Third Pass
A P P E N D I X
Expanding the Dupont
Model: The Scott
Formula
13A
In Chapter 13, the return on equity (ROE) was decomposed into three ratios as follows:
ROE 5
5
Net earnings
Average shareholders’ equity
Net earnings
Net sales
Average total assets
3
3
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 generate net earnings. In the next
section, we show how additional elements can be introduced into the ROE formula to
gain further insight into the company’s profit drivers. This decomposition is followed
by an application of the expanded ROE formula to Canadian Tire’s financial results
for fiscal year 2012. 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 Canadian
Tire’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:
NE 5 Net earnings
S 5 Net sales
TA 5 Average total assets
E 5 Average shareholders’ equity
Using these abbreviations, the ROE formula can be written as
ROE 5
NE
S
TA
3
3
S
TA
E
We add and deduct interest after tax (IAT) to and from net earnings. We also note that
total assets equal liabilities plus shareholders’ equity (TA 5 L 1 E). These changes
produce the following equation:
ROE 5
S
(NE 1 IAT 2 IAT)
(L 1 E)
3
3
S
TA
E
Noting that (L 1 E) / E 5 1 1 L/E, we can expand this equation as follows:
ROE 5
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(NE 1 IAT 2 IAT)
S
3
(NE 1 IAT 2 IAT)
L
S
S
1
3
3
TA
S
TA E
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13A-2
APPENDIX 13A
Expanding the Dupont Model: The Scott Formula
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 5
NE 1 IAT
S
3
IAT
(NE 1 IAT 2 IAT) L
S
S
2
3
1
3
TA
S
TA
E
TA
The expression (NE 1 IAT)/S is a modified version of the profit margin ratio (NE/S),
where interest after tax is added to net earnings. We abbreviate this ratio as PMAT. We
note also that (S/TA) is total assets turnover, which we abbreviate as AT. The expression (NE 1 IAT 2 IAT) / TA can be rewritten as [(NE 1 IAT) / TA 2 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 5 PMAT 3 AT 2
IAT
IAT
L
1 ROA 2
3
E
TA
TA
Rearranging again, we get
ROE 5 PMAT 3 AT 2
IAT
TA
1 ROA 3
5 PMAT 3 AT 1 ROA 3
L IAT L
2
3
E
TA E
L IAT
L
2
3 11
TA
E
E
Noting that 1 1 L/E 5 (E 1 L)/E, and that E 1 L 5 TA, the expression
(IAT / TA) 3 (1 1 L/E) is reduced to IAT / E, which can be expressed as (IAT / L) 3
(L / E). Making these substitutions in the equation above produces the following result:
ROE 5 PMAT 3 AT 1 ROA 3
L IAT L
2
3
E
L
E
The final formula is expressed as follows:
ROE 5 PMAT 3 AT 1 (ROA 2 IAT /L) 3 (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 insight into the effect
of leverage on ROE.1 Managers and analysts can use this formula to assess the relative importance of each ratio 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 net profit margin ratio
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 ratio may necessitate
examination of turnover ratios for specific assets, such as trade receivables, inventories, and fixed assets, in order to identify which assets are causing the low turnover,
such as excessive inventory levels or excess productive capacity.
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APPENDIX 13A
13A-3
Expanding the Dupont Model: The Scott Formula
Application of the Scott Formula to Canadian Tire
To illustrate the application of the Scott formula, we use the financial statements of
Canadian Tire that are printed in Chapter 13. The various elements of the formula are
computed as follows, with statement of financial position amounts computed as the
averages of beginning and end-of-year values:
5 Interest expense 3 (1 2 tax rate) 5 $144.3 3 (1 2 $178.0/$677.2)
5 $106.4 million
PMAT 5 (NE 1 IAT)/S 5 ($499.2 1 $106.4)/$11,427.2 5 0.053
AT 5 S/TA 5 $11,427.2/$12,760.1 5 0.896 (as computed in Chapter 13, Exhibit 13.5)
ROA 5 (NE 1 IAT)/TA 5 ($499.2 1 $106.4)/$12,760.1 5 0.047 (as computed in
Chapter 13, ratio 2)
IAT/L 5 $106.4/[($7,929.8 1 $8,417.8/2] 5 0.0132
IAT
By inserting these numbers in the formula we get the following results:
ROE 5 PMAT 3 AT 1 (ROA 2 IAT/L) 3 (L/E)
5 (0.053 3 0.896) 1 (0.047 2 0.013) 3 1.780
5 0.047 1 0.061 5 0.108
The direct computation of ROE (NE/E) gives the same ratio ($499.2 / $4,586 5 0.109).
The difference of 0.001 is due to rounding.
The Scott formula indicates that Canadian Tire’s operations generated approximately 43 percent (4.7%) of the company’s return on equity (10.8%), and that
57 percent of ROE (6.1%) was contributed by financial leverage. Given the company’s
low cost of borrowing, Canadian Tire has the potential to increase its ROE by increasing its long-term debt.
