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ROCE ROCE CAPITAL TURNOVER CAPITAL TURNOVER GROWTH GROWTH ROIC ROIC LEVERAGE LEVERAGE D/E D/E ROE ROE MARGIN MARGIN VALUE CREATION VALUE CREATION EBIT EBIT ND/E ND/E ROA ROA WACC WACC EVA EVA Goals, Relationships, and Measurement Methods CTO CTO EBITDA EBITDA SURVIVAL SURVIVAL ND/EBITDA ND/EBITDA RISK RISK CAPITAL CAPITAL MARKET-TO-BOOK MARKET-TO-BOOK SALES SALES CASH FLOW CASH FLOW EQUITY EQUITY LIABILITY LIABILITY COST OF EQUITY COST OF EQUITY CAPITAL EMPLOYED CAPITAL EMPLOYED DIVIDEND DIVIDEND EXCESS PROFIT EXCESS PROFIT FINANCIAL STRENGTH FINANCIAL STRENGTH OPERATIONS OPERATIONS FINANCE FINANCE Sven-Erik Johansson GEARING GEARING Mikael Runsten COST OF DEBT COST OF DEBT RETURN RETURN PROFITABILITY PROFITABILITY MARKET PRICE MARKET PRICE EARNINGS EARNINGS PROFIT PROFIT

The Profitability, Financing, and Growth of the Firm

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Art. No 6887 ISBN 978-91-44-16157-0 Third edition 3:1 © Studentlitteratur 1998, 2014, 2023 studentlitteratur.se Studentlitteratur AB, Lund Cover design: Francisco Ortega Printed by Dimograf, Poland 2023

CONTENTS

Preface 7 1 Conceptual Framework 9 2 Profit, rate of return, and growth as conditions for the survival of the firm 11

2.1 2.2 2.3 2.4 2.5

Profit is no measure of profitability 11 The market price for capital 12 Relationships between the market value of equity and the return on equity 13 Relationships between growth, return, and equity ratio 22 Illustrations 24

3 Leverage relationship: the link between return and the liabilities-to-equity ratio 29

3.1 3.2 3.3 3.4

Measures of return on capital 29 Relationships between different return measures 31 Relationships when the values of variables change 35 Illustrations and exercises 40

4 The rate of return, the liabilities-to-equity ratio, and risk 43

4.1 4.2 4.3 4.4

Financial policy considerations and risk 43 Financial policy as a problem of risk 47 Valuation of risk and selection of liabilities-to-equity ratio 49 The interest coverage ratio 53

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Contents

5 Calculation of the rate of return and taxation 57

5.1 5.2 5.3 5.4 5.5

Introduction 57 No temporary or permanent differences 59 Only temporary differences 60 Only permanent differences 62 Illustrations and exercises 66

6 The DuPont relationship and alternative ways to analyze operating performance 69

6.1 6.2 6.3

e split of ROA into a margin and a capital turnover Th component 69 Capital employed or invested capital instead of total assets 77 Exercises 90

7 The relation­­ship between growth, rate of return and the liabilities-to-equity ratio 93

7.1 7.2 7.3 7.4 7.5 7.6

Targets concerning growth 93 Balanced financial growth 94 Growth of equity 97 A few measurement issues 104 Opening or average capital: How do you choose? 106 Illustrations and exercises 107

8 Summary of financial relationships 109

8.1 8.2 8.3 8.4

4

S ummary of relationships with total assets as a capital basis 109 Capital employed and invested capital as capital basis 113 Confusing terminology 114 Illustrations and exercises 117

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9 Cash flow and growth in financial balance 129

9.1 9.2 9.3 9.4 9.5

Cash flow statement 129 Cash flow and targets for return, growth, and leverage 131 Investment capacity at set financial targets 135 Loan repayment required by a ND/EBITDA covenant 138 Illustrations and exercises 146

10 Growth – allowing a changed debt-equity ratio 149

10.1 10.2 10.3

Planned continuous changes 149 Unplanned continuous changes 152 Planned changes of a non-recurring nature 154

11 Management control, return, and growth for a group and its parts 157

11.1 11.2 11.3 11.4 11.5

ontrol via targets for ROCE and financially C stable growth 158 The relationship between ROCE and capacity for growth 161 Control of ROIC and free cash flow 166 Control with the focus on economic profit as an alternative to ROIC 167 Illustrations and exercises 172

12 Returns, growth, and equity valuation 175

12.1 12.2 12.3 12.4 12.5 12.6 12.7

Valuation of Multibrands 175 Future dividends 179 Equity and economic profit 184 Future free cash flow 186 Invested capital and future economic profit 190 A simple benchmark model 192 Summary 199

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Contents

13 Pitfalls of using financial key ratios 201

13.1 13.2 13.3 13.4 13.5 13.6 13.7

Origin of problems 201 Unrealized appreciation of value in fixed assets 203 Expensed intangible investments 205 Growth by acquisition 210 Stakeholders with multiple roles 210 Deliberate improvements 213 Illustrations and exercises 215

Symbols/Definitions References 223 Index 225

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CHAPTER 3

Leverage relationship: the link between return and the liabilities-to-equity ratio

This chapter will define some basic return measures, and then introduce the link between return on assets (ROA) and return on equity (ROE). The amount of liability financing (leverage) and the cost of liabilities (COL) will prove to be important components. The relationship we introduce in the chapter is called the leverage relationship.

