# Average rate of return (ARR)

# Average Rate of Return (ARR) - An Insightful Analysis

## Definition and Calculation

The **Average Rate of Return (ARR)** is a pivotal financial metric reflecting the profitability of investments or projects over their lifetime, expressed as a percentage of the initial investment. The ARR is calculated by dividing the average annual profit by the initial cost of investment.

The formula for ARR is:

ARR = (Average Annual Profit / Initial Investment) x 100%

## Significance of ARR in Business Decision-Making

ARR plays a vital role in capital budgeting, offering a straightforward metric for comparing investment opportunities. It is valued for its simplicity, comparability, and serving as a decision criterion.

However, it's crucial to consider its limitations, such as not accounting for the time value of money, alongside other metrics like NPV and IRR for a comprehensive analysis.

## Industry Example: Solar Energy Investment

Consider *SolarTech Inc.*, evaluating an investment in a new solar farm:

- Initial Investment: $5,000,000
- Total Net Profit over 10 years: $6,000,000
- Average Annual Profit: $600,000

Using the ARR formula:

ARR = (600,000 / 5,000,000) x 100% = 12%

With an ARR of 12%, the solar farm project exceeds SolarTech's minimum acceptance rate of 10%, marking it as a viable investment.

ARR measures the net return each year as a percentage of the capital cost of the investment.

How do I calculate and present it in the exam?

Table 3.2: Average rate of return for Project A ($000) | |

Year | Net Cash Flow |

0 | (50) |

1 | 10 |

2 | 10 |

3 | 15 |

4 | 15 |

5 | 20 |

Net profit | 70 − 50 = 20 |

Net profit per annum |
$$\frac{20}{5}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}4$$ |

ARR |
$$\frac{4}{50}\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}100\text{\hspace{0.17em}}=\text{\hspace{0.17em}}8\%$$ |

**Again, this is what the examiner expects from you when it comes to presenting ARR, so present it this way.**What do all these numbers mean?

Net cash flow column will be given to you in the case study. It is the cash flow businesses expected over the years. Again, you start with 0 and since the number is negative it represents expenditure (in our case $50000). In the net profit section, all we did was add up all the expected cash influx in each year and then subtract the value of the investment. Then we calculated the net profit per annum — what the profit of the firm will be in those five years after subtracting the value of the investment (in our case $20000/5 years = $4000). Then we calculate the ARR using the formula:

$$\text{ARR}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\frac{\text{Total}\text{\hspace{0.17em}}\text{returns}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\text{Capital}\text{\hspace{0.17em}}\text{cost}}{\text{Years}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{use}}}{\text{Capital}\text{\hspace{0.17em}}\text{cost}}\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}100$$

*Don’t worry about memorizing this formula – it will be in your formula booklet in the exam.*

We got that the ARR is 8%.

If we used this method to appraise different investment projects, we would choose the investment that has the highest average rate of return.