Cfa Level 1 - Section 7 Financial Ratios

CFA Level 1 - Financial Ratios Email to Friend Comments

7.1 - Introduction INTRODUCTION Knowing how to calculate and use financial ratios is important for not only analysts, but for investors, lenders and more. Ratios allow analysts to compare a various aspect of a company's financial statements against others in its industry, to determine a company's ability to pay dividends, and more. The material presented in this section is extremely important to know for your exam. The majority of the questions you see on your exam, within the accounting section, will require you to have excellent knowledge on how to calculate and manipulate ratios. You also need to recognize how ratios are interrelated and how the results of two or more other ratios can be used to calculate other ratios. A. ANALYZING FINANCIAL STATEMENTS I. Common-Size Financial Statements Common-size balance sheets and income statements are used to compare the performance of different companies or a company's progress over time. •

A Common-Size Balance Sheet is a balance sheet where every dollar amount has been restated to be a percentage of total assets. o Calculated as follows: Formula 7.1 % value of balance sheet account = Balance sheet account Total Assets

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A Common-Size Income Statement is an income statement where every dollar amount has been restated to be a percentage of sales. o Calculated as follows: Formula 7.2 % value of income statement account = Income statement account Total Sales (Revenues)

Example: FedEx Common Size Balance Sheet and Income Statement At first glance, all numbers stated within FedEx's income statement in figure 7.1, and balance sheet in figure 7.2, can seem daunting. It requires close examination to determine whether operating expenses are increasing or decreasing, or which particular expense comprises the highest percentage total operating expenses. Figure 7.1: FedEx Consolidated Income Statements

However, if we consider the common-size statements in figures 7.2 and 7.4 below, you can tell at first glance how a company is performing in many areas. The common-size income statement informs us that salaries and other comprise the largest percentage of total operating expenses and their most recent net income comprises 3.39% of total 2004 revenues. Alternately, the common-size balance sheet in figure 7.4 quickly shows that receivables comprise a large percentage of current assets and are decreasing, and more. Figure 7.2: FedEx Common-sized Income Statements

Figure 7.3: FedEx Consolidated Balance Sheets

Figure 7.4: FedEx Common-sized Consolidated Balance Sheets

II.Financial Ratios Classification of Financial Ratios Ratios were developed to standardize a company’s results. They allow analysts to quickly look through a

company’s financial statements and identify trends and anomalies. Ratios can be classified in terms of the information they provide to the reader. There are four classifications of financial ratios: 1. Internal liquidity – The ratios used in this classification were developed to analyze and determine a company’s financial ability to meet short-term liabilities. 2. Operating performance - The ratios used in this classification were developed to analyze and determine how well management operates a company. The ratios found in this classification can be divided into ‘operating profitability’ and ‘operating efficiency’. Operating profitability relates the company’s overall profitability, and operating efficiency reveals if the company’s assets were utilized efficiently. 3. Risk profile - The ratios found in this classification can be divided into ‘business risk’ and ‘financial risk’. Business risk relates the company’s income variance, i.e. the risk of not generating consistent cash flows over time. Financial risk is the risk that relates to the company’s financial structure, i.e. use of debt. 4. Growth potential - The ratios used in this classification are useful to stockholders and creditors as it allows the stockholders to determine what the company is worth, and allows creditors to estimate the company’s ability to pay its existing debt and evaluate their additional debt applications, if any. 7.2 - Internal Liquidity Ratios 1. Current Ratio This ratio is a measure of the ability of a firm to meet its shortterm obligations. In general, a ratio of 2 to 3 is usually considered good. Too small a ratio indicates that there is some potential difficulty in covering obligations. A high ratio may indicate that the firm has too many assets tied up in current assets and is not making efficient use to them. Formula 7.3 Current ratio = current assets / current liabilities 2. Quick Ratio The quick (or acid-test) ratio is a more stringent measure of liquidity. Only liquid assets are taken into account. Inventory and other assets are excluded, as they may be difficult to dispose of. Formula 7.4 Quick ratio = (cash+ marketable securities + accounts receivables) current liabilities 3. Cash Ratio The cash ratio reveals how must cash and marketable securities the company has on hand to pay off its current obligations. Formula 7.5 Cash ratio = (cash + marketable securities)/current liabilities 4. Cash Flow from Operations Ratio Poor receivables or inventory-turnover limits can dilute the information provided by the current and quick ratios. This ratio provides a better indicator of a company's ability to pay its short-term liabilities with the cash

