Thus far, we've been careful to use a discount rate that is consistent with the frequency of the cash flows--for example, 1% per month with monthly payments or 10% per year with annual payments. In practice, interest rates are typically stated in one of two ways, as an annual percentage rate calculations or as an annual percentage yield (APY), even though interest may be calculated and paid more often than annually.

The annual percentage rate (APR) is the periodic rate times the number of periods in a year. The APR is a nominal rate, a rate "in name only". The true (effective) annual rate may be different from the APR because of the compounding frequency.

The Compounding frequency is how often interest is compounded. For example, the compounding frequency might be monthly (12 times per year), quarterly (4 times), or annually (once). The periodic rate is an effective rate, but recall that two periods of interest is more than double one. The second period's interest includes interest on the first period's interest.

With m compounding periods per year and a periodic rate of r, the APR is:

APR = (m)(r)

How does compounding frequency affect future value? To answer this question, let's compare yearly, semiannually, quarterly, monthly and weekly compounding for saving $10,000 for a year at a 12% APR.

The future value of $10,000 in one year is shown in below table for all of these compounding frequencies. The APY equals the 12% APR for yearly compounding. But the table shows how the future value and APY increase as the compounding frequency increases.

Another way to understand an APY is to say that it's the total interest earned in a year (annual interest) divided by the principal. That is,

APY = annual interest/principal

For example, the annual interest for monthly compounding is $1268.25, which, divided by $10,000, gives the same 12.68%.

Future Values and APYs for Various Compounding Frequencies

Continuous Compounding

If more frequent compounding increases the future value, what if we compound daily, hourly, or even every minute? These are all examples of discrete compounding, where interest is compounded a finite number of times per year. If interest is compounded an infinite number of times per year, we have continuous compounding.

When m, the compounding frequency, becomes large enough, compounding becomes essentially continuous, Without giving the proof, it turns out that with continuous compounding:

Where e is approximately 2.718². The function  e^x  is called an exponential function. It is usually found on a calculator with either an " " or "exp" on the key.

Unlike an annuity, in some cases future cash flows vary in size. In this post, we demonstrate a few common-sense methods for computing the value of a set of unequal future cash flows and use the present value of cash flows calculator. We'll describe three of these methods through the use of the following example.

Suppose you expect to receive the following cash flows at the times indicated:

Time                 0                    1                    2                    3

Cash flow      $3000          $2000            $8000          $5000         

If the required return is 10%, what is the total present value of these cash flows?

The total present value of these cash flows can be calculated by calculating the present value of each cash flow and then adding them together:

                                          PV = 3000+1818.182+6611.570+3756.574= $15,186.326

This calculation is illustrated in figure 1

An alternative method for calculating the total present value of our set of unequal future cash flows is called the "rollback" method: Start with the most distant cash flow ($5000 at time 3) and discount it back one period (at 10%). Its value at t = 2 is $4545.45 (=5000/1.10). And this amount to the time 2 cash flow of $8000 to get $12,545.45. Discount this amount back one period. Its value at t = 1 is $11,404.96(= 12,545.45/1.10). And the time 1 cash flow to this amount to get $13,404.96. Discount this amount back one period. Its value is $12,186.33 (= 13,404.96/1.10). Finally, this amount plus the $3000 time 0 cash flow equals the total present value of $15,186.33. Figure 2 illustrates the rollback method of calculating a present value.

Finally, many financial calculators provide a third method for valuing this unequal set of future cash flows. Because calculators are not identical, you'll have to use your own calculator's manual to learn how to use this method. There is an important advantage to using this calculator feature: If you already know the present value, but don't know the discount rate, the calculator can automatically compute the expected return for the set of unequal cash flows. This can eliminate the hassle of very tedious trial-and-error calculations.

Thus far, we've calculated a present value (t=0) or a future value at t=n. But suppose we want to know the total value of a set of cash flows at some other point in time. Calculating such a value directly may require extra care, but it uses the same formulas. If you already know the present or future value, calculating such values is quite straightforward. Our next example illustrates this process by building on our last example.

