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7. Formulas and ratios

Syllabus
0264–2027–2028
Section
7
Level
—

7.1. Marketing

Syllabus
0264–2027–2028
Topic
7.1
Level
—

Calculating and interpreting market share

Market share is the percentage of total market sales revenue earned by one business. It compares the business with the whole market over the same period and using the same currency.

\text{Market share (%)}=\frac{\text{sales revenue of the business}}{\text{total sales revenue for the whole market}}\times100

If a business earns 36millioninamarketworth36 million in a market worth120 million, its market share is 36m÷36m ÷120m × 100 = 30%. The units cancel because both revenue figures use millions of dollars; the answer is a percentage.

\text{Business sales revenue}=\frac{\text{market share}}{100}\times\text{total market sales revenue}

For a 30% share of a 120millionmarket:30÷100×120 million market: 30 ÷ 100 ×120m = $36m. A market share of 30% does not mean sales grew by 30%; it means the business earns 30% of the market's total sales revenue for that period.

7.2. Production

Syllabus
0264–2027–2028
Topic
7.2
Level
—

Calculate labour productivity

labour productivity=output per periodnumber of employeeslabour\ productivity=\frac{output\ per\ period}{number\ of\ employees}

If 24 employees produce 9,600 units in a month, labour productivity is 400 units per employee per month. Always state both the output unit and the time period.

Compare like with like. Higher productivity can lower labour cost per unit and increase capacity, but may reflect machinery, product mix or working hours as well as employee effort.

Productivity is output per worker, not total output and not profit. Do not call a workforce less productive merely because it is smaller.

Calculate total variable cost

total variable cost=variable cost per unit×number of unitstotal\ variable\ cost=variable\ cost\ per\ unit\times number\ of\ units

At 6variablecostperunitandoutputof2,500units,totalvariablecostis6 variable cost per unit and output of 2,500 units, total variable cost is15,000. If output doubles and unit variable cost is unchanged, total variable cost doubles.

Use units produced when the cost is incurred in production. Total variable cost is not total cost because fixed costs have not yet been added.

Find variable cost per unit

variable cost per unit=total variable costnumber of unitsvariable\ cost\ per\ unit=\frac{total\ variable\ cost}{number\ of\ units}

If total variable cost is 18,000for3,000units,variablecostperunitis18,000 for 3,000 units, variable cost per unit is6. This reverses the total-variable-cost calculation and gives a cost for one unit.

The result helps calculate contribution, forecast cost at another output level and compare production choices, provided the variable cost per unit is expected to remain stable.

Do not divide total cost by units: that gives average cost and includes fixed cost. Match the total variable cost and output to the same period.

Build total cost

total cost=total fixed costs+total variable coststotal\ cost=total\ fixed\ costs+total\ variable\ costs

With fixed costs of 40,000andtotalvariablecostsof40,000 and total variable costs of30,000, total cost is $70,000. As output changes, the variable part changes while fixed costs normally stay unchanged within the relevant range.

Add totals to totals. Do not add fixed cost to variable cost per unit unless both have first been expressed on the same per-unit basis.

Calculate average cost

average cost=total costnumber of unitsaverage\ cost=\frac{total\ cost}{number\ of\ units}

A total cost of 72,000for6,000unitsgivesanaveragecostof72,000 for 6,000 units gives an average cost of12 per unit. If output rises while fixed cost is spread over more units, average cost may fall.

Compare average cost with selling price to understand the cost margin per unit, and compare periods only after checking changes in scale, product mix and input prices.

Average cost includes both fixed and variable cost. It is not the same as variable cost per unit and it does not by itself give profit per unit.

Calculate break-even output

break ⁣− ⁣even output=fixed costscontribution per unitbreak\! -\! even\ output=\frac{fixed\ costs}{contribution\ per\ unit}

With fixed costs of 48,000andcontributionof48,000 and contribution of12 per unit, break-even output is 4,000 units. At that output, total revenue equals total cost and profit is zero.

A higher selling price or lower variable cost raises contribution and lowers break-even output; higher fixed cost raises it. Use the result to test whether forecast demand is sufficient.

Break-even output is not a sales target that guarantees success. The model assumes stable price, unit variable cost and fixed cost, and that sales equal output.

Find contribution per unit

contribution per unit=selling price per unit−variable cost per unitcontribution\ per\ unit=selling\ price\ per\ unit-variable\ cost\ per\ unit

A product sold for 25withvariablecostof25 with variable cost of15 contributes $10 per unit. Each unit first contributes toward fixed costs; after total contribution covers fixed costs, further contribution becomes profit.

Contribution supports break-even calculations and short-run product decisions. Compare contribution with any capacity constraint and with the effect on demand, quality and longer-term positioning.

Contribution is not profit because fixed costs still have to be paid. A positive contribution does not automatically mean the whole business is profitable.

Calculate the margin of safety

margin of safety=actual sales−break ⁣− ⁣even salesmargin\ of\ safety=actual\ sales-break\! -\! even\ sales

If actual sales are 5,600 units and break-even sales are 4,000, the margin of safety is 1,600 units. Sales could fall by 1,600 units before the business begins making a loss, under the model’s assumptions.

A larger positive margin provides more protection against a demand fall. A zero margin means break-even; a negative result means current sales are below break-even.

Use the same unit and period for actual and break-even sales. Margin of safety is a volume difference, not profit and not automatically a percentage.