it produces from current operations. Formula 7.6 Cash flow from operations ratio = cash flow from operations current liability 5. Receivable Turnover Ratio This ratio provides an indicator of the effectiveness of a company's credit policy. The high receivable turnover will indicate that the company collects its dues from its customers quickly. If this ratio is too high compared to the industry, this may indicate that the company does not offer its clients a long enough credit facility, and as a result may be losing sales. A decreasing receivable-turnover ratio may indicate that the company is having difficulties collecting cash from customers, and may be a sign that sales are perhaps overstated. Formula 7.7 Receivable turnover = net annual sales / average receivables Where: Average receivables = (previously reported account receivable + current account receivables)/2 6. Average Number of Days Receivables Outstanding (Average Collection Period) This ratio provides the same information as receivable turnover except that it indicates it as number of days. Formula 7.8 Average number of days receivables outstanding = 365 days_ receivables turnover 7. Inventory Turnover Ratio This ratio provides an indication of how efficiently the company's inventory is utilized by management. A high inventory ratio is an indicator that the company sells its inventory rapidly and that the inventory does not languish, which may mean there is less risk that the inventory reported has decreased in value. Too high a ratio could indicate a level of inventory that is too low, perhaps resulting in frequent shortages of stock and the potential of losing customers. It could also indicate inadequate production levels for meeting customer demand. Formula 7.9 Inventory turnover = cost of goods sold / average inventory Where: Average inventory = (previously reported inventory + current inventory)/2 8. Average Number of Days in Stock This ratio provides the same information as inventory turnover except that it indicates it as number of days. Formula 7.10

Average number of days in stock = 365 / inventory turnover 9. Payable Turnover Ratio This ratio will indicate how much credit the company uses from its suppliers. Note that this ratio is very useful in credit checks of firms applying for credit. Payable turnover that is too small may negatively affect a company's credit rating. Formula 7.11 Payable turnover = Annual purchases / average payables Where: Annual purchases = cost of goods sold + ending inventory – beginning inventory Average payables = (previously reported accounts payable + current accounts payable) / 2 10. Average Number of Days Payables Outstanding (Average Age of Payables) This ratio provides the same information as payable turnover except that it indicates it by number of days. Formula 7.12 Average number of days payables outstanding = 365_____ payable turnover II. Other Internal-Liquidity Ratios 11.Cash Conversion Cycle This ratio will indicate how much time it takes for the company to convert collection or their investment into cash. A high conversion cycle indicates that the company has a large amount of money invested in sales in process. Formula 7.13 Cash conversion cycle = average collection period + average number of days in stock - average age of payables Cash conversion cycle = average collection period + average number of days in stock - average age of payables 12.Defensive Interval This measure is essentially a worst-case scenario that estimates how many days the company has to maintain its current operations without any additional sales. Formula 7.14 Defensive interval = 365 * (cash + marketable securities + accounts receivable) projected expenditures Where: Projected expenditures = projected outflow needed to operate the company 7.3 - Operating Profitability Ratios Operating Profitability can be divided into measurements of return on sales and return on investment. Return on Sales

1. Gross Profit Margin This shows the average amount of profit considering only sales and the cost of the items sold. This tells how much profit the product or service is making without overhead considerations. As such, it indicates the efficiency of operations as well as how products are priced. Wide variations occur from industry to industry. Formula 7.15 Gross profit margin = gross profit / net sales Gross profit = net sales – cost of goods sold 2. Operating Profit Margin This ratio indicates the profitability of current operations. This ratio does not take into account the company's capital and tax structure. Formula 7.16 Operating profit margin = operating income/net sales Where: Operating income = earnings before tax and interest from continuing operations 3. EBITDA Margin This ratio indicates the profitability of current operations. This ratio does not take into account the company's capital, non-cash expenses or tax structure. Formula 7.17 EBITDA margin = earnings before tax, depreciation and amortization net sales 4. Per-Tax Margin (EBT margin) This ratio indicates the profitability of Company's operations. This ratio does not take into account the company's tax structure. Formula 7.18 Pre-tax margin = Earning before tax/sales 5. Net Margin (Profit Margin) This ratio indicates the profitability of a company's operations. Formula 7.19 Net margin = net income/sales 6. Contribution Margin This ratio indicates how much each sale contributes to fixed expenditures. Formula 7.20 Contribution margin = contribution / sales Where: Contributions = sales - variable cost

