CORPORATE FINANCIAL ANALYSIS - SFU.cablazenko/two.pdf · You should be aware of several limitations of financial ratios in financial analysis (the four ... Industry comparison is

Intro to Finance

1

Introduction to Finance

by George W. Blazenko

All Rights Reserved © 2008, 2014

Chapter 2 Financial

Statements in

Financial Analysis “There's no business like show business, but there are several businesses like accounting.”

– David Letterman

“The average parent may, for example, plant an artist or fertilize a ballet dancer and end

up with a certified public accountant.” – Ellen Goodman (b. 1941), U.S. journalist.

“Goodman’s Victory Garden,” Close to Home, Simon & Schuster (1979).

Financial Statements in Financial Analysis

2

Chapter Two Contents (2.1) Introduction ............................................................................................. 3

(2.2) Recognize the Limitations of Financial Ratios................................. 4 2.2.1 A SPREADSHEET TEMPLATE FOR FINANCIAL RATIOS 8

(2.3) The Income Statement ............................................................................ 9 2.3.2 EBITDA MARGIN 11 2.3.3 DEPRECIATION 12 2.3.4 NET INCOME 13 (2.4) The Accounting Balance Sheet ................................................................ 13 2.4.1 ASSETS 15 (2.5) Invested Capital ........................................................................................ 16 2.5.1 THE FINANCIAL DEFINITION OF INVESTED CAPITAL 17 2.5.2 THE OPERATING DEFINITION OF INVESTED CAPITAL 18 (2.6) Business Returns ...................................................................................... 21 2.6.1 THE RATE OF RETURN ON INVESTED CAPITAL (ROIC) 22 2.6.2 THE RATE OF RETURN ON EQUITY (ROE) 24 2.6.3 THE RELATION BETWEEN ROIC AND ROE 26 2.6.4 WHY ARE ROIC AND ROE BOTH IRRS? 28 (2.7) Free Cash Flow ........................................................................................ 30 2.7.1 THE OPERATING DEFINITION OF FREE CASH FLOW 31 2.7.2 THE FINANCIAL DEFINITION OF FREE CASH FLOW 34 2.7.3 AFTER TAX DISTRIBUTIONS TO CREDITORS 34 2.7.4 NET DISTRIBUTIONS TO SHAREHOLDERS 35 (2.8) Additional Invested Capital Ratios .......................................................... 37 2.8.1 DEBT TO INVESTED CAPITAL 37 2.8.2 TRADE CAPITAL TO INVESTED CAPITAL 38 2.8.3 EBITDA MARGIN AND INVESTED CAPITAL TURNOVER 39 (2.9) Net Working Capital and Liquidity .......................................................... 42 (2.10) Efficiency of Trade Capital Utilization .................................................. 43 2.10.1 TURNOVER RATIOS 43 2.10.2 THE CASH CONVERSION CYCLE 44 (2.11) Summary ................................................................................................. 45 (2.12) Suggested Readings ............................................................................... 47 (2.13) Appendix: Industry Ratios ...................................................................... 48 DEFINITIONS 48 (2.14) Problems ................................................................................................. 50 (2.15) Chapter Index .......................................................................................... 78

Intro to Finance

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(2.1) Introduction Title Page

Financial accounting is the process of producing and disseminating information about the

economic activities of a firm. Accountants prepare annual and quarterly reports, and more

specifically, financial statements, to transmit this information to interested readers. Many groups

require information from financial statements, including shareholders, creditors, employees,

suppliers, government, and social interest groups. Financial statements are general summaries of

economic activity because user groups have diverse interests. Perhaps because of this diversity,

accountants take pains to ensure accuracy of the information presented in financial statements but

they provide no guidance on their use. One goal of this book is to explain how investors use

financial statement information to analyze business and financial investments.

For at least two reasons, communication is weaker between professional accountants and users of

financial statements than between other professionals and their clients. First, accounting

principles and the pronouncements of regulatory agencies tightly constrain the content and

format of statements issued for corporations and especially for publicly traded firms. Second, not

only do users of financial statements have little opportunity to make direct requests of

accountants for individual treatment, but also the users of financial statements must share one set

of statements, in spite of diverse interests.

Since the relation is weak between users of financial statement and producers of financial

statement, a second goal of this book is to provide a framework for those who prepare financial

statement to assess the informational requirements of investors. In this chapter, we integrate ratio

calculations into financial analysis, which we know from Chapter 1 answers the question ― is

this good investment? The perspective that we develop in this chapter has its origins in the

investment industry. We emphasize the perspective of financial analysts, who use financial

ratios to make investment decisions.


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(2.2) Recognize the Limitations of Financial Ratios Title Page

You should be aware of several limitations of financial ratios in financial analysis (the four

questions for any investment from chapter one).

First, there is no objective standard for most ratios. What constitutes a high or a low value for a

ratio is often a question of business judgment rather than business theory. Financial ratios

measure business performance, efficiency, and risk. If used carefully, ratios can be valuable as a

tool to assess the financial health of a firm. For most ratios, however, it is difficult to determine

whether the value of a ratio for a firm is good or bad, high or low. The reason for this

uncertainty is that the theory of business is not yet sufficiently strong to offer absolute standards

for most ratios. Until we have a more complete theoretic picture, we must resort to using relative

rather than absolute comparisons. Relative comparisons include trend analysis and industry

average comparisons of ratios. In trend analysis a financial analyst determines whether a ratio is

improving or deteriorating. In an industry average comparison, an analyst determines whether a

ratio is better or worse than the industry. Neither benchmark answers the question whether the

ratio is good or bad.

There is one exception to the general rule that the theory of business is not sufficiently strong to

give us absolute benchmarks. The exception is the theory of finance. In finance we can

benchmark returns against an opportunity cost rate of return from financial markets, which is a

number. How to calculate financial market opportunity costs is a major objective of this text-

book and all of financial study. With an opportunity cost rate of return from financial markets,

we can answer the question whether business returns are good or bad.

Intro to Finance

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An example of an absolute standard for a return is our first numerical example in this book from

Chapter 1. A firm invests $300,000 today to generate (forecast) $400,000 in one year. We

determined in Chapter 1 that the return on this business investment, calculated as the IRR, is

33.3%. We said (without giving the details) that the opportunity cost rate of return from financial

markets is 7%. This number, 7%, is an absolute standard with which to benchmark the 33.3%

business return. Because the 33.3% is greater than the 7% we said that this was a “good”

investment. The theory of finance is sufficiently strong to give us an absolute standard for

returns.

Any return, like, for example, the rate of return on invested capital (ROIC) or the rate of return

on equity (ROE), that we calculate in this chapter can be benchmarked against financial market

opportunity costs. We reserve that benchmarking for later in this textbook after we have learnt

more about financial markets and how these markets determine opportunity cost rates of return.

It makes little sense to benchmark a firm’s ROIC or ROE against industry averages or past values

of these return ratios. These are relative benchmarks when a much better absolute benchmark is

available. The financial opportunities available to shareholders and other financial asset-holders

are much broader than the particular firm under investigation or even its industry. Investors can

invest in the financial assets of any public company around the world. To recognize this broad

perspective for opportunity costs of investors we must benchmark returns against financial

market returns of about the same risk.

Second, differences between firms' accounting methods limit the comparability of many ratios.

Therefore, where there is a choice as to measure, seek to use ratios that are unaffected by

arbitrary choices of accounting treatment.

Third, some ratios that share the same name are calculated in different ways. Different accounts

can be included or excluded; and broader or narrower interpretations might be employed for

different classes of financial assets. Because theory in this area is not yet strong enough to tell us

exactly what or how to measure, then naturally, different analysts employ different measures, and

in different ways. The set of ratios described in this chapter, which is essentially the same as the

ratios in The Canadian Securities Course text, is well suited to financial analysis.


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An industry average might not be an appropriate objective for your firm. If a whole industry is

inefficient, it makes little sense to applaud a move towards the industry average. On the other

hand, a firm that is better than the industry in any one dimension is not necessarily in peak

financial health. Industry averages conceal significant variation, which typically exists for any

ratio across firms in the industry. One interpretation of this variation is that, even for firms in the

same industry, there is not necessarily a “best” value for a particular ratio. There may, in fact, be

different paths to robust financial condition.

Industry comparison is a narrow perspective on corporate benchmarking. Remember that the

objective of a firm is to maximize shareholder wealth. While you, as an employee of your firm,

may be particularly interested in how the firm performs relative to your competitors, shareholders

have a broader perspective. Shareholders are restricted neither to investing in any one firm, nor

to any one industry. Each firm must compete globally for the financial resources of dispassionate

investors who choose to invest wherever they like, in many different firms and in many different

industries. If an industry performs poorly relative to other industries, each firm in the industry

suffers the financial consequences just as surely as if a firm performs poorly relative to industry

competitors. If your objective is to maximize shareholder wealth, then you must maintain a

broader perspective on performance than the perspective allowed by a simple industry

comparison of ratios.

Fourth, another shortcoming of traditional financial statement analysis is that financial statements

are used as the exclusive source of information. Even though financial statements provide an

analyst with firm-specific information, the theory of business organizations is not yet sufficiently

strong to provide an analytically determined absolute standard against which this information can

be compared. Therefore, ratios are compared with prior time-periods or against industry

standards to assess performance. We can build a consistent conceptual framework from recent

advances in economic and financial theory. In this book, we use discounted cash flow analysis as

a theory of value and we use financial statements and financial market data as inputs.

The broad outline goes like this. Estimate prospective rates of return that a firm can earn for its

suppliers of capital. Compare prospective returns to objective measures of corporate

Intro to Finance

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performance, like the average return on financial assets of equivalent risk. We need firm-specific

information to estimate prospective returns. We also need financial market data to access

investor benchmark opportunity costs. Firm-specific information from financial statements and

financial market information are combined by employing the techniques of discounted cash flow

analysis to establish “intrinsic values” for firms' real assets and financial assets. Armed with

intrinsic-value estimates, we can make informed investment decisions.

In our numerical example from Chapter 1, we might use financial statement data to help us

predict that the rate of return on business investment is 33%. On the other hand, we investigate

financial markets to determine that the opportunity cost of this real asset investment is a 7% rate

of return. Both components of this analysis are crucial to making an informed business decision.

So, financial statements and ratios calculated from these financial statements are at best one ½ of

a complete financial analysis. The other half of our financial analysis is the determination of the

7% opportunity cost rate of return from financial markets. Without this benchmark, we cannot

answer the fourth question of financial analysis ― is this a good investment?

Fifth, a final limitation of using financial statements in our financial analysis is that financial

statements are historical but our theory of value, NPV, has a future (forward) orientation. We

know from Chapter 1 that we determine whether an investment is “good” based on whether NPV

is positive or not. The cash flows that we discount in NPV are predicted future cash flows

(without giving the details). On the other hand, financial accounts recognize only transactions

that have taken place in the past. Nonetheless, the past does bear some resemblance to the future.

So, we can use the financial statements of firms to help us predict future cash flows. In particular,

corporate returns from financial statements, like the rate of return on invested capital or the rate

of return on equity (that we calculate in this chapter), have a persistence property that makes

them invaluable for forecasting future corporate results. The persistence property is that if the

rate of return on invested capital was high last year, it will tend to be high this year. Recognize,

however, that not all returns have this persistence property. For example, because of the special

features of financial markets returns (they are determined from financial asset prices that depend

upon investors’ expectations of the future), these returns do not generally have the persistence

property. Or, possibly better said, returns in financial markets do not have the persistence


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property nearly to the same extent as do corporate returns (like, for example, the rate of return on

invested capital). If the rate of return on a publicly traded company last year was high, then, this

observation tells you little about its expected rate of return for the upcoming year.

Benchmarking is an especially valuable use of ratios. Suppose for example, that we forecast

operating results predicted for a new business venture. If our forecast financial statements

produce financial ratios that are far from the industry average or far from the firm’s historic

experience, then we have grounds to reconsider the assumptions of our planning exercise. In this

way, ratio analysis imposes discipline on assumptions we use in financial planning. We use ratio

analysis again when we discuss financial planning and capital budgeting in later chapters.

2.2.1 A Spreadsheet Template for Financial Ratios Title Page

The worksheet embedded below calculates all ratios we discuss in this chapter for Canadian

Pacifica Railway (CPR). CPR provides rail and freight transport services over a 14,400-mile rail

network serving major Canadian business centers from Montreal to Vancouver and in the US

Midwest and Northeast. CPR is a public company with common shares traded on both the

Toronto Stock Exchange (TSX) and the New York Stock Exchange (NYSE).

Canadian Pacific Railway

The CPR workbook above serves also as a template for ratio analysis of other firms. Required

inputs are the income statement and the balance sheet. The spreadsheet then automatically

calculates each of performance measures we develop in this chapter.

We retrieve CPR data from a database called COMPUSTAT which is a product of Standard and

Poor’s Corporation. This database provides mostly financial statement information on over

10,000 publicly traded North American firms. The graphical user interface is called Research

Insight.1 Research Insight has many predefined reports. Two of these reports are an income

1 Research Insight is available for BUS312 students at the Beedie School of Business, Simon Fraser University, in

the Beedie Computer Lab in Room 2301.

https://docs.google.com/spreadsheets/d/1WwyHN9rLO1jfRIG29ZNx6oHOyRlaBNmMFwxS2VBAPRo/edit?usp=sharing

Intro to Finance

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statement and a balance sheet over the last five fiscal years. We use these two reports to

calculate ratios for CPR in the above EXCEL workbook. In producing these two reports,

Research Insight adjusts the financial statements to standardize accounting conventions and uses

common line items for both the income statement and balance sheet for all companies, which

enhances ratio comparability across companies.

The following section begins our discussion of financial ratios and financial analysis by

describing the two principal financial statements: the income statement and the balance sheet.

(2.2) The Income Statement Title Page

Within the confines of generally accepted accounting principles and other accounting

conventions, the income statement measures the increment to shareholders' wealth over a specific

period of time – generally a quarter or a year. The shareholder orientation of this statement

makes it of central importance to existing and potential shareholders. Income statements appear

in a variety of forms but all satisfy the fundamental relationship:

Net Income = Revenues — Expenses.

Revenue is a measure of the benefit of sales events in a period: price times the number of units

sold summed over the different products and services sold by the firm. In the 2013 income

statement for CPR below we see that Sales for 2013 are $5,765,723 (numbers are in thousands).

A common decomposition of financial statement expenses is Costs of Sales (also referred to as

costs of goods sold), Selling, General and Administrative Expenses, Depreciation, and Interest.

