Average rate of return (ARR) - Top Study Guide

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	$\frac{20}{5} = 4$
ARR	$\frac{4}{50} \times 100 = 8 %$

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:

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

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.

Frequently Asked Questions about Average Rates of Return

What is "Average Rate of Return" on investments? What does it mean? ▼

The Average Rate of Return refers to the simple arithmetic average of the annual returns of an investment over a specific period. It's a way to gauge the historical performance of an investment, showing the typical return achieved per year over the chosen timeframe.

Important Note: The simple average rate of return doesn't account for compounding. A more accurate measure for investment performance over multiple periods is the **Compound Annual Growth Rate (CAGR)**, which smooths out volatility and shows the rate at which an investment would have grown if it compounded at a steady rate each year.

What is the average rate of return on stocks, especially the S&P 500? ▼

Historically, the average annual return for the broader U.S. stock market (often represented by indices like the S&P 500) has been around **10% to 12%** before inflation, over long periods (decades).

However, this is an *average*. Actual returns vary significantly from year to year and depend heavily on the specific stocks or index invested in and the timeframe considered. Past performance is not indicative of future results.

What is the average rate of return on a 401(k) or Roth IRA? ▼

The average rate of return on a 401(k) or Roth IRA is not a fixed number because these are **types of investment accounts, not specific investments**. Their returns depend entirely on the underlying assets you choose to hold within them (e.g., stocks, bonds, mutual funds, ETFs).

If your 401(k) or Roth IRA is primarily invested in diversified stock market funds that track indices like the S&P 500, your long-term average return might align closely with the historical stock market average (around 10-12%). If your investments include more bonds or cash, the average return will likely be lower but potentially less volatile.

How do you calculate the Average Rate of Return? ▼

To calculate the simple average rate of return, you would:

Calculate the annual return for each year in your chosen period.
Sum up the annual returns.
Divide the sum by the number of years in the period.

Simple Average Return = (Sum of Annual Returns) / (Number of Years)

For calculating the average *annual* return that accounts for compounding, you would calculate the Compound Annual Growth Rate (CAGR). The formula for CAGR is more complex and requires the beginning value, ending value, and the number of years.

What is considered a "good" average rate of return on investments? ▼

What is considered "good" is subjective and depends on your investment goals, time horizon, and risk tolerance. However, comparing your returns to relevant benchmarks is a standard practice:

For broad stock market investments, comparing to the historical S&P 500 average (10-12%) is common.
For bond investments, benchmarks like the Aggregate Bond Index are used (historically lower returns than stocks).
For a diversified portfolio, compare to a blended benchmark reflecting your asset allocation.

Consistently achieving returns close to or exceeding relevant market benchmarks, while managing risk, is generally considered successful investing. Remember to consider inflation when evaluating returns, as your "real" return is what matters for purchasing power.