Figure 1

Computing the present value of a set of unequal future cash flows.

Figure 2

The rollback method for calculating a present value.

Annuity payments are a very common financial arrangement. An annuity payout calculation is a series of equal periodic payments. The payments occur regularly, year.

Valuing Annuities

Annuities occur in many different financial transactions. Monthly payments on a car loan, a student loan, or a mortgage are annuities. Monthly rent is an annuity. A paycheck, with a fixed salary, is an annuity. Lease, interest and dividend payments are annuities. Any series of equal, periodic payments is an annuity.

The majority of annuities have end-of-period payments. For example, car loans usually require end-of-month payments. If it's a 48-month loan, the first payment is made at the end of the first month and the 48th (and last) is made at the end of month 48. This kind of annuity, where payments occur at the end of each period, is called an ordinary annuity.

Other annuities, such as for a rental, require beginning-of-period payments. For a 12 month apartment lease, the first rent payment is due at the beginning of the first month and the 12th (and last) is due at the beginning of the 12th month. This kind of annuity, where payments occur at the beginning of each period, is called an annuity due.

We know the timing of payments affects value. Therefore, it's critical to know whether you are dealing with an ordinary annuity or an annuity due. We'll start by analyzing the future and present values of an ordinary annuity. Later, we'll show you how to handle an annuity due.

We started our discussion of the time value of money in the previous posts with an example of depositing money in a savings account. Now consider a savings plan for depositing the same amount every period for n periods. How much will you have at the end of the n periods?

 Let the periodic cash flow, PMT, be the amount deposited at the end of each time period (that is ,

Figure 1

Figure 1 illustrates this calculation. Note that the first payment (at t = 1) earns interest for (n-1) periods, not n periods. Each subsequent payment earns interest for one less period than the previous one. Not that the last payment occurs exactly at the end of the annuity, so it doesn't earn any interest; (1+r)⁰ = 1.

We introduced the concept of present values and future values in our brief discussion of the Time-Value-of-Money Principle in last Posts. We also defined three different rates of return: expected, required and realized. The expected return is the return you expect to earn if you make the investment. 

The required return is the minimum return you must expect to get to be willing to make the investment. The realized return is the return you actually earned on an investment during a given time period. We showed you that finding the present value or the future value of a single cash flow is a simple calculation. After a brief recap, we'll extend its logic to deal with multiple cash flows.

Finding the Future Value of an Investment

The future value (FV) is the value an investment will grow to after a given time period. Let's say you invest $1000 today. Table 1 Shows the amount of money you'll have accumulated at the end of each of the next six years if the bank is paying 10% interest. After one year.
In the second year, you'll earn $110 more -10% interest on your accumulated investment (=[0.10]1100), for a total of

Table 1

Concept of Time Value of Money in Financial Management

Have you ever paid for something with monthly payments? Suppose you wanted to buy a $10,000 car and were told the payments would be $273.11 per month for 48 months. How would you know whether you were being offered a great deal, a fair deal, or a bad deal?
The Time Value of Money

This and next coming posts will teach you how to answer such question; it's devoted entirely to the Time-Value-of-Money Principle. You'll learn how to value at one point in time cash flows that actually occur at other points in time. We develop the logic underlying these calculations and show you procedures for solving problems using a financial calculator. We urge you, however, not to use these calculator procedures like cookbook recipes. Understanding the logic will prepare you to apply the Time-Value-of-Money Principle in the business world to new types of problems, ones that don't fit neatly into classroom examples.

Like you, companies also have to choose among investments and borrowing alternatives. In fact, their success depends on those choices. Financial decisions are measured by their net present value (NPV). Recall that NPV is the present value of the expected future cash flows minus the cost. The NPV is the value created or lost by a decision. Therefore, to be successful, companies must find positive-NPV opportunities and avoid negative-NPV choices.

