OLC SUPPLEMENT – CHAPTER 13

                               THE SCOTT FORMULA

In chapter 13, the return on equity (ROE) was decomposed into three ratios as follows (see
Exhibit 13.2):

                Net income                 Net income            Net sales           Average total assets__ _
ROE =                                  =                x                      x
        Average shareholders’ equity       Net sales        Average total assets Average shareholders’ equity

This expression of the ROE can be decomposed further for a more detailed analysis of the
company’s operating and financial strategies to earn profit. In the next section, we show how we
can introduce additional elements into the ROE formula to gain further insights about the
company’s profit drivers. This decomposition is followed by an application of the expanded ROE
formula to Home Depot’s financial results for fiscal year 2007 (January 30, 2006 – January 28,
2007). The reader who is not interested in the derivation of the expanded formula can skip the
next section and proceed to the expanded analysis of Home Depot’s ROE.

Further Decomposition of the DuPont Formula into the Scott Formula
Let us first introduce the following abbreviations of the various elements of the ROE formula:

NI = Net income
S = Net sales
TA = Average total assets
E = Average shareholders’ equity

Using these abbreviations, the ROE formula can be written as:

ROE = NI x S x TA_
      S    TA   E

We add and deduct interest after tax (IAT) to net income. We also note that total assets equal
liabilities plus shareholders’ equity (TA = L + E). These changes produce the following equation:

ROE = (NI + IAT - IAT) x S x (L + E)
           S             TA     E

Noting that (L + E) / E = 1 + L/E, we can expand this equation as follows:

ROE = [(NI + IAT - IAT) x S ] + [(NI + IAT - IAT) x S x L ]
             S           TA              S          TA  E
We regroup the various elements on the right side of the equation by expanding the first
expression and cancelling out the S in the second expression:

ROE = [NI + IAT x S             IAT x S ] + [(NI + IAT - IAT) x L ]
          S      TA             S TA              TA            E

The expression (NI + IAT)/S is a modified version of the profit margin ratio (NI/S) where interest
after tax is added to net income. We abbreviate this ratio as PMAT. We note also that (S/TA) is
total assets turnover, which we abbreviate as AT. The expression, (NI + IAT - IAT) / TA, can be
rewritten as [(NI + IAT) / TA - IAT / TA]. The first element of this expression is the return on
assets (ROA) as defined in Chapter 13. These refinements to the equation produce the following

                             IAT) + (ROA           IAT) x L_
                            TA                    TA       E

Rearranging again, we get:

                            IAT + ROA x L            IAT x L_
                           TA                E      TA      E

       = PMAT x AT + ROA x L                  IAT x (1 + L)
                           E                  TA            E

Noting that 1 + L/E = (E + L)/E, and that E + L = TA, the expression (IAT / TA) x (1 + L/E) is
reduced to IAT / E, which can be expressed as (IAT / L) x (L / E). Making these substitutions in the
equation above produces the following result:

ROE = PMAT x AT + ROA x L                     IAT x L_
                        E                     L        E

The final formula is expressed as follows:

ROE = PMAT x AT + (ROA                IAT / L) x (L / E)

where IAT / L is the after-tax cost of debt, which is equal to after-tax interest divided by average
liabilities. The first part of this formula reflects the return from operating activities, and the
second part reflects the return to shareholders from using debt to finance the company’s

This expanded version of the ROE formula provides more insights into the effect of leverage on
ROE.1 Managers and analysts can use this formula to assess the relative importance of each ratio

 This decomposition of the ROE formula is attributed to Dr. William Scott, a retired professor, who has taught
accounting and auditing at various Canadian universities.

through its impact on the company’s ROE. Analysts can determine if the company’s ROE is
achieved through successful operations (profit margin and turnover) or by using debt. A low or
deteriorating profit margin would require analysis of the major expense items that resulted in a
low ROE and whether they can be reduced. Similarly, a low total asset turnover may necessitate
examination of turnover ratios for specific assets, such as accounts receivable, inventories, and
fixed assets in order to identify which assets are causing the low turnover, such as excessive
inventory levels, or excess productive capacity.