Costs of Sales measures expenses associated with production: materials and supplies, direct labor

costs, freight-in, heat, light, power, insurance and safety, maintenance and repairs, salaries, and

warehouse costs. Selling, General and Administrative Expenses include all commercial expenses

of operation not directly related to production but incurred in the course of business activity:

sales commissions, advertising expense, marketing expense, freight-out, pension, retirement,

profit sharing, provision for bonus and stock options, and other employee benefits. Occasionally,

depreciation is included in general and administrative expenses.


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Exhibit 2.1: Income Statement Canadian Pacific Railway

PERIOD ENDING 31-Dec-13 31-Dec-12 31-Dec-11 31-Dec-10

Total Revenue 5,765,723 5,719,020 5,084,000 5,013,000

Cost of Revenue 2,100,592 2,325,166 2,253,000 1,957,000

Gross Profit 3,665,131 3,393,854 2,831,000 3,056,000

Operating Expenses

Research Development 0 0 0 0

Depreciation 531,165 541,273 481,000 492,000

Selling General and Administrative 1,400,395 1,550,111 1,400,000 1,440,000

Non Recurring 0 0 0 0

Others

Total Operating Expenses 1,931,560 2,091,384 1,881,000 1,932,000

Operating Income or Loss 1,733,571 1,302,470 950,000 1,124,000

Total Other Income/Expenses Net -397,668 -368,548 -1,800 12,000

Earnings Before Interest And Taxes 1,335,903 933,922 948,200 1,136,000

Interest Expense 278,274 295,240 247,000 259,000

Income Before Tax 1,057,629 638,682 701,200 877,000

Income Tax Expense 235,029 152,641 125,000 221,000

Minority Interest 0 0 0 0

Net Income From Continuing Ops 822,600 486,041 576,200 656,000

Non-recurring Events

Discontinued Operations 0 0 0 0

Extraordinary Items 0 0 0 0

Effect Of Accounting Changes 0 0 0 0

Other Items 0 0 0 0

Net Income 822,600 486,041 576,200 656,000

Preferred Stock And Other Adjustments 0 0 0 0

Net Income Applicable To Common Shares 822,600 486,041 576,200 656,000

effective tax rate 0.2222 0.239 0.178 0.252

Cash Dividends (Total) 229,388 223,940 189,811 174,343

Sales less Costs of Sales equals Gross Income or Gross Profit From Operations. Gross profit is a

measure of the profitability of a firm's production. The term “operations” is typically used in

connection with a firm's fundamental business activity (before distributions are made to suppliers

of capital – like dividends and interest). This separation of operations from financing activity is

of critical importance if one is to disentangle shareholders' benefits from a firm's business

activity and shareholders' benefits from financing activities.

Intro to Finance

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Because gross profit is measured in dollars, inter-firm comparison of gross profit is meaningless

until we consider the size of each firm. Financial analysts facilitate inter-firm comparison by

calculating gross profit margin: gross profit divided by sales. Because gross profit margin is a

percentage, it is comparable across firms. However, because financial accountants have

discretion in the classification of expenses as “cost of goods sold” or “general and

administrative,” the comparability of this ratio across firms is limited. For CPR, 2013 gross

profit is $5,765,723-$2,100,592 = $3,665,131 and gross profit margin is 63.6%.

2.3.2 EBITDA Margin Title Page

Gross profit less selling, general, and administrative expenses (before depreciation and

amortization) equals earnings before interest, tax, depreciation and amortization which is often

abbreviated as EBITDA2. EBITDA measures profitability of a firm's operations, net of both

production and commercial expenses. Financial analysts calculate net operating margin (which

is also referred to as the EBITDA margin) as EBITDA divided by sales.

Sales

EBITDA Margin EBITDA

In 2013, CPR EBITDA margin was $2,264,736/$5,765,723 = 39.3%

The EBITDA margin is designed for comparability across firms because taxes, interest expense,

depreciation and amortization are excluded. These four income statement line items are

influenced by the idiosyncratic characteristics of individual firms. For example, tax expense

varies with firm size, and with the existence of prior year losses that offset current-year taxable

income. Interest expense depends on the amount of debt used by a firm, which is more or less

discretionary. Accountants choose depreciation schedules and this choice need not be the same

even for firms in the same industry. For these reasons, any financial ratio that depends on tax

expense, depreciation, or interest has limited comparability across firms.

2 EBITDA is also typically calculated before the line items “other income” and “extraordinary income” (or loss).

Each of these amounts is either non-recurring or outside the firm’s normal business practice. Therefore, EBITDA as

described in the text above is sometimes referred to as “EBITDA from core operations.” For simplicity, unless

otherwise stated in this book, when we use the term EBITDA we really mean EBITDA from core operations.


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The EBITDA margin is a measure of operating efficiency. It measures the fraction of $1 of sales,

which goes to the “bottom” line after production and commercial expenses (that is, to EBITDA).

In later chapters, we will see that the EBITDA margin is also a measure of “operating risk.” In

the appendix to this chapter, the EBITDA margin is sorted and presented for 302 different

industry averages. The median value for the EBITDA margin for firms in the North American

economy is approximately 10.5%. This value is useful for benchmarking North American firms

with respect to operating efficiency and operating risk.

What question of financial analysis are we investigating with the EBITDA margin? The answer

is the EBITDA margin is a component of return. It is not a return itself. However, when

multiplied by another ratio that we will calculate shortly, you get a business return and returns

are, of course, very important in financial analysis.

2.3.3 Depreciation Title Page

Economic depreciation is the reduced ability of an asset (generally a real asset) to generate future

cash flows. Because the value of an asset depends upon the future cash flow that it produces,

economic depreciation decreases the value of assets. An obvious factor in economic depreciation

is asset usage. Assets used more intensely deteriorate more quickly, and therefore, economic

depreciation should depend on the level of use.

Nonetheless, the objectivity principle of financial accounting requires that financial statements be

prepared from readily verifiable data. Therefore, accountants estimate economic depreciation

according to predefined schedules that are invariant to asset use. For example, the most

commonly used depreciation schedule is straight-line depreciation. Yearly depreciation equals

the cost of the asset, less estimated salvage value, divided by estimated years of useful life.

Shareholders bear the burden of economic asset depreciation and net income recognizes

economic depreciation but only with a crude approximation. This approximation is the

“depreciation” line item that is seen on the income statement as an expense. Note well, however,

that the deduction for depreciation is non-cash expense. Firms do not actual pay, in the sense of

a cash outflow, for depreciation. They do, however, benefit from the tax-deduction for

Intro to Finance

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depreciation allowed by the government for the purpose of income taxation. A tax- deduction is

an expense for tax purposes that decreases taxable-income and, thus, decreases the tax-bill of a

corporation.

2.3.4 Net Income Title Page

Net operating profit less interest, taxes, depreciation and amortization equals net income (often

referred to as earnings). Net income divided by sales is net profit margin. Within the confines of

generally accepted accounting principles (GAAP), net profit margin is the increase in

shareholders' wealth for every dollar increase in sales, or equivalently, the net benefit of sales

activity to shareholders. For this reason, net profit margin is also referred to as return on sales.

Interest is subtracted in the calculation of net profit margin, and therefore, this interpretation is

conditional on the current financial structure of the firm (i.e., the firm's use of debt financing).

Net profit margin is a commonly calculated financial ratio but because it incorporates interest,

taxes, depreciation and amortization, its usefulness for inter-firm comparison is limited. For

inter-firm comparison, the EBITDA margin is a more reliable measure of operating efficiency.

(2.3) The Accounting Balance Sheet Title Page

The purpose of the accounting balance sheet is to summarize resources of the firm available for

conducting business operations (assets) and claims against these assets (liabilities and

shareholders equity). The accounting balance sheet describes transaction amounts rather than

values. On the other hand, it is the purpose of financial analysis to estimate investment values.

Exhibit 2-2 illustrates fiscal year-end balance sheets for 2004 to 2013 for CPR.


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Exhibit 2.2: Balance Sheet CPR

PERIOD ENDING 31-Dec-13 31-Dec-12 31-Dec-11 31-Dec-10

Assets Current Assets Cash And Cash Equivalents 833,882 334,404 46,000 363,000

Short Term Investments 0 0 0 0

Net Receivables 545,266 548,303 608,000 685,000

Inventory 155,119 136,574 136,000 115,000

Other Current Assets 373,226 315,324 51,000 48,000

Total Current Assets 1,907,493 1,334,605 841,000 1,211,000

Long Term Investments 112,814 83,350 164,000 146,000 Property Plant and Equipment (net of

accumulated Depreciation) 12,528,909 13,067,885 12,523,000 12,074,000

Goodwill 0 0 0 0

Intangible Assets 152,298 161,679 189,000 191,000

Accumulated Amortization 0 0 0 0

Other Assets 1,336,843 141,595 140,000 141,000

Deferred Long Term Asset Charges 0 0 0 0

Total Assets 16,038,357 14,789,114 13,857,000 13,763,000

Liabilities Current Liabilities Accounts Payable 1,117,796 1,190,960 1,113,000 1,014,000

Short ST Debt/Current Long Term Debt 177,682 54,228 76,000 284,000

Other Current Liabilities 0 0 0 0

Total Current Liabilities 1,295,478 1,245,188 1,189,000 1,298,000

Long Term Debt 4,406,318 4,655,553 4,611,000 4,059,000

Other Liabilities 935,414 1,679,052 1,705,000 1,594,000

Deferred Long Term Liability Charges 2,729,153 2,090,823 1,786,000 1,957,000

Minority Interest 0 0 0 0

Negative Goodwill 0 0 0 0

Total Liabilities 9,366,363 9,670,616 9,291,000 8,908,000

Stockholders' Equity Misc Stocks Options Warrants 0 0 0 0

Redeemable Preferred Stock 0 0 0 0

Preferred Stock 0 0 0 0

Share Capital 2,137,821 2,177,145 1,821,000 1,825,000

Retained Earnings 4,534,173 2,941,353 2,744,000 3,030,000

Treasury Stock 0 0 0 0

Capital Surplus 0 0 0 0

Other Stockholder Equity 0 0 0 0

Total Stockholder Equity 6,671,994 5,118,498 4,565,000 4,855,000

Liabilities + Equity $16,038,357 $14,789,114 $13,856,000 $13,763,000

Intro to Finance

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2.4.1 Assets Title Page

Assets are commonly categorized as current assets and non-current assets. Current assets are

those assets which are expected to be transformed (in the normal course of business activity) into

cash in the relatively near term (i.e., within a fiscal year). The most commonly described current

assets on the balance sheet are Cash and Marketable Securities, Accounts Receivable, and

Inventories. Marketable securities are financial assets of other corporations or governments held

as short-term investments. Because marketable securities are extremely liquid, they are

considered cash equivalents. Accounts receivable are amounts due from customers less an

estimate of amounts unlikely to be paid (doubtful accounts). Inventories include both finished

product inventories and raw materials inventories. Inventory is recorded at cost of purchase or

production.

When finished goods are sold, the periodic cost of goods sold is incremented and inventory on

the balance sheet is decremented (recall the accounting matching principle). The balance sheet

figure for inventories depends upon whether inventory is decremented by the cost of units first

placed in inventory (first in first out inventory accounting – FIFO) or by the cost of units last

placed in inventory (last in first out inventory – LIFO).

Non-current assets are held by corporations to support production and commercial operations

over a relatively longer horizon than a fiscal year. The most common category of non-current

assets described on an accounting balance sheet is Property, Plant and Equipment (often labeled

fixed assets). These fixed assets are recorded at original cost less accumulated depreciation.

The financial side of the balance sheet – liabilities and shareholders' equity – describes

cumulative (over time) sources of funds used to finance the firm’s assets. Liabilities are

commonly segregated into current liabilities and non-current, or long-term, liabilities. Current

liabilities are expected to be paid within a fiscal year.


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Current liabilities are commonly composed of short-term debt, accounts payable, income taxes

payable, salaries and wages payable, and the current portion of long-term debt. Short-term debt

is formal borrowing by the firm from either commercial banks or by selling short-term debt

securities. The market that trades short-term debt securities is called the money market. The

term money is used because securities that trade in this market have many characteristics of

money. In particular, such debt instruments mature in less than one year and carry minimal risk

of default. Accounts payable are amounts owing suppliers. Wages and salaries payable are

amounts owing employees. These amounts are contained within the line item Accrued Expenses.

The current portion of long-term debt or equivalently Long Term Debt Due in One Year is the

amount of principal on long-term debt that the firm expects to repay over the course of the

upcoming fiscal year.

CPR primary sources of long term financing are long term debt and common equity. At the end

of 2013 CPR long term debt was $4,406,318. Since long term debt due in one year is the amount

of principal on long term debt scheduled to be repaid over the course of the upcoming year, long

term debt on the balance sheet is the amount of principal on long term debt scheduled to be

repaid after one year from today.

CPR has two common equity accounts: Share Capital and Retained Earnings. Share capital is the

expenditure by original founding shareholders plus the sale of new shares to new shareholders

less the repurchase of shares by CPR. Retained earnings is the accumulation of net income over

the years less cash dividends.

(2.4) Invested Capital Title Page

Returns are critically important in financial analysis. We are working toward calculating the

equivalent of the 33.3% business return we calculated in Chapter 1 as an IRR but for real rather

than stylized companies. If a firm invests $300,000 to generate $400,000 in one year, the

business return is 33.3% per annum. In real world financial analysis, if we want a good measure

of return, we need a good measure of expenditure, which is the equivalent of the $300,000 in the

above example. Expenditure is one of the fundamental questions of financial analysis that we

Intro to Finance

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identified in Chapter 1. Financial statements and a balance sheet in particular are not designed to

answer this expenditure question. So, in this section, we rearrange a balance sheet to calculate

expenditure with Invested Capital. We can measure Invested Capital from the corporate

perspective (business investment) or from the financial asset-holder perspective (shareholders

and creditors are the primary financial investors in any corporation). So, there are two

calculations for invested capital: the financial calculation and the operating calculation. We begin

with the financial calculation because Invested Capital originates in the investment industry.

2.5.1 The Financial Definition of Invested Capital Title Page

The total of all funds that have been invested by financial asset-holders in a firm is referred to as

“invested capital.” The term “invested” is used because these funds are associated with

identifiable financial assets sold by the firm. Invested capital is a measure of expenditure by

financial asset-holders rather than a measure of the value of these financial assets. All accounts

on the financial side of the balance sheet that are associated with financial investing are included

in the calculation of invested capital. Invested capital is a commonly used measure in the

investment industry because it provides a good organizing framework for analysis. It helps to

separate the two sides of the “coin” which is the corporation, the operating side and the financial

side.