7.4 - Return on Investment Ratios 1. Return on Assets (ROA) This ratio measures the operating efficacy of a company without regards to financial structure Formula 7.21 Return on assets = (net income + after-tax cost of interest) average total assets OR Return on assets = earnings before interest and taxes average total assets Where: Average total assets = (previously reported total assets + current total assets) 2 2. Return on Common Equity (ROCE) This ratio measures the return accruing to common stockholders and excludes preferred stockholders. Formula 7.22 Return on common equity = (net income – preferred dividends) average common equity Where: Average common equity = (previously reported common equity + current common equity) / 2

3. Return on Total Equity (ROE) This is a more general form of ROCE and includes preferred stockholders. Formula 7.23 Return on total equity = net income/average total equity Where: Average common equity = (previously reported total stockholders' equity + current total stockholders' equity) / 2 4. Return on Total Capital (ROTC) Total capital is defined as total stockholder liability and equity. Interest expense is defined as the total interest expense excluding any interest income. This ratio measures the total return the company generates from all sources of financing. Formula 7.24 Return on total capital = (net income + interest expense) / average total capital 7.5 - Operating Efficiency Ratios

OPERATING EFFICIENCY RATIOS 1. Total Asset Turnover This ratio measures a company's ability to generate sales given its investment in total assets. A ratio of 3 will mean that for every dollar invested in total assets, the company will generate 3 dollars in revenues. Capital-intensive businesses will have a lower total asset turnover than non-capitalintensive businesses. Formula 7.25 Total asset turnover = net sales / average total assets 2. Fixed-Asset Turnover This ratio is similar to total asset turnover; the difference is that only fixed assets are taken into account. Formula 7.26 Fixed-asset turnover = net sales / average net fixed assets 3.Equity Turnover This ratio measures a company's ability to generate sales given its investment in total equity (common shareholders and preferred stockholders). A ratio of 3 will mean that for every dollar invested in total equity, the company will generate 3 dollars in revenues. Formula 7.27 Equity turnover = net sales / average total equity 7.6 - Business Risk Ratios Business Risk – This is risk related a company's income variance. There is a simple method and more complex method: Simple Method The following four ratios represent the simple method of business risk calculations. Business risk is the risk of a company making less money, or worse, losing money if sales decrease. In the declining-sales environment, a company would lose money mainly because of its fixed costs. If a company only incurred variable costs, it would never have negative earnings. Unfortunately, all businesses have a component of fixed costs. Understanding a company's fixed-cost structure is crucial in the determination of its business risk. One of the main ratios used to evaluate business risk is the contribution margin ratio. 1.Contribution Margin Ratio This ratio indicates the incremental profit resulting from a given dollar change of sales. If a company's

contribution ratio is 20%, then a $50,000 decline in sales will result in a $10,000 decline in profits. Formula 7.28 Contribution margin ratio = contribution / sales = 1-(variable cost / sales) 2.Operation Leverage Effect (OLE) The operating leverage ratio is used to estimate the percentage change in income and return on assets for a given percentage change in sales volume. Return on sales is the same as return on assets. If a company has an OLE greater than 1, then operating leverage exists. If OLE is equal to 1 then all costs are variable, so a 10% increase in sales will increase the company's ROA by 10%. Formula 7.29 Operation leverage effect = contribution margin ratio return on sales (ROS) ROS = Percentage change in income (ROA) = OLE * % change in sales 3.Financial Leverage Effect (FLE) Companies that use debt to finance their operations, thus creating a financial leverage effect and increasing the return to stockholders, represent an additional business risk if revenues vary. The financial leverage effect is used to quantify the effect of leverage within a company. It is defined as: Formula 7.30 Financial leverage effect = operating income / net income If a company has an FLE of 1.33, an increase of 50% in operating income would result in a 67% shift in net income. 4.Total Leverage Effect (TLE) By combining the OLE and FLE, we get the total leverage effect (TLE), which is defined as: Formula 7.31 Total leverage effect = OLE * FLE In our previous example, sales increased by $50,000, the OLE was 20% and FLE was 1.33. The total leverage effect would be $13,333, i.e. net income would increase by $13,333 for every $50,000 in increased sales. Complex Method Business risk can be analyzed by simply looking at variations in sales and operating income (EBIT) over time. A more structured approach is to use some statistics. One common method is to gather a date set that's large enough (five to 10 years) to calculate the coefficient of variation. With this approach:

- Business risk = standard deviation of operating income / mean of operating income - Sales variability = standard deviation of sales / sales mean - Another source of variability of operating income is the difference between fixed and variable cost. This is referred to as "operating leverage". A company with a large variable structure is less likely to create a loss if revenues decline. The calculation of variability of operating income is complex and beyond CFA level 1.

