Week 2 Notes:

Financial Statement Analysis and Risk
Return and the Time Value of Money
(rev 2/21/02)

The basic financial accounting equation: The objective of every business firm is to sell its products (services) for more than it cost to produce them. A firm's assets are the resources it uses to produce those products. Assets are reported on a balance sheet. However, not all are reported on the balance sheet. Financial accounting rules limit the resources a firm can report as assets to only those it owns. This is why a firm does not report its most important assets -- its people -- on the balance sheet. Two other criteria that must be satisfied for a resource to become an asset are that the resource has value (i.e., it must help to generate revenue) and it was acquired at a measurable cost.

A firm receives money from two sources with which it purchases its assets, and in exchange it issues two different financial securities. The different securities are classifies as debt and equity, and they differ as to the firm's financial obligation to the holders of these securities. Debt represents money that the firm is legally obligated to pay back. The three major forms of debt are notes, bonds, and loans. The holder of any of these financial securities is legally entitled to repayment of the money lent plus interest. As a group these securities are labeled liabilities on the balance sheet. Equity represents money that the firm's owners have invested in the firm and takes two separate forms. The first is "contributed capital," which is money received when the shares of common stock were first sold to investors. It is labeled "paid-in capital" in the text. The second is "earned capital," which is money received from the operation of the company. It is labeled "retained earnings." The firm has no legal obligation to pay any money to its shareholders. However, many firms do pay money to shareholders in the form of dividends. This is money that is paid out of the money the company has earned from its operations and reduces its retained earnings.

Liabilities can be created in a broader range of transactions than just borrowing money to buy assets. Any time a firm uses a resource and does not pay for that resource at the time it is acquired and used a liability is created. The obligation can short term as well as long term. Short term refers a period less than one year, and long term is any period greater than one year. Before a firm recognizes a liability several criteria must be met. The firm must have to give up something of value to satisfy its obligation, and it cannot get out of the obligation unilaterally. Finally, the obligation is the result of a past transaction and typically cannot be recognized in advance of a transaction. For example, a company signs a contract with a supplier to buy a specified number of components each month. There is no liability at the time the contract is signed because the company has not received anything of value from the supplier. At the time the contract is signed, financial accounting would not record a transaction. Legally the company is committed to fulfilling the contract at the time the contract is signed, but until the merchandise changes hands there is no financial transaction.

The money a firm receives from the sale of its products (services) is called revenue, specifically sales revenue. As we will see later in the course, revenue can come from sources other than sales. The costs incurred by a firm to generate revenue (i.e., produce and sell its products or services) are called expenses. Expenses represent the costs of the various resources that a firm uses in generating revenue. Remember, only some of these resources are assets reported on the balance sheet. The difference between the money earned (revenue) and the costs incurred to generate that revenue (expenses) is net income. Net income is the money that a firm receives as a result of its operation. It is reported as "retained earnings" on the balance sheet. The amount in retained earnings is the sum of all of the money the firm has earned since its inception less all dividends paid. It is important to note that the money in retained earnings has already has been used to purchase additional assets. Revenues, expenses and net income are reported on a firm's income statement.

Revenue results only from the sale of a product or service. The price received is the amount of revenue earned. If the company were to sell one of its assets, such as land it no longer needs, there can be no revenue. If the company receives more money than the land cost, the difference between the sales price and the cost is considered a gain, not revenue. If the company receives less than the cost of the land, that difference would be a loss, not an expense. Gains and losses are included in the income statement just as revenues and expenses are. It is important to remember that revenues only come from the sale of products and services and expenses are the costs of resources used to produce the product or service. If a firm sells an asset, it is not being used to generate revenue.

Financial accounting records the operations of a firm as a series of transactions. Each transaction involves at least two different accounts. These accounts fall into one of the five major categories of accounts - asset, liability, equity, revenue and expense. Accounts from every category could be included in the same transaction. In every transaction there are three possible situations. First, there could be an increase in each account included in the transaction. Second, there could be a decrease in each account. Third, there could be an increase in one or more accounts coupled with a decrease in one or more other accounts. Financial accounting tracks these increases and decreases separately as debits and credits. No matter which of the above situations occurs, the total reported for assets must always equal the total reported for liabilities and equity. This is the basic financial accounting equation, and it is always in balance after every transaction.

