How businesses use percentage changes to analyse figures

Businesses rely on percentage changes to monitor and evaluate their performance across various metrics.

The role of percentage changes in business analysis

• Businesses track percentage increases or decreases in key areas such as sales volume, revenue, profit, and market share to assess progress over time.
• By examining these changes month by month or year by year, trends become visible, revealing whether performance is improving, declining, or staying stable.

Calculating percentage changes in business data

Percentage change measures the relative difference between two figures, providing a standardised way to compare shifts regardless of the absolute values involved.

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 (e.g., current sales)
• Previous figure = The original value (e.g., last period's sales)

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

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Worked example - Calculating percentage change

Sales of sports equipment rose from 4,000 units to 4,800 units over a year. Calculate the percentage change in sales.

Step 1: Identify the values

• Previous figure = 4,000 units
• New figure = 4,800 units

Step 2: Apply the formula

$\text{Percentage change}=\frac{\mathrm{4,800}-\mathrm{4,000}}{\mathrm{4,000}}\times 100$

Step 3: Perform the calculation

$\text{Percentage change}=\frac{800}{\mathrm{4,000}}\times 100=20\%$

Increasing figures by a percentage

Businesses often project future figures by applying a percentage increase to current data, which is useful for forecasting growth in areas like revenue or costs.

Formula for increasing a figure by a percentage

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

Where:

• Previous figure = The starting value (e.g., last year's revenue in £)
• Percentage change = The rate of increase (e.g., 10%)

This formula can also be adapted for decreases by using a negative percentage.

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Worked example - Increasing a figure by a percentage

A firm's profit was £250,000 last year and is expected to increase by 12% this year. Calculate the projected profit for this year.

Step 1: Identify the values

• Previous figure = £250,000
• Percentage change = 12%

Step 2: Apply the formula

$\text{New figure}=\mathrm{250,000}+(\frac{\mathrm{250,000}}{100}\times 12)$

Step 3: Perform the calculation

$\text{New figure}=\mathrm{250,000}+(\mathrm{2,500}\times 12)=\mathrm{250,000}+\mathrm{30,000}=\pounds \mathrm{280,000}$

Converting between percentages, fractions, and ratios

Business data is often expressed in different forms, such as percentages, fractions, or ratios, to suit various analytical needs. Being able to switch between these formats allows for clearer comparisons and insights.

Methods for converting between formats

• Fraction to percentage - Multiply the fraction by 100. For example, if 3/5 of expenses are fixed costs, then 3/5 × 100 = 60% of expenses are fixed costs.
• Percentage to fraction - Divide the percentage by 100 and simplify. For example, 40% becomes 40/100, which simplifies to 2/5.
• Fraction to ratio - Express the fraction as a comparison. For example, if 2/5 of revenue is spent on marketing, the ratio of total revenue to marketing spend is 5:2, meaning for every £5 of revenue, £2 goes to marketing.
• Finding a percentage of a number - Convert the percentage to a decimal (divide by 100) and multiply by the number. For example, 35% of 200 = 0.35 × 200 = 70.

Example conversions in a business context

Consider a company where staff absenteeism is 15% and the average workforce is 600 employees:

• As a fraction - 15% = 15/100 = 3/20
• As a ratio - The ratio of absent staff to total workforce is 15:100, which simplifies to 3:20
• Number affected - 15% of 600 = 0.15 × 600 = 90 employees absent on average

Awareness of misleading data presentations

Data visualisation tools like graphs and charts are commonly used in business reports, but they can sometimes distort information if not presented carefully.

Common issues in data visualisation

• Axis labelling - Axes that do not start at zero or use uneven scales can exaggerate changes, making small differences appear larger.
• Omitted information - Key details, such as time periods or sample sizes, might be left out, leading to incomplete interpretations.
• Biased presentation - Businesses may choose formats that highlight positive aspects while downplaying negatives, so it is important to check for manipulation.

Tips for evaluating data presentations

• Always verify if axes are scaled appropriately and start from zero where relevant.
• Look for any missing context that could alter the meaning of the data.
• Compare multiple sources to ensure the presentation is balanced and accurate.