10.3 Investment Appraisal – Payback and ARR 💰
What is the Accounting Rate of Return (ARR)?
ARR is a quick way to see how much profit you’ll earn each year compared to the money you invest. Think of it as the “interest rate” your investment earns on paper, expressed as a percentage.
How to Calculate ARR
- Determine the average annual profit (or earnings) over the project’s life.
- Divide that average profit by the initial investment cost.
- Multiply the result by 100 to convert it to a percentage.
\$ARR = \frac{\text{Average Annual Profit}}{\text{Initial Investment}} \times 100\%\$
Example: Calculating ARR
Suppose a company spends £50,000 on a new machine that will be used for 5 years. The expected yearly profit from the machine is:
| Year | Profit (£) |
|---|
| 1 | 12,000 |
| 2 | 11,500 |
| 3 | 11,000 |
| 4 | 10,500 |
| 5 | 10,000 |
Step 1 – Average Annual Profit:
\$\frac{12,000 + 11,500 + 11,000 + 10,500 + 10,000}{5} = 11,200 \text{ £}\$
Step 2 – Divide by Initial Investment:
\$\frac{11,200}{50,000} = 0.224\$
Step 3 – Convert to Percentage:
\$0.224 \times 100\% = 22.4\%\$
So the ARR for this machine is 22.4 %.
Interpreting ARR
- ARR tells you the average yearly profit as a percentage of the initial cost.
- Compare the ARR to the company’s required rate of return (hurdle rate). If ARR ≥ hurdle rate, the project is likely acceptable.
- ARR ignores the time value of money – it’s a quick, easy check but not as precise as NPV or IRR.
Exam Tips 📚
- Always show the ARR formula in your answer.
- Explain the meaning of ARR in one sentence (e.g., “ARR is the average annual profit expressed as a percentage of the initial investment”).
- When given a table of profits, calculate the average first, then ARR.
- Remember that ARR does not account for the time value of money; mention this limitation if asked.
- Use the words “acceptable” or “unacceptable” when comparing ARR to the required rate of return.
Quick Analogy 🚀
Think of ARR like a “savings account” for your investment. If you deposit £50,000 and the account earns you £11,200 each year, the interest rate is 22.4 %. If the bank’s minimum required interest rate is 15 %, you’re happy with this account. If it’s 25 %, you’d look for a better one.