**ARR AND PAYBACK**

**(a) **Accounting rate of return (ARR) is a computation of the return on an investment where the annual profit prior to interest and tax is expressed as a percentage of the capital sum invested. There are a number of substitute formulae which can be used to calculate ARR which differ in the way in which they define capital cost. The more general alternative measures available are average annual profit to initial capital invested and average annual profit to average capital invested. The method selected will influence the resulting ARR figure, and for this reason it is important to recognise that the measure may be subject to manipulation by managers seeking approval for their investment proposals. The value meant for average annual profit is calculated subsequent to allowances for depreciation as shown in the example below

If ARR is defined as

Initial capital invested

Average profit (after depreciation) × 100 after that a project which costs $5 million and yields average profits of $1250000 per year after depreciation charges of $500000 per year will give an ARR of 1250000/5000000 × 100 = 25% If the depreciation charged is raised to $750000 per year as a result for example of technological changes which reduce the expected life of an asset, the ARR becomes

1000000/5000000 × 100 = 20%

The attraction of by means of ARR as a method of investment appraisal lies in its simplicity and the ease with which it can be used to specify the impact of a project on a company's income statement. The measure is effortlessly understood and is able to be directly linked to the use of ROCE as a performance measure. However ARR has been criticised for a number of major drawbacks perhaps the most important of which is that it uses accounting profits after depreciation rather than cash flows in order to measure return. This signifies that the capital cost is over-stated in the calculation via both the numerator and the denominator. In the numerator the capital cost is taken into account by means of the depreciation charges used to derive accounting profit but capital cost is also the denominator. The practical consequence of this is to reduce the ARR and thus make projects appear less profitable. This might in revolve result in some worthwhile projects being rejected. letter but that this problem does not arise where ARR is calculated as average annual profit as a percentage of average capital invested.

The most significant criticism of ARR is that it takes no account of the time value of money. A second drawback of ARR already suggested is that its value is dependent upon accounting policies and this can make comparison of ARR figures across different investments somewhat difficult. This possibly important in an international company where accounting policies vary between nations. A further difficulty with the use of ARR is that it doesn't give a clear decision rule. The ARR on any particular investment requires to be compared with the current returns being earned within a business and consequently unlike NPV for example it is impossible to say all investments with an ARR of X or below will always be rejected.

The payback method of investment appraisal is extremely widely used by industry usually in addition to other measures perhaps because like ARR it is effortlessly calculated and understood. The payback approach merely measures the time required for cumulative cash flows from an investment to sum to the original capital invested. Illustration as

Original investment $100000

Cash flow profile Years 1-3 $25000 p.a. Years 4-5 $50000 p.a. Year 6 $5000

The cumulative cash flows are thus

End Year 1 $25,000

End Year 2 $50,000

End Year 3 $75,000

End Year 4 $125,000

End Year 5 $175,000

End Year 6 $180,000

The original amount invested is therefore returned via cash flows some time during the course of Year 4. If cash flows are supposed to be even throughout the year then the cumulative cash flow of $100000 will have been earned halfway through year 4. The payback time period for the investment is therefore 3 years and 6 months. This approach is helpful for companies which are seeking to claw back cash from investments as quickly as possible. At the same time the idea is intuitively appealing as many businessmen will be concerned about how long they may have to wait to get their money back for the reason that they believe that rapid repayment reduces risks. This denotes that the payback approach is commonly used for initial screening of investment alternatives.