Look Out! Note that it is unlikely that the exam will ask you to calculate any ratios relating to business risk that utilize statistics.

7.7 - Financial Risk Ratios FINANCIAL RISK RATIOS Financial Risk – This is risk related to the company's financial structure. Analysis of a Company's Use of Debt 1.Debt to Total Capital This measures the proportion of debt used given the total capital structure of the company. A large debt-tocapital ratio indicates that equity holders are making extensive use of debt, making the overall business riskier. Formula 7.32 Debt to capital = total debt / total capital Where: Total debt = current + long-term debt Total capital = total debt + stockholders' equity 2. Debt to Equity This ratio is similar to debt to capital. Formula 7.33 Debt to equity = total debt / total equity Analysis of the Interest Coverage Ratio 3. Times Interest Earned (Interest Coverage ratio) This ratio indicates the degree of protection available to creditors by measuring the extent to which earnings available for interest covers required interest payments.

Formula 7.34 Times interest earned = earnings before interest and tax interest expense 4.Fixed-Charge Coverage Fixed charges are defined as contractual committed periodic interest and principal payments on leases and debt. Formula 7.35 Fixed-charge coverage = earnings before fixed charges and taxes fixed charges 5.Times Interest Earned - Cash Basis Adjusted operating cash flow is defined as cash flow from operations + fixed charges + tax payments. Formula 7.36 Times interest earned - cash basis = adjusted operating cash flow interest expense 6.Fixed-Charge Coverage Ratio – Cash Basis Formula 7.37 Fixed charge coverage ratio – cash basis = adjusted operating cash flow/fixed charges 7.Capital Expenditure Ratio Provides information on how much of the cash generated from operations will be left after payment of capital expenditure to service the company's debt. If the ratio is 2, it indicates that the company generates two times what it will need to reinvest in the business to keep operations going; the excess could be allocated to service the debt. Formula 7.38 Capital expenditure ratio = cash flow from operations capital expenditures 8. CFO to Debt Provides information on how much cash the company generates from operations that could be used to pay off the total debt. Total debt includes all interest-bearing debt, short and long term. Formula 7.39 CFO to debt = cash flow from operations / total debt 7.8 - Growth Potential Ratios

1. Sustainable Growth Rate Formula 7.40

G = RR * ROE Where: RR = retention rate = % of total net income reinvested in the company or, RR = 1 – (dividend declared / net income) ROE = return on equity = net income / total equity Note that dividend payout is the residual portion of RR. If RR is 80% then 80% of the net income is reinvested in the company and the remaining 20% is distributed in the form of cash dividends. Therefore, Dividend Payout = Dividend Declared/Net Income

Look Out! Students sometimes confuse retention rate with actual dividend declared. Students should read questions diligently.

Let's consider an example:

7.9 - Return on Equity and the Dupont System DuPont System A system of analysis has been developed that focuses the attention on all three critical elements of the financial condition of a company: the operating management, management of assets and the capital structure. This analysis technique is called the "DuPont Formula". The DuPont Formula shows the interrelationship between key financial ratios. It can be presented in several ways. The first is: Formula 7.41 Return on equity (ROE) = net income / total equity If we multiply ROE by sales, we get: Return on equity = (net income / sales) * (sales / total equity) Said differently: ROE = net profit margin * return on equity

