Net assets at 31 December (41,000 − 9,500)	31,500
Net assets at 1 January (30,000 − 8,000)	(22,000)
Increase in net assets	9,500
Less: capital introduced	(2,000)
Add: drawings	6,000
Profit for the year	13,500

This gives the profit figure, but not the revenue and expenses that make it up. To prepare a statement of profit or loss, the individual figures must be rebuilt with the other three tools.

5.2 Receivables and payables ledgers

Credit sales are rarely recorded by such a business, but the opening and closing receivables and the cash received from customers are usually known. Set up a total receivables account, enter everything known, and credit sales are the balancing figure. Credit purchases are found the same way from a total payables account. Remember to include discounts, irrecoverable debts and contras if the question gives them (see Chapter 15, Example 3).

Total receivables account	Total payables account
Opening receivables + credit sales − cash received (and discounts allowed, irrecoverable debts) = closing receivables	Opening payables + credit purchases − cash paid (and discounts received) = closing payables

5.3 Cash and bank ledgers

Summarise the receipts and payments in a cash account (for notes and coins kept in the till) and a bank account. The bank balance can be checked against the bank statement, so the bank account usually balances without a missing figure. The cash account is different: an owner who pays some expenses and takes drawings straight out of the takings rarely records them. Enter the opening and closing cash and all the known receipts and payments; the balancing figure is the missing item — usually drawings, or cash that was stolen.

Total sales often come from the mark-up or margin; credit sales come from the receivables account; and cash sales are the difference. The cash sales then go into the cash account as its main receipt.

5.4 Putting it together

A full question needs the figures in a sensible order: opening capital first, then credit sales and purchases, then cost of sales and total sales, then the cash account, and finally the statements.

Kwame Asante runs a shop in Kumasi and does not keep a full set of books. You find the following for the year ended 31 December 2019.

Balances	1 January 2019 $	31 December 2019 $
Equipment, at carrying amount	12,000	see below
Inventory	8,000	9,000
Trade receivables	5,000	6,200
Bank	3,000	see below
Cash in the till	500	400
Trade payables	4,500	5,300

Summary of the bank statements for the year

	$
Takings paid into the bank	40,000
Received from credit customers	30,800
Paid to suppliers	(58,200)
Rent	(4,800)
General expenses	(2,600)

All purchases are on credit. Wages of $6,000 were paid in cash from the till, and Kwame took the rest of the cash he needed for himself from the till; he kept no record of these drawings. Depreciation on the equipment for the year is $1,200. All goods are sold at a mark-up of 50% on cost.

Required:

Calculate Kwame’s capital at 1 January 2019.
Calculate the credit sales and the purchases for the year.
Calculate the cost of sales, the total sales and the cash sales.
Prepare the cash account and find the drawings, and calculate the bank balance at 31 December 2019.
Prepare the statement of profit or loss for the year and the statement of financial position at 31 December 2019.

(a) Opening capital

Assets 12,000 + 8,000 + 5,000 + 3,000 + 500 = 28,500, less trade payables 4,500 = $24,000.

(b) Credit sales and purchases

Debit	Total Receivables Account		Credit
Balance at 1 January	5,000	Bank — received from customers	30,800
Credit sales (balancing figure)	32,000	Balance at 31 December	6,200
	37,000		37,000

Debit	Total Payables Account		Credit
Bank — paid to suppliers	58,200	Balance at 1 January	4,500
Balance at 31 December	5,300	Purchases (balancing figure)	59,000
	63,500		63,500

(c) Cost of sales, total sales and cash sales

Cost of sales = 8,000 + 59,000 − 9,000 = $58,000.

Total sales = 58,000 × 150/100 = $87,000 (gross profit $29,000).

Cash sales = 87,000 − credit sales 32,000 = $55,000.

(d) Cash and bank

Debit	Cash Account		Credit
Balance at 1 January	500	Bank — takings paid in	40,000
Cash sales	55,000	Wages	6,000
		Drawings (balancing figure)	9,100
		Balance at 31 December	400
	55,500		55,500

Debit	Bank Account		Credit
Balance at 1 January	3,000	Payables	58,200
Cash — takings paid in	40,000	Rent	4,800
Receivables	30,800	General expenses	2,600
		Balance at 31 December	8,200
	73,800		73,800

Drawings are $9,100 and the bank balance at 31 December 2019 is $8,200.

(e) Statements

Statement of profit or loss for the year ended 31 December 2019	$	$
Sales		87,000
Opening inventory	8,000
Purchases	59,000
	67,000
Less: Closing inventory	(9,000)
Cost of sales		(58,000)
Gross profit		29,000
Wages	6,000
Rent	4,800
General expenses	2,600
Depreciation	1,200
		(14,600)
Profit for the year		14,400

Statement of financial position at 31 December 2019	$	$
Non-current assets
Equipment (12,000 − 1,200)		10,800
Current assets
Inventory	9,000
Trade receivables	6,200
Bank	8,200
Cash	400
		23,800
Total assets		34,600
Capital at 1 January 2019		24,000
Add: profit for the year		14,400
Less: drawings		(9,100)
Capital at 31 December 2019		29,300
Current liabilities
Trade payables		5,300
Total capital and liabilities		34,600

Check with the accounting equation: net assets rose from 24,000 to 29,300, an increase of 5,300 = profit 14,400 − drawings 9,100.

6 Test your knowledge

Two quick checks before you move on: work through the flashcards to fix this chapter’s terms and definitions, then sit the objective questions for exam-style practice. Both mark themselves and explain the answers as you go.

Answer the questions one at a time. Your progress is saved so you can leave and come back.

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