Financial Accounting
What is Financial Accounting?
A. Financial Accounting is the:
1. identification
2. measurement, and
3. communication of financial information
4. about the business activities of economic entities
5. to its stakeholders
6. to aid in the decision-making process.
B. What are the business activities?
1. Financing Activities
a. Raising equity capital by attracting investment from business owners, such as common shareholders.
b. Acquiring resources from lenders or by the issuance of bonds.
2. Investing Activities
a. Acquiring productive resources such as property, plant, equipment, technology, legal rights, and other assets necessary to operate the business.
3. Operating Activities
a. Utilization of resources in day-to-day activities to produce goods and/or services.
b. Selling of goods and services to customers.
C. Who are the stakeholders?
1. Anyone that has some type of interest in the company.
2. Most companies have many different stakeholders. The users may be internal or external.
3. Stakeholders include: stockholders, banks, creditors, governmental agencies, management, employees, customers, suppliers, and others.
D. What do stakeholders need to know?
1. Investors
a. The business model, strategies, and competitive advantages of the company.
b. Resources the company owns and the debt it owes.
c. The net income or net loss, cash flows, and whether profits and cash flows are growing over time.
2. Creditors
a. The amount of equity capital in place
b. Resources the company owns and the debt it owes
c. Cash flows and the company’s ability to meet interest and principal payments when due.
E. Financial statements are the principal means through which a company communicates its financial information to external stakeholders. The financial statements most frequently provided are:
· the balance sheet,
· the income statement,
· the statement of cash flows, and
· the statement of owners’ or stockholders’ equity.
1. Balance Sheet (Statement of Financial Position)
a. Presents, as of a specific date:
i. a snapshot of the resources of a entity (assets) and
ii. the claims on the entity (liabilities and shareholders’ equity).
b. Assets = Liabilities + Shareholders’ Equity
2. Income Statement (Profit and Loss Statement)
a. Measures and reports the financial results of an entity’s performance for a period of time.
b. Net Income (loss) = Revenues - Expenses + Gains - Losses
3. Statement of Cash Flows
a. Reports for a period of time the net cash flows from operating, investing, and financing activities.
b. Provides useful information about how an entity is generating and using cash.
c. Is useful to creditors and other stakeholders to help evaluate the entity’s cash- generating ability.
4. Statement of Shareholders’ Equity
a. Provides information about the common shareholders’ equity claims on the company and how those claims changed during the year.
b. Contributed Capital - Amounts contributed by shareholders for an interest in the entity (common stock, additional paid-in capital).
c. Earned Capital
i. Cumulative net income in excess of dividends declared (retained earnings).
ii. Stockholders’ equity effects from the recognition or valuation of certain assets or liabilities (Accumulated Other Comprehensive Income).
5. Other means of communicating financial information include:
a. Financial Statement Notes
i. Companies must provide notes as additional information with the financial statements.
ii. Financial notes explain how the accounts and amounts have been determined.
iii. Provides important details about the accounting principles, methods, and estimates the company has used to measure values of assets, liabilities, equity, revenues, expenses, gains and losses.
b. Management Discussion and Analysis
i. Is an extensive narrative discussion and quantitative analysis from the company’s managers.
ii. Provides managers’ insight into: strategies, evaluation of performance, exposure to business risk factors, and expectations about the future.
c. Managers’ and Independent Auditors’’ Attestations
i. The Sarbanes-Oxley Act of 2002 imposed responsibilities on managers and auditors.
ii. Management is responsible for the financial statements and the underlying accounting and control system that generates the financial statements.
iii. Independent auditors are responsible for assessing a company’s internal control system, designing audit tests, and forming an opinion about the fairness of the amounts reported in the financial statements.
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II. The Need to Develop Standards
A. The accounting profession has developed a common set of standards and procedures known as generally accepted accounting principles (GAAP).
B. These principles serve as a general guide to the accounting practitioner in accumulating and reporting the financial information of a business enterprise. The main controversy in setting accounting standards is, “Whose rules should we play by, and what should they be?”
C. Users of financial accounting standards have both coinciding and conflicting need for information of various types. To meet these needs, companies prepare a set of general purpose financial statements. Users expect these statements to present fairly, clearly, and completely the company’s financial position.
