Calculate and interpret the average (accounting) rate of return (ARR)

Emma and Mo calculate the average rate of return

Businesses often have to make investment decisions. This might involve deciding which piece of equipment or machinery to buy, or whether to move to bigger premises. Any investment is made in the hope that in return the business will see its profits increase.

Anything that can provide information about the potential size of the return from an investment decision can be helpful. This is because a business will know the return it could get from leaving the money it is going to invest in the bank, so it can compare this number with the estimate of the return it could get from investing the money instead. For example, if a business knows that it can gain 1% interest on money in its bank account, then any investment that would use that money should return more than 1% in profit. Otherwise, the business would be better off financially by leaving the money in the bank.

One calculation that can help a business to compare different investment options is the average rate of return (ARR).

Calculating the average rate of return

The average rate of return (ARR) is a way of comparing the profitability of different choices over the expected life of an investment. To do this, it compares the average annual profit of an investment with the initial cost of the investment. This is necessary in order to compare investments that might last for different periods of time.

To calculate the average rate of return, a business will first calculate the average annual profit:

Average annual profit = total profit ÷ number of years

Then use the following formula for the average rate of return:

\[\text{Average rate of return (\%)}=\frac{\text{Average annual profit}}{\text{Cost of investment}} × 100\]

For example, a small local building business has decided to invest in a small excavator, since it will allow jobs to be completed more quickly and therefore more work to be completed.

The owner has identified the excavator that is most suitable, but needs to decide whether to invest in a brand new excavator or a used one. The used excavator may be less reliable and will need to be replaced after four years. The business knows the following:

OptionNewUsed
Cost of excavator£40,000£25,000
Additional profit in year 1£14,000£9,500
Additional profit in year 2£12,000£7,500
Additional profit in year 3£9,000£6,500
Additional profit in year 4£8,000£4,500
Additional profit in year 5£7,000£0
Total additional profit£50,000£28,000
The average rate of return for each option would be calculated as follows:
Average annual profit =£50,000 ÷ 5 = £10,000£28,000 ÷ 4 = £7,000
Average rate of return =(£10,000 ÷ £40,000) × 100 = 25%(£7,000 ÷ £25,000) × 100 = 28%

This shows that buying the used excavator would be the best financial decision, as the return from the money invested would be higher.

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