*Somdett™s after-tax profits are given by 0.6(EBIT $3.2 million).

†

Somdett™s equity is only $60 million.

two of the most commonly used profitability measures: operating return on assets (ROA), return on assets

which equals EBIT/total assets, and ROE, which equals net profits/equity. (ROA)

Somdett is an otherwise identical firm to Nodett, but $40 million of its $100 million of Earnings

assets are financed with debt bearing an interest rate of 8%. It pays annual interest expenses before interest and

of $3.2 million. Table 13.5 shows how Somdett™s ROE differs from Nodett™s. taxes divided by

total assets.

Note that annual sales, EBIT, and therefore ROA for both firms are the same in each of the

three scenarios, that is, business risk for the two companies is identical. It is their financial risk

that differs. Although Nodett and Somdett have the same ROA in each scenario, Somdett™s

ROE exceeds that of Nodett in normal and good years and is lower in bad years.

We can summarize the exact relationship among ROE, ROA, and leverage in the following

equation1

Debt

Tax rate) sROA t

ROE (1 (ROA Interest rate) (13.1)

Equity

1

The derivation of Equation 13.1 is as follows:

Net profit

ROE

Equity

EBIT Interest Taxes

Equity

(1 Tax rate) (EBIT Interest)

Equity

(ROA Assets Interest rate Debt)

(1 Tax rate)

Equity

(Equity Debt) Debt

Tax rate) sROA t

(1 Interest rate

Equity

Equity

Debt

Tax rate) sROA t

(1 (ROA Interest rate)

Equity

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The relationship has the following implications. If there is no debt or if the firm™s ROA

equals the interest rate on its debt, its ROE will simply equal (1 minus the tax rate) times

ROA. If its ROA exceeds the interest rate, then its ROE will exceed (1 minus the tax rate)

times ROA by an amount that will be greater the higher the debt/equity ratio.

This result makes intuitive sense: If ROA exceeds the borrowing rate, the firm earns more

on its money than it pays out to creditors. The surplus earnings are available to the firm™s own-

ers, the equityholders, which raises ROE. If, on the other hand, ROA is less than the interest

rate, then ROE will decline by an amount that depends on the debt/equity ratio.

To illustrate the application of Equation 13.1, we can use the numerical example in Table

13.5. In a normal year, Nodett has an ROE of 6%, which is 0.6 (1 minus the tax rate) times its

ROA of 10%. However, Somdett, which borrows at an interest rate of 8% and maintains a

debt/equity ratio of 2/3, has an ROE of 6.8%. The calculation using Equation 13.1 is

8%)2„3]

ROE 0.6[10% (10%

4„3%)

0.6(10% 6.8%

The important point is that increased debt will make a positive contribution to a firm™s ROE

only if the firm™s ROA exceeds the interest rate on the debt.

Note also that financial leverage increases the risk of the equityholder returns. Table 13.5

shows that ROE on Somdett is worse than that of Nodett in bad years. Conversely, in good

years, Somdett outperforms Nodett because the excess of ROA over ROE provides additional

funds for equityholders. The presence of debt makes Somdett more sensitive to the business

cycle than Nodett. Even though the two companies have equal business risk (reflected in their

identical EBIT in all three scenarios), Somdett carries greater financial risk than Nodett.

Even if financial leverage increases the expected ROE of Somdett relative to Nodett (as it

seems to in Table 13.5), this does not imply the market value of Somdett™s equity will be

higher. Financial leverage increases the risk of the firm™s equity as surely as it raises the ex-

pected ROE.

>

1. Mordett is a company with the same assets as Nodett and Somdett but a debt/eq-

Concept

uity ratio of 1.0 and an interest rate of 9%. What would its net profit and ROE be

CHECK in a bad year, a normal year, and a good year?

13.4 RATIO ANALYSIS

Decomposition of ROE

To understand the factors affecting a firm™s ROE, including its trend over time and its per-

formance relative to competitors, analysts often “decompose” ROE into the product of a se-

ries of ratios. Each component ratio is in itself meaningful, and the process serves to focus the

analyst™s attention on the separate factors influencing performance. This kind of decomposi-

tion of ROE is often called the Du Pont system.

One useful decomposition of ROE is

Net profit Pretax profit EBIT Sales Assets

ROE

Pretax profit EBIT Sales Assets Equity

(1) (2) (3) (4) (5)

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Table 13.6 shows all these ratios for Nodett and Somdett under the three different economic

scenarios. Let us first focus on factors 3 and 4. Notice that their product gives us the firm™s

ROA EBIT/assets.

Factor 3 is known as the firm™s operating profit margin, or return on sales (ROS). ROS profit margin or

shows operating profit per dollar of sales. In an average year, Nodett™s ROS is 0.10, or 10%; return on sales

in a bad year, it is 0.0625, or 6.25%, and in a good year, 0.125, or 12.5%. (ROS)

Factor 4, the ratio of sales to assets, is known as asset turnover (ATO). It indicates the The ratio of operating

efficiency of the firm™s use of assets in the sense that it measures the annual sales generated profits per dollar of

by each dollar of assets. In a normal year, Nodett™s ATO is 1.0 per year, meaning that sales of sales (EBIT divided

by sales).

$1 per year were generated per dollar of assets. In a bad year, this ratio declines to 0.8 per

year, and in a good year, it rises to 1.2 per year.

asset turnover

Comparing Nodett and Somdett, we see that factors 3 and 4 do not depend on a firm™s

(ATO)

financial leverage. The firms™ ratios are equal to each other in all three scenarios.