The below table gives one definition of Invested Capital in common use by investors applied to

CPR for 2012. You will see shortly why we use 2012 rather than 2013. This table tells us that at

the end of 2012, the financial asset-holders of CPR (creditors and common shareholders) have

invested over 13.5 billion dollars into the financial assets of CPR. Note carefully, however, that

this is an expenditure calculation. The value of CPR financial assets may have increased or

decreased since their original investment of financial asset-holders. Invested Capital is an

expenditure calculation and not a value calculation.


18

Exhibit 2.3: Financial Definition of Invested Capital: CPR 2012

ST Debt plus Current Portion of LT Debt

LT Debt and other LT Liabilities

Deferred Taxes

Preferred Shares

Share Capital

Retained Earnings

Other Financial Assets

$54,228

4,655,553+1,679,052+2,090,823=$8,479,656

0

0

$2,177,145

$2,941,353

0

Invested Capital in the Financial Calculation $13,598,154

If we define “debt” as short-term debt plus long-term debt plus other long-term liabilities, then

“debt” for CPR for year-end 2012 is $54,228 + $8,479,656 = $8,479,656. If we define “Equity”

(that is, book equity) as the sum of Share Capital and Retained Earnings, then “Equity” at year-

end 2012 for CPR is $2,177,145 + $2,941,353 = $5,118,154. You should locate both these

numbers in the Invested Capital Balance Sheet in exhibit 2-4 below, which summaries our

investigation of expenditure for this company.

2.5.2 The Operating Definition of Invested Capital Title Page

If invested capital in the financial calculation measures the amount that financial asset-holders

have invested in the financial assets of a firm, then the other side of the coin (the corporation)

measures business investment by the corporation for the benefit of all financial asset-holders

(generally creditors and common shareholders). This is the operating definition of invested

capital.

Firms make two general types of business investments. First, firms invest in what might be

termed their “trading” function. Firms make trades associated with the two components of the

income statement, revenues and expenses. Sales represent trades that firms make with their

customers. Expenses represent trades that the firm makes with their suppliers, employees,

landlords, and the government. Firms must make an investment into short-term assets in order to

support this trading function. For example, accounts receivable are held to support credit sales.

Inventories are held to ensure that sales can take place when requested by customers. Some of

Intro to Finance

19

these short-term investments can be financed with deferred payments associated with trades that

the firm makes with product and service suppliers. These deferred payments are measured on the

accounting balance sheet as, for example, “accounts payable,” “wages payable,” and “income

taxes payable.” Income taxes payable can be thought of as a deferred payment for the

infrastructure services provided by the government. The net amount which firms must hold to

support the trading function associated with their operations is referred to as “trade capital.”

Trade capital equals current assets minus current liabilities on the balance sheet but excluding

from current liabilities those accounts that are purely financial in nature. The excluded accounts

are related to financial asset investing and are not operational in nature (that is, they exist for

financial investors to earn a rate of return, which is not the case, for example, for accounts

payable). Accounts that reasonably can be excluded are dividends payable, short-term debt, and

the current portion of long-term debt.

Trade capital is similar to net working capital. Net working capital is defined as current assets

less current liabilities. The difference between trade capital and net working capital is that trade

capital excludes any current liability that is financial and exists because an investor is looking to

earn a rate of return. For 2012, we calculate Canadian Pacific’s Trade Capital as all of their

Current Assets less Accounts Payable. TC12 = $1,334,605 - $1,190,960 = $143,645. Exhibit 2-4

below gives this number as part of Invested Capital for CPR in the operating calculation for year-

end 2012.

The second business investment that firms make is net fixed assets (plus other long-term

business investments). This investment is required to support the long-term production and

commercial activities of the firm. Net Fixed Assets (NFA) equal the cost basis of fixed assets,

net of accumulated depreciation. For CPR we measure long term business investment as Plant,

Property, and Equipment (Net of Accumulated Depreciation) plus Other Long Term Assets

(Intangible Assets and Other Assets). So, for year-end 2012 for CPR their NFA plus other long-

term business investments in Exhibit 2-4 is: NFA12+Other =13,067,885+161,679+141,595 =

$13,454,509.


20

The sum of trade capital, net fixed assets and other assets (as appropriate) equals invested capital.

In exhibit 2-4 below, Invested Capital for CPR at year-end 2012 is: IC12 = 143,645+13,454,509 =

$13,598,154. So, at year-end 2012, the total business investment of CPR, short-term and long-

term, is over 13.5 billion dollars.

The amount financial asset-holders have invested in the firm must equal the equal the business

investments of the firm. In exhibit 2-4 below, we rearrange the accounting balance sheet into an

Invested Capital Balance Sheet. The “right-hand side” shows the investments made by financial

asset-holders. The “left hand-side” shows business investment by the firm. In either case, the

financial perspective or the operating perspective, expenditure as measured by invested capital at

year-end 2012 for CPR is $13,454,509. So, our invested capital balance sheet balances!

Invested Capital Balance Sheet

Canadian Pacific Railway

Invested Capital Operating 31-Dec-13 31-Dec-12 31-Dec-11 31-Dec-10 31-Dec-09

Trade Capital 789,697 143,645 -272,000 197,000 611,400

NFA+Other 14,130,864 13,454,509 13,016,000 12,552,000 11,936,300

Invested Capital 14,920,561 13,598,154 12,744,000 12,749,000 12,547,700

Invested Capital Financial

Debt 8,248,567 8,479,656 8,178,000 7,894,000 8,104,100

Equity 6,671,994 5,118,498 4,565,000 4,855,000 4,443,300

Invested Capital 14,920,561 13,598,154 12,743,000 12,749,000 12,547,400

ROIC (BOP) 0.076 0.056 0.061 0.068

ROE (BOP) 0.161 0.106 0.119 0.148

effective tax rate 0.222 0.239 0.178 0.252 0.128

debt/IC 0.553 0.624 0.642 0.619 0.646

implied interest rate on debt 0.033 0.036 0.031 0.032

Exhibit 2-4: Invested Capital Balance Sheet

Intro to Finance

21

(2.6) Business Returns Title Page

We design and calculate the invested capital balance sheet in Exhibit 2-4 above because we need

a good measure of expenditure for a good return measure. Returns are critically important in

financial analysis. In our first numerical example of this book, a firm invests $300,000 to

generate $400,000 in one year. If the opportunity cost rate of return from financial markets is 7%

per annum, the NPV (wealth creation) for financial asset-holders and shareholders in particular is

$73,832. Because this number exceeds zero, we conclude in chapter 1 that this is a “good”

business investment and should be undertaken by the firm. However, it is hard to assess without

further analysis whether this is an exceptional good investment or only a marginally good

business investment. Because we all have a basic understanding of what constitutes a good or a

bad rate of return from financial markets (in fact, the 7% in the above example give us this

understanding), if we can calculate business returns then we can assess whether this investment is

exceptionally good or only marginally good.

There are two principal business returns and, further, they relate one to the other. The first is the

rate of return that a firm earns when it makes its business investments. We call this rate of return

the rate of return on invested capital (ROIC) and we typically calculate it after depreciation and

after tax. So, we call it the rate of return on invested capital after-tax and after depreciation. In

addition, because financial asset-holders finance business investments, we sometimes referred to

this return as the rate of return that a firm earns for all its financial asset-holders (generally

creditors and common shareholders). Second, we have a special interest in shareholders because

of our presumption that the primary objective of managers in operating a business is to maximize

shareholders’ wealth. So, our second business return measures the return a business earns for

shareholders specifically. We call this return the rate of return on equity (ROE). In the following

two sections, we investigate these two business returns. Then, we investigate how ROIC and

ROE relate to one another and how one is a relative benchmark for the other. Finally, we answer

the question why both ROIC and ROE are IRRs.


22

The principal determinants of business returns and opportunity cost rates of return are very

different. The primary determinants of opportunity cost rates of return are interest rates in the

economy and risk because investors in financial market trading determine opportunity cost rates

of return. On the other hand, the principal determinant of business returns (both ROIC and ROE)

is corporate profitability. Don’t confuse business returns with opportunity cost rates of return.

2.6.1 The Rate of Return on Invested Capital (ROIC) Title Page

The rate of return on invested capital is the rate of return on a firm’s business investment for all

financial asset-holders. It is not a rate of return on market-value (like a share price, for example)

but a rate of return on expended funds. The comparison of rates of return on expended funds to

rates of return on market values (opportunity cost rates of return) is an important corporate

performance benchmark we develop in this book.

The rate of return on invested capital (before tax and before depreciation) is EBITDA divided by

invested capital at the beginning of the period (BOP). Any financial return calculation uses funds

invested at the beginning of the investment period relative to benefits received over the course of

the period. We abbreviate the rate of return to invested capital as ROIC.

ROIC = Rate of Return on Invested Capital (ROIC) = (b.o.p.) Capital Invested

EBITDA

There are a number of variants and more comprehensive measures for ROIC. In particular, the

rate of return on invested capital after-tax and after depreciation is EBIT times one minus the

corporate tax rate divided by invested capital at the beginning of the period. The return

recognizes not only forecast replacement of deteriorated assets (with depreciation) but also taxes

arising from business investment and deductibility of depreciation for tax purposes3.

3 The distinction between financial statement depreciation and depreciation for tax is not made in this return.

Intro to Finance

23

ROIC after- tax and after depreciation = (b.o.p.) Capital Invested

rate) tax-(1EBIT

For CPR for 2013, EBIT from Exhibit 2-1 is $1,335,903. Also from Exhibit 2-1, the effective tax

rate (Income Tax Expense divided by Income before Tax) for CPR for 2013 is 22.22%. Since

beginning of period for 2013 is end of period for 2012, ICBOP is IC12 from the invested capital

balance sheet in Exhibit 2-4, which is 13,598,154. Because we anticipated IC12 for the 2013

ROIC for CPR, we discussed above Invested Capital in the operating and financial calculations

for 2012 rather than for 2013.

ROIC after-tax and after depreciation for CPR for 2013 is,

ROIC13 = 1,335,903 (1-0.2222)

7.6%13,598,154

At the beginning of this chapter we said that the theory of business is not sufficiently strong to

give us absolute standards for most ratios and, thus, most ratios we benchmark with relative and

weaker benchmarks like trend analysis or industry comparison. However, the exception to this

statement is returns from finance. Because ROIC is a return, we can benchmark it with an

opportunity cost from financial markets, which is a number and, thus, an absolute standard. We

learn later in this book how to calculate opportunity cost rates of return from financial markets to

benchmark the business returns. However, we have to learn more about financial markets in

upcoming chapters before we can calculate these opportunity cost rates of return and determine

the above business return for CPR is high or low.

Ignoring “other income,” which corporations sometime have, we can write ROIC after tax and

after depreciation in the following form. Because stylized companies we give in end-of-chapter

problems will not have “other income” this return calculation might be useful for you,

ROIC after-tax after depreciation = (1-tax rate)

Invested Capital (b.o.p.)

EBITDA deprec


24

2.6.2 The Rate of Return on Equity (ROE) Title Page

If the primary objective of managers is maximizing shareholders’ wealth, then an important

measure of corporate performance is the rate of return that the firm earns on funds originally

invested by shareholders. We calculate the rate of return on equity (ROE) as net income divided

by “book equity” at the beginning of the period,

ROE = Net Income available to common

Book Equity (b.o.p.)

Net income for 2013 for CPR in Exhibit 2.1 is $822,600. Book Equity (BOP) for 2013 is Book

Equity 2012 in the Invested Capital balance sheet in Exhibit 2-4, which is $5,118,498. Thus,

2013 ROE for CPR is,

ROE = Net Income 822,600

16.1%Book Equity (b.o.p.) 5,118,498

We have a three observations about this return. First, like our discussion above for ROIC we do

not know immediately whether 16.1% is high or low. However, because ROE is a return, we can

benchmarked it with an absolute standard, which is an opportunity cost from financial markets.

We learn later in this book how to calculate opportunity cost rates of return from financial

markets to determine whether ROE13 = 16.1% is high or low.

Second, notice that ROE13 = 16.1% > ROIC13 =7.6%. There are two primary reasons why

ROE>ROIC (although it is not always the case). We identify these two reasons in End of Chapter

Question #5.

Third, ROE and ROIC (after tax and after depreciation) are relative benchmarks for one another.

As we said above, the primary determinant of business returns, both ROIC and ROE, is corporate

profitability. Because corporate profitability is common to both, they tend to move together.

When one is high, both are high, and ROE exceeds ROIC. If one is low, both are low, and ROIC

exceeds ROE. The converse of these statements is also true. If ROE > ROIC (like for CPR in

Intro to Finance

25

2013), then both business returns are relatively high and this is a relative good year for corporate

profitability for this firm. We cannot yet say whether ROE or ROIC is high or low because we

don’t yet have an opportunity cost rate of return as an absolute benchmark, but we do know that

2013 was as relatively good year for corporate profitability for CPR. Because ROE and ROIC

move together (that is, when one is high they are both high), there must be a formal relation

between them. We identify this relation in the following section.

However, before we develop this relation, we do one more thing with ROE. A second way to

calculate ROE beyond the above (and the following section) is with the “Dupont” formula, which

multiplies three ratios together: net profit margin, invested capital turnover, and invested-capital

to equity. These ratios are sometimes called the “levers” of performance because ROE increases

as they increase. However, we warn the reader that if managers increase ROE by increasing the

IC to Equity ratio (that is, they use more debt to finance their business investments), then risk

borne by shareholders also increases. So, increasing ROE by increasing a firm’s “financial

leverage” is not necessarily a good thing.

ROE =Net Profit Margin Invested Capital Turnover Invested Capital to Equity

= Net Income

Sales

(b.o.p.) IC

Sales

(b.o.p.)Equity

(b.o.p.) IC =

Net Income

Equity (b.o.p.)

Net profit margin measures profitability per dollar of sales for shareholders. Invested capital

turnover measures sales per dollar of business investment. The invested capital to equity ratio is a

financial leverage ratio that measures invested capital per dollar of equity. For CPR in 2012,

invested capital to equity is $13,598,154/5,118,498=2.66. Net profit margin for 2013 is

$822,600/5,765,723= 14.3%. Invested-capital turnover (BOP) is 5,765,723/13,598,154=0.424.