3.1

Measures of return on capital

Return on capital is generally defined as the relationship between an accountingbased earnings measure1 and an accounting-based capital measure, i.e.: Return =

Earnings Capital

This relationship expresses the return which the capital generates. Calculations of the return can refer to various measures of capital, for example equity or total assets (which in turn correspond to the sum of equity and liabilities).

The choice of the earnings measure will depend on the capital measure we select. This is clarified with a simplified example. (This example will be the basis for the evolving discussion in this book and will thus be developed in stages. The reader is therefore advised to study it closely).

1 We will use the terms earnings and profit as synonyms.

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3 Leverage relationship: the link between return and …

Main example 3.1

The company which our main example describes reports the following financial position and results, shown here in a simplified form: Balance Sheet

Assets 1,000

Income Statement Equity 400

Earnings before interest expense (EBIE) 80 Interest expense –24 Earnings before tax (EBT) 56

Liability 600

(The amounts are denominated in million EUR in this example and throughout the book.)

Three useful rate of return metrics are derived from this information.

1 Return on equity (ROE) =

Earnings before tax 56 = = 14% Equity 400

2 Cost of liabilities (COL) =

Interest expense 24 = = 4% Liabilities 600

3 Return on assets (ROA) = Earnings before interest expense = 80 = 8% Assets 1,000

ROA =

30

80 = 8% 1,000

Assets 1,000

Equity 400

ROE =

56 = 14% 400

Liability 600

COL =

24 = 4% 600

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3 Leverage relationship: the link between return and …

Return on equity (ROE) is calculated on the basis of the earnings after interest expense. We have so far ignored the company’s income taxes in the example. The effect of taxes on the rate of return metrics is dealt with further in Chapter 5. The average cost of liabilities (COL) is the return which lenders obtain, on average, on the capital they have lent to the company.

For the time being, we will disregard the problems associated with the measurement of interest expenses and with the criteria for selecting the liabilities to be included in the metric. We will return to these questions in Chapter 6.

Return on assets (ROA) is calculated based on earnings before interest expense. It is important to note this as it gives the ratio the important feature of being independent of the mix of financing the company has chosen. This measure of return is consequently unaffected by the company’s financial policy (defined as its choice of capital structure), but otherwise dependent upon company policy as regards pricing, product policy, market policy, investment policy, and so on.

When using the above definitions, the rate of return is expressed as a decimal, i.e., 0.08 = 8 percent. In mathematical operations, it is appropriate to denote it in decimal form, while in other situations it may be preferable to express it as a percentage. For the sake of simplicity, we will use the variable names above to express both decimal and percentage values.

If no liabilities and no interest expenses exist, then ROE will be equal to ROA. If there is a difference between ROE and ROA, it thus depends upon the presence of liabilities and the interest expenses which accompany them, and the actual difference depends upon the company’s financial policy. The relationship between these return metrics is analyzed in more detail in the next section.

3.2

Relationships between different return measures

The return on equity (ROE) is dependent on the return on total assets (ROA), and on the average cost of total liabilities (COL) as well as the liabilities-toequity ratio (L/E). Let us examine this relationship with the help of our main example. We will call total assets A, liabilities L, and equity E.

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3 Leverage relationship: the link between return and …

Main example 3.2

The earnings after interest expense (56) are split in the following way: one component corresponds to the return which is obtained on all assets in the company, and thus also on the assets financed by the equity

the other component is what the shareholders earn on borrowed capital, when it is invested within the company giving a return on total assets of 10% at a margin of 4% in relation to the cost of liabilities which is 6%

ROA × E 0.08 × 400 = 32

ROA =

80 = 8% 1,000

(ROA – COL) × L (0.10 – 0.06) × 600 = 24

Assets 1,000

Equity 400

ROE =

(32 + 24) = 14% 400

Liability 600

COL =

24 = 4% 600

We have now split the earnings which are assigned to equity, i.e., the earnings before tax (after interest expense, 56). To split return on equity (ROE) in the same way, the different income components must be divided by the amount of equity. We consequently divide both ROA × E and (ROA–COL) × L by E and get the following expressions. Note that the expression after each equation sign is only a mathematical simplification.