Similarly, factor 1, the ratio of net income after taxes to pretax profit, is the same for both The annual sales

firms. We call this the tax-burden ratio. Its value reflects both the government™s tax code and generated by each

dollar of assets

the policies pursued by the firm in trying to minimize its tax burden. In our example, it does

(sales/assets).

not change over the business cycle, remaining a constant 0.6.

While factors 1, 3, and 4 are not affected by a firm™s capital structure, factors 2 and 5 are.

Factor 2 is the ratio of pretax profits to EBIT. The firm™s pretax profits will be greatest when

there are no interest payments to be made to debtholders. In fact, another way to express this

ratio is

Pretax profits EBIT Interest expense

EBIT EBIT

We will call this factor the interest-burden (IB) ratio. It takes on its highest possible

value, 1, for Nodett, which has no financial leverage. The higher the degree of financial lever-

age, the lower the IB ratio. Nodett™s IB ratio does not vary over the business cycle. It is fixed

at 1.0, reflecting the total absence of interest payments. For Somdett, however, because inter-

est expense is fixed in a dollar amount while EBIT varies, the IB ratio varies from a low of

0.36 in a bad year to a high of 0.787 in a good year.

TA B L E 13.6

Ratio decomposition analysis for Nodett and Somdett

(1) (2) (3) (4) (5) (6)

Net Compound

Profit Pretax EBIT Sales Leverage

Pretax Profit Sales Assets Assets Factor

ROE Profit EBIT (ROS) (ATO) Equity (2) (5)

Bad year

Nodett 0.030 0.6 1.000 0.0625 0.800 1.000 1.000

Somdett 0.018 0.6 0.360 0.0625 0.800 1.667 0.600

Normal year

Nodett 0.060 0.6 1.000 0.100 1.000 1.000 1.000

Somdett 0.068 0.6 0.680 0.100 1.000 1.667 1.134

Good year

Nodett 0.090 0.6 1.000 0.125 1.200 1.000 1.000

Somdett 0.118 0.6 0.787 0.125 1.200 1.667 1.311

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ROS ATO ROA

TA B L E 13.7

Differences Supermarket chain 2% 5.0 10%

between ROS Utility 20% 0.5 10%

and ATO

across

industries

Factor 5, the ratio of assets to equity, is a measure of the firm™s degree of financial lever-

age. It is called the leverage ratio and is equal to 1 plus the debt/equity ratio.2 In our numeri-

leverage ratio

cal example in Table 13.6, Nodett has a leverage ratio of 1, while Somdett™s is 1.667.

Measure of debt to From our discussion in Section 13.2, we know that financial leverage helps boost ROE

total capitalization only if ROA is greater than the interest rate on the firm™s debt. How is this fact reflected in the

of a firm.

ratios of Table 13.6?

The answer is that to measure the full impact of leverage in this framework, the analyst

must take the product of the IB and leverage ratios (that is, factors 2 and 5, shown in Table

13.6 as column 6). For Nodett, factor 6, which we call the compound leverage factor, remains

a constant 1.0 under all three scenarios. But for Somdett, we see that the compound leverage

factor is greater than 1 in normal years (1.134) and in good years (1.311), indicating the posi-

tive contribution of financial leverage to ROE. It is less than 1 in bad years, reflecting the fact

that when ROA falls below the interest rate, ROE falls with increased use of debt.

We can summarize all of these relationships as follows:

ROE Tax burden Interest burden Margin Turnover Leverage

Because

ROA Margin Turnover

and

Compound leverage factor Interest burden Leverage

we can decompose ROE equivalently as follows:

ROE Tax burden ROA Compound leverage factor

Table 13.6 compares firms with the same ROS and ATO but different degrees of financial

leverage. Comparison of ROS and ATO usually is meaningful only in evaluating firms in the

same industry. Cross-industry comparisons of these two ratios are often meaningless and can

even be misleading.

For example, let us take two firms with the same ROA of 10% per year. The first is a su-

permarket chain and the second is a gas and electric utility.

As Table 13.7 shows, the supermarket chain has a “low” ROS of 2% and achieves a 10%

ROA by “turning over” its assets five times per year. The capital-intensive utility, on the other

hand, has a “low” ATO of only 0.5 times per year and achieves its 10% ROA by having an

ROS of 20%. The point here is that a “low” ROS or ATO ratio need not indicate a troubled

firm. Each ratio must be interpreted in light of industry norms.

Even within an industry, ROS and ATO sometimes can differ markedly among firms pur-

suing different marketing strategies. In the retailing industry, for example, Neiman-Marcus

pursues a high-margin, low-ATO policy compared to Wal-Mart, which pursues a low-margin,

high-ATO policy.

2 Equity Debt

Assets Debt

1 .

Equity Equity

Equity

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13 Financial Statement Analysis

TA B L E 13.8

Growth Industries financial statements, 2001“2003 ($thousands)

2000 2001 2002 2003

Income statements

Sales revenue $100,000 $120,000 $144,000

Cost of goods sold (including depreciation) 55,000 66,000 79,200

Depreciation 15,000 18,000 21,600

Selling and administrative expenses 15,000 18,000 21,600

Operating income 30,000 36,000 43,200

Interest expense 10,500 19,095 34,391

Taxable income 19,500 16,905 8,809

Income tax (40% rate) 7,800 6,762 3,524

Net income 11,700 10,143 5,285

Balance sheets (end of year)

Cash and marketable securities $ 50,000 $ 60,000 $ 72,000 $ 86,400

Accounts receivable 25,000 30,000 36,000 43,200