There are also various limitations in ROI analysis. Centrally incurred expenses and assets may be allocated, and such allocations are subject to many arbitrary interpretations. A major criticism is a manager's ability to manipulate income for showing a higher ROI. R&D and other critical expenditures may be delayed to achieve a higher income and a higher ROI even though the long-term survival of the firm may be jeopardized. ROI maximization can also distort the proper allocation of a firm's resources. For example, an invesemtnet with ROI of 14%, where cost of capital is 10%, may be rejected if current ROI is 16%, because such a project would reduce the overall ROI for the firm. The latter problem is solved by using residual income in place of ROI. Another shortcoming of ROI is variations in the use and interpretation of the concepts of income and investment. Should income be the amount before or after interest and taxes? Is investment net of accumulated depreciation? Should investment be at cost or replacement value?

The author believes that using income before interest and after taxes is a more appropriate numerator in the ROI equation rather than net income. The amount of interest paid is a financing question and can be addressed better when determining return on equity. Measuring gross investment at cost and preferably at replacement cost gives a better approximation of investment value. Otherwise, with higher depreciation, higher returns on investment will continue to show.

An Expanded Approach to ROI

The following discussion focuses on the formula approach to ROI analysis and offers a few suggestions for further expansion of ROI to enhance its usefulness and overcome part of its weaknesses.

Problem 1. ROI is too compact and a clearer analysis requires breaking down ROI into margin and turnover:

ROI = Income/Investment

Solution 1. The Dupont formula approach of breaking down ROI into margin and turnover is well-known and well-utilized.

ROI = (Income/Sales) * (Sales/Investment)

Problem 2. Income is a good measure when determining return on equity, but it may be inappropriate when measuring ROI. Interest is a financing issue and must not be confused with investing questions.

Solution 2. Expand the above formula so that income will be inclusive of interest.

ROI = (Income + Interest)/Sales * (Sales/Investments

Problem 3. Investment at historical value may be irrelevant in measuring return on investment. Using replacement cost of investment may be more appropriate.

Solution 3. Add a factor to investment to convert investment from historical cost to replacement cost.

ROI = (Income + Interest)/Sales) * (Sales/Investment + Adj.)

Further Analysis

Based on the above information, ROI may now be analyzed on a four- factor basis. The factors are as follows:

Factor 1. Margin = (Income + Interest)/Sales

Factor 2. Turnover = Sales/(Investment + Adjustment Factor)

Factor 3. Financing Ratio = Income/(Income + Interest)

Factor 4. Investment Adjustment = (Investment + Adj.)/Investment

The following abbreviations for the expanded ROI formula are used:

* I = Income;

* T = Interest;

* S = Sales;

* V = Investment at cost;

* A = Investment adjustment factor;

* MV = Market value of equity;

* E = Stockholders' equity;

* L = Liabilities;

* ROE = Return on equity;

* ROI = (I + T)/S * S/(V + A) * I/(I + T) * (V + A)/V.

Factor 3 shows income as a percentage of income plus interest. Factor 4 shows replacement cost. Accordingly, when using the first two factors in ROI measurement, we see margin in terns of income exclusive of financing questions and turnover based on replacement cost of assets.

Return on Equity: A Closer Look

The expanded formula of ROI can now be modified to determine ROE as an extension of ROI measurement. ROE can be described as income as a percentage of equity.

ROE = INCOME/EQUITY

The income figure should be net of interest and taxes. The equity taken from accounting records is at historical cost. A more realistic figure is equity adjusted to market value. As such, we will add two factors to the above ROI formula to transform it into an expanded version of ROE.

Factor 5 shows the leverage that is liabilities plus equity divided by market value of equity. Note that the numerator comes from the accounting records whereas the denominator is computed by determining the market value of the outstanding shares. Also because liabilities plus equity equals the investment amount, we can use the investment number in this equation.

Factor 6 makes the final adjustment by determining market value of shares as a percentage of book value of shares. Accordingly, the ROE formula exclusive of the latter adjustment would show return on equity as a percentage of market value of shares. This expanded analysis of ROE can be illustrated in the following formula:

ROE = (I + T)/S * S/V + A) * I/(I + T) * (V + A)/V * (V/MV) * (MV/E)

The six components and a numerical illustration are explained below:

Factor 1. Illustrates margin where income is inclusive of interest because interest is a financing issue and must be dealth with separately in computation of ROE.

Factor 2. Represents investment turnover where investment is adjusted to replacement cost of assets.

Factor 3. Represents income as a percentage of income before interest.

Factor 4. Represents replacement cost as a percentage of actual cost of assets.

Factor 5. Represents the leverage where equity is measured in terms of market value.

Factor 6. Represents market value of shares as a percentage of historical cost of equity.

The following numbers are used to calculate the expanded ROI and ROE:

* Income = $25,000;

* Interest = $10,000;

* Sales = $200,000;

* Investment = $100,000;

* Adjustment = $20,000 (add to investment to convert to replacement cost);

* Market value of shares = $62,500;

* Book value of shares = $50,000; ROI (four-factor analysis):

(25,000 + 10,000)/200,000 * 200,000/(100,000 + 20,000) * 25,000/(25,000 + 10,000) * (100,000 + 20,000)/100,000 = .25

Factor 1 income inclusive of interest amounts to 17.5% of sales.

Factor 2 turnover amounts to 1.667 times based on replacement cost of assets.

Factor 3 income as a percentage of income before interest amounts to 71.14%.

Factor 4 replacement cost of assets amounts to 120% of historical cost of assets.

ROI = .175 * 1.667 * .7143 * 1.2 = 25%

This is the same as taking income of $25,000 as a percentage of investment of $100,000 which amunts to 25%. The above four-way analysis provides a deeper meaning and understanding of all the components of ROI. The suggested method alleviates some of the problems and criticisms associated with ROI analysis as well.

Factor 3 shows how much of income is retained after tax is paid out, and factor 4 illustrates the added cost of investment due to inflation and other factors.

Expanded ROE

As explained earlier, the ROI computed above is the starting point to which factor 5, representing leverage computed as a liabilities plus equity (investment at cost) as a percentage of market value of shares outstanding, and factor 6 which shows market value of shares as a percentage of book value of shares are added.

ROE = ROI * (V/MV) * (MV/E) ROE = .25 * (100,000/62,500) * (62,500/50,000) ROE = .25 * 1.6 * 1.25 = 50%

Factor 5 amounts to 1.6, indicating that the leverage, considering current market value of shares, is 1.6 times.

Factor 6 amounts to 1.25, indicating that market value of shares is 1.25 times book value of shares. The ultimate result of 50% agrees with the shortcut computation of income over equity of $25,000 and $50,000, respectively.

The four-factor analysis of ROI and the six-factor analysis of ROE provide significant additional information to management for analysis and interpretation of the financial results of the firm and substantially improve the usefulness of such information.