Financial ratios are used by analysts, investors, lenders and managers to judge a company's financial performance and condition. Still, Comparing Companies Financial Ratios and financial analysis is more of an art than a science. The set of ratios that proves most useful in any particular application depends on the company being analyzed, the purpose of the analysis and the analyst's judgments. Lenders typically are most concerned with the company's liquidity, coverage and leverage ratios. They may believe that the greater the liquidity and the lower the leverage, the greater the likelihood that interest and principal payments will be made on time. Managers are also likely to be concerned with the profitability of the enterprise. They must be concerned with turnover ratios and profitability measures too, because these ratios show how effectively the company is using its assets. Shareholders are most concerned with investment returns. As a result, common stockholders tend to emphasize profitability ratios, return on common stockholders equity and market value ratios.

Financial information can be obtained from the company itself as well as from financial service companies, government agencies, trade associations and many other sources. Information is increasingly available in electronic form instead of in a printed medium. Table No. 1 provides examples of several important providers of financial information.

Analysts, investors and managers face a number of challenging and interesting situations whenever they undertake financial statement analysis. Several important tools you can use and several problems you may encounter are described and discussed below.

Earlier in the posts, we presented a set of basic financial ratios. As we noted then, however, many other ratios are used to meet the needs of specialized analysts representing particular clienteles or focusing on specific industries. Fortunately, each specialty tends to use a limited set of ratios. Unfortunately, the names of financial ratios are not standardized. A particular ratio might have several names (as does the acid test ratio and the quick ratio). Even more disturbing is the fact that many ratios called by the same name have different definitions.

For example, when calculating an inventory turnover ratio, some analysts use the end-of-year inventory in the denominator, as we did. But others use an average of the inventory over the year. Also, some analysts use sales in the numerator of the inventory turnover ratio instead of cost of goods sold.

Similarly, the P/E may be calculated in different ways. It's most often calculated (and reported in the financial press) by dividing the current market price by the last year's EPS (that is, total EPS for the last four quarters). Alternative P/Es are constructed by dividing the current market price by the forecasted earnings per share for the next year.

As you can see, unlike a rose, a ratio by any other name (or even by the same name) may not smell as sweet. Therefore, whenever ratios are supplied by others, you must know their exact definition if they are to be of any use.

    Major Sources of Financial Information

One tool used to assess the financial health of a company is called discriminant analysis. This statistical procedure combines several variables (such as a company's financial ratios)into a single score in an attempt to classify the company into one of various groupings. Such analysis can be used to predict significant events, such as bankruptcy or a bond rating change. 

In the case of bond ratings, the rating predicted by discriminant analysis is compared with the actual rating. For example, a discriminant analysis might reveal that a company whose bonds are currently rated BBB has financial characteristics more similar to those companies whose bonds are rated A. This would suggest that the bonds have lower default risk than the BBB rating would indicate. The analysis would predict an improvement in the rating. 

Discriminant analysis models are also used for evaluating commercial loans, consumer loans and credit card applications. Such models are often called credit scoring models. As the likelihood of default.

Cross-Sectional analysis evaluates a company's financial ratios against industry averages or averages for a selected set of comparable companies. As you would expect from the Behavioral Principle, more meaningful comparisons are often possible using specific companies. Table 2 shows selected financial ratios from the Annual Statement Survey published by

    Selected Ratios for SIC# 5942, Retailer-Books

Robert Morris Associates. The information in the table illustrates the distribution of a financial ratio within an industry.

Suppose you're interested in book retailers. Table 2 divides the firms into three size classes and shows the 25th percentile, 50th percentile and 75th percentile of five ratios for this industry. The industry averages are broken down further by company size, as measured by most recent total annual sales. For example, for the smallest companies, the 25th percentile current ratio (25% are below this amount) is 0.9. The 50th percentile (median) current ratio is 1.5 and the 75th percentile current ratio is 2.5. Using this kind of information, a company can compare itself to other companies of similar size in the same industry.

Beyond simple industry/size comparisons, many companies engage in benchmarking. Benchmarking is a comparison to a more specific set of benchmark companies. For example, suppose the Olin Corporation wants to compare itself to Dow Chemical, DuPont, Monsanto and Union Carbide. Table 3 provides the ratios for all five companies. As you can see, Olin is most like Union Carbide, Olin's inventory turnover, receivables turnover and total asset turnover are higher than those of Dow, DuPont, and Monsanto, but similar to those of Union Carbide. Day's sales outstanding and the days sales in inventory are below the benchmark companies, except for Union Carbide.

