Annuity Depreciation

Annuity depreciation crops up within the context of divisional performance management when using return on investment and / or residual income as performance measures.

Example

Division X is currently generating a ROI of 12%. It is considering a new project. This requires an investment of $1.4 million and is expected to yield net cash inflows of $460,000 per annum for the next four years. None of the initial investment will be recoverable at the end of the project.

The company has a cost of capital of 8%. Annual accounting profits are to be assumed to equal annual net cash inflows less depreciation,and tax is to be ignored.

Required:

(a)Calculate and comment of the NPV of the project.

(b)Calculate and comment on the ROI and RI of the project.

(c)Calculate and comment on the ROI and RI of the project using annuity depreciation.

(d)Calculate and comment on the ROI and RI of the project at the project IRR of 12%.

Solution:

(a) NPV calculation

NPV =123,520

Conclusion: the project has a positive NPV and is therefore worthwhile accepting from the company's point of view.

(b) ROI and RI

Conclusion: If the manager's performance is measured (and rewarded) on the basis of RI or ROI, he is unlikely to accept the project. The first year's RI is negative, and the ROI does not exceed the company's cost of capital until year 2, or the ROI currently being earned until year 3. Divisional managers will tend to take a short-term view. More immediate returns are more certain, and by year 3 he may have moved jobs.

(c )ROI and RI using annuity depreciation

Annuity depreciation is calculated as follows:

Step 1: Calculate the equivalent annual cost (EAC) of the initial investment

EAC = Initial investment ÷ cumulative discount factor at the company's cost of capital

         = $1.4m ÷ 3.312

         = $422,705

Step 2: Calculate annual depreciation

Annual depreciation = EAC - interest on opening NBV

         e.g for year 1 = 422,705 - (1,400,000 × 8%)

                                = $310,705

The ROI and RI can now be calculated as follows:

Conclusion: The project now has an equal, positive, RI over its life, which will encourage the manager to invest, a decision compatible with that using NPV.

However, there is still a problem if ROI is used as the performance measure, in that the short-term low rate of return may not encourage investment in what is, in fact, a worthwhile project. A way round this is to use annuity depreciation at a different rate that will ensure a level ROI over the project life. The rate to be used will be the IRR of the project.

(d) ROI and RI using annuity depreciation at the project IRR

12% is now used instead of 8% in computing both the EAC of the investment and the interest on capital, yielding the following results:

Conclusion:

The ROI and the RI is now level over the project life, ensuring a consistent decision whether the short-term or long-term view is taken. Using 12% as an appraisal rate for the project yields consistent results under all three methods (NPV, ROI and RI) i.e. the project is at break-even.

This somewhat contrived approach is probably less useful than the one above when RI is used to assess performance.

In addition, the use of annuity depreciation does not produce helpful results when cash flows are uneven.

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Tags:	annuity depreciation;ROI;RI;return on investment;residual income;divisional performance management