 Accrual accounting: A business firm's present and potential creditors and shareholders require timely information regarding the financial performance of a business firm. To facilitate this analysis, financial accounting separates this performance into fiscal years. A company's fiscal year can begin at any point in time and continues for next twelve months. Its income statement reports its financial performance over this period. The firm's balance sheet shows its financial position at the end of the fiscal year.

There are two methods of financial accounting that are used to measure how well a company is doing financially. They are cash accounting and accrual accounting. Almost all business firms use accrual accounting. Many small business firms use cash accounting. People use cash accounting when they calculate their income taxes. The difference between them is simply the point in time when revenues and expenses are recorded. Cash accounting records revenue when a company receives the cash from the sale of its products and services from its customers. Expenses are recorded when the company pays out cash for the resources it uses to produce products and services. Accrual accounting records revenue when it is earned, i.e., when the company has completed what the customer has requested. This point in time can be simply when merchandise is exchanged for cash. It would also be at the point in time when merchandise is sold on credit. The seller will record revenue at the point in time when title to merchandise legally passes to the buyer. What happens when the customer has paid cash in advance of receiving the merchandise? At the time the cash is received, the seller has not done what the buyer has asked, and therefore, there can be no revenue recorded. The cash would be recorded along with a liability ("unearned revenue") because the seller now has an obligation to deliver merchandise to the buyer. When delivery takes place, the seller would record the revenue and remove the liability.

Revenue cannot be earned without using resources to produce the products and services being sold. The costs of these resources are expenses in the same fiscal year as the revenue that they helped to generate is earned. An expense would be recorded if a resource's cost were paid in cash at the time it was acquired and used. An expense would also be recorded if a resource was acquired and used but not paid for. A liability would be created at that time and removed when the cash was paid. As stated previously, a resource may or may not be an asset of a firm. If it is an asset of the firm, the expense recorded would be an estimate of the asset's cost that has been used to produce products and services in the current fiscal year. In this situation, the value of the asset on the balance sheet would be reduced by the same amount as the expense that is recorded.

Accrual accounting provides a better measure of the financial performance of a firm that continuously sells many different products and services, and it permits a more accurate comparison of a single company's financial performance across fiscal years.

Nonbusiness (not-for-profit and government) organizations use a different financial accounting system, known as "fund accounting." There is no "net income" in these organizations because there are no equityholders. Fund accounting is based on the concept of "stewardship." Its purpose is to provide information as to how much money was raised and whether that money was spent according to the spending plan or budget. You can review some notes on fund accounting by following this link:

Asset valuation: There are only two ways a firm can record the cost of a resource. The cost can be capitalized, i.e., the resource becomes an asset and the cost is reported on the balance sheet. This resource is owned by the firm and will generate revenue over two or more fiscal years. A portion of that cost would become an expense in each of the years. If a resource's cost is not capitalized, it is expensed. The cost is reported on the current fiscal year's income statement.

When an asset is purchased, there can be costs in addition to its purchase price that will be capitalized. A company purchases some land on which there is a building that must be torn down. The cost of demolishing the building will be capitalized along with the purchase price as the cost of the land. If there were any unpaid taxes associated with the land, the amount paid would be added to the cost of the land on the balance sheet. The value of every tangible asset - land, building, equipment - on the balance sheet includes all of the costs incurred in getting the asset in a location and condition for use. If some equipment had to be installed and tested, these costs plus the purchase price are the cost of the equipment on the balance sheet.

Intangible assets are another major type of asset. These assets provide the company with certain rights and privileges that can be used to generate revenue. For example, a company leases a warehouse. The lease gives the firm the right to use the warehouse for the period specified in the lease. The company does not own the building. The lease represents the company's legal right to use the warehouse. The lease is an intangible asset. Other intangible assets include patents, trademarks, and copyrights. Their value on the balance sheet is determined by the costs the firm incurred in developing and registering them and not the money that they could earn for the company. Goodwill is an important intangible asset. It will only appear on a balance sheet if the company has acquired another firm at a cost that exceeded the fair market value of the acquired firm's assets. A company will never report the goodwill it has created with its customers because its value cannot be measured objectively. In summary, the value of every asset, tangible and intangible, reflects the costs that the firm incurred in acquiring the asset.

