### Learning Outcomes

- Calculate the accounting rate of return

One easy way to take future cash flows into account is to borrow a financial accounting ratio analysis to compute an estimated rate of return on the investment.

The Accounting Rate of Return (ARR) formula is as follows:

ARR = average annual profit / average investment

Calculating ARR is actually a five-step process:

- Calculate total net cash inflows for the project.
- Calculate total depreciation expense.
- Subtract the depreciation expense from total net cash inflows to get net profit (accounting income).
- Divide accounting income by the project lifespan to get the average annual net profit.
- Divide average annual net profit by average cost of the investment (net investment / 2).

For JuxtaPos, we saw that total net cash inflows for the refurbish option was $88,000, and total net cash inflows for the purchase of a new machine was $136,000. To get accounting income, we subtract total depreciation expense from cash flows. The refurbish is completely depreciated at $56,000, but the new machine is only depreciated down to its residual value of $10,000. Over the life of the project, the company would only take $70,000 in depreciation (e.g. $7,000 per year if it is depreciated on a straight-line basis).

As shown in the table below, using steps 1-4 of the five-step process, we get $4,000 in average annual net profit for the refurbish project and $6,600 for the purchase. However, the purchase option is much more expensive than refurbishing, so which is better? The payback period on the refurbish was quicker than the purchase.

Refurbish | Purchase New | |
---|---|---|

Total net cash inflows | $ 88,000 | $ 136,000 |

Depreciation on machine | $ 56,000 | $ 70,000 |

Accounting income | Single Line$ 32,000 | Single Line$ 66,000 |

Operating life in years | 8 | 10 |

Average annual net profit | Single Line$ 4,000Double line | Single Line$ 6,600Double line |

Investment | $ 56,000 | $ 80,000 |

Residual value | $ – | $ 10,000 |

Net investment (depreciable value) | Single Line$ 56,000 | Single Line$ 70,000 |

Divided by: | 2 | 2 |

Average amount invested | Single Line$ 28,000Double line | Single Line$ 35,000Double line |

Accounting rate of return | 14.29%Double line | 18.86%Double line |

Our average investment for the refurbish was $56,000/2 = $28,000 (average of $56,000 in year 0 and $0 in Year 8) and the average investment for the purchase was $70,000 / 2 = $35,000.

The yield then, also called *return on investment*, was $4,000 / $28,000 for the refurbish, which comes to 14.29%, and $6,600 / $35,000 for the purchase, which comes to 18.86%. In both cases, the rate of return is higher than our 10% hurdle rate, but the purchase yields a higher overall rate of return and therefore looks like the better investment in the long term.

To review, the formula is Average Annual Profit/Average Investment, where:

- Average Annual Profit = Total profit over Investment Period / Number of Years
- Average Investment = (Book Value at Year 1 + Book Value at End of Useful Life) / 2

The book value at the end of the project should be equal to the residual value. However, remember that residual value is the amount of proceeds expected to be realized on the sale of the asset. It is not necessarily the market value since an asset may be disposed of other than by selling.

You’ll find variations on this calculation. Some accountants may use the total investment rather than an average. It would be possible to use the discounted cash flows instead of the nominal, but that would be a much more difficult calculation. Remember that managerial accounting does not have codified rules like financial accounting. As long as you are consistent in your methods, the ARR will give you a solid comparative metric.

Here is an explanation and example:

You can view the transcript for “Accounting Rate of Return (ARR)” here (opens in new window).

Before we tackle the more sophisticated methods of analyzing capital investments in the next section, check your understanding of the ARR.