7.3. Business finance

Syllabus
0264–2027–2028
Topic
7.3
Level
—

Calculate revenue

revenue=selling price per unit×number of units soldrevenue=selling\ price\ per\ unit\times number\ of\ units\ sold

Selling 3,200 units at 15eachproducesrevenueof15 each produces revenue of48,000. Use units sold, not units produced, and keep the price and sales volume in the same period.

Revenue is money earned from sales before costs are deducted. It is not profit and it is not necessarily the same as cash received during the period.

Calculate gross profit

gross profit=revenue−cost of salesgross\ profit=revenue-cost\ of\ sales

Revenue of 90,000andcostofsalesof90,000 and cost of sales of54,000 give gross profit of $36,000. Gross profit shows what remains after the direct cost of the goods sold, before operating expenses.

A change can come from selling price, sales mix, purchase prices, production efficiency or inventory valuation. Compare gross profit margin as well as the absolute amount.

Do not deduct all business expenses here. Rent, administration and other operating expenses are deducted later to reach profit.

Calculate profit

profit=total revenue−total costs=gross profit−expensesprofit=total\ revenue-total\ costs=gross\ profit-expenses

If gross profit is 36,000andoperatingexpensesare36,000 and operating expenses are21,000, profit is $15,000. The equivalent revenue-minus-total-cost route must give the same result when the figures use the same definitions and period.

Profit rewards risk and can finance growth, but its meaning improves when compared with revenue or capital employed. A larger business may earn more profit yet have weaker profitability.

Profit is not cash flow: credit sales, inventory purchases, loan repayments and non-cash expenses can make cash movement different.

Calculate working capital

working capital=current assets−current liabilitiesworking\ capital=current\ assets-current\ liabilities

Current assets of 70,000andcurrentliabilitiesof70,000 and current liabilities of46,000 give working capital of $24,000. This is the short-term resource buffer available within the operating cycle.

Negative working capital may indicate payment pressure. Very high working capital may indicate excess inventory, slow receivables or idle cash, so compare composition, timing and industry practice.

Working capital is a balance-sheet difference, not cash, revenue or profit. Positive working capital does not guarantee immediate liquidity.

Calculate profit margin

profit margin=profitrevenue×100profit\ margin=\frac{profit}{revenue}\times100

Profit of 18,000fromrevenueof18,000 from revenue of120,000 gives a profit margin of 15%. The business retains 15 cents of profit from each dollar of revenue after all relevant costs.

A fall may reflect weaker prices, higher cost of sales or rising expenses. Compare periods and competitors, then identify the specific cause before recommending action.

Use profit, not gross profit, in the numerator. A higher margin can coexist with lower total profit if sales volume falls sharply.

Calculate gross profit margin

gross profit margin=gross profitrevenue×100gross\ profit\ margin=\frac{gross\ profit}{revenue}\times100

Gross profit of 42,000onrevenueof42,000 on revenue of140,000 gives a gross profit margin of 30%. This leaves 30% of revenue to cover operating expenses and profit.

A lower margin may result from discounts, higher input cost, waste or a different sales mix. It focuses on the relationship between sales and cost of sales before other expenses.

Do not confuse gross profit margin with profit margin. A stable gross margin does not prevent final profit from falling when operating expenses rise.

Calculate return on capital employed

ROCE=profitcapital employed×100ROCE=\frac{profit}{capital\ employed}\times100

Profit of 50,000fromcapitalemployedof50,000 from capital employed of400,000 gives ROCE of 12.5%. It measures profit generated for each unit of long-term finance invested.

Compare ROCE over time, with similar businesses and with the cost of finance. A rise may come from higher profit, more efficient asset use or a reduction in capital employed; the cause matters.

ROCE is not profit margin: its denominator is capital employed, not revenue. A high ROCE from ageing or underinvested assets may not be sustainable.

7.4. Liquidity ratios

Syllabus
0264–2027–2028
Topic
7.4
Level
—

Calculating the current ratio

The current ratio compares a business's current assets with its current liabilities. It shows how many units of current assets exist for each one unit of current liabilities.

\text{Current ratio}=\frac{\text{current assets}}{\text{current liabilities}}

If current assets are 250,000andcurrentliabilitiesare250,000 and current liabilities are200,000, the current ratio is 250,000÷250,000 ÷200,000 = 1.25. Write the result as 1.25:1 or simply 1.25. The matching currency units cancel.

A result of 0.8:1 means 0.80ofcurrentassetsforeach0.80 of current assets for each1 of current liabilities. It is a ratio, not 0.8%, and no ×100 step is used.

Calculating the acid-test ratio

The acid-test ratio compares current assets excluding inventory with current liabilities. Subtract inventory before dividing; this is the step that distinguishes it from the current ratio.

\text{Acid-test ratio}=\frac{\text{current assets}-\text{inventory}}{\text{current liabilities}}

If current assets are 60,000,inventoryis60,000, inventory is40,000 and current liabilities are 30,000:(30,000: (60,000 - 40,000)÷40,000) ÷30,000 = 0.67. Write 0.67:1 or 0.67; small rounding differences such as 0.66 may follow from recurring decimals.

Do not divide inventory by current liabilities or subtract inventory after dividing. With non-negative inventory, the acid-test ratio cannot exceed the current ratio calculated from the same figures.