The cost of all tangible assets, except land, and all intangible assets eventually get expensed. The cost goes from the balance sheet to the income statement. For tangible assets this cost is called depreciation expense. For intangible assets it is called amortization expense. The amount of the expense recorded each fiscal year is an estimate. There is no way to calculate exactly how much of an asset's cost should be expensed in a specific year. When a depreciation expense or an amortization expense is recorded, it results in a reduction in the value of the asset on the balance sheet. For tangible assets the value of the asset on the balance sheet is reduced indirectly. Each year's depreciation amount is added to a separate account, called accumulated depreciation, which has a negative balance. When the amount in the accumulated depreciation account is added to the asset's value, or original cost, this is called the asset's book value. Eventually, the balance in the accumulated depreciation account could equal the asset's original value. The asset would have a zero book value, and there would no additional depreciation expense. The asset is fully depreciated.

For intangible assets the process is typically a little different. An intangible asset's value is reduced directly on the balance sheet each time an amortization expense is recorded. Some firms do use an accumulated amortization account similar to accumulated depreciation. This account would collect each year's amortization amount and have a negative balance. When it is combined with the intangible asset's original value, which remains constant, the result is the asset's book value.

The number of years over which an asset is depreciated or amortized will depend on the estimated useful life of the asset, which is the period of time the asset is expected to generate revenue. For tangible assets this period of time is based on experience. Intangible assets, such as leases and patents have definite useful lives. Goodwill doesn't. In those situations where there is no specific time period, accounting procedures require the time period to be less than 40 years.

Bond valuation: A bond is a debt obligation of the firm, which obligates the firm to repay the principal with interest. The value of the bond on the balance sheet at the time the bond is issued is the principal or the amount of money the company received. All long-term liabilities are valued similarly. This is the present value of the expected cash payments from the bond (annual coupon payment plus the face value of the bond at maturity) discounted at the market interest rate for the bond. Market interest rates are determined by the investors who buy the bonds and are different for bonds with different degrees of risk. The risk of a bond is the uncertainty an investor has that the company will pay all the cash it promised. Bonds with higher degrees of risk will have higher market interest rates.

The interest expense each period is determined by taking the principal or the amount still owed at the beginning of the period multiplied by the market interest rate at the time the bond is issued. The market interest rate for a bond remains constant over time. It was determined at the time the bond was issued. However, a bond's principal and interest expense usually do change over time because most bonds sell at a discount, below its face value, or at a premium, above its face value. In both situations over time the principal approaches the face value. The principal of a bond selling at a discount increases over time. The principal of a bond selling at a premium will decrease over time. At maturity the principal of every bond exactly equals its face value. Because interest expense is equal to principal time the market rate of interest, interest expense changes as the principal changes. For a bond selling at a discount, the interest expense increases each year as the principal increases. For a bond selling at a premium. The interest expense decreases each year as the principal decreases.

The value of all liabilities on the balance sheet, not just long-term debt such as bonds, is the present value of the money owed, interest and principal. This process of valuation is tied to the "time value of money."

Equity valuation: The shares of stock issued by a business firm are divided into two different categories - preferred stock and common stock. Preferred stockholders get paid dividends before the common stockholders receive theirs. The amount is usually fixed. The money common stockholders pay for their shares goes into two accounts - common stock and paid-in-capital. A firm assigns a par value to its common stock, which is usually a lot less than the market price. The par value of a share times the number of shares issued is the amount in the common stock account. The difference between the market price and the par value times the number of shares issued goes into the paid-in-capital account. As stated previously, the money the company earns from its operations less any dividends paid out goes into the retained earnings account.

If a company repurchases its own common stock to put in an employee pension fund, the value of the shares purchased is put into an equity account called treasury stock. This account has a negative balance, which reduces the total amount of equity outstanding for the firm.

The usefulness and limitations of financial ratios: Financial ratios are used to analyze the financial performance of business firms. Investors and creditors use financial ratios to uncover a firm's strengths and weaknesses. The various line items on the balance sheet and income statement are used in these ratios.