Trends in financial ratios and of common-size statement items are studied very carefully by managers and analysts. Changes in a company's liquidity, financial leverage, asset turnover, or profitability ratios over time can be very meaningful.

Asset Turnover Ratios for Benchmark Company Group

General economic conditions, industry conditions, specific managerial decisions, or simply good or bad luck might explain what is happening. Table 4 shows an eight-year series of profitability ratios for three companies. Notice how the net profit margin, return on assets and return on equity declined significantly from 1988 until 1993 for Chrysler. In 1994 and 1995, Chrysler recovered dramatically. Compare Chrysler's ratios to those of McDonald's and PepsiCo, the soft drink and food conglomerate. The profitability ratios for McDonald's and PepsiCo were fairly stable. The patterns in these ratios imply that Chrysler is a riskier company than McDonald's and PepsiCo.

The structure of financial statements underlies many models that companies build for internal as well as external use. For example, a company applying for a bank loan might be required to submit historical financial statements as well as projected (what are called pro forma) financial statements for the next several years. Banks use such projected statements to help judge the likelihood the company will be able to repay the loan. Other models are used internally by management to plan the company's future investments and financing.

Financial decisions should be based on current and expected future conditions. However, as we emphasized in the previous posts, accounting statements are historical in the United States and many other countries. In particular, we showed how several factors, such as inflation, can distort the balance sheet.

Inflation can also distort a company's reported income. When a company gets an inflated price from selling its finished goods from inventory, it appears to have had higher income. However, it must then in turn pay an inflated price for the cost of goods to replenish its inventory for the next sale. If the company uses the so called LIFO (last in, first out) convention to overcome this problem, that will distort its balance sheet by understating the inventory value. 

Fixed assets also will have to be replaced at inflated prices in the future. However, U.S. tax laws compute depreciation on a historical cost basis. This too inflates the company's income. Taxes are paid on this overstated income, which further impinges on cash flow.

In fact, inflation is the major reason for using common-size and common-base-year financial statements. Many, but not all, of the distortions caused by inflation are reduced by scaling the information by a common base.

Some countries with high inflation rates, such as Mexico, actually require that accounting statements be adjusted for inflation. With out such adjustments, meaningful interperiod 

    Time-Series Profitability Ratios for Chrysler, McDonald's and PepsiCo (All ratios are in percent)

comparisons or comparisons among companies can be almost impossible. As Mexico becomes a larger trading partner with the United States, in part because of the North American Free Trade Agreement (NAFTA), accounting for differences in inflation will remain important to all stakeholders in Mexican companies.

In the previous posts, we noted how accounting standards can differ substantially across countries. This is an additional significant impediment to using and interpreting financial information. In addition, there are the problems of language translation and foreign currency conversion. There are other differences as well. Auditing standards vary. Disclosure ranges from fairly open to almost completely secret. Legal systems, business practices, educational levels and management sophistication all vary widely. In fact, even seemingly similar countries, such as the United States and Great Britain, have differences that can surprise you. Just as it takes considerable effort to learn to read and interpret U.S. financial statements, it takes additional effort to learn how to understand those from other countries.

There is no unique set of theoretically correct financial ratios. A manager's decisions, such as those about a company's liquidity or leverage, are not simple decisions. A business is a complex and dynamic organization. Most decisions involve some sorts of trade-offs, frequently including the Principle of Risk-Return Trade-Off. For example, a company can lower its risk by maintaining greater liquidity, but that's likely to reduce profitability. A company can lower its risk by using less debt, but that too will reduce the stockholder's expected return. Such decisions require judgment and analysis.

