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*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
Bodie’Kane’Marcus: IV. Security Analysis 13. Financial Statement © The McGraw’Hill
Essentials of Investments, Analysis Companies, 2003
Fifth Edition




458 Part FOUR Security Analysis


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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Fifth Edition




459
13 Financial Statement Analysis


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
Bodie’Kane’Marcus: IV. Security Analysis 13. Financial Statement © The McGraw’Hill
Essentials of Investments, Analysis Companies, 2003
Fifth Edition




460 Part FOUR Security Analysis


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
Bodie’Kane’Marcus: IV. Security Analysis 13. Financial Statement © The McGraw’Hill
Essentials of Investments, Analysis Companies, 2003
Fifth Edition




461
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

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