III. Parties Involved in the Standard Setting Process
A. What prompted the standard setting process?
1. After the stock market crash in 1929 and the Great Depression, there were calls for increased government regulation and supervision—especially of financial institutions and the stock market.
2. As a result, the federal government established the Securities and Exchange Commission (SEC) to help develop and standardize financial information presented to stockholders.
a. The SEC is a federal agency and administers the Securities Act of 1933 and the Securities Exchange Act of 1934 and several other acts.
b. Most companies that issue securities to the public or are listed on a stock exchange are required to file audited financial statements with the SEC.
c. In addition, the SEC has the legal authority to prescribe the accounting practices and standards to be employed by companies that fall within its jurisdiction.
3. At the time the SEC was created, it encouraged the creation of a private standards- setting body. As a result, accounting standards have generally been developed in the private sector either through the American Institute of Certified Public Accountants (AICPA) or the Financial Accounting Standards Board (FASB).
a. The SEC has affirmed its support for the FASB by indicating that financial statements conforming to standards set by the FASB will be presumed to have substantial authoritative support.
b. Over its history, the SEC’s involvement in the development of accounting standards has varied. In some cases, the private sector has attempted to establish a standard, but the SEC has refused to accept it. In other cases, the SEC has prodded the private sector into taking quicker action on setting standards.
IV. AICPA – American Institute of Certified Public Accountants - 1887
A. The first group appointed by the AICPA to address the issue of uniformity in accounting practice was the Committee on Accounting Procedure (CAP).
1. This group served the accounting profession from 1939 to 1959.
2. During that period, it issued 51 Accounting Research Bulletins (ARBs) that narrowed the wide range of alternative accounting practices then in existence.
B. In 1959, the AICPA created the Accounting Principles Board (APB).
a. The major purposes of this group were
1. to advance the written expression of accounting principles,
2. to deter-mine appropriate practices, and
3. to narrow the areas of difference and inconsistency in practice.
b. The APB was designated as the AICPA’s sole authority for public pronouncements on accounting principles.
c. Its pronouncements, known as APB Opinions, were intended to be based mainly on research studies and be supported by reason and analysis.
C. In 1971, a committee, known as the Study Group on Establishment of Accounting Principles (Wheat Committee), was set up to study the APB and recommend changes in its structure and operation. The result of the Study Group’s findings was the demise of the APB and the creation of the Financial Accounting Standards Board (FASB) in 1973.
D. FASB – Financial Accounting Standards Board
1. The FASB represents the current rule-making body within the accounting profession.
2. The mission of the FASB is to establish and improve standards of financial accounting and reporting for the guidance and education of the public, which includes issuers, auditors, and users of financial information.
3. The FASB differs from the predecessor APB in the following ways:
a. Smaller membership (7 versus 18 on the APB).
b. Full-time remunerated membership (APB members were unpaid and part- time).
c. Greater autonomy (APB was a senior committee of the AICPA).
d. Increased independence (FASB members must sever all ties with firms, companies, or institutions).
e. Broader representation (it is not necessary to be a CPA to be a member of the FASB).
4. Two basic premises of the FASB are that in establishing financial accounting standards:
a. it should be responsive to the needs and viewpoints of the entire economic community, not just the public accounting profession, and
b. it should operate in full view of the public through a “due process” system that gives interested persons ample opportunity to make their views known.
V. Due Process
A. The FASB issues two major types of pronouncements:
1, Accounting Standards Updates. The Updates amend the Accounting Standards Codification, which represents the source of authoritative accounting standards, other than standards issued by the SEC.
a. Each Update explains how the Codification has been amended and also includes information to help the reader understand the changes and when those changes will be effective.
b. They are considered GAAP and must be followed in practice.
2. Financial Accounting Concepts. The SFACs represent an attempt to move away from the problem-by-problem approach to standard setting that has been characteristic of the accounting profession.
a. The Concept Statements are intended to form a cohesive set of interrelated concepts, a conceptual framework, which will serve as tools for solving existing and emerging problems in a consistent manner.
b. Unlike FASB statements, the Concept Statements do not establish GAAP.
