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Formulae Quiz

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Formulae Quiz

Although students are supplied with a formulae sheet in the examination (both Paper 1 and Paper 2), please note that not all equations / formulae in the IB Business Management course are included in this formulae sheet (see pages 87 and 88 of the official IB Business Management guide, May 2017).

Can you state at least 10 quantitative techniques / terms from the syllabus that are included in the formulae sheet?

The following formulae are included in the formula sheet for students in the final examinations (both Paper 1 and Paper 2).

Formulae for ratio analysis (SL/HL)

Profitability ratios (SL/HL): Gross profit margin (GPM) and Net profit margin (NPM)

G r o s s space p r o f i t space m a r g i n space equals fraction numerator G r o s s space p r o f i t over denominator S a l e s space r e v e n u e end fraction cross times 100

N e t space p r o f i t space m a r g i n space equals fraction numerator N e t space p r o f i t space left parenthesis b e f o r e space i n t e r e s t space a n d space t a x right parenthesis over denominator S a l e s space r e v e n u e end fraction cross times 100

Liquidity ratios (SL/HL): Current ratio and Acid test (quick) ratio

C u r r e n t space r a t i o space equals fraction numerator C u r r e n t space a s s e t s over denominator C u r r e n t space l i a b i l i t i e s end fraction

A c i d space t e s t space r a t i o equals fraction numerator C u r r e n t space a s s e t s space minus S t o c k s over denominator C u r r e n t space l i a b i l i t i e s end fraction

Efficiency ratio (SL/HL): Return on capital employed (ROCE)

Capital employed = Loan capital (also known as long-term liabilities) + Share capital + Accumulated retained profit

R O C E space equals fraction numerator N e t space p r o f i t space left parenthesis b e f o r e space i n t e r e s t space a n d space t a x right parenthesis over denominator C a p i t a l space e m p l o y e d end fraction cross times 100

Efficiency ratios (HL only): Stock turnover (days or times), Debtor days, Creditor days, and Gearing ratio

There are two ways to measure the stock turnover ratio (by number of days or number of times):

S t o c k space t u r n o v e r space r a t i o space left parenthesis n u m b e r space o f space d a y s right parenthesis space equals fraction numerator C o s t space o f space g o o d s space s o l d over denominator A v e r a g e space s t o c k end fraction

S t o c k space t u r n o v e r space left parenthesis n u m b e r space o f space d a y s right parenthesis space equals fraction numerator A v e r a g e space s t o c k over denominator C o s t space o f space g o o d s space s o l d end fraction cross times 365

where cost of goods sold (COGS) is an approximation of total credit purchases by the business, and where

A v e r a g e space s t o c k space equals fraction numerator O p e n i n g space s t o c k space plus thin space C l o sin g space s t o c k over denominator 2 end fraction

D e b t o r space d a y s space r a t i o space left parenthesis n u m b e r space o f space d a y s right parenthesis space equals fraction numerator D e b t o r s over denominator T o t a l space s a l e s space r e v e n u e end fraction cross times 365

where total sales revenue is an approximation of the firm's total credit sales.

C r e d i t o r space d a y s space r a t i o space left parenthesis n u m b e r space o f space d a y s right parenthesis space equals fraction numerator C r e d i t o r s over denominator C o s t space o f space g o o d s space s o l d end fraction cross times 365

where the cost of goods sold (COGS) is an approximation of the firm's total credit purchases.

G e a r i n g space r a t i o equals fraction numerator L o a n space c a p i t a l over denominator C a p i t a l space e m p l o y e d end fraction cross times 100

Where the firm's capital employed = Loan capital (or long-term liabilities) + Share capital + Accumulated retained profit.

