How businesses use percentage changes to analyse performance

Businesses rely on percentage changes to evaluate shifts in key metrics such as sales volume, revenue, profit and market share. This helps in monitoring progress and spotting patterns over periods like months or years.

Calculating percentage changes and increasing figures by percentages

Percentage changes measure the relative difference between two figures, often used to assess business growth or decline.

Formula for percentage change

$\text{Percentage change}=\frac{\text{new figure}-\text{previous figure}}{\text{previous figure}}\times 100$

Where:

• New figure = The updated value (£, units, etc.)
• Previous figure = The original value (£, units, etc.)

A positive result indicates an increase, while a negative shows a decrease.

Formula for increasing a figure by a percentage

$\text{New figure}=\frac{\text{percentage change}\times \text{previous figure}}{100}+\text{previous figure}$

Where:

• Percentage change = The rate of increase (%)
• Previous figure = The original value (£, units, etc.)

Worked example - Calculating percentage change

A business's revenue rises from £38,000 last year to £47,500 this year. Calculate the percentage change in revenue.

Step 1: Identify the values

• Previous figure = £38,000
• New figure = £47,500

Step 2: Apply the formula

$\text{Percentage change}=\frac{\pounds \mathrm{47,500}-\pounds \mathrm{38,000}}{\pounds \mathrm{38,000}}\times 100$

$\text{Percentage change}=\frac{\pounds \mathrm{9,500}}{\pounds \mathrm{38,000}}\times 100=25\%$

Worked example - Increasing a figure by a percentage

A company plans to raise its product price from £25 by 8%. Calculate the new price.

Step 1: Identify the values

• Previous figure = £25
• Percentage change = 8%

Step 2: Apply the formula

$\text{New figure}=\frac{8\times \pounds 25}{100}+\pounds 25$

$\text{New figure}=\frac{\pounds 200}{100}+\pounds 25=\pounds 2+\pounds 25=\pounds 27$

Converting between percentages, fractions and ratios

Percentages, fractions and ratios are interconnected ways to express proportions, useful in business for tasks like analysing profit margins or cost breakdowns.

Methods for converting between percentages and fractions

• Fraction to percentage - Multiply the fraction by 100.
• Percentage to fraction - Divide the percentage by 100 and simplify.

Understanding ratios

A ratio compares two or more quantities, showing their relative sizes. It is written as figures separated by colons.

Expressing fractions as percentages and ratios

When a fraction shows a part of a whole, it can be converted to a percentage or ratio.

For example, if 2/5 of a firm's costs are for materials:

• As a percentage - 2/5 × 100 = 40% of costs are for materials.
• As a ratio - 2 parts materials to 5 parts total costs, or total costs to materials is 5:2. This means for every £5 of costs, £2 goes to materials.

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Worked example - Converting fractions to percentages and ratios

If 2/7 of a business's workforce is in sales, express this as a percentage and as a ratio of sales staff to total workforce.

Step 1: Convert to percentage

Percentage = 2/7 × 100 = 28.6% (rounded to one decimal place)

Step 2: Express as a ratio

Ratio of sales to total workforce = 2:7

Step 3: Interpretation

This means approximately 28.6% of the workforce is in sales, or for every 2 sales staff, there are 7 staff in total.

Calculating labour turnover

Labour turnover measures the rate at which employees leave a business, expressed as a percentage.

Formula for labour turnover

$\text{Labour turnover (\%)}=\frac{\text{number of staff leaving}}{\text{average number of staff employed}}\times 100$

Where:

• Number of staff leaving = Total employees who departed in the period
• Average number of staff employed = Mean number of workers over the period

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Worked example - Calculating labour turnover

A company had an average of 95 employees last year, and 15 staff left during that time. Calculate the labour turnover percentage.

Step 1: Identify the values

• Number of staff leaving = 15
• Average number of staff employed = 95

Step 2: Apply the formula

$\text{Labour turnover (\%)}=\frac{15}{95}\times 100$

$\text{Labour turnover (\%)}=\mathrm{0.15789...}\times 100=15.8\%\text{ (rounded to one decimal place)}$

Points of caution when analysing business graphs and charts

Businesses often use graphs and charts to present data, but these can be misleading if not examined carefully.

Key cautions for analysing data presentations

• Axes labelling - Check if labels are clear and units are consistent.
• Axes starting point - Graphs where axes do not start at zero can exaggerate changes.
• Omitted information - Important details might be left out.
• Biased presentation - Businesses may choose formats that highlight positive aspects.