B. A second type of update is a consensus of the EITF.
1. In 1984, the FASB created the Emerging Issues Task Force (EITF).
2. The purpose of the Task Force is to reach a consensus on how to account for new and unusual financial transactions that have the potential for creating differing financial reporting practices.
3. The EITF can deal with short-term accounting issues by reaching a consensus and thus avoiding the need for deliberation by the FASB and the issuance of an FASB Statement.
VI. GAAP – Generally Accepted Accounting Principles
A. Generally accepted accounting principles (GAAP) are those principles that have substantial authoritative support.
1. Accounting principles that have substantial authoritative support are those found in FASB Statements, Interpretations, and Staff Positions; APB Opinions; and Accounting Research Bulletins (ARBs).
2. If an accounting transaction is not covered in any of these documents, the accountant may look to other authoritative accounting literature for guidance.
B. FASB Accounting Standards Codification (ASC)
1. The Codification is an electronic database that integrates and topically organizes U.S. GAAP into one coherent body of literature.
2. The Codification became effective on July 1, 2009.
3. The FASB developed the Codification to achieve three goals:
a. Simplify user access by organizing and categorizing all authoritative U.S. GAAP in one database.
b. Ensure the codified content accurately represented all U.S. GAAP.
c. Create a codification research system that is up to date, including the most recently released standards.
4. The Codification is now the only source of authoritative GAAP for U.S. companies to determine how to record their transactions, events, or circumstances, and how to report the results in their financial statements.
5. The Codification did not change GAAP, only repackaged it.
VII. International Accounting Standards
A. The IASB and IFRs
1. The IASB is the international accounting standard setter, establishing IFRS which are required or permitted in roughly 130 countries.
2. As the parent organization of the IASB, the IFRS Foundation consists of a group of Trustees that is responsible for fund-raising, appointing IASB members, and overseeing the effectiveness of the IASB.
3. The IASB includes 16 members from various countries.
4. Following a similar process as the FASB, the IASB studies the topic, issues a discussion paper, issues an Exposure Draft, evaluates comments, and drafts the proposed standard.
5. If approved by 10 of the 16 members, the proposed standard becomes an International Financial Reporting Standard (IFRS).
B. Convergence of FASB and IASB Accounting Standards
1. The SEC mandates corporations are subject to U.S. GAAP or IFRS.
2. International convergence of accounting standards refers to both a goal and the path chosen to reach it.
3. The ultimate goal of convergence is a single set of high-quality, international accounting standards that companies worldwide would use for both domestic and cross-border financial reporting.
4. The path toward that goal has been the collaborative efforts of the FASB and the IASB to both improve U.S. GAAP and IFRS and eliminate or minimize the differences between them.
5. Major projects have been completed to achieve convergence of accounting standards for: consolidated financial statements, fair value measurement, financial statement presentation and revenue recognition.
C. The SEC and International Convergence
1. In 2007 the SEC decided to allow foreign companies to use IFRS rather than U.S. GAAP, agreed to accept IFRS-based filings (in Form 20-F), and decided that these companies do not need to reconcile how differences between IFRS and U.S. GAAP affect their reported financial statements.
2. Professional accountants must be fluent in U.S. GAAP and IFRS and well informed about their differences.
VIII. Ethics in the Accounting Profession
A. Accountants serve the greater good of society and owe a responsibility of ethics and fairness to all stakeholders, whose interests are sometime conflicting.
B. Accountants face ethical dilemmas, situations in which an accountant must make a decision about what is the “right” (ethical) action to take in given circumstances.
C. Professional accounting organizations have established codes of ethics for their members.
D. The AICPA has adopted the Code of Professional Conduct (CPC).
E. The CPC includes six principles that express the basic tenets of ethical and professional conduct and call for an unswerving commitment to honorable behavior, even at the sacrifice of personal advantage.