ROE is, thus,

ROE = 0.143 0.424 2.66 = 16.1%


26

2.6.3 The Relation Between ROIC and ROE Title Page

ROE and ROIC (after tax and after depreciation) move in tandem with one another. That is, if

ROIC is great, then ROE is great as well. The following equation gives the formal relation

between ROE and ROIC (after tax and after depreciation),

(1 )* * *D

Debt BVEROIC t r ROE

IC IC

where t is the corporate tax rate, rD is the interest rate that a firm pays on its debt, Debt is debt

outstanding on the invested capital balance sheet, BVE is the book value of equity on the invested

capital balance sheet, and IC is invested capital.

In business analysis, the “short-term” is generally taken to be up to one year hence. In the above

relation, we presume that most corporate characteristics are constant in the short-term (that is, we

presume Dr , t, and /Debt IC to be constant in the short-term). However, in business analysis we

cannot assume SALES to be constant in the short-term (or the long-term). Since corporate

profitability depends upon SALES and business returns depend upon corporate profitability, we

do not presume ROIC or ROE to be constant in the short-term but rather ROE and ROIC move in

tandem with one another according to the above relation. When one is great the other is great and

vice versa.

In Question 39 of end of chapter problems you calculate ROIC after tax and after depreciation in

two ways. First, as (EBITDA-deprec)*(1-t)/IC (see above). And, second, as the right side of

(1 )* * *D

Debt BVEROIC t r ROE

IC IC . Of course, if you do this question correctly, the two

methods give you the same value for ROIC.

In discussions above, we calculate all terms in the above equation for CPR in 2013 with the

exception of rD, the interest rate that CPR pays on its debt (on average over all of the types of

debt that CPR uses, short-term, long-term, etc). Because we know all other terms in this

equation we can calculate the one that we do not know, rD, the interest rate that CPR pays on its

debt. We call this calculation the implied interest on debt (that is, implied by the above formula).

Intro to Finance

27

Exhibit 2.4 calculates CPR’s implied interest rate on debt for a number of years. For example,

this interest rate is 3.3% per annum in 2013. Amazing what one can do with financial statements!

Depending upon corporate profitability in any particular year, sometimes ROIC>ROE and

sometimes ROIC<ROE. So, it must be possible that ROIC and ROE exactly equal one another.

In this case, set ROIC=ROE in the above formula and do a little algebra. In particular, because

1Debt BVE

IC IC (that is, Debt+BVE=IC), (1 )* DROIC ROE t r . This result represents a

type of financial break-even for shareholders. If a firm makes business investments at the same

rate that it borrows (after corporate tax), then ROIC and ROE equal one another and both equal

the after-tax interest rate on debt. Thus, we can make the following statement.

Profitability for a business in a particular year is relatively good if the rate of return on invested

capital after tax and after depreciation exceeds the after tax cost interest rate on their debt and, in

addition, in this case, ROE exceeds ROIC. The vice versa is also true. Profitability for a business

in a particular year is relatively bad if the rate of return on invested capital after tax and after

depreciation is below the after tax cost interest rate on their debt and, in addition, ROIC exceeds

ROE. We can also say that if ROE>ROIC in a particular year, then corporate profitability is

relatively good for that firm in that year. Amazing! I think we have learnt something!

End of chapter problems give numerous opportunities to test your understanding of the above

relation between ROIC, ROE, and other financial variables.

Just before we leave business returns and their relations, don’t make the mistake of concluding

from our above discussion that if a firm makes business investments at a return above the after-

tax interest rate on its debt that debt-financing for business investments is preferable for

shareholder wealth maximization compared to equity financing. That conclusion is not justified

for reasons that are not likely immediately obvious to you. You need to take advanced finance

courses if you want to study questions of that nature.

There are some timing issues that can be important in the above relation between ROIC and

ROE. If we use ROIC and ROE with beginning of period IC and BVE and, if we use beginning

of period DEBT, IC, and BVE for DEBT/IC and EQUITY/IC, then we presume that any debt


28

repayment or incremental borrowing is at period-end. If alternatively, this debt transaction was at

the beginning of the period, then we need end-of-period amounts for DEBT, BVE, and IC in

DEBT/IC, BE/IC, ROIC, and ROE.

2.6.4 Why are ROIC and ROE both IRRs? Title Page

The author of this book has a confession to make. The numerical example that we presented in

chapter 1, a firm invests $300,000 to generate $400,000 in one year, is not a typical business

investment. The reason it is not typical is that most business investments have no predefined

termination or maturity. I think we should focus on things that are typical rather than atypical.

So, let’s consider a typical business investment that has no predefined termination. Suppose that

a business plans an investment for which the required expenditure today once (that is, the

investment) is $I. The “benefit” of this business investment is a cash flow (this is, free cash flow

in the upcoming section) is $c per annum indefinitely starting in one year. The opportunity cost

rate of return from financial markets for financial investments of about the same risk is r% per

annum.

For this typical business investment, the NPV is,

cNPV PV I I

r

Net Present Value (NPV) is always Present Value (PV) less expenditure (I). Notice in PV above,

we divide by “r” rather than “1+r.” In the numerical example of chapter 1, for a similar term, we

divided by “1+r,” so what is the difference?

The unity in “1+r” indicates we (as the business investor) want one dollar back (in one period,

which is typically one year) per one dollar of business investment. Plus, we want (really we want

for shareholders) compensation for time (one year) and risk. The opportunity cost rate of return

“r” embeds a financial market compensation for time and risk. So, rather, when we divide by “r”

in PV above, we are anticipating (it might not always be true) that this is a “good” business

investment (NPV>0) and we will commence the business investment today. Now, if this is a

Intro to Finance

29

good business investment today and if the business environment does not unduly adversely

deteriorate in a year or the following year or the following year, etc., then this will always be a

good business investment and, thus, we never want to terminate it. If we anticipate never wanting

to terminate this business investment, we never want the dollar back per dollar of original

business investment. Terminating the business destroys what we believe to be a “good”

investment. Thus, in the PV above, we divide by “r” rather than “1+r.” We want compensation

for time and risk for our shareholders but we never want back the dollar per dollar of original

business investment.

If we never get capital (original business investment) back, how can our business have value?

After the business investment the value of the business has nothing to do with capital but,

alternatively, with future cash-flow that capital generates. Remember that our theory of value is

future oriented not past oriented. The value of the business after the business investment is

PV=c/r and expenditure on business capital (I) does not appear in this calculation. We could

prove these statements mathematically (I don’t think you want me to do this) but this is the

business explanation of PV above.

Now, any IRR is the “hypothetical” opportunity cost rate of return that makes NPV equal zero.

So, for a typical business investment, we find the IRR from,

0c

NPV IIRR

Solve this equation to find that the IRR for a typical business investment is,

cIRR

I

So, now we can answer the question why ROIC and ROE are both IRRs.

For ROIC after-tax and after depreciation, c=(EBITDA-deprec)*(1-t) and I=IC. So, because

ROIC=(EBITDA-deprec)*(1-t)/IC, which is c/I, ROIC is an IRR.


30

Similarly, for ROE, c=NI (net income) and I=BVE (book value of equity). So, ROE=NI/BVE,

and because we can identify “c” and “I,” in IRR=c/I, ROE is also an IRR. I love IRRs!

(2.7) Free Cash Flow Title Page

Cash flow is the lifeblood of any firm. Firms with abundant cash flow thrive and grow; firms

strangled by insufficient cash flow wither and die. Even short periods of inadequate cash flow

have traumatic effects on firms and their employees. It is critically important, therefore, that you

be able to trace and evaluate the flow of cash through your firm. Cash flow is investigated in this

subsection using the concept of free cash flow. Free cash flow (FCF) plays a very important role

in financial analysis. In later chapters of this book, predicted future free cash flow is the

foundation of corporate valuation, the method we use for setting the value of a firm’s assets in

place. Likewise, predicted incremental free cash flow from a new business venture is central to

the evaluation of prospective business investments that we analyze in chapter 9. Because of

these important uses of free cash flow, it is essential to develop this concept early in our study of

corporate financial analysis.

For a typical business investment (see above), c

NPV Ir

. In this equation, “c” is FCF. So,

FCF (generally in the operating calculation below) is what we discount in NPV analysis as

financial analysts to establish the value to shareholders of business investments. Since FCF is

paid out to financial asset holders (the financial calculation of FCF below), it is the source of

value of all the financial assets of a business for creditors and shareholders.

Let us begin with a casual and intuitive description of free cash flow. Free cash flow is the net

amount of cash that flows into a firm as the result of operations. Inflows arise from past business

investments. In the current period, the firm bears the “fruit” of past investment. In addition, the

firm might make additional business investments. These investments are composed of both short

and long-term business investments. The difference between these two cash flows (the first is

typically an inflow and the second is typically an outflow) is free cash flow. The adjective “free”

refers to the fact that this net cash flow is available (i.e., free) and is distributed in one way or the

Intro to Finance

31

other to financial asset holders. This relationship between cash flow arising from operations and

distributions to financial asset holders implies that there is both a financial and an operating

definition of free cash flow.

2.7.1 The Operating Definition of Free Cash Flow Title Page

We can calculate Free Cash Flow (FCF) as Funds From Operations (FFO) less incremental

investment:

Free Cash Flow = FFO - Incremental Investment

FFO is the “benefit” of past business investment.

There are a number of ways to calculate funds from operations. First,

FFO = [EBITDA + Other Income – Deprec] × (1 – tax rate) + Deprec

EBITDA is before other income. Deprec is “depreciation” for tax purposes. This amount can

differ but (for simplicity) we presume it is the same as depreciation for financial statement

purposes.4 The above calculation for FFO is called the top down calculation because it begins

near the top of a typical income statement.

For CPR for 2013, EBITDA=$2,264,736 (see our calculation of EBITDA-margin above where

we used this number), Other Income is -397,668 (see 2013 income statement above), so, EBITDA

+ Other Income = $2,264,736-$397,668 = $1,867,068. CPR’s 2013 Deprec=531,165. Their 3013

effective tax rate is 22.22%. So, FFO (top down) for CPR for 2013 is,

FFO (top down) = [ 1,867,068–531,165] × (1 –0.2222) + 531,165=1,570,200

There is also a “bottom up” calculation for FFO.

4 If depreciation for tax purposes differs from depreciation for financial reporting purposes then a business has

“Deferred Income Tax” on its income statement that we add back in calculating FFO as a “non-cash” charge in

addition to financial statement “Depreciation.”


32

FFO (bottom up) = Net Income + Depreciation + other non-cash charges +After-Tax Interest

FFO (bottom up) = 822,600 +531,165+278,274*(1-0.2222) = 1,570,200

(net income for 2013 is 822,600, depreciation is 531,165, dollar interest is 278,274, the effective

tax rate is 22.22%).

Now, let’s calculate incremental business investment for 2013 for CPR. We know from our

discussion of invested capital that businesses make two primary business investments. The short-

term investment is Trade Capital (TC) and the long-term business investment is Net Fixed Assets

(NFA).5 Incremental business investment for a period is incremental trade capital plus

incremental depreciable asset investment (plus other long-term business investments) that we

measure as Capital Expenditure (CAPX).

The IC balance sheet in Exhibit 2-4 has Trade Capital as a component. The symbol Δ represents

change over a period (end of period EOP minus beginning of period BOP).

13 12EOP BOPTC TC TC TC TC 789,697-143,645=$646,052

We can rearrange an accounting calculation to determine CAPX.

EOP BOPNFA NFA CAPX deprec .

So,

CAPX NFA deprec

5 Plus possibly other long-term business investments.

Intro to Finance

33

Exhibit 2-4 has NFA (plus other long-term investments) and depreciation for 2013 for CPR is

531,165. So, for CPR for 2013,

13CAPX NFA deprec 14,130,864-13,454,509+531,165 = $1,207,520.

We can now calculate FCF in the operating calculaton. Free cash flow is FFO less incremental

business investment.

FCF FFO TC CAPX

For CPR for 2013,

13FCF = 1,570,200 - 646,052 - 1,207,520 = -$283,372.

Because this amount is negative, CPR has a Free Cash Flow deficit. On the other hand, firms

that have positive FCF have a Free Cash Flow surplus. Zero is a benchmark for FCF. However,

for any firm at any time, positive or negative FCF is not necessarily good or bad. An

investigation of why a firm has negative or positive FCF might lead to a conclusion on whether

these amounts are good or bad. The best we can do is identify the common characteristics of

firms with negative FCF (and vice versa for positive FCF firms).

Firms with a FCF Deficit Have the Following Common Characteristics

1. Growth Oriented with Large Business Investments

2. New Ventures that have Not Yet Completed Business

Investments for their Start-up Phase

3. Low Profitability


34

In order to survive in the long term firms eventually must have positive FCF. However, FCF

deficits in the near term are not necessarily bad. A FCF deficit indicates that a firm is investing

more in new business investments than it can “finance” from its operations. Therefore, it must

sell new financial assets to investors to makeup this deficit. As long as these investments are

productive – that is, they are positive NPV and create wealth, they should be made by the firm.

As financial analysts, we expect that eventually when anticipated FFO benefits of these new

investments begin to accrue and/or incremental investment slows down, FCF will turn positive.

2.7.2 The Financial Definition of Free Cash Flow Title Page

For our purposes, the operating definition of FCF is probably more important than is the financial

calculation. However, there is information content to the financial calculation for FCF, which

measures the sum of all net out flows from s firm to financial asset-holders. If FCF is negative

then the net flow is from financial asset-holders to the firm.

Free Cash Flow =

After Corporate Tax Net Distributions to Debt-holders

plus

Net Distributions to Shareholders

plus

Net Distributions to Other Financial Asset-Holders.

Each of these distributions represents the flow of cash from the firm to financial asset holders.

2.7.3 After Tax Distributions to Creditors Title Page

Net distributions to debtholders is after-tax interest plus principal repayments less the sale of new

debt over the period in question.

After-corporate-tax interest rather than interest itself is used in this calculation for two reasons.

First, interest is tax deductible for the firm, and therefore, the actual cost to the firm of making a

dollar of interest payment is lesser by the rate of taxation (presuming the firm is in a tax-paying

position). Second, in financial analysis, it is conceptually important to separate the operating

Intro to Finance

35

activities of a firm from its financing activities. Because the benefit of interest deductibility to a

firm arises from a financial activity (i.e., borrowing), this benefit (from the firm’s perspective)

should be attributed to this financing activity in the free cash flow calculation. In other words,

from the firm’s perspective, the “cost” of making interest payments to debtholders is less because

of this benefit.

During 2013 CPR paid interest of 278,274 (see income statement above). Their effective tax rate

for 2013 is 22.22%. So, the after-tax cost of their dollar interest payment is,

After Tax Cost of Dollar Interest 278,274*(1-0.2222) = $216,435

Net new borrowing, which is the difference between the sale of new debt and principal

repayments can be found by taking the difference between end-of-period and beginning-of-period

debt (both short-term and long-term) on the invested capital balance sheet.