Other formulae (SL/HL)

Investment appraisal (SL/HL): Average rate of return (ARR)

A v e r a g e space r a t e space o f space r e t u r n space left parenthesis A R R right parenthesis equals fraction numerator left parenthesis t o t a l space r e t u r n s space c a p i t a l space cos t right parenthesis space divided by space y e a r s space o f space u s e over denominator C a p i t a l space cos t end fraction cross times 100

Investment appraisal (HL): Net present value (NPV)

N e t space p r e s e n t space v a l u e space left parenthesis N P V right parenthesis space equals space begin inline style sum for p r e s e n t space v a l u e s space o f space r e t u r n of end style open square brackets negative o r i g i n a l space cos t close square brackets

Capacity utilization and productivity (HL only)

C a p a c i t y space u t i l i z a t i o n space r a t e equals fraction numerator A c t u a l space o u t p u t over denominator P r o d u c t i v e space c a p a c i t y end fraction cross times 100

P r o d u c t i v i t y space r a t e space equals fraction numerator T o t a l space o u t p u t over denominator T o t a l space i n p u t end fraction

Note: The Guide states the following formula for calculating the productivity rate (although in reality it is highly uncomon to  express labour productivity as a percentage figure).

P r o d u c t i v i t y space r a t e space equals fraction numerator T o t a l space o u t p u t over denominator T o t a l space i n p u t end fraction cross times 100

Also, as stated in the Guide, on page 89, a discount table will be provided for HL students within the examination paper when required to answer the question, i.e. if and only if there is a question that requires students to calculate the NPV.

A copy of the discount table is provided here for reference only. The relevant figures will be provided as part of the question and exam paper should this topic come up in an actual HL examination.

Years

Discount rate

4%

6%

8%

10%

20%

1

0.9615

0.9434

0.9259

0.9091

0.8333

2

0.9246

0.8900

0.8573

0.8264

0.6944

3

0.8890

0.8396

0.7938

0.7513

0.5787

4

0.8548

0.7921

0.7350

0.6830

0.4823

5

0.8219

0.7473

0.6806

0.6209

0.4019

6

0.7903

0.7050

0.6302

0.5645

0.3349

7

0.7599

0.6651

0.5835

0.5132

0.2791

8

0.7307

0.6271

0.5403

0.4665

0.2326

9

0.7026

0.5919

0.5002

0.4241

0.1938

10

0.6756

0.5584

0.4632

0.3855

0.1615

Now, can you state at least 10 quantitative techniques / terms from the syllabus that are not included in the formulae sheet?

In fact, you will find that there are actually more quantitative techniques / terms / equations in the IB Business Management syllabus that are not included in the formulae sheet than there are actually included on pages 87 - 88 of the syllabus guide. Do warn students about this as they may become overly reliant on the published formulae sheet in their exams.

Take a look here for some examples of quantitative techniques / terms from the IB syllabus that are not included in the formulae sheet. HL examples are shown in italics.

  1. 4-part moving averages

  2. Absenteeism rate

  3. Average costs (AC)

  4. Average fixed costs (AFC)

  5. Average variable costs (AVC)

  6. Break-even output (or break-even quantity)

  7. Buffer stock (minimum stock level)

  8. Capital employed

  9. Closing balance (cash flow)

  10. Contribution per unit (or unit contribution)

  11. Cost of goods sold (COGS)

  12. Cost of sales (COS)

  13. Cost to buy (CTB)

  14. Cost to make (CTM)

  15. Current assets

  16. Current liabilities

  17. Declining balance depreciation

  18. Gross profit

  19. Labour productivity

  20. Labour turnover rate*

  21. Lead times

  22. Margin of safety (or safety margin)

  23. Market share

  24. Net assets

  25. Net cash flow (NCF)

  26. Net current assets

  27. Net profit

  28. Net profit before interest and tax (NPBIT)

  29. Opening balance (cash flow forecasts)

  30. Payback period (PBP)

  31. Profit

  32. Reducing-balance annual depreciation

  33. Re-order level (stock control)

  34. Re-order quantity (stock control)

  35. Sales forecasting - Seasonal, cyclical and random variations

  36. Sales revenue (or total revenue)

  37. Straight-line annual depreciation

  38. Target profit

  39. Target price

  40. Total costs (TC)

  41. Total fixed costs (TFC)

  42. Total variable costs (TVC)

  43. Unit contribution (or contribution per unit)

  44. Variances analysis

  45. Working capital.

* Labour turnover is an AO2 in the DP Business Management syllabus, but in reality it is more difficult/less meaningful to teach this without referring to how it is calculated. The labour turnover rate (AO4) has been included in the new syllabus (first teaching in 2022).

 Top tip!

In addition to the above formulae, not included in the formulae sheet for the final exams, students must ensure they also learn how to construct the following, using the format prescribed by the IB:

Refer to pages 90 - 91 in the syllabus guide for further details.