Likewise, an outside analyst must exercise judgment and draw on experience to understand a company's financial position. People outside the company must be aware of the possibility that managers are manipulating the company's financial information through careful decision making involving such things as choices of accounting treatments, timing of decisions and public relations. Alternative accounting treatments can alter the picture of the company's financial statements. A certain amount of manipulation of financial information, which is called window dressing, is legally permissible and fairly routine. As an outside user of financial information, you should be carefully skeptical. If you are providing financial information about your company, you should recall our admonition about ethics. Avoid unethical manipulations. They can be fraudulent and land you in prison!

Corporate practice must deal with ever-increasing complexity and that's part of what managers are paid for. If you're not an accounting major, you still must understand a critical mass of accounting to be an intelligent user of accounting information.

Comparing Companies Financial Ratios and financial statement analysis is useful in at least two ways. First, it provides a structure for understanding the dynamics of a company. For example, how would some event affect a company? Is it good or bad; is it significant or insignificant; how does it affect specific parts of the company? A financial framework allows you to more quickly understand the importance of new information.

Manager and investors are concerned with the return on common stockholder’s equity (ROE). An important linkage between ROE and three other ratios has been called Du Pont Analysis, named for the large chemical company that popularized its use. ROE can be expressed as the product of three other ratios, the net profit margin, the total asset turnover and the equity multiplier.

Return on equity= (Net profit margin)(Total asset turnover)(Equity multiplier)-------------------------(1)

 Net income/Stockholders equity=(Net income/Sales)(Sales/Total assets)(Total assets/Stockholders equity)

Financial Analysts and managers find it helpful to calculate financial ratios when interpreting a company's financial statements. A financial ratios is simply one quantity divided by another. You'll find almost any decision that uses accounting information relies on financial ratios that focus on specific aspects of the company. The number of financial ratios that might be created is virtually limitless, but there are certain basic ratios that are frequently used. These ratios can be placed into six classes; liquidity ratios, asset turnover ratios, leverage ratios, coverage ratios, profitability ratios and market value ratios.

Recall that liquidity refers to how quickly and efficiently (in the sense of low transaction costs) an asset can be exchanged for cash. Liquidity ratios provide a measure of the company's liquidity, that is, its ability to meet its financial obligations on time. Four widely used liquidity ratios are the current ratio, quick ratio, working capital ratio and the cash ratio.

The most commonly used measure of overall liquidity is the current ratio

Current ratio = Current assets/Current liabilities = 1816/1460= 1.24x ----------------- (1)

The current ratio measures the number of times the company's current assets cover its current liabilities. The higher the current ratio, the greater the company's ability to meet its short term obligations as they come due. A widely held but conservative rule of thumb holds that a current ratio of 2.0 is an appropriate target for most companies. In fact, the average current ratio for companies included in the S&P 500 is about 1.5.

Inventories are considered current assets, so they are included in the current ratio calculation. Inventories, however are less liquid than marketable securities and accounts receivable. This is because it is normally more difficult to turn inventory into cash on short notice. Thus analysts often exclude inventories from the numerator in the current ratio and calculate the quick ratio (also called the acid test ratio).

Quick (Acid test) ratio=Current assets - Inventories/Current liabilities=1816-661/1460=0.79x ------(2)

Another widely held but rough rule of thumb holds that a quick ratio of at least 1.0 is desirable. The average S&P 500 company has a quick ratio of about 0.9.

Net working capital (or, simply, working capital) is the difference between current assets and current liabilities. The working capital ratio is simply net working capital expressed as a proportion of sales.

Working capital ratio = Current assets - Current liabilities/Sales = 1816-1460/11,394 = 3.1% -------(3)

Net Working capital is often considered a measure of liquidity. This ratio shows the amount of liquidity relative to sales.

The cash ratio is calculated by dividing cash and equivalents by total assets.

Cash ratio = Cash and equivalents/ Total assets = 215/10,538 = 2.0%  ----------------------------------(4)

Cash and equivalents (which include marketable securities) is the most liquid asset. The cash ratio simply shows the proportion of its assets that the company is holding in the most liquid possible form.

Asset turnover ratios are designed to measure how effectively a company manages its assets. A business faces fundamental decisions about how much to invest in assets such as receivable, inventories and fixed assets and then it has the responsibility of using these assets effectively. Several ratios have evolved that focus on the management of specific assets as well as total assets.