The second is: Formula 7.42 Return on equity (ROE) = net income / total equity If in a second instance we multiply ROE by assets, we get: ROE = (net income / sales) * (sales / assets) * (assets / equity) Said differently: ROE = net profit margin * asset turnover * equity multiplier Uses of the DuPont Equation By using the DuPont equation, an analyst can easily determine what processes the company does well and what processes can be improved. Furthermore, ROE represents the profitability of funds invested by the owners of the firm. All firms should attempt to make ROE as high as possible over the long term. However, analysts should be aware that ROE can be high for the wrong reasons. For example, when ROE is high because the equity multiplier is high, this means that high returns are really coming from overuse of debt, which can spell trouble. If two companies have the same ROE, but the first is well managed (high net-profit margin) and managed assets efficiently (high asset turnover) but has a low equity multiplier compared to the other company, then an investor is better off investing in the first company, because the capital structure can be changed easily (increase use of debt), but changing management is difficult. More Useful Dupont Formula Manipulations The DuPont formula can be expanded even further, thus giving the analyst more information. Formula 7.43 ROE = (net income / sales) * (sales / assets) * (assets / equity) If in a third instance we substituted net income for EBT * (1-tax rate), we get: ROE =(EBT/sales) * (sales / assets) * (assets / equity)* (1-tax rate) Formula 7.44 ROE = (net income / sales) * (sales / assets) * (assets / equity) If in a forth instance we substituted EBT for EBIT - interest expense, we get: ROE = [EBIT / sales * sales / total assets – interest / total assets] * total assets / equity * [1 – tax / net before tax] Said differently: ROE = operating profit margin * asset turnover – interest expense rate * equity multiplier * tax retention 7.10 - Uses and Limitations of Financial Ratios

Benchmarking Financial Ratios Financial ratios are not very useful on a stand-alone basis; they must be benchmarked against something. Analysts compare ratios against the following: 1.The Industry norm – This is the most common type of comparison. Analysts will typically look for companies within the same industry and develop an industry average, which they will compare to the company they are evaluating. Ratios per industry are also provided by Bloomberg and the S&P. These are good sources of general industry information. Unfortunately, there are several companies included in an index that can distort certain ratios. If we look at the food and beverage ratio index, it will include companies that make prepared foods and some that are distributors. The ratios in this case would be distorted because one is a capital-intensive business and the other is not. As a result, it is better to use a crosssectional analysis, i.e. individually select the companies that best fit the company being analyzed. 2.Aggregate economy - It is sometimes important to analyze a company's ratio over a full economic cycle. This will help the analyst understand and estimate a company's performance in changing economic conditions, such as a recession. 3.The company's past performance – This is a very common analysis. It is similar to a time-series analysis, which looks mostly for trends in ratios. Limitations of Financial Ratios There are some important limitations of financial ratios that analysts should be conscious of: • •

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Many large firms operate different divisions in different industries. For these companies it is difficult to find a meaningful set of industry-average ratios. Inflation may have badly distorted a company's balance sheet. In this case, profits will also be affected. Thus a ratio analysis of one company over time or a comparative analysis of companies of different ages must be interpreted with judgment. Seasonal factors can also distort ratio analysis. Understanding seasonal factors that affect a business can reduce the chance of misinterpretation. For example, a retailer's inventory may be high in the summer in preparation for the back-to-school season. As a result, the company's accounts payable will be high and its ROA low. Different accounting practices can distort comparisons even within the same company (leasing versus buying equipment, LIFO versus FIFO, etc.). It is difficult to generalize about whether a ratio is good or not. A high cash ratio in a historically classified growth company may be interpreted as a good sign, but could also be seen as a sign that the company is no longer a growth company and should command lower valuations. A company may have some good and some bad ratios, making it difficult to tell if it's a good or weak company.

In general, ratio analysis conducted in a mechanical, unthinking manner is dangerous. On the other hand, if used intelligently, ratio analysis can provide insightful information. 7.11 - Basic Earnings Per Share I. Introduction Simple and Complex Capital Structures A simple capital structure is one that contains no potential dilutive securities. A company with a simple structure will have only common stockholders, preferred stockholders and nonconvertible debt. Companies with simple capital structures only need to report basic EPS. A complex structure refers to one that contains potential dilutive securities. A company with a complex structure in addition to what is included in a company’s simple capital structure will also include warrants and/or options and/or convertible debt instruments. - Companies that have a complex capital structure must report earnings per share (EPS) on a basic and fully diluted basis. EPS is simply the net income that is attributable to common shareholders divided by the number of shares outstanding. If a company has a complex capital structure, it means that a portion of their dilutive securities may be converted to equity at some point in time. Since EPS basic does not take into account these dilutive securities, EPS basic will always be greater than EPS fully diluted. Basic Earnings Per Share (EPS) EPS basic does not consider potential dilutive securities. A company with a simple capital structure will calculate only a basic EPS, which is defined as: Formula 7.45

Basic EPS =

(net income – preferred dividends)_____ weighted average number of shares outstanding

Since we are interested only in the net income that belongs to common stockholders, preferred dividends are subtracted. Dividends, whether paid in cash or stock, or the additional dividend that is attributable to participating preferred shares must also be deducted. Note: - Dividends declared to common stockholders are not subtracted from ESP as they belong to common stockholders. - Preferred stock dividends are the current year's dividend only. (a) If none are declared, then calculate an amount equal to what the current dividend would have been. (b) Don't include dividends in arrears. (c) If a net loss occurs, add the preferred dividend.