ROA × E = ROA E (ROA – COL) × L L = (ROA – COL) × E E

The sum of these two simplified components must equal ROE and we thus conclude: L ROA + (ROA – COL) × = ROE E or with numbers: 8% + (8% – 4%) ×

32

600 = 14% 400

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3 Leverage relationship: the link between return and …

The relationships between the return on equity (ROE), the return on total assets (ROA) and the average cost of liabilities (COL) which we have described with the example above, can thus be summarized in the following basic equation, the leverage relationship: ROE = ROA + (ROA – COL) ×

L E

(3–1)

We call the ratio L/E the liabilities-to-equity ratio. In the example, it is 600/400 = 1.5, which is equivalent to an equity ratio of 0.4 or 40 percent.

The difference between ROA and COL is defined as the financial margin on borrowed capital, or, for the sake of simplicity, the financial margin.

The financial margin multiplied by the liabilities-to-equity ratio renders the contribution which the borrowed capital makes to the return on equity.

In the main example, this contribution is (8% – 4%) × 1.5 = 6 percent. We define this as the leverage contribution going forward. We will analyze the leverage contribution with respect to different types of liabilities in Chapter 6.

By way of conclusion, we return to the example and see that the return on equity (14 percent) is equal to the sum of the return on total assets (8 percent) and the leverage contribution (6 percent).

In situations where the focus is on calculating a required return on total assets rather than explaining the return on equity, it may be appropriate to express the return on total assets (ROA) as a function of the return on equity (ROE) and the average cost of liabilities (COL). From the basic formula (3-1), we can derive the expression for ROA, after substituting A for (E+L): ROA = ROE ×

E L + COL × A A

(3–2)

With the help of (3-2), it is easy to derive how great ROA must be in order to achieve a set target rate for ROE with a certain objective for the equity ratio (E/A), as well as satisfying lenders’ yield requirements at that equity ratio.

When we know the initial value for E and the required ROE, we can determine the required size of the earnings after interest expense. When L and the required value for COL are known, the firm’s interest expenses (= lenders’ requirements for compensation) can be determined. The requirements for earnings before interest expense and ROA can then also be determined. This chain of requirements, which begins with ROE and the bottom line on the © S T U D E N T L I T T E R AT U R

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3 Leverage relationship: the link between return and …

income statement, can be illustrated with the help of the main example and an “upside-down” income statement and balance sheet.

Main example 3.3

The required ROE as determined by the stock market is assumed to be 14 percent, and initially the equity is 400. The target set by management for the equity ratio is 40 percent, and the expected cost of liabilities (COL) is 4 percent. Based on these assumptions, the required earnings before interest expense are derived in the following way.

Balance sheet

Required return

Income statement (required earnings)

Equity 400

ROE = 14%

Earnings before tax 0.14 × 400 =

56

Liability 600

COL = 4%

+ Interest expense 0.04 × 600 =

24

= Earnings before interest expense

80

Assets 1,000

80 1,000 ROA = 8% =

The required ROA can also be calculated directly using the equation 3-2: ROA = 14% × 0.40 + 4% × 0.60 = 8% If, in addition, there is a target for the company’s revenue, e.g., 1,600, the earnings before interest expense (EBIE) must equal 5 percent of revenue (=80/1,600). Introducing such links to a required profit margin is developed further in Chapter 6.

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3.3

Relationships when the values of variables change

Based on the basic formula (3-1) for the relationship between different measures of return, it is also possible to precisely define the relationships between changes in the measures. With the help of the main example, we will study the relationships between changes in return on total assets, the average cost of liabilities, and the liabilities-to-equity ratio, and changes in the return on equity. The analysis will consist of two steps. First, we will study the effect on the return on equity of a change in the return on total assets in a situation where the liabilities-to-equity ratio and average cost of total liabilities remain constant. Thereafter, we will study how the return on equity is affected when the return on total assets, the liabilities-to-equity ratio, and the average cost of liabilities change simultaneously.

Main example 3.4

Assume that ROA increases from 8 percent in the initial example to 10 percent. Assume further that L/E and COL remain unchanged.

ROE = ROA + (ROA – COL) ×

L E

basic formula

14% = 8% + (8% – 4%) × 1.5

initial conditions

19% = 10% + (10% – 4%) × 1.5

ROA has increased

The increase in ROA of 2 percentage points causes ROE to increase from 14 percent to 19 percent. The increase in ROE (5 percentage points) can be derived from the increase in ROA (2 percentage points) multiplied by 1 + the L/E ratio (5% = 2% × 2.5).

