*This feature is a continuation of an earlier publication on how managers could effectively strategise and manage complex investment decisions to ensure profitability of their respective firms. Discussions in the previous write-up ended on some capital budgeting methods.*

**Accounting Rate of Return (ARR)**

A division of the firm’s average after-tax profit by its initial investment capital gives us the Accounting Rate of Return. It is also determined when we divide net income (NI) by average investment capital. Net income, in this case, is equivalent to the cash flows of a given time period (CFt) minus depreciation (Dep). That is, NI = CFt – Dep. The average investment capital is the sum of the beginning and ending investment values divided by two. Presently, most managers measure the accounting rate of return as the ratio of net income to the book value of tangible assets. This implies there are some similarities between the accounting rate of return and the return on assets (ROA). Table 2 provides an illustration of how the accounting rate of return for Project E can be calculated. The assumption underlying these computations is the firm uses a straight-line depreciation of $300 on a yearly basis.

**Table 2: Accounting Rate of Return for Project E**

**Cash Flows**

**Year E – Dep. Amount = Net Income ****÷**** DVOI* = ARR**

0 $(1,500) – – $1,500 –

1 150 300 (150) 1,200 (12.50%)

2 300 300 0 900 0.00%

3 450 300 150 600 25.00%

4 600 300 300 300 100.00%

5 1,875 300 1,575 0 ∞

*DVOI implies Depreciated Value of Investment

An important observation from the data in Table 2 is, as the depreciated value of the assets declines, the accounting rate of return increases (even with a constant measurement of net income). The accounting rate of return for the firm in year five is infinitive (∞). But it is argued that, for organisations with large asset portfolios, the book value of fixed assets after depreciation has been computed would be equivalent to fifty percent (50%) of the fixed assets’ original value. The United States Department of Commerce notes the ratio of net-to-gross tangible assets for all United States manufacturing firms is 51%. If we apply this to Project E, we can conclude the average value of tangible assets throughout the life of the project is $750 [($1,500 + $0) / 2 = $750]. It is argued the fluctuation of net income would be less, even if it were related to the average value of the tangible assets. However, any attempt to measure summarily, the useful life of the project may not be logical.

The accounting rate of return fails to consider the time value of money in its measurement process. The return on equity (ROE), also called net worth or net assets, is determined as the ratio of net income to average owners’ equity. The ** accounting equation** states:

*assets equal liabilities plus owners’ equity (A = L + OE)*. The value of assets used in the computation process is the net value (Total Tangible Assets less Accumulated Depreciation). The implication is, the reported amount for owners’ equity is affected by depreciation. This suggests there is a relationship between the accounting rate of return and return on equity. Thus, setbacks associated with the accounting rate of return may be identified in the computation of the return on owners’ equity. To some finance experts, the proposition of the accounting rate of return that about 50% of assets are depreciated is true for the entire manufacturing population. However, this proposition may not hold when individual firms or industries are considered; the proposition may not hold when new and emerging firms require huge investments in new fixed assets:

For the all manufacturing universe, ARR’s assumption that assets are about 50 percent depreciated turns out to be factually correct. However, for individual [firms] and even industries, this assumption that fixed assets are about one-half depreciated may not be correct. For new and growing [firms] where [significant investments] are being made for new plant and equipment, the ratio of net to gross fixed assets would be much higher than 50 percent. This would bias the measured return on equity downward because the denominator would be higher than for the average corporation. (Weston and Copeland, 1992, p. 309)

The ratio of net to total tangible assets may be below 50% for firms that are old and exhibit maturity in their operations. In such situations, the return on equity reported may be higher than usual. The relationship between accounting rate of return and return on owners’ equity implies the ARR would be understated in areas that would require management’s attention; the ARR would be overstated in areas that management would have to withdraw its economic resources. As stated earlier, the ARR could also be derived from the division of average after-tax profit by the initial investment capital. Using the data in Table 1, we compute the ARR for Project G as follows.

Where:

I0 = Initial investment capital

t = Time period of cash flow

n = Number of years for the project

The ARR for Project G is

ARR = [(-$1,500 + $150 + $1,350 + $150 – $150 – $600) / 5] ÷ $1,500

= (-$600 / 5) ÷ $1,500

= (-$120 / $1,500)

= -0.08 x 100% = **-8%**

The accounting rates of return (ARRs) for the four projects are:

- Project E, ARR = 25%
- Project F, ARR = 22%
- Project G, ARR = -8%
- Project H, ARR = 26%

Our computations reveal management would select Project H if the ARR is used in making investment decisions; it provides the highest return among the alternatives. Irrespective of how the cash inflows for Project H occur, the ARR would still recognise Project H as the ideal one for the firm. The reason is time value of money has no prominence in the measurement of ARR. Ideally, corporate executives would prefer positive future cash flows to negative ones – the current order of cash flows from Project H would be preferred to the opposite.

** ****Cash Pay Back (PB)**

The payback period measures the expected number of years required to recover an initial capital investment in a project. The first formal technique that was used to evaluate capital budgeting projects was the payback period. The payback periods for the four projects outlined in Table 1 are listed below:

- Project E, Payback = 4 years
- Project F, Payback = 3 years
- Project G, Payback = 2 years
- Project H, Payback = 4 years

A strict adherence to the payback concept reveals managers would opt for Project G because it has the shortest payback period among the four mutually exclusive alternatives. It is easy to use the payback method; it helps companies in financial difficulties to know how quickly they could regain their investments. The major problem associated with the payback method is its failure to discount cash flows, and to consider negative cash flows that occur in subsequent periods. Failure to discount means managers may be indifferent in their choice between Project G and another project with a cash flow of say, $1,400 in year one and a cash flow of $100 in year two. By selecting project G, the firm would be ignoring the negative cash flows, -$750 [-$150 + (-$600)] that would occur in years four and five. The payback method is not ideal because it fails to exhibit the first and second essential features discussed earlier.

Ebenezer M. Ashley (PhD)

*The Author is **a Senior Consultant at Ghana Investment Services Centre and Founder of Eben Consultancy*

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