Principles of the AICAP Code of Professional Ethics
Topic 7:
Conceptual Framework for Financial Reporting
I. Conceptual Framework
A. A conceptual framework in accounting is important because rule-making should be built on and relate to an established body of concepts. The benefits of a soundly developed conceptual framework are as follows:
1. Guide the FASB in establishing accounting standards.
2. It should be easier to issue a coherent set of standards and rules.
3. Establish objectives and concepts to guide financial statement preparers and auditors to resolve questions and make appropriate judgements
4. Increase user’s understandability of and confidence in financial reporting
5. Enhance financial statement comparability across companies and over time.
B. The FASB’s conceptual framework is developed in a series of concept statements (collectively the Conceptual Framework). The conceptual framework has the following 3 levels:
1. First level: The objective of financial reporting, the “why” or purpose of accounting.
2. Second level: The qualitative characteristics and the elements of financial statements, which form a bridge between the 1st and 3rd levels.
3. Third level: Recognition, measurement, and disclosure concepts, the “how” or implementation.
II. Need for a Conceptual Framework:
A. Build on and relate to an established body of concepts
B. Issue more useful and consistent pronouncements over time
C. Increase financial statement users’ understanding of and confidence in financial reporting
D. Enhance comparability among companies’ financial statements
E. Provide a framework for solving new and emerging practical problems.
III. First Level: Basic Objective (SFAC #5, #8)
A. The basic objective of financial reporting is the foundation of the conceptual framework and requires that general-purpose financial reporting provide information about the reporting entity that is useful to present and potential equity investors, lenders, and other creditors in making decisions about providing resources to the entity.
B. Information Useful in Decision Making
1. Information useful to external users(investors, lenders, and other creditors) in assessing expected returns.
a. Decisions by existing and potential investors about buying, selling, or holding equity instruments
b. Decisions by existing and potential investors about buying, selling or holding debt instruments.
2. Information useful in assessing the amounts, timing, and uncertainty of the prospective company cash flows.
3. Information about economic resources and claims on the company.
a. To identify the company’s resources, obligations, financial strengths and weaknesses, and to assess its liquidity and solvency.
b. To specify the types of resources in which the company has invested, as well as the types of the claims on the company.
c. To indicate the potential future cash flows from the company’s resources and the ability of the resources to satisfy the claims on the company.
4. Information about changes in the company’s resources and claims.
a. Provide information about the financial performance which causes the company’s resources and claims on the company resources to change during the period.
b. Information concerning the company’s net income, comprehensive income, and their components is useful to external users in: 1) evaluating management’s performance, 2) estimating the company’s “earning power” or other amounts that are representative of persistent long-term income producing ability, 3) predicting future income and net cash flows, and 4) assessing the risk of investing in or lending to the company.
C. In order to understand general-purpose financial reporting, users need reasonable knowledge of business and financial matters.
IV. Second Level: Fundamental Concepts (SFAC #8, #6)
A. Companies must decide what type of information to disclose and how to disclose it. These choices are determined by which method or alternative provides the most decision-useful information. The qualitative characteristics of accounting information distinguish better and more useful information from inferior and less useful information.
B. The overriding criterion for evaluating accounting information is that it must be useful for decision making. To be useful, it must be understandable.
C. Fundamental Qualities
The fundamental qualities of accounting information are:
1. Relevance – information that is capable of making a difference in a decision. Relevant information has:
a. Predictive value means that the information can help users form expectations about the future.
b. Confirmatory value means that the information provides feedback which validates or refutes expectations based on previous evaluations.
c. Materiality means that information is material if omitting it or misstating it could influence decisions that users make on the basis of the reported financial information.
2. Faithful representation – numbers and descriptions match what really happened or existed. Comprised of:
a. Completeness means that all information necessary to understand the information being reported is provided.
b. Neutrality means that the information is unbiased. It is not manipulated to achieve a predetermined result or to influence users’ behavior in a particular direction
c. Free from error means that the information is measured and described as accurately as possible.
D. Enhancing Qualities
Enhancing qualities complement the fundamental qualities and include:
1. Comparability means that companies record and report information in a similar manner. Consistency is another type of comparability and means the company uses the same accounting methods from period to period.
2. Verifiability means that independent people using the same methods arrive at similar conclusions.
3. Timeliness means that information is available before it loses its relevance.
4. Understandability means that reasonably informed users should be able to comprehend the information that is clearly classified and presented.
E. Basic Elements
An important aspect of developing an accounting theoretical structure is the body of basic elements or definitions. Ten basic elements that are most directly related to measuring the performance and financial status of a business enterprise are f ormally defined in SFAC No. 6. These elements are defined below.