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3 Leverage relationship: the link between return and …

The relationship between the changes we have studied in the example above can be expressed as: L ∆ROE = ∆ROA × d1 + n E

(3–3)

+5 = +2 × (1 + 1.5)

from the example

Δ indicates change; ΔROA will accordingly be used from now on to mean the change in ROA. We consequently state that the higher the liabilities-to-equity ratio, the greater the impact on ROE of a change in ROA. This is known as the leverage effect (also called the gearing effect).

Main example 3.5

In this case, we assume the following simultaneous changes in relation to the initial conditions: a) ROA increases from 8% to 10% b) L/E increases from 1.5 to 2 c) COL increases from 4% to 5% ROE = ROA + (ROA – COL) ×

L E

basic formula

14% = 8% + (8% – 4%) × 1.5

initial conditions

20% = 10% + (10% – 5%) × 2

ROA, L/E, COL have increased

The changes cause ROE to increase by 6 percentage points, from 14 percent to 20 percent. This increase can be explained by the sum of three different components. The increase in ROE is equal to the sum of i) the increase in ROA (2 percentage points), ii) the initial financial margin multiplied by the increase in L/E, i.e., (+8% – 4%) × 0.5 = 2 percentage points, and iii) the increase in the financial margin multiplied by the new L/E ratio + (2% – 1%) × 2 = 2 percentage points. In this example, each component explains 2 percentage points.

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With the help of symbols used earlier, this can be expressed as: ∆ROE = ∆ROA + + (ROA – COL) × ∆

L E

L L + (∆ROA – ∆COL) × d + ∆ n E E

(3–4)

We conclude with a graphic illustration of how the return on equity varies in line with the return on total assets. In Figure 3.1 the relationship between ROE and ROA is shown given a constant cost of liabilities (COL) and different levels of the liabilities-to-equity ratio (L/E) and keeping the average cost of total liabilities constant.

It is evident from the slopes of the lines in Figure 3.1 (on the next page), that the greater the liabilities-to-equity ratio (L/E), the greater the effect on the return on equity (ROE) for any given change in the return on total assets (ROA).

In Figure 3.2, we keep the liabilities-to-equity ratio constant at 2.0 and instead show the relationship between ROE and ROA given three different levels of COL. As can be seen, the lines shift in parallel to the right, implying that when COL increases, a higher ROA is required to reach a certain ROE. The following chapter considers the significance of the relationships described in the basic formula for the analysis and planning of a company’s financial policy.

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L =4 E

L ROE = ROA + (ROA – COL) × E

L =3 E

40%

L =2 E

35%

L =1 E

30% 25% 20% ROE 15% 10% 5% 0% –5%

0% –5%

5%

10%

15%

ROA

–10% –15% –20% FIGURE 3.1 The relationship between ROE and ROA, with a constant COL (4%), but varying the liabilities-to-equity-ratio (L/E).

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ROE = ROA + (ROA – COL) ×

L E

COL = 2%

40%

COL = 4% 35%

COL = 6%

30% 25% 20% ROE 15% 10% 5% 0% –5%

0% –5%

5%

10%

15%

ROA

–10% –15% –20% FIGURE 3.2 The relationship between ROE and ROA, with a constant L/E = 2, but varying levels of the cost of liabilities (COL).

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Sven-Erik Johansson (1924–2015) was Professor of Business Administration at Stockholm School of Economics. He also served as a consultant and an auditor for several Swedish listed companies. Mikael Runsten has a PhD in Business Administration from Stockholm School of Economics, and he has many years of experience of management training. He is a co-owner of Bild & Runsten AB, which specialises in financial learning for company management teams.

The Profitability, Financing, and Growth of the Firm Goals, Relationships, and Measurement Methods How profitable does a company have to be to ensure its long-term survival? How is a company’s equity ratio determined? What are the relationships between return on capital employed, growth and changes in the equity ratio? These are some of the questions discussed in this book, which has been a highly esteemed textbook at universities and colleges, as well as in leadership training, for over 30 years. The authors present an accounting-based model for an integrated analysis of a company’s profitability, financing and growth.

In this third edition, the examples have been updated and a number of new sections have been added, but above all the form and language have been revised to make the book more accessible.

The book is intended primarily to be used on courses in accounting and finance. Many people who work in business and finance will also find it offers invaluable help in their professional role.

There is also a website which contains practical exercises, illustrations and Excel models: studentlitteratur.se/6887.

”

This classic book on financial statement analysis, first published in 1983, is in our mind the best Swedish text book in business administration ever. It is easy to be impressed by how much knowledge the authors have managed to include […].

Complicated relationships are explained in a pedagogical way.

InvestingByTheBooks, May 26, 2015

Third edition

Art. No 6887

studentlitteratur.se