The previous topic found the total profit from the change in net assets. To prepare a full statement of profit or loss, the accountant needs the lines inside it: sales, purchases, cost of sales and expenses. These are usually not recorded, but they can be rebuilt.
The tools are Memorandum accounts, which are working ledgers used only to find a missing figure, and Cost structures, which use the gross profit margin or mark-up to find cost of sales or lost inventory.
This topic covers those tools and ends with a complete question that combines them. It follows the statement of affairs and the capital method, and it uses the margin and mark-up conversions that were introduced in the ratio topic. It appears as a 20-mark question in several past diets. The next topic covers not-for-profit accounts.
In 30 seconds
Use a Receivables memorandum account to find sales: opening receivables + sales = money received + bad debts + closing receivables, so sales is the balancing figure. Use a Payables memorandum account to find purchases the same way. Use a Cash and bank memorandum account to find a missing figure such as drawings.
Use Margin (profit as a percentage of sales) or Mark-up (profit as a percentage of cost) to find cost of sales or sales. A mark-up of 25% is a margin of 25 ÷ 125 = 20%. Missing inventory = (opening inventory + purchases − cost of sales) − inventory that is left. Then prepare the statements and check that profit agrees with the net assets method.
Memorandum control accounts
A memorandum account is not part of the ledger. It is a working used to calculate a missing figure.
Sales. If sales were not recorded, you may know receivables at the start (from last year’s statement) and at the end (from unpaid invoices), the money banked from customers, and bad debts. Sales are the balancing figure. Cash sales that were not banked can be found from the increase in cash in hand plus any expenses paid in cash from the till.
The example: receivables ₦650 at the start and ₦720 at the end, bad debt written off ₦800, money banked ₦58,600 and cash sales not banked ₦300.
| Receivables memorandum account | ₦ | ₦ | |
|---|---|---|---|
| Opening balance | 650 | Money banked | 58,600 |
| Sales (balancing figure) | 59,770 | Cash sales not banked | 300 |
| Bad debt written off | 800 | ||
| Closing balance | 720 | ||
| Total | 60,420 | Total | 60,420 |
In a vertical form: opening receivables 650, less closing 720, is an increase of 70 (subtract), then add money banked 58,600, cash sales 300 and bad debts 800: sales = 58,600 + 300 + 800 + 720 − 650 = ₦59,770. Receivables of ₦2,400 at the start and ₦1,800 at the end, with ₦12,500 banked and bad debts of ₦200, give sales of 12,500 + 200 + 1,800 − 2,400 = ₦12,100.
Purchases. The same approach applies to payables: opening payables + purchases = payments + closing payables. With payables of ₦1,200 at the start and ₦1,800 at the end, and ₦18,700 paid to suppliers, purchases = 18,700 + 1,800 − 1,200 = ₦19,300. With payables of ₦1,400 and ₦1,900, and ₦11,300 paid, purchases are 11,300 + 1,900 − 1,400 = ₦11,800.
Cash and bank memorandum accounts
A cash and bank memorandum account lists all receipts and payments and the opening and closing balances. It may reveal a missing figure such as drawings, because the owner often takes cash without recording it. Example. Opening cash in hand was ₦100 and bank ₦2,400. Receipts were ₦51,700. Payments were ₦38,200 to suppliers and ₦3,400 to employees. Closing cash was ₦150 and bank ₦5,200. Total on the debit side is 100 + 2,400 + 51,700 = 54,200.
Known payments and closing balances are 38,200 + 3,400 + 150 + 5,200 = 46,950, so drawings are the balancing figure, ₦7,250.
Margin, mark-up and cost structures
A business usually has a standard gross profit. It may be quoted as a Margin (percentage of sales) or a Mark-up (percentage of cost). Selling price is cost plus gross profit, so if the mark-up is 25%, cost is 100 and sales 125. The gross profit is then 25 ÷ 125 = 20% of sales. To convert: margin = mark-up ÷ (100 + mark-up), and mark-up = margin ÷ (100 − margin). A 20% margin is a 25% mark-up, and a margin of 40% is a mark-up of 40 ÷ 60 = 66.7%.
Practice table. Fill in the missing figures using cost of sales = opening inventory + purchases − closing inventory.
| ₦ | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Sales | 8,000 | 15,000 | 10,000 | 20,000 |
| Opening inventory | 1,000 | 2,000 | 1,000 | 2,000 |
| Purchases | 5,000 | 8,700 | 7,500 | 15,000 |
| Closing inventory | (1,200) | (1,500) | (500) | (2,000) |
| Cost of sales | 4,800 | 9,200 | 8,000 | 15,000 |
| Gross profit | 3,200 | 5,800 | 2,000 | 5,000 |
| Margin on sales | 40% | 38.7% | 20% | 25% |
| Mark-up on cost | 66.7% | 63% | 25% | 33.3% |
More than one cost structure. A company has sales of ₦1,000. Sixty per cent is type A at a mark-up of 20%. Type B has a margin of 30% and a cost of ₦154. Total gross profit is ₦184. Type A sales are 600, so cost is 600 ÷ 1.2 = 500 and gross profit 100. Type B sales are 154 ÷ 0.7 = 220, gross profit 66. Type C sales are 1,000 − 600 − 220 = 180, gross profit is 184 − 100 − 66 = 18, cost 162 and margin 10%.