13 12EOP BOPDEBT DEBT DEBT DEBT DEBT = 8,248,567- 8,479,656 = -$231,089

The fact that this number is negative indicates that CPR has paid down some of their debt during

2013. Paying down debt is a payment out from CPR to a financial asset-holder and thus will have

a positive sign in the FCFFIN calculation. If the above number had been positive, then CPR would

have undertaken incremental borrowing during 2013, which is a flow into CPR from a financial

asset-holder, and which, thus, would have a negative sign in the FCFFIN calculation.

Principal Repayment = $231,089

2.7.4 Net Distributions to Shareholders Title Page

Net distributions to shareholders equal the sum of dividends plus any share repurchases less new

issues of shares.

The information section at the bottom of the income statement in Exhibit 2-1 tells us that CPR

paid dividends in total of 229,388 to shareholders in 2013.


36

Dividends = $229,388

Of course, dividends flow out from CPR to a financial asset-holder and, thus, dividends have a

positive sign in the FCFFIN calculation.

In addition, CPR might have either sold new shares to shareholder or repurchased shares from

their existing shareholders. To find out whether CPR did either of these two things, recall that

book equity is the sum of share capital and retained earnings. BVE stands for book value of

equity,

BVEEND=BVEBEG + NI – DIV + NEW ISSUE - REPURCHASE OF SHARES

NI stands for Net Income and DIV stands for Dividends. For CPR in 2013 (see exhibits 2-4 and

2-1 for the numbers),

BVE2013 = 6,671,994 = 5,118,498 + 822,600 – 822,600 + NewIssue - ShareRepurchase

Rearrange to find,

NewIssue - ShareRepurchase = 960,284

Because this number is negative, in 2013, CPR had a sale of new shares (new issue) in the

amount of $960,284. This net new issue is a flow into CPR from a financial asset-holder and,

thus, has a negative sign in FCFFIN. On the other hand, if this amount had been negative, it

would be a net share repurchase that puts cash in the hand of a financial asset-holder (former

shareholders), and therefore, this amount would have a positive sign in FCFFIN.

The financial definition of FCF applied to CPR for 2013 is

After Tax Interest $216,435

Debt Repayment $231,089

Dividends $229,388

Intro to Finance

37

Net Share Repurchase -$960,284

Free Cash Flow Financial -$283,372

FCF in the financial definition in the above table equals FCF in the operating calculation as it

should The financial definition of FCF tells us how a firm has distributed a FCF surplus to its

financial asset holders or how it has financed a FCF deficit from its financial asset holders. In

2013, CPR sold new shares to new shareholders to pay down some debt and finance their large

CAPX of 1.2 billion dollars.

(2.8) Additional Invested Capital Ratios Title Page

There is often too much information on an accounting balance sheet that is not required for

financial analysis at least in the first instance. So, the invested capital balance sheet in exhibit 2-4

summarizes the expenditure question with a small number of measures. With these measures we

can learn quite a bit about the nature of business investment made by a corporation and how that

investment was financed. We can calculate a number of interesting ratios with invested-capital

and its component parts.

2.8.1 Debt to Invested Capital Title Page

The debt to invested capital ratio measures the fraction of business investment that the

corporation finances with debt. This is one of a set of “financial leverage” ratios. This is a risk

measure because as a firm uses more debt to finance their business investments they impose

greater risk on their shareholders. So, a financial leverage ratio is important for the risk question

of financial analysis that we identified in chapter 1.

The debt to invested capital ratio is:

Debt-to-Invested Capital = Capital Invested

s)liabilitie other debt term-long debt term-(short Debt


38

For CPR at the end of 2012 the debt to invested-capital ratio is 8,479,656/13,598,154 = 0.624.

This ratio indicates that 62.4% of CPR’s business investment is financed with debt. The industry

averages reported in the appendix of this chapter indicate that a typical value for debt to invested

capital is in the range of 40 to 50%. A comparison of CPR with this benchmark means that CPR

uses more debt than does a typical business. There are two reasons why an analyst might be

interested in debt use. First, debt imposes additional risk on shareholders beyond the risk

associated with business operations. We investigate this issue in more detail in chapter 3.

Second, because interest is tax-deductible, debt reduces a firm’s taxes payable.

2.8.2 Trade Capital to Invested Capital Title Page

A second invested capital ratio is trade capital to invested capital. This ratio measures the

fraction of the firm’s business investment that is short-term and held to support the trading

function of the firm. Other things equal (in particular, the level of a firm’s sales), firms would

prefer to reduce their trade capital investment. If a firm can maintain sales but decrease trade

capital, the rate of return on invested capital, the rate of return that the firm earns for all financial

asset-holders increases. The trade-off between lesser trade capital and reduced sales is referred to

as a firm’s trade capital (or working capital) problem.

Trade Capital-to-Invested Capital = Capital Invested

Capital Trade

For CPR at the end of 2013, the trade-capital-to-invested capital ratio is $789,697/14,920,561 =

5.3%. The appendix to this chapter reports trade-capital-to-invested capital for industry

averages. Notice that the range of industry averages is from approximately zero to over 80%.

This wide range indicates that for many firms, trade capital is an important component of

business investment. Recognition of this fact is important for focusing the financial planning and

analysis efforts of these firms. When planning for expansion of business activity, all firms, and

these firms in particular, should recognize incremental trade capital investment that is invariably

required.

Intro to Finance

39

2.8.3 EBITDA Margin & Invested Capital Turnover Title Page

A third invested-capital ratio is invested capital turnover. Invested capital turnover is a measure

of the ability of a business to generate sales from business investment. Other things equal, firms

that can increase sales without an increase in invested capital are more efficient. Below we

calculate invested-capital turnover6 as sales for the period divided by invested capital (b.o.p.),

Invested Capital Turnover = (b.o.p.) Capital Invested

Sales

The 2013 invested capital turnover ratio for CPR is $5,765,723/13,598,154=0.424.

Invested capital turnover is an inverse measure of “capital intensity.” Firms that require great

business investments to generate a dollar of sales are said to be capital intense. Firms that

require large fixed asset investment, which often have payoffs over many years (for example,

utilities), have low invested-capital turnover. While firms have some influence over their

invested-capital turnovers (for example, revenues depend upon product pricing), the example of

utilities highlights the fact that invested capital turnover is, in large part, based on the technology

of the industry in which a firm operates. For firms in North America, the median invested-

capital turnover ratio is approximately 1.7 (see the industry average ratios in the appendix).

Using the definitions of EBITDA margin and invested capital turnover, you can illustrate that the

rate of return on invested capital before depreciation and before tax is the product of the EBITDA

margin and invested capital turnover.

ROIC = EBITDA Margin Invested Capital Turnover

ROIC = Sales

EBITDA

(b.o.p.) Capital Invested

Sales

6Rather than invested capital turnover, accountants tend to use asset-turnover, which is yearly sales divided by the

book-value of all of a firm’s assets.


40

ROIC = (b.o.p.) Capital Invested

EBITDA

EBITDA margin and invested capital turnover are related to each other. As is evident from the

industry averages in the appendix, industries with low invested capital turnover tend to have high

EBITDA margins.

The reason for this relationship is a combination of the returns required by financial-asset

investors and competition faced by firms in their product markets. These relationships highlight

the inextricable co-dependent relationship between the operations of firms and financial markets.

No firm can ignore this relationship.

Why does there exist an inverse relationship between invested capital turnover and EBITDA

margin? Here is a thought experiment meant to give you the intuition.

Assume that financial markets expect the same ROIC from all firms. Call this the benchmark

ROIC. A firm that earns precisely the benchmark ROIC has just enough cash flow to pay every

investor’s opportunity cost of capital. Any firm that earns a return above the benchmark ROIC

accumulates more wealth than is needed to cover its investors’ opportunity cost. The fortunate

investors own the extra wealth, so the market prices of their financial assets (i.e., the tradable

values of common shares, bonds, preferred shares, etc.) increase. If such exceptional

performance persists, these firms can easily attract additional funds for investment in their

business. On the other hand, a firm that earns less than the benchmark ROIC cannot pay investors

as much as they can earn elsewhere. If such performance persists, investors will not invest in the

securities of lagging firms. Without capital, under-performing firms will be forced to liquidate.

To take the argument one step further, consider the effect of competition in product markets. If

firms in a particular industry earn a ROIC in excess of the benchmark, not only is this particular

firm likely to expand its operations, but also competitors are likely to enter the industry and the

Intro to Finance

41

product market the firm in question. Thus, a firm’s operations depend (at least in part) upon

whether firms have ROIC’s which exceed or fall short of the benchmark ROIC.

Entry by competitors tends to undermine increases in product price and ease shortages in

products. On the other hand, if an industry cannot earn its benchmark ROIC, firms shut down,

industry supply shrinks and product prices rise. These observations imply that, at least over the

long-term, ROIC’s of firms (even across industries) will tend toward the financial market

benchmark.

We mentioned above that invested capital turnover is in large part determined by the industry in

which a firm operates. For example, firms in the utility industry tend to be capital intense and

have low invested capital turnovers. If ROIC for every firm tends to the industry ROIC

benchmark, but some firms in have relatively low invested capital turnover, then (other things

equal) they are likely to have relatively great EBITDA margins. The reason for this negative

association between invested capital turnover and EBITDA margin is the influence of financial

markets on product pricing (given the level of competition in the industry).

Consider the electrical utility industry. For utilities to get earn an adequate rate of return for their

suppliers of capital, they must offset a relatively low invested capital turnover with a relatively

large EBITDA margin. This EBITDA margin is not reduced (at least significantly) by product

price-competition because of barriers to entry in the industry associated with low invested capital

turnover (i.e., high required fixed asset investment). In addition, if competitors were to enter the

product market, product prices would fall, and ROIC would drop below the industry ROIC

benchmark. Then the industry is unattractive for additional investment. Firms consolidate or

leave the industry until product prices tend to increase. EBITDA returns to its original level and

equilibrium is achieved once more between the product market and the financial market.


42

(2.9) Net Working Capital and Liquidity Title Page

Liquidity of any investment is a measure of the likelihood that it can be sold (i.e., liquidated)

without value loss. Long-term assets are often difficult to liquidate. Thus, in the hypothetical

case of forced liquidation of a firm’s operating investment, it is of interest to know whether a

firm could pay all its current liabilities from only its current assets. Presuming no value loss in

this liquidation (in other words, presuming that current assets can be liquidated dollar for dollar

as they are represented on the accounting balance sheet), the ability of a firm to meet its current

liabilities is measured by the current ratio. The current ratio is calculated as current assets

divided by current liabilities.

Current Ratio = sLiabilitie Current

Assets Current.

Is a declining current ratio good news or bad news for a firm? The answer to this question is that

it depends upon the firm’s circumstances. The current ratio should not be used independently of

other information and other analysis of a firm’s financial health. A declining current ratio that is

associated with profit growth might be interpreted to mean which a firm is making more efficient

use of its trade capital. On the other hand, a declining current ratio that is accompanied by a

profit decline might be an indication that the firm is having financial difficulties.

In the hypothetical exercise of liquidating a firm’s current assets and paying off current liabilities,

financial analysts often recognize that there is more potential for value loss when inventories are

liquidated than when other current assets are liquidated. The quick ratio, which is a more

exacting measure of liquidity than the Current Ratio, is current assets less inventory divided by

current liabilities.

Quick Ratio = sLiabilitie Current

Inventory-Assets Current

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43

(2.10) Efficiency of Trade Capital Utilization Title Page

For many firms, an important component of their business investment is trade capital. Recall

that if firms can reduce trade capital without reducing sales, the rate of return on invested capital

increases to the benefit of all financial asset-holders in the firm, including shareholders. It is

important, therefore, to assess the efficiency of a firm’s trade capital utilization.

2.10.1 Turnover Ratios Title Page

Financial analysts use three turnover ratios to measure the number of times (on average) that the

major current asset accounts of a firm are “zeroed” (or liquidated) during a year, accounts

receivable turnover, inventory turnover, and accounts payable turnover. To calculate each

turnover ratio, we divide an income statement line item by the current account balance that it

“generates.”

Account receivable turnover is Sales divided by Accounts Receivable.

Accounts Receivable Turnover = Receivable Accounts

Sales

The number of days it takes to collect a dollar of receivables is the accounts receivable collection

period. The accounts receivable collection period is the number of days during the year divided

by the receivable turnover.

Accounts-Receivable Collection Period = Turnover Receivable Accounts

365

Inventory turnover is cost of goods sold divided by inventory.

Inventory Turnover = Inventory

SoldGoods of Cost

The number of days it takes to sell or use inventory is the inventory conversion period, which is

the number of days during the year divided by inventory turnover.


44

Inventory Conversion Period = TurnoverInventory

365

Accounts payable turnover is Cost of Goods Sold divided by Accounts Payable.

Accounts Payable Turnover = Payable Accounts

SoldGoods of Cost

The number of days it takes to make payments is the accounts payable deferral period. The

accounts payable deferral period is calculated as the number of days during the year divided by

accounts payable turnover.

Accounts Payable Deferral Period = Turnover Payable Accounts

365

2.10.2 The Cash Conversion Cycle Title Page

The cash conversion cycle is a summary measure of a firm’s trade capital utilization. It measures

the length of time (in days) a dollar is “outside” the firm as it circulates through the firm’s

fundamental trade capital accounts: inventory, accounts receivable, and accounts payable. All

else equal, firms would like to minimize the cash conversion cycle. The cash conversion cycle is

calculated as the inventory conversion period plus the accounts receivable collection period less

the accounts payable deferral period.

Cash Conversion Cycle equals

Inventory Conversion Period

Plus Accounts Receivable Collection Period

Less Accounts Payable Deferral Period

There is no absolute standard for the cash conversion cycle, and therefore, firms use trend

analysis and industry comparisons to determine whether cash conversion is improving or

deteriorating. Soenen (1993) reports the cash conversion cycle for a number of different

industries. It is unusual, however, for a firm to have a negative cash conversion cycle. Similarly,

it is possible, but not likely, for a firm to have negative trade capital. These firms often have

Intro to Finance

45

considerable market power over many small suppliers that they can force to finance their current

assets. Since most firms do not have this type of market power, negative cash conversion cycles

and negative trade capital are not common.