The receivables turnover ratio is:

Receivables turnover = Annual credit sales/ Accounts receivable = 11,394/650 = 17.53x-------------(5)

It measures the number of times the accounts receivable balance "turns over" during the year. Note that annual credit sales, which give rise to receivables, are used in the numerator. If a figure for annual credit sales is not available, the company's net sales figure is used instead. Making that substitution is like assuming all sales were credit sales.

A closely related figure is the days sales outstanding (DSO). It is the number of days in a year divided by the receivables turnover ratio.

Days sales outstanding = 365/Receivables turnover= Accounts receivable/Annual credit sales/365=365/17.53=20.8 days --------------------------------------------------------------------------------(6)

The days sales outstanding shows approximately how many days on average it takes to collect the company's accounts receivable. The days sales outstanding is also called the average collection period.

A more detailed picture of the company's accounts receivable can be obtained by preparing an aging schedule for accounts receivable. An aging schedule shows the amounts of receivables that have been outstanding for different periods, such as 0 to 30 days, 30 to 60 days, 60 to 90 days and more than 90 days. An example of an accounts receivable aging schedule is given in the below table. An external analyst typically lacks the detailed information in an aging schedule unless the company has chosen to provide it. Of course, managers within the company want this information to help monitor the quality of their accounts receivable.

A measure of the effectiveness of inventory management is the inventory turnover ratio, which is calculated as follows.

Inventory turnover = Cost of goods sold/Inventory = 6742/661 = 10.20x--------------------------------(7)

Inventory turnover is a good estimate of how many times per year the inventory is physically turning over. In the past, some analysts calculated the inventory turnover by dividing net sales by inventory. However, this calculation overstates the turnover rate of physical inventory.

Another way to measure inventory turnover is the days sales in inventory ratio. This is the time for "one turnover". For example, if inventory turnover were 12.0x, one turnover would be 1/12 of a year, which in days is 30.42 (=365/12). For Anheuser-Busch, it is 

Days sales in inventory= 365/Inventory turnover =Inventory/Cost of goods sold/365=365/10.20=35.8days----------------------------------------------------------------------------------(8)

The days sales in inventory ratio estimates the average time inventory stays with the company before it's sold.

Finally, two more ratios show how productively the company is using its assets. They are the fixed asset turnover ratio and the total asset turnover ratio.

Fixed asset turnover = Sales/Net fixed assets = 11,394/7524=1.51x -------------------------------------(9)

Total asset turnover = Sales/Total Assets = 11,394/10538=1.08x ---------------------------------------(10)

These two ratios show the sales volume generated per book value dollar of fixed assets and total assets, respectively. Because total assets is never smaller than fixed assets, the total asset turnover is virtually always smaller than the fixed asset turnover.

Accounts Receivable Aging Schedule

Financial leverage is the extent to which a company is financed with debt. The amount of debt a company uses has both positive and negative effects. The more debt, the more likely it is that the company will have trouble meeting its obligations. Thus the more debt, the higher the probability of financial distress and even bankruptcy. Furthermore, the chance of financial distress, and debt obligations generally, may create conflicts of interest among the stakeholders.

Despite this , debt is a major source of financing. It provides a significant tax advantage, because interest is tax deductible, as we noted in this post. Debt also has lower transaction costs and is generally easier to obtain. Finally, debt affects how the company's stakeholders bear the risk of the company. One particular effect is that debt makes the stock riskier because of the increased chance of financial distress. These factors are discussed at length later in the book. At this point, suffice it to say that leverage is very important, and leverage ratios measure the amount of (financial) leverage.

Three common leverage ratios are the debt ratio, the debt/equity ratio, and the equity multiplier. The debt ratio is the proportion of debt financing.