Set up a table of sales, cost and profit for each product and fill in the easy figures first.
Missing inventory
If inventory is lost in a fire or stolen, find what it should have been and deduct what remains. Example. A warehouse fire at the year end leaves inventory with a cost of ₦2,000. Opening inventory was ₦16,000, purchases ₦115,000 and sales ₦140,000, and the mark-up is 25%. Gross profit = 20% × 140,000 = 28,000, so cost of sales = 112,000. Inventory that should be there = 16,000 + 115,000 − 112,000 = 19,000. Lost in the fire = 19,000 − 2,000 = ₦17,000.
Practice question. Inventory at 1 March was ₦127,000, March purchases ₦253,000 and March sales ₦351,000, at a standard gross profit of 30% of sales. Inventory in good condition at 31 March was ₦76,000. Cost of sales = 70% × 351,000 = 245,700. Goods available are 127,000 + 253,000 = 380,000. Lost = 380,000 − 76,000 − 245,700 = ₦58,300. Closing inventory from a mark-up of 40% on cost: sales 98,000 give cost of sales 98,000 ÷ 1.4 = 70,000, so closing inventory = 5,000 + 71,200 − 70,000 = ₦6,200.
A complete question
A full question usually gives a bank summary, balances at two dates and some adjustments. The order is:
- Opening capital from the opening assets and liabilities.
- Sales from the receivables memorandum account, adding cash sales.
- Purchases from the payables memorandum account, then cost of sales.
- Expenses adjusted for accruals and prepayments, plus depreciation.
- The statement of profit or loss.
- The statement of financial position, with closing capital = opening capital + profit − drawings.
Question (Alji Binuyo). Credit sales are 5,600 + sales = 36,584 + 7,860, so credit sales are ₦38,844,000 and total sales 38,844 + 12,476 = ₦51,320,000. Purchases are 21,149 + 6,900 − 6,380 = 21,669, cost of sales 4,118 + 21,669 − 6,278 = 19,509 and gross profit 31,811. Electricity is 246 + 172 − 140 = 278 and rent and rates are 84 + 712 − 120 = 676. Depreciation is 10% of the cost of ₦15,000, which is 1,500. Administration expenses total 22,788, so profit is ₦9,023,000. Opening capital is 21,750 − 6,520 = 15,230, so closing capital is 15,230 + 9,023 − 1,800 = 22,453, and the statement of financial position totals ₦29,525,000.
The ideas in more depth
Slips in the question. The question gives non-current assets with a “cost of ₦150,000,000”, but with a carrying amount of ₦10,600,000 and accumulated depreciation of ₦4,400,000 the cost is ₦15,000,000, and 10% of that is the depreciation of ₦1,500,000 that the solution uses. The additional information also shows opening payables as ₦6,300, but the working uses ₦6,380, and only ₦6,380 makes the statement of financial position balance.
The sales note says “₦51,000,000” where the statement correctly shows ₦51,320,000, and the total of liabilities in the capital working shows ₦7,780 where the correct total is 6,380 + 140 = ₦6,520. The profit, assets and capital in the solution are right.
Background. A cross-check is to compare the profit with the profit found from the change in net assets. Any difference signals an error or an unrecorded item. Discounts allowed and received go through the receivables and payables memorandum accounts as well as the money banked or paid, and bad debts reduce receivables.
Worked example: Lekki Provision Store
Scenario. Lekki Provision Store keeps no sales or purchases records. Receivables were ₦120,000 at the start and ₦150,000 at the end. Customers paid ₦1,400,000, bad debts of ₦10,000 were written off and discounts of ₦5,000 were allowed. Cash sales were ₦80,000. Payables were ₦90,000 and ₦110,000. ₦900,000 was paid to suppliers and discounts received were ₦6,000. Inventory was ₦60,000 at the start and ₦70,000 at the end. The opening bank balance was ₦20,000 and the closing balance ₦50,000.
Bank payments for expenses were ₦330,000. Required: sales, purchases, gross profit and drawings.
- Credit sales.
150,000 + 1,400,000 + 10,000 + 5,000 − 120,000 = 1,445,000.
With cash sales of 80,000, total sales = ₦1,525,000. - Purchases.
900,000 + 6,000 + 110,000 − 90,000 = ₦926,000. - Cost of sales and gross profit.