The table below compares the various components of the Scott formula for fiscal
years 2010–2012. The results show (1) a gradual decrease in profit margin over the
three years, (2) an increase of the total asset turnover ratio that partially offset the
decrease in profit margin, and (3) reduced reliance on debt during the last three years.
The decrease in ROA in 2011 and 2012 is caused by the decrease in profit margin during this period. Furthermore, the decrease in debt relative to equity in 2011 and 2012
contributed to the decrease in return on assets for both years.
Fiscal Year
2012
Operating Return
(PMAT 3 AT)
2010
1
1
ROE
0.061
5
0.108
0.062
5
0.110
5
0.108
[(0.048 2 0.017) 3 1.936]
(0.059 3 0.821)
0.048
5
[(0.048 2 0.013) 3 1.780]
(0.054 3 0.886)
0.048
Return from Leverage
[(ROA 2 IAT / L) 3 L / E]
[(0.047 2 0.013) 3 1.780]
(0.053 3 0.896)
0.047
2011
1
1
0.060
The Scott formula for Canadian Tire’s competitors shows that RONA’s ROE for
fiscal 2012 benefited from a relatively higher asset turnover, but it had lower net
profit margin and lower debt-to-equity ratios than those of Canadian Tire. In contrast, Richelieu Hardware had a much higher profit margin ratio and a much higher
operating return than both Canadian Tire and RONA. However, Richelieu Hardware
did not benefit as much as Canadian Tire from the use of debt to finance the acquisition of assets.
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13A-4
APPENDIX 13A
Expanding the Dupont Model: The Scott Formula
Company
RONA
Operating Return
(PMAT 3 AT)
20.002
1
ROE
5
0.010
5
0.168
(0.137 2 0.0) 3 0.229
(0.081 3 1.693)
1
0.137
5
(0.012 2 0.017) 3 0.455
(0.007 3 1.748)
0.012
Richelieu
Hardware
Return from Leverage
(ROA 2 IAT / L) 3 L / E
1
0.031
Refinements to the Scott Formula3
We noted in endnote 2 that the calculated cost of debt for Canadian Tire is relatively
low because we divided interest expense (after tax) by total liabilities. However, not
all liabilities reported on the statement of financial position 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 statement of financial position items may need to be
restructured in order to highlight the operating capital that leads to operating returns
and the financial capital that results in interest payments to lenders. The assets and
liabilities reported on a statement of financial position can be regrouped into the following main components:4
Assets
Operating assets
Financial assets
Total assets
OA
FA
OA 1 FA
Liabilities and Equity
Operating liabilities
Financial liabilities
Shareholders’ equity
Total liabilities and equity
OL
FL
SE
OL 1 FL 1 SE
To distinguish operating items from financial items, we could restructure the statement
of financial position by deducting operating liabilities from operating assets and financial assets from financial liabilities as follows:
Assets
Operating assets
Less: Operating liabilities
Net operating assets
OA
(OL)
NOA
Liabilities and Equity
Financial liabilities
Less: Financial assets
Net financial liabilities
Shareholders’ equity
Net financial liabilities and equity
FL
(FA)
NFL
SE
NFL 1 SE
If financial assets exceed financial liabilities, then the net financial assets will appear
on the assets side of the statement of financial position. 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 statement of financial position appear
below.5 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 assets (NFA). If financial
liabilities exceed financial assets, then a net financial liability (NFL) will result.
The sum of NOA and NFA (or the difference between NOA and NFL) equals shareholders’ equity.
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APPENDIX 13A
13A-5
Expanding the Dupont Model: The Scott Formula
1
1
1
1
1
5
2
2
2
2
5
1
1
5
2
2
2
5
5
Restructured Statement of Financial Position
Net operating assets
Cash
Accounts receivable
Inventories
Prepaid expenses and other current assets
Property, plant, and equipment
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 statements of financial position of Canadian Tire for fiscal years
2010–2012, which follow, indicate that Canadian Tire had net financial liabilities for
fiscal years 2010 through 2012. Normally, net financial liabilities result in net interest expense, and net financial assets yield net interest income. For Canadian Tire, this
observation is true for all fiscal years. 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 STATEMENTS OF FINANCIAL POSITION
CANADIAN TIRE CORPORATION, LIMITED
(amounts in millions)
Dec. 29,
Dec. 31,
Jan. 1,
2012
2011
2011
Net Operating Assets
Receivables, net
$ 5,016.3
$ 4,911.0
$ 4,724.9
Merchandise inventories
1,503.3
1,448.6
901.0
Other current assets
44.6
74.8
157.7
Property and equipment, net
3,438.6
3,438.3
3,300.6