There are five major categories of ratios:The first are the liquidity ratios. These focus on a firm's cash and other current assets and its current liabilities. These indicate the extent to which a firm can make the required payments on its maturing debt obligations. Examples of liquidity ratios are current ratio, quick ratio, and days sales outstanding. The current ratio should be greater than one. The value of current liabilities is typically more definite than the value of a firm's current assets. For example, the inventory on the balance sheet of a firm is carried at its cost. When the company will sell the inventory and the price the company will receive when it is sold is uncertain. As a result, more than one dollar in assets is needed to ensure sufficient money to pay the liabilities. However, the ratio shouldn't be too high. Money invested in current assets is not earning any new revenue. Too much money in current assets is money that could be invested in the revenue producing assets like new buildings and equipment. The amount in current assets should only be sufficient to pay off the liabilities. The quick ratio may be less than one because it excludes the least liquid of the current assets, i.e., the amount money that the inventory will provide is more uncertain than the accounts receivable. The days sales outstanding reflects the time it takes for a firm to collect its accounts receivable. Lower values of this ratio are better because the cash represented by the accounts receivable is being collected more quickly. The longer accounts receivable are outstanding, the more likely it is that the company may not collect all or some of the amount owed.

The second category of ratios is leverage ratios. They measure the extent to which a firm is using debt financing. Debt provides financial leverage for the owners or shareholders of a firm. The money paid to a firm's debtholders is fixed. If the firm invests the money wisely and it generates lots of new revenue, the shareholders benefit because the amount paid to debtholders does not depend on how well the company does financially. The amount of debt a company can hold responsibly does vary by industry. The more certain the revenue is for an industry, the more debt the firms in it are likely to issue. Types of leverage ratios are debt ratio and times interest earned. There can be various definitions of the debt ratio. For this course it will be defined as long-term debt divided by long-term debt plus all equity. This ratio will always be less than one. The current amount of debt is hard to specify. Some firms won't issue any debt. Usually some debt is preferred because it does offer advantages to a firm's shareholders. The industry average is usually a good yardstick as to what is an appropriate amount of debt. Times interest earned will always be greater than one. This ratio can be as large as possible.

The third category of ratios is asset management ratios. These ratios measure how effectively a firm is managing its assets. Examples are inventory turnover and total asset turnover. The higher the inventory turnover is the faster a firm is turning inventory into revenue. The total asset turnover reflects the same idea. Assets are used to generate revenue. The higher the level of sales per dollar of assets, the more effective management is in using their assets to generate revenue.

The fourth category is profitability ratios. These ratios show the combined effects of liquidity, asset management, and debt on the operating performance of a firm. In other words, they indicate how efficiently a company earns net income for its shareholders. Examples are profit margin, return on assets, and return on equity. For profit margin higher values reflect lower costs and more net income, which is good. Generally higher values of ROA and ROE are good. The exception might be if a company does not have an effective investment policy in place to buy the assets it needs to generate revenue over the long run. The high ROA and ROE could be the result of a company using its assets to create good short-term performance at the expense of good long-term performance.

The final category is market ratios. These measure the firm's acceptance by investors in the market. The most important is the price-to-earnings ratio. A higher P/E ratio reflects confidence by investors in greater earnings in the future. However, buying a stock that has a high P/E ratio can be risky because any bad news about the company's future profitability can cause a sharp drop in the price of the stock. "Normal" P/E ratios are typically between 10 and 20. A low P/E ratio can either be a company that has severe financial problems or one, which is just in temporary financial trouble and could be a good investment in the long run. An investor must investigate these stocks carefully because the firm may not recover from its current financial problems.

Financial ratios are used for three purposes. The first is to standardize financial statement information so that comparisons can be made between companies in the same industry and between different industries. The second is to compare the financial performance of the same company over time. The final purpose is to highlight individual strengths and weaknesses of a company.

Financial statement analysis has many limitations. Comparing a firm's ratios with industry averages is difficult when a firm operates many divisions in different industries. General Electric is such a company. Because its financial statements are broken out a little, some comparisons can be made. Companies in the financial services industries, such as GE Capital, have ratios that are fundamentally different from manufacturing companies. Industry ratios represent average performance, which may not be necessarily good. Another problem is that inflation distorts a firm's balance sheet. The current value of the assets on the balance sheet may be quite different from their initial cost, reflected on the balance sheet. Seasonal factors can also distort ratios. Excessively high inventories can mask problems, or they could represent preparations for the upcoming selling season. Companies can manipulate their financial statements to a limited degree. They can sell off inventory at bargain prices at the end of the fiscal year to lower the inventory number on the balance sheet. Such techniques can make statements and ratios look better than they actually are. Companies do have a choice, although limited, as to how they report certain transactions. These different operating and accounting practices distort comparisons. Finally, it may be difficult to tell if a particular ratio is good or bad and difficult to determine whether a firm's ratios are, on balance, good or bad. It is essential that a firm's ratios are compared together and not individually. For example, a firm might have a low current ratio compared to other firms in the same industry. If its inventory turnover was high and its days sales outstanding was low, the firm might not need a lot of current assets because it is converting its inventory into sales and sales into cash more quickly than other firms in its industry.