- EPS is calculated for each component of income: income from continuing operations, income before extraordinary items or changes in accounting principle, and net income. Calculating the Weighted Average Number of Shares Outstanding The weighted average number of shares outstanding (WASO) is: Formula 7.46 The # of shares outstanding during each month, weighted by the # of months those shares were outstanding. Included are the impacts of all stock dividends and stock splits effective during the period and those announced after the end of the reporting period but before the financial statements are issued. Furthermore, all prior periods must be restated to facilitate comparative analysis. 7.12 - Dilutive Effect of Splits and Dividends Since in the Financial Statements section we described stock dividends and splits, here we will focus on their effects by considering an example. Example 1: Cash Dividend In 2004, Company ABC generated a net income of $12 million and paid a dividend of $1 million to preferred stockholders. Other information:

The first step is to average out the number of months the shares were outstanding:

Answer: Basic EPS = $12 million – $1 million / 3.8 million = $2.89 Example 2: Stock Splits and Dividends Stock splits and dividends are applied to all shares issued prior to the split and to the weighted average number of shares at the beginning of the period. In other words, if in this quarter a company declares a 2-to-1 stock split, then double the number of outstanding shares of prior months. Furthermore, if the company declares in Q3 a stock dividend of 10%, then increase the number of shares outstanding by 10% of prior months. Shares that are repurchased from treasury after the stock split and dividends should not be adjusted. Other information:

The first step is to account for the stock dividend in Q3:

The second step is average out the number of month the shares were outstanding:

Answer: Basic EPS = $12m –$1m/ 4.28m = $2.57 7.13 - Dilutive Securities Dilutive Securities are securities that are not common stock in form, but allow the owner to obtain common stock upon exercise of an option or a conversion privilege. The most common examples of dilutive securities are: stock options, warrants, convertible debt and convertible preferred stock. These securities would decrease EPS if exercised or if they were converted common stock. In other words, a dilutive security is any securities that could increase the weighted number of shares outstanding. If a security after conversion causes the EPS figure to increase rather than decrease, such a security is an antidilutive security, and it should be excluded from the computation of the dilutive EPS. For example, assume that the company XYZ has a convertible bond issue: 100 bonds, $1,000 par value, yielding 10%, issued at par for the total of $100,000. Each bond can be converted into 50 shares of the common stock. The tax rate is 30%. XYZ’s weighted average number of shares, used to compute basic EPS, is 10,000. XYZ reported an NI of $12,000, and paid preferred dividends of $2,000. What is the basic EPS? What is the diluted EPS? 1) Compute basic EPS: i. Basic EPS = (12,000 – 2,000) / (10,000) = $1.00 2) Compute diluted EPS: i. Find the adjustment to the denominator: 100 * 50 = 5,000 ii. Find the adjustment to the numerator: 100 * $1000 * 0.1 * (1 - 0.3) = $7,000 3) Find diluted EPS: i. Diluted EPS = (12,000 – 2,000 + 7,000) / 10,000 + 5,000 = $1.13 If Basic EPS > the fully diluted ESP, then the security is anti-dilutive. In this case, Basic EPS = $1.00 is less than the fully diluted ESP, and the security is not anti-dilutive.

