Calculating average rate of return (ARR)

Average rate of return (ARR) is a calculation of the average return on an investment each year over its lifespan. It helps businesses compare different investment options over the project's expected duration.

Formula for average annual profit

$\text{Average annual profit}=\frac{\text{total profit}}{\text{number of years}}$

Where:

• Total profit = Sum of all yearly profits minus initial investment (£)
• Number of years = Lifespan of the investment

Formula for ARR

$\text{ARR (\%)}=\left(\frac{\text{average annual profit}}{\text{cost of investment}}\right)\times 100$

Where:

• Average annual profit = Profit averaged over the investment's lifespan (£)
• Cost of investment = Initial amount invested (£)

The ARR calculation process

1. Work out the total profit by adding up all yearly profits and subtracting the initial investment.
2. Find the average annual profit by dividing the total profit by the number of years in the investment's lifespan.
3. Calculate ARR by dividing the average annual profit by the cost of investment and multiplying by 100.

A higher ARR indicates a more successful investment. What counts as a strong ARR varies by business and investment size; for example, 6% might be worthwhile for a large £12 million project but not for a small £850 one.

Worked example - Calculating ARR

A business invests £30,000 in new equipment with a 5-year lifespan. The yearly profits are £5,000 in year 1, £6,000 in year 2, £7,000 in year 3, £8,000 in year 4, and £9,000 in year 5. Calculate the ARR.

Step 1: Identify the values

• Cost of investment = £30,000
• Yearly profits: £5,000; £6,000; £7,000; £8,000; £9,000
• Number of years = 5

Step 2: Calculate total profit

Total profit = (£5,000 + £6,000 + £7,000 + £8,000 + £9,000) - £30,000 = £35,000 - £30,000 = £5,000

Step 3: Calculate average annual profit

$\text{Average annual profit}=\frac{\pounds \mathrm{5,000}}{5}=\pounds \mathrm{1,000}$

Step 4: Calculate ARR

$\text{ARR (\%)}=\left(\frac{\pounds \mathrm{1,000}}{\pounds \mathrm{30,000}}\right)\times 100=3.33\%$

Understanding gross and net profit

Gross profit shows the earnings after subtracting the direct costs of producing goods, while net profit accounts for all expenses, providing a fuller picture of financial performance. Revenue is the total income from selling goods or services over a period.

Formula for revenue

$\text{Revenue}=\text{sales price}\times \text{quantity sold}$

Where:

• Sales price = Price per unit (£)
• Quantity sold = Number of units sold

Formula for gross profit

$\text{Gross profit}=\text{revenue}-\text{cost of sales}$

Where:

• Revenue = Total sales income (£)
• Cost of sales = Direct costs of producing goods (£)

Formula for net profit

$\text{Net profit}=\text{gross profit}-(\text{operating expenses}+\text{interest})$

Where:

• Gross profit = Profit after direct costs (£)
• Operating expenses = Indirect costs like rent and utilities (£)
• Interest = Costs from loans (£)

Calculating gross and net profit margins

Profit margins express profits as a percentage of revenue, helping businesses assess efficiency. A good margin depends on the industry; higher is generally better, but some sectors like supermarkets operate on low margins with high sales volumes.

Gross profit margin

$\text{Gross profit margin}=\frac{\text{gross profit}}{\text{revenue}}\times 100$

Where:

• Gross profit = Revenue minus cost of sales (£)
• Revenue = Total sales income (£)

Gross profit margin represents the portion of each pound of revenue not spent on direct production costs. It can be improved by raising prices or cutting direct costs.

Net profit margin

$\text{Net profit margin}=\frac{\text{net profit}}{\text{revenue}}\times 100$

Where:

• Net profit = Profit after all costs (£)
• Revenue = Total sales income (£)

Net profit margin shows the share of revenue kept after all expenses. It is often higher for small, new businesses with fewer indirect costs, but tends to fall as companies expand and indirect expenses rise.

Worked example - Calculating gross and net profit margins

A business has revenue of £200,000, cost of sales of £110,000, operating expenses of £40,000, and interest of £8,000. Calculate the gross profit margin and net profit margin.

Step 1: Identify the values

• Revenue = £200,000
• Cost of sales = £110,000
• Operating expenses = £40,000
• Interest = £8,000

Step 2: Calculate gross profit

$\text{Gross profit}=\pounds \mathrm{200,000}-\pounds \mathrm{110,000}=\pounds \mathrm{90,000}$

Step 3: Calculate gross profit margin

$\text{Gross profit margin}=\frac{\pounds \mathrm{90,000}}{\pounds \mathrm{200,000}}\times 100=45\%$

Step 4: Calculate net profit

$\text{Net profit}=\pounds \mathrm{90,000}-(\pounds \mathrm{40,000}+\pounds \mathrm{8,000})=\pounds \mathrm{42,000}$

Step 5: Calculate net profit margin

$\text{Net profit margin}=\frac{\pounds \mathrm{42,000}}{\pounds \mathrm{200,000}}\times 100=21\%$