Industry classification: Companies have been classified by industry according to the Standard Industrial Classification (SIC), which was originally developed by the Office of Management and Budget to facilitate statistical and economic analysis and reporting of the state of the U.S. economy based on enterprises engaged in production, trade, and service. The SIC system assigned each company a four-digit code which specified the primary industry in which they operated. Effective in 1997 the SIC system has been replaced with the North American Industry Classification System. NAICS has been developed in cooperation with Statistics Canada; Mexico's Instituto Nacional de Estadistica, Geografia e Information; and the U.S. Office of Management and the Budget, Economic Classification Policy Committee. The NAICS provides common industry definitions that cover the economies of the three North American countries and will aid in statistical economic analyses for all three countries. The NAICS is being used to collect and report 1997 economic information for American and Canadian companies and 1998 information for Mexican companies. For additional information, you can visit the National Technical Information Service web site.

There are three major references, which contain the financial ratios of specific industries: Robert Morris Associates Annual Statement Studies published by the Robert Morris Associates, D&B Industry Norms and Key Business Ratios published by Dun & Bradstreet, and Almanac of Business and Industrial Financial Ratios published by Prentice Hall. Each calculates the ratios on the basis of different groupings of companies within the same industry. The Robert Morris Associates Annual Statement Studies is the most comprehensive with the financial information of companies. Each industry data set, sorted by SEC code and compiled from bank loan requests, includes ratios and common size financial statement percentages segregated by sales size and quartile. The Dun & Bradstreet publication uses the four-digit SIC code but provides only general financial information. The Almanac provides detailed financial information but combines companies according to the first three-digits of their SIC code. When using any of these publications, be sure you know how the ratios are calculated. Ratios for the different sources may have the same label but can be calculated differently. All three references are available in most libraries.

There is another way to calculate "industry" averages for financial ratios. For example, any reference source, such as The Value Line Investment Survey, which groups companies by major product line can be used. You simply calculate the ratios for five or more companies in the group with your company and use that as an industry average.  

The relationship between risk and return: The term "risk" can have several meanings. In a financial context many people use risk to refer to the chance that they will lose their money if they invest it in common stock or bonds. This is not a useful definition because, if people believe they will lose their money, they won't make the investment. A definition of risk must recognize that people make investments even though they aren't sure how much money they will make. Therefore, financial risk is defined as the chance that the actual return (or actual cash flows) of a single financial security or a portfolio of securities that investors receive will be different from the expected return (or expected cash flows) that they anticipated. This reflects the fact that the future return of a financial security is not a single value but part of a probability distribution of returns, in which different returns can have different probabilities of occurrence.

Although most people don't like uncertainty, they will accept all kinds of risk if the expected reward is sufficient to compensate them for the risk they are taking. People invest in risky financial securities because they expect a return commensurate with this risk. As the risk increases, so must the reward. People exhibiting this characteristic are said to be risk-averse. People have different tolerances for risk. Some people need a very high return to compensate them for a specific level of risk while others will accept a lower return for the same risk. People who demand the higher return are more risk-averse while those who accept the lower return are less averse to risk. This is an important premise in finance.

Let's use a nonbusiness example. Most people travel a highway to get to work rather than side streets even though the chance of a serious accident is greater. Why? The benefit from using the high-speed road (time saved) is deemed worth the risk. Can a person be wrong? Can a person misjudge the risk? Absolutely. This is why people listen to traffic reports on the radio and television to help them select the route that has the highest risk-reward combination for them. Will everyone use a highway to get to work even if they can? Probably not. For some people the likely reward is simply not large enough for them to accept the risk. These same ideas guide people's investment decisions. People will do a considerable amount of research for an investment opportunity to determine if the expected return is sufficiently large to compensate them for the risk. Not all people will judge the expected benefit from an investment worth the risk. This is why some people invest only in relatively risk-free investments, such as insured savings accounts and Treasury securities, while others buy the common stock of companies in bankruptcy.