(2.11) Summary Title Page

Financial accounting is the process of producing and disseminating information about the

economic activities of a firm. Annual and quarterly reports, and more specifically financial

statements, transmit this information to interested individuals and groups. Users of financial

statement information include shareholders, creditors, employees, suppliers, government, and

social interest groups. Financial statements are general-purpose summaries of economic activity

because user groups have diverse interests. A goal of this electronic book is, therefore, to

describe how investors can use financial statement information to analyze a firm as a potential

investment.

Financial accountants – the producers of financial statements – differ from other professional

groups because they rarely if ever meet directly with users of their services. Not only must

financial accountants interpret needs of users, but they must also jointly satisfy user groups

whose informational requirements differ. Since the relationship between financial statement

users and producers is weak, this electronic book is intended not only for users but also for

producers of financial statements as a framework with which to assess the informational

requirements of investors. An important aspect of this electronic book is a framework for

interpreting and reorienting financial statement information for investment analysis.

This chapter begins the development of this framework by describing the two principal financial

statements: the income statement and the balance sheet.

In this chapter, we integrate ratio calculations with a discussion of the use of financial statements.

This integration is intended to illustrate the use, rather than preparation, of financial statements.

The perspective adopted in this chapter has its origins in the financial industry. Because financial


46

analysts use financial ratios to make investment decisions, their perspective is generally more

insightful than the perspective of those who prepare financial statements.

Intro to Finance

47

(2.12) Suggested Readings Title Page

1. The Canadian Securities Course. Toronto: The Canadian Securities Institute, 1995.

2. Robert C. Higgins. Analysis for Financial Management, fifth ed. Chicago: Irwin, 1998.

3. Erich A. Helfert. Techniques of Financial Analysis, eighth ed. Chicago: Irwin, 1994.

4. Diana R. Harrington and Brent D. Wilson. Financial Analysis, third ed. Chicago: Irwin,

1989.

5. Kenneth Hackel and Joshua Livant Cash Flow and Security Analysis, Chicago, Business-

One Irwin, 1992.

6. Soenen, L.A, “Cash Conversion Cycle and Corporate Profitability,” Journal of Cash

Management (July/August, 1993), 53-57.

7. G.I. White, A.C. Sondhi, D. Fried. The Analysis and Use of Financial Statements. New York:

John Wiley & Sons, 1994.


48

(2.13) Appendix: Industry Ratios Title Page

In this appendix a number of industry-average financial ratios are reported. The data are from the

COMPUSTAT database, which is maintained and distributed by Standard and Poors

Corporation. The COMPUSTAT database is a commonly used source of firm-specific financial

data for both practicing financial analysts and academics. Firms included in the database are

selected by Standard and Poors based on investor interest. All firms trade on the NYSE, the

ASE, or the OTC stock exchanges in the United States. Some Canadian firms that have their

shares “interlisted” on one of these exchanges are also included. The data is from (by and large)

quarterly financial statements of firms. The time interval of the data is from (approximately) the

beginning of 1989 to the end of 1999. Each industry average is based on the ratios of at least five

firms.

DEFINITIONS

SIC is the standard industry code classification of industries. In the low thousands, firms are

from the extractive industries where little processing is required. The middle thousands are

processing and manufacturing firms. The higher thousands are retail and service companies.

INVESTED CAPITAL is debt included in current liabilities plus the book-value of common

equity plus the book-value of preferred equity plus short-term debt plus long-term debt plus other

liabilities plus deferred tax.

EBITDA MARGIN is average earnings before interest, tax, depreciation, and amortization

divided by average sales.

CONTRIBUTION MARGIN is a statistical estimate of a firm’s contribution-margin per dollar

sales which is defined as (revenues - variable costs)/revenues. Contribution-margin tends to be

greater than EBITDA-margin because contribution-margin is “before” fixed expenses while

EBITDA-margin is “after” fixed expenses. However, in the following tables, there are some

industries for which contribution-margin is lesser than EBITDA margin. This discrepancy arises

because contribution-margin is an estimate and is therefore subject to estimation variation. In

fact, all ratios should be interpreted as estimates of actual firm characteristics. For those who are

statistically inclined, contribution-margin is estimated as the slope coefficient in the simple linear

regression of annual EBITDA against annual sales.

INVESTED-CAPITAL TURNOVER is average of quarterly sales times 4.0 divided by the

average of invested capital. The multiplication by 4 is required to transform quarterly sales to a

yearly equivalent.

DEBT TO INVESTED-CAPITAL is the average of short-term debt plus long-term debt plus

“other liabilities” divided by the average of invested capital.

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TRADE-CAPITAL TO INVESTED-CAPITAL is the average of trade capital divided by the

average of invested capital. Trade-capital is current assets less current liabilities (excluding short-

term debt, the current portion of long-term debt, and dividends payable from current liabilities).

TRADE-CAPITAL TO SALES is the average of trade capital divided by the average of

annualized sales. Trade-capital is current assets less current liabilities (excluding short-term

debt, the current portion of long-term debt, and dividends payable from current liabilities).

REVENUE BASED RISK is the fraction of EBITDA variability that is explained by sales. This

measure is between 0 and 1. A high value indicates that relatively more EBITDA variability

arises from sales. Firms which have high revenue based risk tend to be “marketing” types of

firms. On the other hand, a value of revenue-based-risk close to zero indicates that relatively

more of EBITDA variability arises from cost factors (for example, unpredictable changes in

fixed or variable costs). Firms that are more production oriented and have less established

technologies tend to have lesser values for revenue based risk. For those who are statistically

inclined, “revenue based risk” is the coefficient of determination (i.e., R2) in the simple linear

regression of annual EBITDA against annual sales.

Industry Ratios

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(2.14) Problems

1. Financial Statements and Free Cash Flow. Title Page

Based on the following information for ABC Ltd., prepare an income statement for 1999 and

balance sheets for 1998 and 1999. Assume a flat 40% tax rate throughout. Next, for 1999,

calculate Funds From Operations, Change in Invested Capital, and Free Cash Flow. Find net

distributions to debtholders and net distributions to shareholders. Verify that free cash flow is

equal to the sum of net after corporate tax distributions to debtholders and net distributions to

shareholders. There is no deferred tax in this problem, so you can reasonably assume that

financial statement depreciation and depreciation for tax are equal.

Selected Information for ABC, Ltd

(All figures in thousands)

1998 1999

Sales $3,790 $3,990

Production Costs 2,043 2,137

Depreciation 975 1,018

Interest 225 267

Dividends 200 205

Current Assets 2,140 2,346

Net Fixed Assets 6,770 7,087

Accounts Payable 994 1,126

Long-term Debt 2,869 2,956

Solution

2. Invested Capital, ROIC, Trade-Capital, Free Cash Flow. Title Page

ABC Co. Ltd. has the following year-end accounting balance sheet.

Current Assets $500,000 Accounts Payable $200,000

Net Fixed Assets $1,500,000 Short-Term Debt 400,000

Equity 1,400,000

Equity on the balance sheet represents the sum of all the accounting “equity” accounts. Expected

sales for the upcoming year are $4,500,000. Costs of goods sold are 65% of sales and other

operating expenses are $850,000. The interest rate on ABC’s short-term debt is 10% per annum.

ABC’s tax-rate is 23%. ABC expects to maintain the level of its short-term debt into the

indefinite future.

a) Calculate ABC’s invested capital turnover, EBITDA margin, and rate of return on

invested capital (before tax, no depreciation in this problem).

https://drive.google.com/file/d/0B0oJRUS-4qjQZ3JmeTNjQ01fTDA/view?usp=sharing

Intro to Finance

51

b) ABC anticipates no capital expenditure in the upcoming year. ABC expects to pay

dividends equal to net income. Find free cash flow, net after corporate tax distributions

to debtholders and net distributions to shareholders. Does ABC have a free cash flow

surplus or deficit? If ABC has a free cash flow deficit, how is it financed? If ABC has a

free cash flow surplus, how is it distributed?

c) ABC intends to expand its operations. Sales are expected to increase by $1,000,000 per

annum. In addition, “other” operating expenses will increase by $200,000 per annum.

Costs of goods sold, as a fraction of sales is not expected to change. This expansion

requires a one-time incremental investment of $400,000 in trade capital and a capital

expenditure in the amount of $300,000. ABC intends to finance these expenditures with

long-term debt. Does ABC’s before tax rate of return on invested capital (for the entire

firm) increase or decrease as the result of the expansion?

d) What is the after tax IRR on the business expansion?

Solution

3. Rate of Return on Assets and Rate of Return on Invested Capital. Title Page

Compare and contrast the rate of return on “invested capital” and the rate of return on

“assets” as measures of corporate performance for evaluating the financial health of a firm.

Solution

https://drive.google.com/file/d/0B0oJRUS-4qjQMU1McmVqc0dUalk/view?usp=sharing

https://drive.google.com/file/d/0B0oJRUS-4qjQMXhQTE1mUXVET2c/view?usp=sharing


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4. The EBITDA Margin. Title Page

The range for EBITDA margin for industries in the North American economy is from

approximately zero to about 60%. What characteristics of industries lead to high or low

EBITDA margin? Explain and discuss.

Solution

5. ROA versus ROIC Title Page

This question is adapted from Analysis for Financial Management by Robert C. Higgins, fifth ed.

Chicago: Irwin, 1998.

The rate of return on assets is a commonly used ratio that is calculated as net income divided

by the accounting definition of assets. The purpose of this question is to illustrate that the

rate of return on invested capital is a better measure of the rate of return on business

investment. In this question, invested capital and “assets” are the same. Ignore depreciation

in this problem.

You have the following information for ABC Co. Ltd.

Earnings before interest and tax $100

Interest Expense 5

Earnings before tax 95

Tax at (30%) 28.5

Earnings after tax 66.5

Assets = Invested Capital = $500, Equity = $450

a) Calculate ABC’s ROE, ROA, and ROIC times one minus the tax-rate.

b) Suppose that ABC recapitalizes by selling $200 million in debt at 10% per annum. ABC

uses the proceeds of this financial-asset sale to repurchase $200 million of its common

shares. Presume that this recapitalization has no effect on ABC’s operating performance

(in other words, ROIC is not expected to change after the recapitalization). Calculate

ABC’s ROE, ROA, and ROIC times one minus the tax rate. Explain why ROA is an

inadequate measure of the rate of return to business investment.

c) Give two reasons for the increase in ROE after the recapitalization. Discuss some of the

advantages and disadvantages of debt use by firms.

Solution

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6. The EBITDA Margin. Title Page

Explain the significance of EBITDA margin in financial analysis.

Solution

7. Free cash flow and net distributions to financial asset-holders. Title Page

ABC is a non-growing firm: it retains no earnings and pays all residual cash flows after

interest and tax to shareholders as dividends. ABC is financed with common shares and

short-term debt. ABC’s trade capital equals inventory plus accounts receivable less accounts

payable. Ignore depreciation for reporting and tax in this problem.

ABC sells widgets. Projected sales are 1,000,000 units per annum into the future. Product

price is $2.80 per unit. Costs of goods sold equal 60% of Sales. General and administrative

expenses are $100,000 per annum. ABC’s accounts receivable turnover is 6.5. Inventory

turnover is 5.5. Accounts payable turnover is 4.0.

ABC’s past expenditure into capital assets is $2,225,000. ABC has financed its operations

(in part) with $1,000,000 in short-term debt that pays interest at a rate of 12% per annum

(paid annually). ABC’s only other financial asset is common equity. ABC anticipates to

make no additional expenditures in the foreseeable future on capital assets. ABC pays annual

dividends equal to Net Income, and therefore, ABC is a non-growing firm. The corporate tax

rate is 35%. There are 1,000,000 shares of ABC stock, which trade on the Newton stock

exchange.

a) Find the rate of return on equity for ABC.

b) Decompose ABC’s rate of return on equity into the product of net profit margin, asset-

turnover, and the asset to equity ratio. In these calculations, use invested-capital as your

definition of assets.

c) ABC is contemplating a change in its product pricing policy, which may require changes

in its trade-capital investment. If ABC reduces its product price to $2.70 per unit it

anticipates an increase in per unit sales to 1,200,000 units per annum. As the result of

increase in per annum dollar sales, what will be the new level of trade capital for ABC?

Accounts receivable turnover, inventory turnover, and accounts payable turnover are not

expected to change.

The remaining parts of this problem relate to the policy change described in (c).

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d) ABC repurchases no shares over the year. In addition, they sell no new shares. ABC will

use short-term debt for any required financing (at the end of the year). How much will

ABC need to borrow at the end of the year?

e) Find Funds from operations for ABC. Find incremental business investment. Find Free

Cash Flow.

f) Find Net Distributions to Shareholders. Find Net Distributions to Debtholders.

Solution

8. ROE Title Page

Consider the following invested capital balance sheet for ABC Company for year-end 1994.

Trade Capital 3,200,000 s.t. debt 1,900,000

Common Equity 600,000

Net Fixed Assets 800,000 Retained Earnings 1,500,000

ABC has a contribution margin per dollar sales of 20%. (Contribution margin is defined as

unit product/service price minus unit variable cost dividend by unit price). Fixed costs per

annum (before depreciation) are $200,000. Dollar sales for the upcoming year are expected

to be $3,000,000. The interest rate on short-term debt is 10% per annum. ABC expects no

incremental business investment for the year. ABC’s tax-rate is 35%. Depreciation for tax

and reporting is 15% per annum.

a) Find expected net income for the upcoming year.

b) Find after-tax expected funds from operations.

c) Calculate the rate of return on equity.

Solution

9. The Current Ratio. Title Page

A firm has current assets of $500,000. What is the change in the current ratio (now equal to

2.0) if the following actions are taken independently? In other words, you should have five

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55

separate responses for the five parts of this problem below. Other than the common

information given on current assets and the current ratio, information from no one part of the

question should be used in any other part.

a) pays $77,500 of accounts payable with cash.

b) collects $43,000 in accounts receivable.

c) purchases merchandise worth $51,300 on account.

d) Sells production machinery for $90,000.

e) Sells merchandise on account that cost $53,500. Gross profit margin is 33%.

Solution

10. Financial Analysis. Title Page

There are three principal questions a financial analyst or investor must investigate for any

investment. Identify these questions. Suppose you are a financial analyst who is charged

with evaluating the performance of a corporation over the recent past. Discuss the measures

and ratios that you might calculate to answer or investigate these questions for the firm under

consideration.

Solution

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11. Ratio Analysis in EXCEL. Title Page

Below is an embedded “workbook” composed of three worksheets. The first worksheet is an

income statement and the second is a balance sheet. In the third worksheet, calculate the

indicated financial ratios for each of the years 1990-1993. In every cell of this solution

template, you should replace the “X” cell identifier with a spreadsheet formula that uses

inputs from the first two worksheets to calculate the indicated ratio. The tax rate for the firm

in this problem is 36%. A suggested solution is contained in the second embedded workbook

entitled “Solution”.

