Capital Investment and Average Rate of Return

• Machinery: a bakery might replace a worn oven or a manufacturer might install a new production line. New machinery can increase output, improve quality or reduce the cost of making each item.
• Buildings: a retailer might buy another shop, while a manufacturer might extend a factory or add a warehouse. These investments provide space for expansion, serving more customers or holding more stock.
• Vehicles: a wholesaler might buy delivery vans to reach customers further away and control its deliveries rather than relying on a courier.

These decisions link business functions. For example, a new production line may increase what operations can produce, require employees to be trained and give marketing more products to sell. Finance must assess the cost and expected return.

What average rate of return measures

Average rate of return, or ARR, measures the average annual profit from an investment as a percentage of its initial cost. It helps a business judge the expected financial return and compare projects of different sizes.

There are two stages:

$$\text{Average annual profit} = \frac{\text{total profit over the project's life}}{\text{number of years}}$$ $$\text{ARR} = \frac{\text{average annual profit}}{\text{initial investment}} \times 100$$

The first calculation spreads the total profit evenly across the project's life. This produces an average: it does not mean the actual profit will be identical every year. The second calculation expresses that annual average relative to the amount invested.

Calculating ARR from profit

The following figures are forecasts.

Suppose a bakery is considering machinery costing £40,000, expected to generate £60,000 total profit over five years.

Its average annual profit is $60{,}000 \div 5 = £12{,}000$.

Its ARR is $12{,}000 \div 40{,}000 \times 100 = 30\%$.

This means the machinery is forecast to generate an average annual profit of 30p for every £1 initially invested.

For a building project costing £100,000, with forecast total profit of £80,000 over eight years, average annual profit is $80{,}000 \div 8 = £10{,}000$. ARR is therefore $10{,}000 \div 100{,}000 \times 100 = 10\%$.

The building produces a larger total profit than the machinery, but a lower average annual percentage return. Total profit alone does not account for the size of the investment or the number of years involved.

Calculating ARR when total returns are given

Sometimes a question gives total returns before the initial investment cost has been deducted, rather than giving total profit. In that case, first deduct the investment cost.

For a vehicle project, assume a van costs £25,000 and its forecast total returns over five years are £45,000, after running costs but before deducting the purchase cost.

• Total profit: $45{,}000 - 25{,}000 = £20{,}000$.
• Average annual profit: $20{,}000 \div 5 = £4{,}000$.
• ARR: $4{,}000 \div 25{,}000 \times 100 = 16\%$.

The van is forecast to generate an average annual profit equal to 16% of its initial cost.

Using the result in a decision

A higher ARR indicates a greater average annual profit relative to the initial investment. On ARR alone, the machinery project is more attractive than the van or building project.

However, forecast profits are uncertain, and a business must be able to afford the initial cost. The project's purpose also matters: a delivery van may be essential for supplying customers even if another project has a higher ARR. The percentage supports a decision; it does not make the decision by itself.

If total returns are given before deducting the initial investment, calculate total profit first:

$$\text{Total profit} = \text{total returns} - \text{initial investment}$$

Interpret the percentage

A higher ARR means a higher average annual profit relative to the original cost. It allows comparison between projects of different sizes, but forecasts, affordability and business needs also affect the decision.