Application of the Scott Formula to Home Depot
To illustrate the application of the Scott formula, we use the financial statements of Home Depot
that are printed in Chapter 13. The various elements of the formula are computed as follows, with
balance sheet amounts computed as the averages of beginning and end-of-year values:

IAT      = Interest expense x (1 – tax rate) = $392 x (1 – $3,547/$9,308) = $242.6 million
PMAT = (NI + IAT)/S = ($5,761 + $242.6) / $90,837 = 0.066
AT       = S / TA = $90,837 / $48,334 = 1.88 (as computed in Chapter 13, ratio 7)
ROA = (NI + IAT)/TA = ($5,761 + $242.6)/$48,334 = 0.124 (as computed in Chapter 13, ratio 2)
IAT/L = $242.6 / [($17,496 + $27,233) / 2] = 0.0112
L/E      = [($17,496 + $27,233) / 2] / [($26,909 + $25,030) / 2] = 0.861

By inserting these numbers in the formula we get the following results:

ROE = PMAT x AT + (ROA IAT / L) x (L/E)
    = (0.066 x 1.88) + (0.124 – 0.011) x 0.861
    = 0.124 + 0.097 = .221

The direct computation of ROE (NI/E) gives the same ratio ($5,761 / $25,970 = 0.221).

The Scott formula indicates that Home Depot’s operations generated approximately 55 percent
(12.4%) of the company’s return on equity (22.1%), and that 45 percent of ROE (9.7%) was
contributed by financial leverage. Given the company’s low cost of borrowing, Home Depot has
the potential to increase its ROE by increasing its long-term debt.

  This after-tax interest rate is rather low because we have divided interest expense by all the liabilities, both current
and long-term. In reality, companies incur interest mainly on their short-term bank loans and notes, and long-term
debt (including the current portion). But, interest is not incurred on other current liabilities and non-current
liabilities, especially if these liabilities consist primarily of accounts payable and accrued liabilities as in the case of
Home Depot. Note 2 to Home Depot’s 2007 financial statements indicates that the company had $2,159 million in
long-term debt at the end of its 2007 fiscal year, and $1,359 million at the end of its 2006 fiscal year for an average
amount of $1,762 million. Interest charges for the year totalled $110 million including $40 million that was
capitalized. Hence, the average interest rate on Home Depot’s long-term debt is approximately 6.25 percent
($110/$1,762), and its after-tax interest rate is 3.95 percent [6.25 x (1 – .368)]. Given that we used interest expense
of $70, which excludes the portion that was capitalized, and divided this amount by total liabilities instead of long-
term debt, the average after-tax interest rate of 1.1 percent understates the company’s true after-tax cost of borrowing
of 3.95 percent.

     The table below compares the various components of the Scott formula for fiscal years
2004-2007. The results show (1) a decrease in profit margin in 2007 after successive increases in
2004-2006, (2) a deterioration of the total asset turnover, (3) and increased reliance on debt. The
decrease in asset turnover was offset by an increase in profit margins during the years 2004-2006
so that ROA increased during this period. Furthermore, the increased use of debt resulted in an
increasing return from leverage, which helped in increasing ROE over time, from 20.4 percent in
2004 to 22.1 percent in 2007. This illustration shows clearly the effect of financial leverage on

                     Operating Return Return from Leverage
     Fiscal Year     (PMAT x AT) + [(ROA – IAT / L) x L/E]                          =    ROE

         2007        (0.066      x 1.880) + [(0.124      – 0.011)      x 0.861] =        0.221
                              0.124                        0.097

         2006        (0.073      x 1.957) + [(0.143      – 0.006)      x 0.631] =        0.229
                              0.143                        0.086

         2005        (0.069      x 1.993) + [(0.138      – 0.003)      x 0.577] =        0.215
                              0.138                        0.077

         2004        (0.067      x 2.011) + [(0.135      – 0.004)      x 0.527] =        0.204
                              0.135                        0.069

The Scott formula for Home Depot’s competitors shows that RONA’s ROE for fiscal 2007
benefited from a relatively higher asset turnover but lower profit margin and lower debt-to-equity
ratios than those of Home Depot. In contrast, Canadian Tire has a much lower asset turnover
ratio, but it relied on a relatively high level of debt to increase the return from leverage and hence

                      Operating Return      Return from Leverage
       Company        PMAT x AT        + (ROA – IAT / L) x L/E                       =    ROE

         RONA          (0.045      x 2.410) + [(0.109      – 0.018)     x 0.824] =        0.184
                                0.109                        0.075

     Canadian Tire     (0.049      x 1.410) + [(0.069      – 0.016)     x 1.164] =        0.131
                                0.069                        0.062

Refinements to the Scott Formula3
We noted earlier, in footnote 2, that the calculated cost of debt for Home Depot is relatively low
because we have divided interest expense (after tax) by total liabilities. However, not all
liabilities reported on the balance sheet result in interest expense. Consequently, the amount that
is used for liabilities should be limited to those financial liabilities that attract interest.
Furthermore, many companies invest in financial assets (e.g., marketable securities, bonds) that
generate interest income which offsets interest expense. These financial assets should probably
be netted against financial liabilities. For this reason, the balance sheet items may need to be
restructured in order to highlight the operating capital that leads to operating returns and the
financial capital which results in interest payments to lenders. The assets and liabilities reported
on a balance sheet can be regrouped into the following main components4:

