The meaning and formula for ARR

Accounting rate of return (ARR), also known as average rate of return, is a method used to evaluate the potential profitability of an investment project. It calculates the average annual profit as a percentage of the average amount invested, providing a measure of the return expected over the project's lifespan.

Formula for ARR

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

Where:

• Average annual profit = Total profit divided by the number of years in the project's lifespan (£)
• Average investment = (Initial capital cost + residual capital value) / 2 (£)

Formula for average investment

$\text{Average investment}=\frac{\text{initial capital cost}+\text{residual capital value}}{2}$

Where:

• Initial capital cost = The starting amount invested in the project (£)
• Residual capital value = The estimated value of the investment at the end of its lifespan (£)

Steps in calculating ARR

The five stages of ARR calculation:

1. Add up all positive net cash flows over the project's lifespan.
2. Subtract the initial investment cost from the total net cash flows to find the total profit.
3. Divide the total profit by the number of years in the project's lifespan to get the average annual profit.
4. Calculate the average investment by adding the initial capital cost and residual capital value, then dividing by 2.
5. Divide the average annual profit by the average investment and multiply by 100 to obtain the ARR percentage.

Worked example - Calculating ARR

A business is considering a project with an initial capital cost of £120,000 and a residual capital value of £20,000 at the end of its 4-year lifespan. The net cash flows are £40,000 in year 1, £35,000 in year 2, £45,000 in year 3, and £30,000 in year 4. Calculate the ARR for this project.

Step 1: Calculate total net cash flows

Total net cash flows = £40,000 + £35,000 + £45,000 + £30,000 = £150,000

Step 2: Calculate total profit

Total profit = £150,000 - £120,000 = £30,000

Step 3: Calculate average annual profit

Average annual profit = £30,000 ÷ 4 = £7,500

Step 4: Calculate average investment

Average investment = (£120,000 + £20,000) ÷ 2 = £70,000

Step 5: Calculate ARR

$\text{ARR}=\left(\frac{\pounds \mathrm{7,500}}{\pounds \mathrm{70,000}}\right)\times 100\approx 10.71\%$

Interpreting and comparing ARR results

ARR provides a percentage that represents the average annual return on the investment over its entire lifespan.

Ways to compare ARR:

• With other projects - Compare the ARR of different investment options to identify the most profitable one.
• Against a criterion rate - Measure it against the business's minimum required return, such as a target percentage set by management.
• With interest rates - Evaluate it relative to the annual interest rate on loans to see if the project offers a better return than borrowing costs.

ARR is often used alongside other methods, like payback period, to provide a fuller picture by balancing profitability with the timing of cash flows.

Advantages and disadvantages of ARR

ARR is a popular tool for appraising investment projects due to its focus on overall returns, but it has limitations related to timing and accuracy.

Advantages of using ARR

• Considers all cash flows - Includes every net cash flow over the project's life, unlike methods that stop at a certain point.
• Emphasises profitability - Directly links to key business goals by measuring average returns.
• Easy to understand and compare - The percentage result is straightforward and can be quickly evaluated against other projects or targets.
• Simple assessment against targets - Can be readily checked against a business's required rate of return.

Disadvantages of using ARR

• Overlooks cash flow timing - Treats all cash flows equally, regardless of when they occur.
• Ignores differences in payback - Projects with similar ARR values may vary greatly in how quickly they recover costs.
• Relies on potentially inaccurate forecasts - Includes later cash flows, which are harder to predict reliably.
• Does not account for time value of money - Fails to discount future cash flows to reflect their present value.