Template Solution

12. Calculate Free Cash Flow. Title Page

The following information is available on the financial accounts of ABC Corporation.

1999

Sales 1,600

Cost of Goods Sold 800

General and Administrative Expenses 250

Interest 50

Depreciation 40

tax at 40% 184

1998 1999

Accounts Receivable 150 ?

Inventory 200 ?

Net Fixed Assets ? ?

Short Term Debt 500 ?

Accounts Payable 100 ?

Equity ? ?

NOTE: “Equity” represents the sum of all of the accounting equity accounts.

The following additional financial information is available for ABC.

The rate of return on invested capital (b.o.p.) after tax and after depreciation for 1999 is

15.3%. This return is calculated as EBITDA less depreciation times one minus the tax rate

divided by beginning of period invested capital. Dividends for 1999 are $85. ABC paid off

its short-term debt in 1999 and sold additional common shares. In 1999, inventory turnover

was 4.0, the accounts payable deferral period was 40 days, and the cash conversion cycle was

60 days. The component ratios of the cash conversion cycle are calculated using 365 days in

a year. In addition, these ratios use only the 1999 financial statements (i.e., not beginning of

period balance sheet amounts). Capital expenditure in 1999 was $135.

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Required : Based on the information at hand, find free cash flow using both the operational

and the financial definitions for 1999.

Solution

13. Calculate Free Cash Flow. Title Page


1999

Sales ?

Cost of Goods Sold ?


Interest 50

Depreciation 40

tax at 40% 274

1998 1999

Accounts Receivable 150 200

Inventory ? ?

Net Fixed Assets ? 3056


Accounts Payable ? 100

Equity ? ?



The rate of return on invested capital (b.o.p.) after tax and after depreciation for 1999 is

15.0%. This return is calculated as EBITDA less depreciation times one minus the tax rate

divided by beginning of period invested capital. Dividends for 1999 are $95. ABC

incremented the level of its short-term debt by $300 in 1999. ABC repurchased $200 of its

outstanding shares in 1999. Incremental investment in trade capital in 1999 was $145. In

1999, inventory turnover was 4.0, the accounts receivable collection period was 40 days. The

accounts receivable collection period is calculated using 365 days in a year. In addition,

inventory turnover and the accounts receivable collection period use only the 1999 financial

statements (i.e., not beginning of period balance sheet amounts).

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Required: Based on the information at hand, find free cash flow using both the operational

and the financial definitions for 1999.

Solution

14. Free Cash Flow and the Invested Capital Balance Sheet. Title Page


1996

Sales 2,000

Cost of Goods Sold 1,400


Interest 60

depreciation (which equals depreciation for tax) 35

corporate tax rate ?

1995 1996

Accounts Receivable 268 ?

Inventory 100 ?

Net Fixed Assets 3000


Accounts Payable 200 ?

Equity ? 2,517



ABC has a trade capital to sales ratio of 10% (i.e., trade capital for the end of the fiscal year

divided by sales for that same year). ABC has financed its operations with short-term debt and

with common equity. Dividends for 1996 are $95. ABC borrowed additional short-term debt in

1996. They also repurchased $200 of shares in 1996. Free cash flow in 1996 was $25.

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Required: Based on the information at hand, and the definition(s) of free cash flow, determine

the invested capital balance sheet for ABC for both 1995 and 1996. For each year find trade

capital, net fixed assets, short-term debt and “equity.” What was ABC’s corporate tax rate in

1996? What was ABC’s expenditure for plant property and equipment for 1996 (i.e., capital

expenditure)? Find free cash flow for 1996 using the operating definition.

Solution

15. Optimal Trade Capital. Title Page

Comment on the following assertion. “If a firm can reduce its trade capital usage, then it

should definitely do so.”

Solution

16. Cash Flow. Title Page

ABC has a contribution margin of 20% and fixed costs of $450,000 per annum. Their

corporate tax rate is 40%. For financial statement purposes, ABC takes depreciation charges

on its net fixed assets at the rate of 5% per annum on the declining balance. Capital cost

allowance is the same as financial statement depreciation. As of December 31, 1996, ABC

has financed its business investment with short-term debt and with common equity. ABC has

a trade capital to sales ratio of 12%. This ratio is calculated as trade capital at the end of the

year divided by yearly sales for the associated year (for example trade capital at December

31, 1996 divided by yearly sales ended December 31, 1996). This ratio is not expected to

change in the foreseeable future. ABC has net fixed assets of $250,000 at December 31,

1996.

ABC is doing some short term financial planning. They predict sales, for the year ending

December 31, 1997, of $3,000,000. Their invested capital turnover based on this prediction

and December 31, 1996 invested capital is 3.0 (i.e., predicted 1997 sales divided by year-end

1996 invested capital is 3.0). If ABC requires any financing to accommodate their 1997

sales, they plan to increment (or decrement) their short term borrowing. If ABC borrows, or

repays existing short-term debt, they plan to do so at the end of 1997. The interest rate on

short-term debt is 10% per annum. ABC’s predicted 1997 net income is $42,000. ABC

expects to pay no dividends to their shareholders in 1997. ABC expects no capital

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expenditures or asset sales in 1997. ABC expects no share repurchases or new share issues in

1997.

a) (10 marks) Use 1997 predicted net income to help you determine short-term debt at

December 31, 1996. What is invested capital at December 31, 1996? Calculate ABC’s

predicted 1997 rate return on equity (using beginning of period equity).

b) (10 marks) Does it appear that ABC will need incremental short-term borrowing (at the

end of 1997) or can they pay down some of their short-term debt? What is the most likely

reason for the change in ABC’s debt use?

c) (10 marks) For 1997, calculate ABC’s free cash flow using both the operating and the

financial definitions.

d) (10 marks) Without doing any numerical calculations, do you believe that ABC’s

operating leverage has increased or decreased between 1996 and 1997? Explain.

Solution

17. Free Cash Flow and the Rate of Return on Invested Capital. Title Page


1997

Sales ?

Cost of Goods Sold ?

General and Administrative Expenses ?

Interest 35

Depreciation (which equals depreciation for tax) 100

Corporate tax (at 40%) ?

Net Income ?

1996 1997

Accounts Receivable 250 275

Inventory 150 175


Short Term Debt ? 400

Accounts Payable 200 225

Equity ? ?


The following additional financial information is available for ABC:

For both 1996 and 1997, ABC had a trade capital to invested capital ratio of 25% (trade

capital at the end of the year divided by invested capital at the end of the year). ABC has

financed its operations with short-term debt and with common equity. ABC undertakes

borrowing or repayment of debt at the end of the year. Therefore, ABC’s interest charge on

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61

its income statement is equal to outstanding short-term debt at the beginning of 1997 (end of

1996) times the interest rate on this debt which is 7% per annum. Dividends for 1997 are

$95. ABC issued shares for $200 in 1997.

Required: Based on the information at hand, and the definition(s) of free cash flow

developed in class, find free cash flow for 1997 using both the operating and the financial

definitions. Find ABC’s 1997 rate of return on invested capital, after tax and after

depreciation, using beginning of period invested capital.

Solution

18. Free Cash Flow and the Rate of Return Equity. Title Page


1998

Depreciation $30

Interest 10

1997 1998

Trade Capital 150 ?

Short-term Debt ? 250

Net Fixed Assets 300 ?

Equity 350 ?

NOTES: “Equity” represents the sum of all of the accounting equity accounts (e.g., share-

capital plus retained earnings). You can presume that depreciation for tax and for financial

statement purposes is the same, and therefore, there is no deferred income tax in this

problem.

Any incremental short-term borrowing undertaken by ABC during 1998 was at the end of the

year. Therefore, ABC’s interest expense for 1998 is the interest rate on short-term debt times

short-term debt at the beginning of 1998 (end of 1997). Alternatively, if instead, ABC paid

down any short-term debt during 1998, this was also done at the end of 1998. ABC has

financed its business activity with short-term debt and with common equity. In 1998, ABC’s

rate of return on equity (ROE) was 20%. ROE is calculated with equity at the end of 1998.

ABC paid dividends of $26 during 1998. ABC had no share issues or share repurchases

during 1998. Also in 1998, ABC’s EBITDA margin was 25%. Their trade capital to sales

ratio was 30%, both trade capital and sales are measured at the end of 1998. ABC’s tax rate

is 40%.

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Required: Using both the operating and the financial definitions, find ABC’s free cash flow

for 1998.

Solution

19. Ratios. Title Page

Discuss briefly how each of the following five ratios is calculated and what each is intended to

measure:

(a) EBITDA margin,

(b) debt to assets,

(c) times interest earned,

(d) quick ratio (acid test ratio),

(e) asset turnover.

Solution

20. Incremental Business Return Title Page

Generally, ABC Company Ltd. has been a non-growing firm. Per annum sales have been

$8,000,000. However, as the result of a favourable international trade agreement between

Canada and the United States, in the upcoming year, sales are expected to increase to

$10,000,000 per annum and remain at this higher level indefinitely into the future.

ABC has a trade capital to sales ratio of 20% and an invested-capital turnover ratio of 1.25.

Trade capital to sales is calculated as trade capital at the beginning of the year divided by

sales for the upcoming year. Invested-capital turnover is calculated as sales for the upcoming

year divided by invested-capital at the beginning of the year. ABC’s depreciation is 5% of

net fixed assets at the beginning of any year. Subsequent to the change in sales, these ratios

and rates are expected to remain unchanged. Depreciation for tax equals financial statement

depreciation. ABC makes maintenance capital expenditures at year-end equal to financial

statement depreciation. Maintenance capital expenditures “maintain” the quality of ABC’s

assets and prevent revenue deterioration.

Generally, other than in the upcoming year, ABC makes no capital expenditures for the

purpose of growth. However, at the beginning of the upcoming year, to accommodate the

increased level of permanent sales, incremental trade capital assets and additional depreciable

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Intro to Finance

63

assets will be needed. In addition, as the result of the increase in depreciable assets, per

annum year-end maintenance capital expenditures will also increase. Thereafter, because

ABC will be once more a non-growing firm (that is, trade capital will not increase and capital

expenditure for the purpose of growth will again be zero).

ABC’s contribution margin per dollar sales is 25%. The tax-rate is 40%. Find the rate of

return on ABC’s incremental business investment after tax and after depreciation

(equivalently, after tax and after additional maintenance capital expenditures) arising from

the greater expected level of dollar sales.

Solution

21. Free Cash Flow, Invested Capital, Financial Statements Title Page


1999

EBITDA ?

Depreciation ?

Interest ?

1998 1999

Trade Capital ? 200

Short-term Debt ? ?


Equity ? 520

Invested Capital 500 850



statement purposes is the same, and therefore, there is no deferred income tax in this problem

.

ABC’s net incremental borrowing for 1999 was $120. Because this borrowing was at the end

of 1999, ABC’s interest expense for 1999 is the interest rate on short-term debt times short-

term debt at the beginning of 1999 (end of 1998). The interest rate on ABC’s short-term debt

is 10% per annum. ABC made net capital expenditures of $365 at the end of 1999. Because

these capital expenditures were at the end of 1999, ABC’s depreciation expense for 1999

(also depreciation for tax) is a rate for depreciation times net fixed assets at the beginning of

1999 (end of 1998) prior to the capital expenditure. The depreciation rate is 5% per annum.

ABC paid dividends to shareholders of $50 during 1999. ABC’s tax rate is 40%. ABC had a

free cash flow deficit of $100 for 1999.

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64

Required: Find ABC’s rate of return on invested capital for 1999, before tax and before

depreciation, using beginning of period invested capital. Was ABC a net seller of common

shares or a net repurchaser of its common shares in 1999?

Solution

22. The Relation Between ROIC and ROE Title Page

Today, ABC has invested capital of $4,000,000. Trade capital and net fixed assets are 34% and

66% of invested capital respectively. Invested capital has been financed with short-term debt

and with common equity. The interest rate on short-term debt is 10% per annum. ABC’s tax

rate is 40%. Depreciation is 5% of beginning-of-period net fixed assets. No capital expenditures

are required for the upcoming year. Based on predicted sales in the upcoming year, ABC’s

EBITDA is $1,000,000. Other things equal, ABC’s rate of return on equity (using beginning of

period equity) at predicted sales for the upcoming year, is equal to their predicted rate of return

on invested capital after tax and after depreciation (using beginning of period invested capital)

plus 10%. That is at predicted sales, ROE=ROIC+0.10.

Required: What is ABC’s beginning of period (i.e., today) debt to equity ratio?

Solution

23. The Relation Between ROIC and ROE Title Page


2013

EBITDA ?

Depreciation ?

Interest ?

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65

2013

Trade Capital 200

Short-term Debt ?


Equity ?

Invested Capital 1,000

NOTES: “Equity” represents the sum of all of the accounting equity accounts (e.g., share-capital

plus retained earnings). You can presume that depreciation for tax and for financial statement

purposes is the same, and therefore, there is no deferred income tax in this problem .

ABC neither borrowed incrementally nor repaid short-term debt during 2013, and therefore, its

interest expense for 2013 is the opening balance for 2013 (same as the closing balance) times the

interest rate on its short-term debt, which is 6.25% per annum. ABC’s tax rate is 40%.

ABC’s rate of return on invested capital for 2013, after tax and after depreciation, using end of

period invested capital is 27%. ABC’s ROE for 2013 using end of period book equity is 42.5%.

Required: Find ABC’s debt to equity ratio for 2013.

Solution

24. ROA and ROE. Title Page

ABC has return on equity (ROE) of 24 percent and a return on assets (ROA) of 16%.

Required: Find ABC’s debt to equity ratio.

Solution

25. Relation Between ROIC and ROE Title Page


2013

EBITDA ?

Depreciation ?

Interest ?

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2013

Trade Capital ?

Short-term Debt 400


Equity ?

Invested Capital ?



statement purposes is the same, and therefore, there is no deferred income tax in this

problem .

The interest rate on ABC’s short-term debt is 8% per annum. ABC’s tax rate is 40%.

ABC’s rate of return on equity (ROE) for 2013 using end of period book equity is 16.8%.

Their rate of return on invested capital for 2013, after tax and after depreciation, using end

of period invested capital, is 12%.

Required: Find ABC’s 2013 year-end invested capital.

Solution

26. ROA, ROE, and Net Profit Margin Title Page

ABC company limited has a 4 percent net profit margin, a return on equity (ROE) of 32 percent,

a return on assets (ROA) of 16 percent.