Debt ratio= Total debt/Total assets=10,538 - 4620/10,538=5918/10,538=0.56x-----------------------(11)

The debt/equity ratio is a simply rearrangement of the debt ratio and expresses the same in formation on a different scale. Whereas the debt ratio can be as small as zero but, assuming positive equity, is always less than 1.0, the debt/equity ratio ranges from zero to infinity. The debt/equity ratio is 

Debt/equity ratio=Total debt/Stockholders equity=5918/4620=1.28x-----------------------------------(12)

The equity multiplier is yet another representation of the same information. It shows how much total assets the company has for each dollar of equity. The equity multiplier is 

Equity multiplier = Total assets/Stockholders equity=10,538/4620=2.28x -----------------------------(13)

All three of the leverage ratios are widely used. As we have said, they are simply different representations of the same information. If you know any one of them, you can derive the other two. For example, suppose a company has a debt ratio of 0.40x, so it's 40% debt financed. From this we know that the company is 60% equity financed. Therefore, the company's debt/equity ratio is 40/60=0.67x. Because total assets are equal to 100% of the financing (the balance sheet identity, A=L+SE), the equity multiplier is 100/60=1.67. Generalizing we have 

Debt/equity ratio = Debt ratio/1.0 - Debt ratio

Equity multiplier=Debt/equity ratio + 1.0 = 1.0/1.0-Debt ratio

Because it does not make any difference which of the three measures is used, we use the debt ratio throughout this post and its related for simplicity and consistency.

Coverage ratios show the number of times a company can "cover" or meet a particular financial obligation. The times interest earned ratio, which is also called the interest coverage ratio, measures the number of times the income available to pay interest charges covers the company's interest expense. It is Earnings Before Interest and Income Taxes (EBIT) divided by the company's interest expense. For Anheuser Busch, EBIT is 1767 (=operating profit (1776) plus nonoperating profit(-9). So the time interest earned ratio is

Times-interest-earned ratio=EBIT/Interest expense=1767/200=8.84x----------------------------------(14)

Many companies lease or rent assets that require contractual payments. Long term leases are reported on the balance sheet and the periodic lease payments are included in the company's interest expense. Rental agreements are different. They are not on the balance sheet. Renting an asset is an alternative to owing it. (Rental payments are therefore an alternative to the interest payments the company would make if it borrowed the money to buy the same assets). Rental expense is reported in the notes to the financial statements. For these companies, the fixed charge coverage ratio is useful, where fixed charges consist of interest expense plus rental payments.
Fixed charge coverage ratio=EBIT+Rental payments/Interest charges + Rental payments=1767+5/200+5=8.64x------------------------------------------------------------------------------(15)

The cash flow coverage ratio is the company's operating cash flows divided by its payment obligations for interest, principal, preferred stock dividends and rent.

Cash flow coverage ratio = EBIT+Rental payments + Depreciation/Prefferred stock
                                           
                             Rental payments + Interest charges + dividends /1-T+repayment/1-T-------------(16)

Cash flow coverage ratio = 3.01x

Note that two of the financial obligations in the denominator of the cash flow coverage ratio are divided by (1-T), where T is the marginal income tax rate. Rental payments and interest charges are tax deductible expenses. Only one dollar of before tax cash flow is required to meet one dollar of these obligations. In contrast, preferred stock dividends and principal repayments must be made out of after tax cash flows. As a consequence, they are divided by (1-T) to calculate the equivalent before tax operating cash flow necessary to meet them. For example, with a marginal tax rate of 40% and a $100 non tax deductible obligation, the company needs $166.67 (=100/(1-0.4) of before tax dollars to meet this obligation. Note that the $166.67 before tax cash flow provides $100 after taxes of $66.67 (=[0.40]166.67).
Profitability Ratios
Profitability ratios focus on the company's effectiveness at generating profit. They reflect the operating performance, its riskiness and the effect of leverage. We'll look at two kinds of profitability ratios, profit margins, which measure performance in relation to sales and return ratios, which measure performance relative to some measure of the size of the investment.
Gross profit is the difference between sales and the cost of goods sold. Gross profit is critical because it represents the amount of money remaining to pay operating costs, financing costs and taxes and to provide for profit. The gross profit margin is the amount of each sales dollar left over after paying the cost of goods sold.