60,000 + 926,000 − 70,000 = 916,000.
Gross profit = 1,525,000 − 916,000 = ₦609,000, a margin of 39.9%. - Drawings.
Bank: opening 20,000 + customers 1,400,000 = 1,420,000.
Payments: suppliers 900,000, expenses 330,000 and closing 50,000, a total of 1,280,000.
Drawings = ₦140,000. - Fire at another store.
Mark-up is 30%, so margin is 30 ÷ 130 = 23.1%.
With sales of 520,000, cost of sales is 520,000 ÷ 1.3 = 400,000.
If inventory at the start was 90,000 and purchases 400,000, the inventory that should remain is 90,000, so if 25,000 survived, 65,000 was lost.
Common mistakes in the exam
- Using the margin as if it were a mark-up, or the reverse.
- Using sales as the total of money banked, forgetting opening and closing receivables.
- Forgetting bad debts and discounts allowed in the receivables account, and discounts received in the payables account.
- Leaving out cash sales that were not banked.
- Finding purchases but not cost of sales.
- Not adding unpaid expenses and removing prepayments when finding the expense for the year.
- Taking the lost inventory as the whole amount of the opening inventory, rather than the balancing figure.
- Forgetting drawings when preparing the closing capital.
Quick revision
- Sales: opening receivables + sales = receipts + bad debts + closing receivables.
- Purchases: opening payables + purchases = payments + closing payables.
- Margin = mark-up ÷ (100 + mark-up). Mark-up = margin ÷ (100 − margin).
- Cost of sales = opening inventory + purchases − closing inventory.
- Lost inventory = expected closing inventory − inventory remaining.
Practice questions
These are original questions in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one first.
Section A style: multiple choice
Question 1. Receivables were ₦650 at the start and ₦720 at the end. ₦58,600 was banked from customers, a bad debt of ₦800 was written off, and cash sales of ₦300 were not banked. Sales are:
- ₦58,500
- ₦59,470
- ₦59,770
- ₦60,420
Show the answer
C. 58,600 + 300 + 800 + 720 − 650 = 59,770.
Question 2. Payables were ₦1,200 at the start and ₦1,800 at the end, and ₦18,700 was paid to suppliers. Purchases are:
- ₦19,300
- ₦18,100
- ₦20,500
- ₦17,500
Show the answer
A. 18,700 + 1,800 − 1,200 = 19,300.
Question 3. A mark-up of 25% on cost is a margin on sales of:
- 25%
- 33.3%
- 75%
- 20%
Show the answer
D. 25 ÷ 125 = 20%.
Question 4. A margin of 20% on sales is a mark-up on cost of:
- 20%
- 25%
- 80%
- 16.7%
Show the answer
B. Profit 20 on a cost of 80 is 25%.
Question 5. Sales are ₦140,000 and the mark-up is 25%. Gross profit is:
- ₦35,000
- ₦25,000
- ₦28,000
- ₦32,000
Show the answer
C. Margin is 20%, so 20% × 140,000 = 28,000.
Question 6. Cost of sales is ₦112,000, opening inventory ₦16,000 and purchases ₦115,000. The inventory that should be on hand is:
- ₦19,000
- ₦3,000
- ₦131,000
- ₦243,000
Show the answer
A. 16,000 + 115,000 − 112,000 = 19,000.
Question 7. Sales are ₦351,000 at a gross margin of 30%. Cost of sales is:
- ₦105,300
- ₦456,300
- ₦351,000
- ₦245,700
Show the answer
D. 70% × 351,000 = 245,700.
Question 8. In a receivables memorandum account, the balancing figure is normally:
- Cash received
- Sales
- Bad debts
- Opening receivables
Show the answer
B. Sales are the unknown when receipts, bad debts and balances are known.
Question 9. A missing figure for the owner’s drawings is normally found from:
- A cash and bank memorandum account
- The receivables account
- The trial balance
- The appropriation account
Show the answer
A. Drawings are the balancing figure in the cash and bank summary.
Question 10. Opening inventory is ₦5,000, purchases ₦71,200 and sales ₦98,000, with a mark-up of 40% on cost. Closing inventory is:
- ₦71,200
- ₦70,000
- ₦6,200
- ₦5,000
Show the answer
C. Cost of sales = 98,000 ÷ 1.4 = 70,000. Closing = 5,000 + 71,200 − 70,000 = 6,200.
Section B style: written questions
Question 11 (10 marks). (a) Explain how sales are found from a receivables memorandum account. (5 marks) (b) Explain how purchases are found from a payables memorandum account. (5 marks)
Question 12 (20 marks). Gusau Traders keeps no books. At the start of the year it had equipment (carrying amount) ₦200,000, inventory ₦70,000, receivables ₦140,000 and bank ₦30,000, and payables of ₦85,000. At the end of the year inventory was ₦90,000, receivables ₦160,000, bank ₦55,000 and payables ₦95,000. Customers paid ₦1,250,000 and cash sales banked were ₦150,000. ₦820,000 was paid to suppliers and ₦310,000 for expenses. Bad debts written off were ₦8,000, discounts allowed ₦4,000 and discounts received ₦5,000. Depreciation is ₦20,000. Drawings are not known.