    Assets                                              Liabilities and Equity

    Operating assets                     OA             Operating liabilities                        OL
    Financial assets                     FA _           Financial liabilities                        FL
                                                        Shareholders’ equity                         SE    _
    Total assets                      OA + FA           Total liabilities and equity            OL + FL + SE

To distinguish operating items from financial items, we could restructure the balance sheet by
deducting operating liabilities from operating assets and financial assets from financial liabilities
as follows:

    Assets                                              Liabilities and Equity

    Operating assets                      OA            Financial liabilities                           FL
    Less: Operating liabilities          (OL)           Less: Financial assets                         (FA)
                                                        Net financial liabilities                      NFL
                                                        Shareholders’ equity                            SE _
    Net operating assets                 NOA            Net financial liabilities and equity         NFL + SE

If financial assets exceed financial liabilities, then the net financial assets would appear on the
assets side of the balance sheet. The net operating assets generate operating returns and the net
financial liabilities are associated with net interest expense to determine the effect of financial
leverage on ROE.

The main elements of a restructured balance sheet appear on the next page5. Operating assets are
listed first followed by operating liabilities, and the difference is computed as net operating assets
(NOA). Similarly, financial liabilities are deducted from financial assets to obtain net financial
  This section has benefited from an article by Thomas W. Scott titled “Structuring Ratio Analysis Using the Scott
Formula” that appeared in Canadian Accounting Education and Research News, a quarterly publication of the
Canadian Academic Accounting Association, Autumn 2002, pp. 12-14.
  See, for example, Stephen H. Penman, Financial Statement Analysis & Security Valuation (New York: McGraw-
Hill Irwin, 2001), p. 216.
  Scott, 2002, p. 13.

assets (NFA). If financial liabilities exceed financial assets, then a net financial liability (NFL)
would result. The sum of NOA and NFA (or the difference between NOA and NFL) equals
shareholders’ equity.

                                   Restructured Balance Sheet

                            Net Operating Assets
                        +   Accounts receivable
                        +   Inventories
                        +   Prepaid expenses and other current assets
                        +   Property, plant and equipment
                        +   Investments
                        +   Goodwill and other intangibles
                        =   Operating assets
                        –   Accounts payable
                        –   Accrued expenses
                        –   Future income tax liabilities
                        –   Other long-term liabilities
                        =   Net operating assets (NOA)

                            Net Financial Assets
                            Cash equivalents
                        +   Short-term investments
                        +   Long-term investments
                        =   Financial assets
                        –   Bank loans
                        –   Notes payable
                        –   Long-term debt including current portion
                        =   Financial liabilities
                            Net financial assets (NFA)

                        = Shareholders’ equity

The restructured balance sheets of Home Depot for fiscal years 2003–2007, which appear on the
next page, indicated that Home Depot had net financial assets for fiscal years 2003-2005 and net
financial liabilities for the next two years. Normally, net financial liabilities result in net interest
expense and net financial assets yield net interest income. For Home Depot, this observation is
true for fiscal years 2003, 2006 and 2007, but does not hold for fiscal years 2004 and 2005. Net
interest expense may be associated with net financial assets if interest accrued on financial
liabilities exceeds interest earned on financial assets, and vice versa.

                                 Restructured Consolidated Balance Sheets
                                   The Home Depot, Inc. and Subsidiaries
                                           (amounts in millions)
                                                       Jan. 28, Jan. 29, Jan. 30,                Feb. 1,      Feb. 2,
                                                          2007     2006     2005                   2004         2003
Net Operating Assets
 Receivables, net                                              3,223       2,396      1,499       1,097        1,072
 Merchandise Inventories                                      12,822      11,401     10,076       9,076        8,338
 Other Current Assets                                          1,341         665        450         303          254
 Net Property and Equipment                                   26,605      24,901     22,726      20,063       17,168
 Goodwill, net                                                 6,314       3,286      1,394         833          575
 Other Assets                                                  1,001         601        228         129          244
Operating Assets                                              51,306      43,250     36,373      31,501      27,651