7.14 - Calculating Basic and Fully Diluted EPS in a Complex Capital Structure There are some basic rules for calculating basic and fully diluted ESP in a complex capital structure. The basic ESP is calculated in the same fashion as it is in a simple capital structure. Basic and fully diluted EPS are calculated for each component of income: income from continuing operations, income before extraordinary items or changes in accounting principle, and net income. To calculate fully diluted EPS: Diluted EPS = [(net income – preferred dividend) / weighted average number of shares outstanding - impact of convertible securities - impact of options, warrants and other dilutive securities] Other form: (net income – preferred dividends) + convertible preferred dividend + (convertible debt interest * (1-t)) Divided by weighted average shares + shares from conversion of convertible preferred shares + shares from conversion of convertible debt + shares issuable from stock options. To understand this complex calculation we will look at each possibility: If the company has convertible bonds, use the ifconverted method: 1.Treat conversion as occurring at the beginning of the year or at issuance date, if it occurred during the year (additive to denominator). 2.Eliminate related interest expense, net of tax (additive to numerator). If the company has convertible preferred stock, use the if-converted method: 1. Eliminate preferred dividend from numerator (decrease numerator). 2. Treat conversion as occurring at the beginning of the year or at issuance date, if it occurred during the year (additive to denominator). Furthermore, use the most advantageous conversion rate available to the holder of the security. Options and warrants use the treasury-stock method: 1.Assume that exercise occurred at the beginning of the year or issue date, if it occurs during the year. 2.Assume that proceeds are used to purchase common stock for treasury stock. 3.If exercise price < market price of stock, dilution occurs. 4.If exercise price > market price, securities are anti-dilative and can be ignored in the diluted EPS calculation. Example: Company ABC has: - Net income of $2m and 2m weighted average number of shares outstanding for the accounting period.

- Bonds convertible to common stock worth $50,000: 50 at $1,000, with an interest of 12%. They are convertible to 1,000 shares of common stock. - A total of 1,000 convertible preferred stock paying a dividend of 10% and convertible to 2,000 shares of common stock, with a par of $100 per preferred stock. - A total of 2,000 stock options outstanding, 1,000 of which were issued with an exercise price of $10 and the other 1,000 of which have an exercise price of $50. Each stock option is convertible to 10 common stocks. - A tax rate of 40%. - Stock whose average trading price is $20 per share. Calculate the fully diluted EPS 1.Convertible debt Assume conversion: If the debt is converted, the company would have to issue an additional 50,000 (50*1,000) common stock. As a result the WASO would increase to 2,050,000. Since the debt would be converted, no interest would have to be paid. Interest was $6,000 per annum. The interest expense would flow through to common stockholders but not before the IRS get a portion of it. So net of taxes the company would have generated an additional $3,600 [(6,000*(1-40%)] in net income. Adjusted WASO: 2,050,000 Adjusted net income: $2,003,600 2.Convertible preferred stock Assume conversion: If the stock is converted the company would have to issue an additional 2,000 shares of common stock. As a result the WASO would increase to 2,052,000. Since the preferred dividend would no longer be issued the company would not have to pay $1,000 dividends (100*1,000*10%). Since dividends are not tax deductible, there are no tax implications. So the company would have generated an additional $1,000 in net income attributable to common stockholders. Adjusted WASO: 2,050,000 Adjusted net income: $2,003,600 Preferred dividend is reduced to zero 3.Stock options If-converted method: Say there are 1,000 stock options in the money (exercise price < market price of stock). The holders of the stock option can convert their options into stock for a profit at any point and time. Say 1,000 stock options are out of the money (exercise price > market price of stock). The holders of the stock option would not convert their options, because it would be cheaper to purchase the stock on the open market. The out-of-the-money option can be ignored. The in-the-money options need to be accounted for.

Here is how in-the-money options are accounted for: 1)Calculate the amount raised through the exercise of options: 1000 * 10 *$10 = $100,000 2)Calculate the number of the common shares that can be repurchased using the amount raised through the exercise of options (found in step #1): $100,000 / 20 = 5,000 3)Calculate number of common shares created by the exercise of the stock options: 1000 * 10 = 10,000 4)Find the net number by which the number of new common shares, created as result of the stock options exercised (found in step #3), exceed the number of common shares repurchased at the market price with proceeds received from the exercise of the options (found in step #2): 10,000 – 5,000 = 5,000 5) Find the total number of shares if the stock options are exercised: add weighted average number of shares to what you found in step #4: 2,052,000 + 5,000 = 2,057,000 Fully diluted EPS= 2,000,000 + 3,600 - 6,000 + 6,000 = 2,003,600 = 0.974 2,000,000 +50,000 + 2,000 +5,000 2,057,000 Presentation and disclosure Simple capital structure a. Basic EPS is presented for income from continuing operations, income before extraordinary items or change in accounting principle, and net income. b. Reported for all accounting periods presented c. Prior-period EPS is restated for any prior-period adjustments. d. Footnotes are required for stock splits and stock dividends. Complex capital structure a. Basic and fully diluted EPS are presented for income from continuing operations, income before extraordinary items or change in accounting principle, and net income. b. Reported for all accounting periods presented c. Prior-period EPS is restated for any prior-period adjustments. d. Footnotes are required for diluted EPS.