(a) Calculate sales and purchases. (6 marks) (b) Calculate the drawings. (3 marks) (c) Prepare the statement of profit or loss. (7 marks) (d) Prepare the statement of financial position. (4 marks)
A further written question
Question 13 (10 marks). A business has sales of ₦2,000. Product P is 1,000 of sales at a mark-up of 25%. Product Q has sales of 600 at a margin of 40%. Product R is the rest of the sales. Total gross profit is ₦560. Calculate the sales, cost of sales and gross profit for each product, and the margin on product R. (10 marks)
Model answers
Show the model answer to Question 11
(a) Set up a receivables account. On the debit side put the opening balance and sales. On the credit side put the money received from customers, bad debts and discounts allowed, and the closing balance. Sales are the balancing figure: sales = cash received + bad debts + discounts + closing receivables − opening receivables. Add cash sales to find total sales. (b) Set up a payables account.
On the credit side put the opening balance and purchases. On the debit side put the cash paid to suppliers, discounts received and the closing balance. Purchases are the balancing figure: purchases = cash paid + discounts + closing payables − opening payables.
Show the model answer to Question 12
(a)
- Credit sales.
160,000 + 1,250,000 + 8,000 + 4,000 − 140,000 = 1,282,000. - Total sales.
1,282,000 + 150,000 = ₦1,432,000. - Purchases = 820,000 + 95,000 + 5,000 − 85,000 = ₦835,000.
(b)
- Bank.
30,000 + 1,250,000 + 150,000 = 1,430,000. - Payments 820,000 + 310,000 + closing 55,000 = 1,185,000.
- Drawings = ₦245,000.
(c)
- Sales 1,432,000.
- Cost of sales 70,000 + 835,000 − 90,000 = 815,000.
- Gross profit 617,000.
- Expenses 310,000 + depreciation 20,000 + bad debts 8,000 + discounts allowed 4,000 − discounts received 5,000 = 337,000.
- Profit ₦280,000.
(d)
- Opening capital.
(200,000 + 70,000 + 140,000 + 30,000) − 85,000 = 355,000. - Closing capital.
355,000 + 280,000 − 245,000 = 390,000. - Assets: equipment 180,000, inventory 90,000, receivables 160,000, bank 55,000, total 485,000.
- Payables 95,000.
- Capital 390,000 + payables 95,000 = 485,000.
Show the model answer to Question 13
P: sales 1,000, cost 1,000 ÷ 1.25 = 800, gross profit 200. Q: sales 600, gross profit 40% = 240, cost 360. R: sales 2,000 − 1,000 − 600 = 400. Gross profit = 560 − 200 − 240 = 120, cost 280. Margin on R = 120 ÷ 400 = 30%. Totals: sales 2,000, cost of sales 1,440, gross profit 560.
Pathfinder on Incomplete records: margins, control accounts and missing figures
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
From the previous syllabus. A trader keeps single-entry books. Gives opening balances and cash book information and asks for the receivables control account (2 marks), the payables control account (2 marks), the opening capital (2 marks), the statement of profit or loss (8 marks) and the statement of financial position (6 marks).
Revise first: Memorandum control accounts
From the previous syllabus. A trader kept only a record of takings and payments, with cash banked and cheques drawn for business and private use. Asks for the cash book (6½ marks), the payables control account (2½ marks), the receivables control account (2 marks), the statement of profit or loss (5 marks) and the statement of financial position (4 marks).
Revise first: Cash and bank memorandum accounts
From the previous syllabus. A pharmacy owner has a summary of her bank account for the year. Asks for sales and purchases (10 marks), the statement of profit or loss (5 marks) and the statement of financial position (5 marks).
Revise first: A complete question
From the previous syllabus. Asks for the sales from a gross margin of 40%, the profit on a sale at a 20% mark-up, and the gross profit from a profit margin of 5%.
Revise first: Margin, mark-up and cost structures
Expect an item on finding sales or purchases from a control account, on converting a mark-up to a margin, or on inventory lost in a fire or theft. Check Section A of every diet you practise.
Revise first: Missing inventory
Source: ICAN Pathfinder, Financial Accounting. Diets covered: November Diet, 2014, May Diet, 2015, November Diet, 2016, May Diet, 2019, May Diet, 2021 and May Diet, 2022. All are on the previous syllabus. Diets before November 2014, and November Diet, 2024 onwards, are not covered here.
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