Gross profit margin=Gross profit/Sales=Sales-Cost of goods sold/Sales=4652/11,394=40.8%-----(17)

The net profit margin measures the profit that is available from each dollar of sales after all expenses have been paid, including cost of goods sold, selling, general and administrative expenses, depreciation interest and taxes.

Net profit margin = Net income before extraordinary items/Sales=994/11,394=8.7%----------------(18)

Note that the gross profit margin and net profit margin are identical to the percentages of sales for gross profit and net profit on the common size income statement.

Unlike profit return ratios express profitability in relation to various measures of the investment in the company. Their potential usefulness is inherently limited, however, because they are based on book values. Three ratios are commonly used, return on assets, earning power and the return on equity.
Return on assets (ROA) corresponds to the net profit margin, except that net income is expressed as a proportion of total assets.

ROA=Return on assets=Net income/Total assets=994/10,538=9.4%------------------------------------(19)

Earning power is EBIT divided by total assets.

Earning Power = EBIT/Total Assets = 1767/10,538=16.8%----------------------------------------------(20)

The difference between ROA and earning power is due to debt financing. Net income is EBIT minus interest and taxes, so ROA will always be less than earning power. Earning power represents the "raw" operating results, whereas ROA represents the combined results of operating and financing.

Return on equity (ROE) is the return on common stock holders equity.

ROE=Return on common Stockholders equity=Earnings available for common stock before extraordinary items/Common stockholders equity=994/4620/21.5%------------------------------------(21)
Where common stockholders equity includes common stock (at par value), capital surplus and retained earnings. ROE shows the company's residual profits as a proportion of the book value of common stockholders equity. The amount of financial leverage affects both the numerator and denominator of the ROE. Typically, ROE is greater than ROA for healthy companies. In bad years, however, ROE can be below ROA. This is because financial leverage increases the risk of the stock, as we noted earlier.

Market Value Ratios

At the time the 1992 statements were prepared, the price of Anheuser Busch common stock was $58.50 per share. Analysts look at several ratios that use the market value of the company's common stock.
The price/earnings ratio (P/E) is the market price per share of common stock divided by the earnings per share (EPS)

P/E=Price/earnings ratio=Market price per share/Earnings per share=58.50/3.48=16.8x-------------(22)

Negative earnings make EPS negative. Which in turn make the P/E negative. Also, when EPS gets close to zero, the P/E becomes extremely large, because of dividing by the EPS. In such cases, the P/E is not considered economically meaningful. As a result, the P/E is not generally reported when EPS is negative or excessively small.
The earnings yield is another form of the same information. It is the reciprocal.

Earnings yield= Earnings per share/Market price per share=3.48/58.50=5.95%-----------------------(23)

EPS is in the numerator of the earnings yield and so avoids the division by zero problem. So, unlike the P/E the earnings yield does not "break down" when EPS is negative or excessively small. A very small EPS simply leads to a very small earnings yield. A negative EPS simply represents such losses as a negative return, a rate of losing value.
The ratio of dividends per share to market price per share is called the dividend yield.

Dividend yield = Dividend per share/Market price per share=1.20/58.50=2.05%---------------------(24)

Many companies are not currently paying a cash dividend. Such companies will have a dividend yield of zero. The decision to pay cash dividends is essentially a choice between paying out earnings to the owners or reinvesting the money in the company.
Finally, the market to book ratio is the market price per share divided by the book value per share. The book value per share is total common equity divided by the number of common shares outstanding. At year end 1992, Anheuser-Busch's book value per share was $16.17(=4620/285.69).

Market to book ratio=Market price per share/Book value per share=58.50/16.17=3.62x-------------(25)

The market to book ratio is a very rough index of a company's historical performance. The higher the ratio, the greater is market value relative to book value. A high ratio says the company has created more in market value than the GAAP rules have recorded in book value. The implied message is that the company has done well. Of course, as we noted earlier, there are many possible explanations for a difference between market and book values. Although the implied message of a high market to book ratio is likely to be correct in most cases, additional information is generally needed to reach a confident conclusion. Financial Analysts and managers find it helpful to calculate financial ratios when interpreting a company's financial statements.