There is some constancy in the investment decisions of people. Given the choice between two investments with the same degree of risk, everyone will prefer the investment with the higher expected return. Likewise, given the choice between two investments with the same expected return, everyone will prefer the investment with the lower risk. It is when two investments have different risk-return combinations that people's preferences will vary. Below are two sets of probability distributions, one based on returns and one based on cash, for two different investment opportunities. The expected return is the same for both as is their expected cash flow. Because financial risk is defined as the chance the actual return (or cash flow) will vary from the expected return (or cash flow), the investment opportunity on the left is less risky. The risk of an individual asset is its standard deviation. Because the investment opportunity on the left has a smaller standard deviation, it has less risk than the opportunity on the right. There is a greater chance its actual return will be closer to its expected return and the investor will receive $110. Because the expected return for both opportunities is the same, people will prefer the investment on the left.

In the market this situation would not last very long. Because of its higher risk, the price of the investment on the right will fall relative to the investment on the left. People will pay less for the investment on the right because its payoff is less certain. Thus, its expected return will rise relative to the investment on the left. The final result is that, because both investments promise the same amount of money but have different levels of risk, they will have different prices and, thus, different expected returns.

People typically invest in a portfolio of securities rather than buying just one or two securities because they can lower their risk. The risk of a portfolio of securities is also measured by its standard deviation. This measure is dependent on more than the variances of the individual securities. It is also dependent on the covariance between the different pairs of securities. These covariance terms are incorporate the correlation between the returns of the securities. The concept of correlation is pretty simple. If the return of one security increases whenever the return of another increases or decreases when the other decreases, the two securities would be positively correlated. If the returns of both increased or decreased by the same percentage, the two securities would be perfectly positively correlated. This is one end of the correlation spectrum. The degree of correlation is measured by the correlation coefficient. If two securities are perfectly positively correlated, he correlation coefficient is +1.0. If the return of one increased while the return of another decreased, the two would be negatively correlated. If they increased or decreased by the same percentage as another decreased, they would be perfectly negatively correlated with a correlation coefficient of -1.0. This is the other end of the correlation spectrum. Usually the correlation falls in between these two extremes. For example, a correlation coefficient of zero (0) would mean that the two securities are not correlated at all. Changes in the return of one security have no relationship to changes in the return of the other. The returns for most stocks are positively correlated. This is why people pay uses stock indexes, such as the Dow Jones Industrial Average and the Standard&Poors 500, to gauge the performance of the market as a whole. As long as the returns of two securities are not perfectly positively correlated, the standard deviation of the portfolio will decrease as the number of securities in the portfolio increases. This is the benefit of diversification.

If you are interested, here is a simple portfolio example.

Time value of money: People make their decisions in fundamentally the same way. The first step is to identify the available alternatives. There must be two or more from which to choose. If there is only one alternative, there is no choice and, therefore, no decision to be made. Second, all benefits and costs of each alternative are identified. Third, a value is placed on these benefits and costs by the decision-maker so that they can be combined. Fourth, those alternatives for which the benefits are greater than the costs are directly compared, and the alternative whose net benefit is greatest is selected. Once the decision is made, it may turn out that the best alternative was not selected. A cost may have been underestimated or a benefit overvalued, which could have us wishing we had made another choice. It is important to note that every decision-making technique tries to identify which alternative is best before a choice is made.

Economic decision-making tries to improve the quality of the decision making process by objectively measuring the dollar value associated with the benefits and costs of each alternative. This permits the different alternatives to be directly compared. Unfortunately, the economic value of a dollar decreases over time. If someone gave us a choice between receiving $100 today and $100 next year, we would choose the $100 today. Why is it that we would we rather have that money in our hand today than to have the same amount in our hand in one year? The answer is simple. There is an opportunity cost associated money. If we had that $100 today, we could save it or spend it or do nothing with it. Just possessing it has value. This economic concept is called the time preference for money.

The time preference for money means a single dollar today is valued more highly than a single dollar to be received in one year. Therefore, in order to compare an alternative's benefits and costs whose dollars are either received or paid out at different points in time, it is necessary to use dollars that have the same economic value. This only occurs when the dollars are to be received or paid out at the same point in time. The decision-maker's opportunity cost is used to convert the economic value of all dollars into an equivalent amount of dollars at the same point in time. Only dollars at the same point in time can be directly added (benefits) or subtracted (costs). The time value of money (TVM) is a series of relationships that makes this conversion possible.

Here are a set of notes that cover the basics of the time value of money.