Required:

(a) Find ABC’s asset turnover ratio.

(b) Find ABC’s debt to equity ratio.

Solution

27. ROIC and ROE Title Page


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Intro to Finance

67

2008

EBITDA 400

Depreciation 25

Interest ?

2008

Trade Capital ?

Short-term Debt ?

Net Fixed Assets ?

Equity 600

Invested Capital ?






interest rate on its short-term debt, which is 8% per annum. ABC’s tax rate is 40%.

ABC’s rate of return on invested capital for 2008, after tax and after depreciation, using end of

period invested capital equals its 2008 ROE using end of period equity.

Required: Find ABC’s 2008 interest expense (in dollars).

Solution

28. ROIC Versus ROE Title Page


2008

EBITDA 600

Depreciation 40

Interest

2008

Trade Capital ?

Short-term Debt ?

Net Fixed Assets ?

Equity ?

Invested Capital ?

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68




The interest rate on ABC’s short-term debt is 9% per annum. ABC paid down no debt during

2008, and therefore, their opening debt balance for 2008 equals their closing 2008 debt balance.

ABC’s tax rate is 40%.

ABC’s rate of return on equity (ROE) for 2008 using end of period book equity is 20%. Their

year-end 2008 debt to invested capital ratio is 25%.

Required: Find ABC’s 2008 Invested Capital.

Solution

29. ROIC Title Page

Comment on the following assertion. “A primary determinant of a firm’s rate of return on

invested capital (after tax and after depreciation) is corporate debt use.” Use no numerical

examples in your response. A complete response is required for full marks.

Solution



2008

EBITDA 700

Depreciation 520

Interest 100

2008

Trade Capital ?

Short-term Debt ?

Net Fixed Assets ?

Equity ?

Invested Capital ?

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69

NOTES: “Equity” is the sum of all of the accounting equity accounts (e.g., share-capital plus

retained earnings). You can presume that depreciation for tax and for financial statement


ABC paid down no debt during 2008, and therefore, their opening debt balance for 2008 equals

their closing 2008 debt balance. ABC’s tax rate is 40%. ABC’s 2008 rate of return on equity

(with 2008 year-end book equity) equals their 2008 rate of return on invested capital (after tax,

after depreciation, with 2008 year-end invested capital).

Required: Find ABC’s year-end 2008 equity to invested capital ratio (2008 year-end equity

divided by 2008 year-end invested capital).

Solution



2008

EBITDA ?

Depreciation 400

Interest ?

2008

Trade Capital ?

Short-term Debt 900

Net Fixed Assets ?

Equity ?

Invested Capital ?

NOTES: “Equity” is the sum of all of the accounting equity accounts (e.g., share-capital plus

retained earnings). You can presume that depreciation for tax and for financial statement




interest rate on its short-term debt, which is 10% per annum. ABC’s tax rate is 40%. ABC’s rate

of return on invested capital for 2008, after tax and after depreciation, using end of period

invested capital is 20%. ABC’s 2008 ROE using end of period equity is 26%.

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70

Required:

(a) Find ABC’s 2008 year-end Invested Capital.

(b) Find ABC’s 2008 EBITDA.

Solution


Comment on the following assertion. “When a firm does well on its business investments, that

is, EBITDA is high, the rate of return on invested capital (ROIC) is correspondingly high and

exceeds the rate of return on equity (ROE). On the other hand, when a firm does poorly on its

business investments, ROIC is low and is below ROE.” State whether or not you agree with the

assertion and then explain why. Use no numerical examples in your response. A complete

response is required for full marks.

Solution

33. Free Cash Flow Title Page


1999

EBITDA ?

Depreciation 20

Interest 25

1998 1999

Trade Capital ? ?

Short-term Debt ? 300


Equity 520 ?

Invested Capital ? 850




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71

ABC’s did some incremental borrowing during 1999. Because this borrowing was at the end of

1999, ABC’s interest expense for 1999 is the interest rate on short-term debt times short-term

debt at the beginning of 1999 (end of 1998). The interest rate on ABC’s short-term debt is 10%

per annum. ABC made net capital expenditures (e.g. net of disposals) of $165 at the end of

1999. Because these capital expenditures were at the end of 1999, ABC’s depreciation expense

for 1999 (also depreciation for tax) is a rate for depreciation times net fixed assets at the

beginning of 1999 (end of 1998) prior to the capital expenditure. The depreciation rate is 5%

per annum. ABC paid dividends to shareholders of $50 during 1999. ABC’s tax rate is 40%.

ABC had a free cash flow surplus of $100 for 1999.

Required: Find ABC’s rate of return on invested capital for 1999, after tax and after

depreciation, using beginning of period invested capital. Was ABC a net purchaser or seller of

its own common shares in 1999? What was is the amount of shares sold or repurchased?

Solution



1999

EBITDA ?

Depreciation ?

Interest 25

1998 1999

Trade Capital 180 200

Short-term Debt ? ?


Equity ? 520

Invested Capital 850 ?




ABC’s did some incremental borrowing during 1999. Because this borrowing was at the end of

1999, ABC’s interest expense for 1999 is the interest rate on short-term debt times short-term

debt at the beginning of 1999 (end of 1998). The interest rate on ABC’s short-term debt is 8%

per annum. ABC made net capital expenditures (e.g. net of disposals) of $365 at the end of

1999. Because these capital expenditures were at the end of 1999, ABC’s depreciation expense

for 1999 (also depreciation for tax) is a rate for depreciation times net fixed assets at the

beginning of 1999 (end of 1998) prior to the capital expenditure. The depreciation rate is 5%

https://drive.google.com/file/d/0B0oJRUS-4qjQU2g3YUtxbTcwdTg/view?usp=sharing


72

per annum. ABC paid dividends to shareholders of $50 during 1999. ABC’s tax rate is 40%.

ABC had a free cash flow deficit of $100 for 1999.

Required: Find ABC’s rate of return on invested capital for 1999, after tax and after

depreciation, using beginning of period invested capital. Was ABC a net seller of its common

shares or a net purchaser of its common shares in 1999? What is the dollar amount of shares sold

or repurchased?

Solution



2003

EBITDA 450

Depreciation ?

Interest ?

2002 2003

Trade Capital 550 ?

Short-Term Debt ? ?


Equity 800

Invested Capital ? ?

NOTES: "Equity" represents the sum of all of the accounting equity accounts (that is, share-


statement purposes is the same, and therefore, there is no deferred income tax or future income

tax liability in this problem .

ABC repaid $200 of their short-term debt at year-end 2003. Therefore, ABC's 2003 interest

expense is the interest rate on short-term debt times short-term debt at the beginning of 2003

(year-end 2002). The interest rate on ABC's short-term debt is 8% per annum. ABC made capital

expenditures of $365 at year-end 2003. Because these capital expenditures were at year-end,

ABC’s 2003 depreciation expense (also depreciation for tax) is a rate for depreciation times Net

Fixed Assets at the beginning of 2003 (year-end 2002). The depreciation rate is 5% per annum.

ABC paid dividends to shareholders of $X during 2003. ABC's tax rate is 40%. Also, during

2003, ABC sold new shares to new shareholders in the amount of $125 (no shares were

repurchased). ABC’s 2003 free cash flow was $253.

https://drive.google.com/file/d/0B0oJRUS-4qjQakR4TnNUMkYzRnc/view?usp=sharing

Intro to Finance

73

Required: How much did ABC pay in dividends (in total rather than per share) to shareholders

during 2003?

Solution

36. Free Cash Flow


2003

EBITDA 450

Depreciation ?

Interest ?

2002 2003

Trade Capital ? ?

Short-Term Debt ? ?

Net Fixed Assets 300 630

Equity 517 700

Invested Capital ?





ABC's 2003 interest expense is the interest rate on short-term debt times short-term debt at the

beginning of 2003 (year-end 2002). The interest rate on ABC's short-term debt is 8% per annum.

ABC made capital expenditures of $365 at year-end 2003. Because these capital expenditures

were at year-end, ABC’s 2003 depreciation expense (also depreciation for tax) is a rate for

depreciation times Net Fixed Assets at the beginning of 2003 (year-end 2002). ABC paid

dividends to shareholders of $50 during 2003. ABC's tax rate is 40%. Also, during 2003, ABC

sold new shares to new shareholders in the amount of $100 (no shares were repurchased).

ABC’s 2003 free cash flow was $253.

Required: Determine the amount of ABC’s short-term debt repayment or the increment to

short-term debt borrowing at year-end 2003.

Solution

https://drive.google.com/file/d/0B0oJRUS-4qjQcU4zekgxdVdMbUk/view?usp=sharing

https://drive.google.com/file/d/0B0oJRUS-4qjQTXRyakE0OGZGSW8/view?usp=sharing


74



2008

EBITDA ?

Depreciation ?

Interest 35

2013 2008

Trade Capital 650 ?

Short-Term Debt ? ?


Equity 900






ABC repaid $200 of their short-term debt at year-end 2008. The interest rate on ABC’s debt is

10% per annum. ABC made capital expenditures of $385 at year-end 2008. Because these

capital expenditures were at year-end, ABC’s 2008 depreciation expense (also depreciation for

tax) is a rate for depreciation times Net Fixed Assets at the beginning of 2008 (year-end 2013).

The depreciation rate is 5% per annum. ABC paid dividends to shareholders of $X during 2008.

ABC's tax rate is 40%. Also, during 2008, ABC sold new shares to new shareholders in the

amount of $125 (no shares were repurchased). ABC’s 2008 free cash flow was $353.

Required:

(a) Determine ABC’s 2008 dividend payment, $X.

(b) Determine ABC’s 2008 rate of return on invested capital, after tax and after depreciation,

using beginning of period invested capital.

Solution

https://drive.google.com/file/d/0B0oJRUS-4qjQRkRlUWh0dkpQWkk/view?usp=sharing

Intro to Finance

75



2008

EBITDA ?

Depreciation ?

Interest ?

2013 2008

Trade Capital 845

Short-Term Debt 540 480

Net Fixed Assets 640 ?

Equity ? ?






ABC repaid some of their short-term debt at year-end 2008. The interest rate on ABC’s debt is

10% per annum. ABC made capital expenditures of $105 at year-end 2008. Because these

capital expenditures were at year-end, ABC’s 2008 depreciation expense (also depreciation for

tax) is a rate for depreciation times Net Fixed Assets at the beginning of 2008 (year-end 2013).

The depreciation rate is 5% per annum. ABC paid dividends to shareholders of $55 during 2008

(in total rather than per share). ABC's tax rate is 40%. ABC’s 2008 free cash flow was $283.

Required: Determine ABC’s 2008 rate of return on invested capital after tax and after

depreciation using beginning of period invested capital.

Solution

39. ROIC and ROE: Title Page

The following information is available on the financial accounts of ABC Ltd.

2006

EBITDA 400

Depreciation 40

Interest 60

https://drive.google.com/file/d/0B0oJRUS-4qjQUnFCc1VxVGNyODQ/view?usp=sharing


76

2006

Trade Capital 200

Short-term Debt 600


Equity 400

Invested Capital ?




The interest rate on ABC’s short-term debt is 10% per annum. ABC’s tax rate is 40%.

a). Find ABC’s rate of return on invested capital for 2006, after tax and after depreciation, using

end of period invested capital.

b). Find ABC’s ROE for 2006 using end of period book equity.

c). Show that the ROIC from part “a” of this question can also be calculated as the after

corporate tax interest rate on debt times the debt to invested capital ratio plus the ROE from part

“b” of this question times the equity to invested capital ratio. That is:

(1 )* * *Debt Equity

ROIC t r ROEInvested Capital Invested Capital

,

where “r” is the interest rate on debt and “t” is the corporate tax rate. This relation says that the

firm’s ROIC, the rate of return that the firm earns for all financial asset-holders, is a weighted

average of the rates of return that the firm earns for the specific financial asset-holders (in this

problem, the creditors and the common shareholders).

Solution

https://drive.google.com/file/d/0B0oJRUS-4qjQR2hjWGY1VDJsUU0/view?usp=sharing

Intro to Finance

77

40. A Benchmark for ROIC and ROE

ABC Company has debt and common equity in its financial structure. The interest rate on ABC

Company’s debt is 10% per annum. The corporate tax rate is 40%. In 2006, ABC’s ROIC (after

tax and after depreciation) equals ROE. For 2006 what was ABC’s ROIC?

Solution

https://drive.google.com/file/d/0B0oJRUS-4qjQSlpPRGxXZ2RDOEE/view?usp=sharing


78

(2.15) Chapter Index Title Page

accounts payable, 57

Accounts payable, 57

accounts payable deferral period, 85

accounts payable turnover, 84

Accounts Receivable, 56

accounts receivable collection period, 84

accounts receivable turnover, 84

assets, 54

balance sheet, 54

business investments, 59

capital expenditure, 71, 74

capital intensity, 80

Capital Surplus, 57

cash conversion cycle, 85

Common stock, 57

COMPUSTAT, 49

costs of goods sold, 50

current assets, 56, 60

current liabilities, 60

Current liabilities, 57

current portion of long-term debt, 57

current ratio, 83

debt to invested capital, 79

Debt-to-Invested Capital, 78

depreciation, 53

dividends, 76

earnings, 54

EBITDA, 52

EBITDA margin, 52, 80

Economic depreciation, 53

financial analysis, 50

financial definition of FCF, 75

financial ratios, 50

financial statement analysis, 47

free cash flow, 71

Funds from operations, 72

General and Administrative Expenses, 50

generally accepted accounting principles, 50,

54

Gross Profit, 51

gross profit margin, 52

income statement, 50

income taxes payable, 57

industry averages, 47

Inventories, 56

inventory conversion period, 84

inventory turnover, 84

invested capital, 58, 59, 61, 72

invested capital balance sheet, 61

invested capital turnover, 80

Liquidity, 83

Long Term Debt Due in One Year, 57

maximization of shareholders’ wealth, 65

maximize shareholder wealth, 47

net fixed assets, 60

Net fixed assets, 60

net income, 54

net profit margin, 54

net working capital, 60

non-current assets, 56

operating definition of invested capital, 59

opportunity cost returns, 45

Property, Plant and Equipment, 56

quick ratio, 83

rate of return on equity, 46, 65

rate of return on invested capital, 63, 79

Research Insight, 49

Retained earnings, 57

share repurchase, 76

shareholders' wealth, 54

short-term debt, 57

Standard and Poor’s Corporation, 49

the rate of return on invested capital, 46

trade capital, 60, 71, 79

Trade capital, 60

Treasury Stock, 57

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