Goodwill and intangible assets, net
1,089.9
1,110.0
361.4
40.4
36.8
34.6
Other assets
Operating Assets
11,133.1
11,019.5
9,480.2
Deposits
(2,422.8)
(2,284.5)
(1,880.1)
Trade and other payables
(1,631.3)
(1,640.9)
(1,179.9)
Provisions
(240.6)
(247.0)
(221.3)
Income tax payable
(5.5)
(3.9)
—
Other long-term liabilities
(213.4)
(205.7)
(137.1)
(77.7)
(66.1)
—
Deferred income taxes
Operating Liabilities
4,591.3
4,448.1
3,418.4
Net Operating Assets
6,541.8
6,571.4
6,061.8
Jan. 3,
2010
$ 4,862.5
933.0
150.8
3,281.6
335.4
46.1
9,609.4
(2,060.3)
(1,192.9)
(247.6)
—
(127.5)
—
3,628.3
5,981.1
(continued)
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13A-6
APPENDIX 13A
Expanding the Dupont Model: The Scott Formula
RESTRUCTURED CONSOLIDATED STATEMENTS OF FINANCIAL POSITION
CANADIAN TIRE CORPORATION, LIMITED
(amounts in millions)
Dec. 29,
Dec. 31,
Jan. 1,
2012
2011
2011
Cash and cash equivalents
1,015.5
325.8
568.9
Short-term investments
168.9
196.4
196.7
Long-term receivables
681.2
668.9
726.9
Long-term investments
182.7
128.2
75.8
Financial Assets
2,048.3
1,319.3
1,568.3
Bank indebtedness
(86.0)
(124.8)
(118.0)
Short-term borrowings
(118.9)
(352.6)
(100.6)
Loans payable
(623.7)
(628.7)
(687.0)
Current portion of long-term debt
(661.9)
(27.9)
(354.2)
(2,336.0)
(2,347.7)
(2,365.4)
Long-term debt, excluding current portion
Financial Liabilities
3,826.5
3,481.7
3,625.2
(1,778.2)
(2,162.4)
(2,056.9)
Net Financial Assets (Liabilities)
4,763.6
4,409.0
4,004.9
Total Shareholders’ Equity
EXCERPTS FROM CONSOLIDATED STATEMENTS OF EARNINGS
CANADIAN TIRE CORPORATION, LIMITED
For the Years Ended
(amounts in millions)
Dec. 30, 2012
Dec. 31, 2011
Net finance costs
$126.2
$132.2
Jan. 3,
2010
885.8
60.9
802.3
48.8
1,797.8
(83.7)
(163.0)
(757.4)
(690.6)
(2,441.1)
4,135.8
(2,338.0)
3,643.1
Jan. 1, 2011
$135.7
The various components of the Scott formula are recomputed for Canadian Tire 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 dropped steadily from 2010
to 2012. On the other hand, the total asset turnover ratio increased in 2011 and again
in 2012. The total asset turnover ratio is also higher than the previous computation
because NOA are lower than total assets in a traditional statement of financial position.
Fiscal Year
2012
Return on Net
Operating Assets
(PMAT 3 AT)
1
2011
(0.054 3 1.644)
2010
(0.059 3 1.530)
0.089
0.091
5
ROE
5
0.109
5
0.111
5
0.116
[(0.090 2 0.047) 3 0.430]
(0.052 3 1.743)
0.090
Return from Leverage
[(ROA 2 IAT / L) 3 L / E]
1
0.019
[(0.089 2 0.046) 3 0.501]
1
0.022
[(0.091 2 0.047) 3 0.575]
1
0.025
The results for RONA and Richelieu Hardware indicate that net operating assets made
a greater contribution to ROE than previously indicated in the initial decomposition of
their ROE. Both RONA and Richelieu Hardware did not benefit from the use of debt
to increase ROE. In fact, the return from leverage was negative for both companies,
and reduced their ROE.
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APPENDIX 13A
Company
RONA
Return on Net
Operating Assets
(PMAT 3 AT )
1
1
5
ROE
20.004
5
0.010
5
0.168
[(0.194 2 0.004) 3 20.133]
(0.081 3 2.40)
0.194
Return from Leverage
(ROA 2 IAT/L) 3L/E
[(0.014 2 0.046) 3 0.127]
(0.006 3 2.258)
0.014
Richelieu
Hardware
13A-7
Expanding the Dupont Model: The Scott Formula
1
20.026
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.
Endnotes
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.
2This after-tax interest rate is rather low because we divided interest expense by all the
liabilities, both current and non-current. 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 and non-current liabilities, especially if these
liabilities consist of trade payables and accrued liabilities, provisions, and other non-interestbearing liabilities, as in the case of Canadian Tire. Note 25 to Canadian Tire’s 2012 financial
statements indicates that the company had $3,006 million in long-term debt at the end of its
2012 fiscal year, and $2,997 million at the end of its 2011 fiscal year, for an average amount of
$3001.5 million. Interest expense for the year totalled $144.3 million, including $3.8 million
that was capitalized. Hence, the average interest rate on Canadian Tire’s long-term debt is
approximately 4.81 percent ($144.3/$3,001.5), and its after-tax interest rate is 3.54 percent
[4.81 3 (1 2 0.263)]. Given that we used interest expense of $144.3, 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 1.3 percent understates the company’s true after-tax
cost of borrowing of 3.54 percent.
3This 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.
4See, for example, Stephen H. Penman, Financial Statement Analysis & Security Valuation
(New York: McGraw-Hill Irwin, 2001), p. 216.
5Scott, 2002, p. 13.
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