OLC SUPPLEMENT – CHAPTER 13
EXPANDING THE ROE PROFIT DRIVER ANALYSIS:
THE SCOTT FORMULA
In chapter 13, the return on equity (ROE) was decomposed into three ratios as follows (see
Exhibit 13.2):
ROE =
Net income
=
Average shareholders’ equity
Net income
Net sales
x
Net sales
x
Average total assets__ _
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
S
TA
IAT x S ] + [(NI + IAT - IAT) x L ]
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
expression:
ROE = (PMAT x AT
IAT) + (ROA
IAT) x L_
TA
TA
E
Rearranging again, we get:
ROE = PMAT x AT
IAT + ROA x L
IAT x L_
TA
TA
E
= PMAT x AT + ROA x L
E
E
IAT x (1 + L)
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
E
IAT x L_
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
operations.
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
1
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.
2
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.
2
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 longterm 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.
3
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
ROE.
Fiscal Year
Operating Return
Return from Leverage
(PMAT x AT) + [(ROA – IAT / L) x L/E]
=
ROE
2007
(0.066
x 1.880) + [(0.124
0.124
– 0.011)
0.097
x 0.861] =
0.221
2006
(0.073
x 1.957) + [(0.143
0.143
– 0.006)
0.086
x 0.631] =
0.229
2005
(0.069
x 1.993) + [(0.138
0.138
– 0.003)
0.077
x 0.577] =
0.215
2004
(0.067
x 2.011) + [(0.135
0.135
– 0.004)
0.069
x 0.527] =
0.204
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
ROE.
Company
Operating Return
Return from Leverage
PMAT x AT
+ (ROA – IAT / L) x L/E
=
ROE
RONA
(0.045
x 2.410) + [(0.109
0.109
– 0.018)
0.075
x 0.824] =
0.184
Canadian Tire
(0.049
x 1.410) + [(0.069
0.069
– 0.016)
0.062
x 1.164] =
0.131
4
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
Operating assets
Financial assets
Total assets
Liabilities and Equity
OA
FA _
OA + FA
Operating liabilities
Financial liabilities
Shareholders’ equity
Total liabilities and equity
OL
FL
SE
_
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
Less: Operating liabilities
OA
(OL)
Net operating assets
NOA
Financial liabilities
Less: Financial assets
Net financial liabilities
Shareholders’ equity
Net financial liabilities and equity
FL
(FA)
NFL
SE _
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.
4
See, for example, Stephen H. Penman, Financial Statement Analysis & Security Valuation (New York: McGrawHill Irwin, 2001), p. 216.
5
Scott, 2002, p. 13.
3
5
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
Cash
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.
6
Restructured Consolidated Balance Sheets
The Home Depot, Inc. and Subsidiaries
(amounts in millions)
Jan. 28, Jan. 29, Jan. 30,
2007
2006
2005
Net Operating Assets
Receivables, net
Merchandise Inventories
Other Current Assets
Net Property and Equipment
Goodwill, net
Other Assets
Operating Assets
Feb. 1,
2004
Feb. 2,
2003
3,223
12,822
1,341
26,605
6,314
1,001
51,306
2,396
11,401
665
24,901
3,286
601
43,250
1,499
10,076
450
22,726
1,394
228
36,373
1,097
9,076
303
20,063
833
129
31,501
1,072
8,338
254
17,168
575
244
27,651
Accounts Payable
Accrued Salaries and Related Expenses
Sales Taxes Payable
Deferred Revenue
Income Taxes Payable
Other Accrued Expenses
Other Long-Term Liabilities
Deferred Income Taxes
Operating Liabilities
Net Operating Assets
(7,356)
(1,295)
(475)
(1,634)
(217)
(1,936)
(1,243)
(1,416)
(15,572)
35,734
(6,032)
(1,068)
(488)
(1,757)
(388)
(1,560)
(1,172)
(946)
(13,411)
29,839
(5,766)
(1,055)
(412)
(1,546)
(161)
(1,578)
(763)
(1,309)
(12,590)
23,783
(5,159)
(801)
(419)
(1,281)
(175)
(1,210)
(653)
(967)
(10,665)
20,836
(4,560)
(809)
(307)
(998)
(227)
(1,127)
(491)
(362)
(8,881)
18,770
Net Financial Assets
Cash and Cash Equivalents*
Short-Term Investments
Notes Receivable
Financial Assets
Current Installments of Long-Term Debt
Long-Term Debt, Excluding Current Installments
Financial Liabilities
Net Financial Assets (Liabilities)
Total Stockholders' Equity
600
14
343
957
(18)
(11,643)
(11,661)
(10,704)
25,030
793
14
348
1,155
(513)
(2,672)
(3,185)
(2,030)
26,909
506
1,659
369
2,534
(11)
(2,148)
(2,159)
375
24,158
1,103
1,749
84
2,936
(509)
(856)
(1,365)
1,571
22,407
2,188
65
107
2,360
(7)
(1,321)
(1,328)
1,032
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,
2007
2006
2005
2004
Net interest expense (income)
365
81
14
3
Feb. 2,
2003
(42)
7
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.
Fiscal
Year
Return on Net
Operating Assets
(PMAT x AT)
2007
(0.066
x 2.771) + [(0.183
0.183
– 0.035)
0.036
x 0.245]
= 0.219
2006
(0.073
x 3.040) + [(0.222
0.222
– 0.031)
0.006
x 0.032]
= 0.228
2005
(0.069
x 3.276) + [(0.225
0.225
– (–0.009) x –0.042]
–0.010
2004
(0.066
x 3.273) + [(0.217
0.217
– (–0.001) x –0.062] = 0.204
–0.013
Return from Leverage
+ [(ROA – IAT / L) x L/E]
= ROE
= 0.215
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.
Company
Return on Net
Operating Assets
PMAT x AT
Return from Leverage
+ (ROA – IAT / L) x L/E
=
ROE
RONA
(0.045
x 3.316) + [(0.149
0.149
– 0.048)
0.031
x 0.303] =
0.180
Canadian Tire
(0.049
x 3.540) + [(0.173
0.173
– (–0.155) x –0.118] =
– 0.039
0.134
8
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.
9