 Accounts Payable                                            (7,356)     (6,032)     (5,766)     (5,159)      (4,560)
 Accrued Salaries and Related Expenses                       (1,295)     (1,068)     (1,055)       (801)        (809)
 Sales Taxes Payable                                           (475)       (488)       (412)       (419)        (307)
 Deferred Revenue                                            (1,634)     (1,757)     (1,546)     (1,281)        (998)
 Income Taxes Payable                                          (217)       (388)       (161)       (175)        (227)
 Other Accrued Expenses                                      (1,936)     (1,560)     (1,578)     (1,210)      (1,127)
 Other Long-Term Liabilities                                 (1,243)     (1,172)       (763)       (653)        (491)
 Deferred Income Taxes                                       (1,416)       (946)     (1,309)       (967)        (362)
Operating Liabilities                                       (15,572)    (13,411)    (12,590)    (10,665)      (8,881)
Net Operating Assets                                          35,734      29,839      23,783      20,836      18,770

Net Financial Assets
  Cash and Cash Equivalents*                                     600         793         506       1,103        2,188
  Short-Term Investments                                           14         14       1,659       1,749           65
  Notes Receivable                                               343         348         369          84          107
Financial Assets                                                 957       1,155       2,534       2,936        2,360
  Current Installments of Long-Term Debt                         (18)      (513)         (11)      (509)           (7)
  Long-Term Debt, Excluding Current Installments            (11,643)     (2,672)     (2,148)       (856)      (1,321)
Financial Liabilities                                       (11,661)     (3,185)     (2,159)     (1,365)      (1,328)
Net Financial Assets (Liabilities)                          (10,704)     (2,030)         375       1,571        1,032
Total Stockholders' Equity                                    25,030     26,909      24,158      22,407       19,802
* Home Depot did not disclose its cash equivalents separately, so we classified both cash and cash equivalents as
  financial assets.

                           Excerpts from Consolidated Statements of Earnings
                                 The Home Depot, Inc. and Subsidiaries
                                          (amounts in millions)
                                                                  For the Years Ended
                                                      Jan. 28, Jan. 29, Jan. 30, Feb. 1,                    Feb. 2,
                                                         2007     2006     2005     2004                      2003

Net interest expense (income)                                    365          81          14          3        (42)

The various components of the Scott formula are recomputed for Home Depot by replacing TA
with NOA, L with NFL(A), and IAT with net interest expense (income) after tax. The results
below confirm that profit margin was relatively stable during the period 2004-2006, but dropped
significantly in 2007. On the other hand, the asset turnover ratio shows a steady decrease over the
last three years. The asset turnover ratio is also higher than the previous computation because
NOA are lower than total assets in a traditional balance sheet.

                    Return on Net
       Fiscal      Operating Assets           Return from Leverage
       Year       (PMAT x AT)           + [(ROA – IAT / L) x L/E]                = ROE

       2007       (0.066      x 2.771) + [(0.183     – 0.035)       x 0.245]     = 0.219
                           0.183                        0.036

       2006       (0.073      x 3.040) + [(0.222     – 0.031)       x 0.032]     = 0.228
                           0.222                        0.006

       2005       (0.069      x 3.276) + [(0.225     – (–0.009) x –0.042]        = 0.215
                           0.225                        –0.010

       2004       (0.066      x 3.273) + [(0.217     – (–0.001) x –0.062] = 0.204
                           0.217                        –0.013

The net financial assets for fiscal years 2004 and 2005 result in negative returns from leverage,
which reduce the return from net operating assets. However, the net financial liabilities for fiscal
years 2006 and 2007 produce positive returns. These results indicate that Home Depot’s use of
debt, particularly in 2007, improved the return to shareholders’ equity.

The results for RONA and Canadian Tire indicate that net operating assets made a greater
contribution to ROE than previously indicated in the initial decomposition of their ROE on page
4. RONA did benefit from the use of debt to increase ROE, but Canadian Tire did not. Although
the interest rates on Canadian Tire’s long-term debt are mostly in the range of 4.95 percent to
6.32 percent, its cash equivalents and loans receivable exceeded its financial liabilities, thus
resulting in a negative interest rate, a negative leverage ratio, and a negative contribution from
financial leverage.

                      Return on Net
                     Operating Assets           Return from Leverage
      Company        PMAT x AT             + (ROA – IAT / L) x L/E                 =   ROE

        RONA         (0.045      x 3.316) + [(0.149      – 0.048)     x 0.303] =       0.180
                              0.149                        0.031

    Canadian Tire    (0.049      x 3.540) + [(0.173      – (–0.155) x –0.118] =        0.134
                              0.173                        – 0.039

In conclusion, the decomposition of the Dupont formula into various components highlights the
main drivers of a company’s return on equity and draws management’s attention to areas that
need improvement. Analysts may use the details provided by the Scott formula to evaluate the
performances of companies and make appropriate recommendations for investment purposes.


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