Take the Dynamic Quiz below to see how many of the formulae your students know...

What is the formula for calculating the closing balance in a cash flow?

The closing balance is the amount of cash in the business at the end of a reporting trading period (such as the end of the week or end of the month). Hence, the correct formula is Closing balance = Opening balance + Cash inflow - Cash outflow, i.e. Opening balance + Net cash flow.

What is the formula for calculating straight-line annual depreciation? (HL Only)

The straight-line annual depreciation method reduces the value of an asset by a pre-determined fixed amount. Hence the formula is the Purchase Cost ÷ Useful lifespan to get the annual amount of depreciation

What is the formula for calculating sales revenue?

Sales revenue is the money a firm earns from selling its goods and/or services. Hence, the formula is Unit price × Quantity sold (or Price × Quantity)

What is the formula for calculating Average Fixed Cost?

The average fixed cost (AFC) is simply the total fixed costs of the firm spread over the number of units of output, so is calculated by using the formula Total Fixed Costs ÷ Output level

What is the formula for calculating capital employed?

Capital employed refers to the sum of internal and external sources of finance for a business. Hence, this is comprised of loan capital (external sources) plus share capital and retained profits (both internal sources)

What is the formula for determining the cost to make? (HL Only)

The cost to make refers to how much a firm must pay if it produces goods for which it intends to sell to  consumers (rather than the costs of buying the goods to resell to customers). The formula is: Cost to make = TFC + (AVC × Q) or TFC + TVC, where:

TFC = Total fixed costs

AVC = Average variable costs

Q = Quantity

TFC = Total fixed costs, and

TVC = Total variable costs

What is the formula for calculating a firm's cost of sales (COS)?

The cost of sales (COS) are the direct costs of trading, so are calculated by using the formula: Opening stock + Purchases – Closing stock.

What is the formula for calculating gross profit?

Gross profit is also referred to as trading profit, i.e. the difference between sales revenue and the direct costs of production (cost of goods sold)

What is the formula for calculating the net cash flow?

The net cash flow (NCF) is simply the difference between cash inflow and cash outflow per time period, usually per month.

What is the formula for calculating labour productivity?

Labour productivity is the output per worker, so is calculating by the formua total output / number of workers.

What is the formula for calculating net current assets? (HL Only)

As the name suggests, the term net current assets is the difference between current assets and current liabilities. Hence the correct formula is Current assets – Current liabilities.

What is the formula for determining break-even?

Break-even is determined by the formula Total fixed costs ÷ (P – AVC) x Quantity, i.e. Total fixed costs ÷ Unit contribution

What is the formula for calculating current assets?

Current assets are items of value owned by the business, intended for trading purposes (unlike fixed assets). These comprise of stocks (inventory), cash, and debtors

What is the formula for calculating current liabilities?

Current liabilities are sums of money owed within the (current) tax year, i.e. Overdraft + Tax + Dividends + Creditors

What is the formula for calculating the reducing-balance annual depreciation? (HL Only)

The reducing-balance annual depreciation method reduces the value of an asset by a predetermined percentage each year. Hence, it can be calculated using the formula Purchase cost – Cumulative depreciation (or the Historic cost – Cumulative depreciation).

What is the formula for calculating net current assets?

As the name suggests, the term net current assets is the difference between current assets and current liabilities. Hence the correct formula is Current assets – Current liabilities.

What is the formula for calculating the margin of safety?

The safety margin is the difference between a firm's actual sales volume (how much it sells) and how much it needs to sell in order to break even). Therefore, the correct formula is Margin of safety = Level of demand – Break-even quantity.

What is the formula for calculating profit?

Profit (before interest and tax) is the financial surplus of a firm after all its direct costs (or cost of sales) and indirect costs (expenses) have been paid, i.e., Profit = Gross profit – Expenses.

What is the formula for determining the cost to buy? (HL Only)

The cost to make refers to how much a firm must pay if it purchases products which it intends to resell to the consumer (rather than the costs of producing the product in-house). The formula is: Cost to buy = Price × Quantity.

What is the formula for calculating profit?

Profit is the positive difference between a firm's sales revenue (or Total revenue) and its costs of production (or Total costs)

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