1. Assets. Probable future economic benefits obtained or controlled by a particular entity as a result of past transactions or events.
2. Liabilities. Probable future sacrifices of economic benefits arising from present obligations of a particular entity to transfer assets or provide services to other entities in the future as a result of past transactions or events.
3. Equity. Residual interest in the assets of an entity that remains after deducting its liabilities. In a business enterprise, the equity is the ownership interest.
4. Investments by Owners. Increases in net assets of a particular enterprise resulting from transfers to it from other entities of something of value to obtain or increase ownership interests (or equity) in it. Assets are most commonly received as investments by owners, but that which is received may include services or satisfaction or conversion of liabilities of the enterprise.
5. Distributions to Owners. Decreases in net assets of a particular enterprise resulting from transferring assets, rendering services, or incurring liabilities by the enterprise to owners. Distributions to owners decrease ownership interests (or equity) in an enterprise.
6. Comprehensive Income. Change in equity (net assets) of an entity during a period from transactions and other events and circumstances from nonowner sources. It includes all changes in equity during a period except those resulting from investments by owners and distributions to owners.
7. Revenues. Inflows or other enhancements of assets of an entity or settlement of its liabilities (or a combination of both) during a period from delivering or producing goods, rendering services, or other activities that constitute the entity’s ongoing major or central operations.
8. Expenses. Outflows or other using up of assets or incurrences of liabilities (or a combination of both) during a period from delivering or producing goods, rendering services, or carrying out other activities that constitute the entity’s ongoing major or central operations.
9. Gains. Increases in equity (net assets) from peripheral or incidental transactions of an entity and from all other transactions and other events and circumstances affecting the entity during a period except those that result from revenues or investments by owners
10. Losses. Decreases in equity (net assets) from peripheral or incidental transactions of an entity and from all other transactions and other events and circumstances affecting the entity during a period except those that result from expenses or distributions to owners.
V. Third Level: Recognition and Measurement Concepts (SFAC #5, #7)
The third level of the framework consists of concepts that implement the basic objective of level one. These concepts explain how companies should recognize, measure, and report financial elements and events.
A. Four Basic Assumptions:
1. Economic Entity Assumption. Economic activity can be identified with a particular unit of accountability in a manner that assumes the company is separate and distinct from its owners or other business units.
a. An individual, department, division, or an entire industry could be considered a separate entity if we choose to define it in this manner.
b. The entity concept does not necessarily refer to a legal entity. A parent and its subsidiary are separate legal entities, but merging their activities together does not violate the entity assumption.
2. Going Concern Assumption. In the absence of contrary information, a company is assumed to have a long life. The current relevance of the historical cost principle is dependent on this assumption.
a. Only when liquidation is imminent is the assumption inapplicable. In this situation a revaluation of the assets and liabilities can provide information that closely approximates the company’s net realizable value.
3. Monetary Unit Assumption. Money is the common denominator of economic activity and provides an appropriate basis for accounting measurement and analysis.
a. The monetary unit is assumed to remain relatively stable over the years in terms of purchasing power.
b. In essence, this assumption disregards any inflation or deflation in the economy in which the company operates.
4. Periodicity Assumption. The economic activities of a company can be divided into artificial time periods for the purpose of providing the company’s periodic reports.
B. Basic Accounting Principles:
Certain basic principles are followed by accountants in recording and reporting the transactions of a business entity. These principles relate to how assets, liabilities, revenues, and expenses are to be identified, measured, and reported.
4 Basic Accounting Principles:
1. Measurement Principle. A ‘mixed-attribute’ system permits the use of various measurement bases.
a. Historical Cost Principle. Acquisition cost is considered a reliable basis upon which to account for assets and liabilities of a company. Historical cost has an advantage over other valuations, as it is thought to be verifiable.
b. Fair Value Principle. Fair value is defined as the price that would be received to sell an asset or paid to transfer a liability in on orderly transaction between market participants at the measurement date. Recently, GAAP has increasingly called for the use of fair value measurements in the financial statements.
1. To increase consistency and comparability in fair value measures, the FASB established a fair value hierarchy provides insight into the priority of valuation techniques to use to determine fair value.
Level 1: Observable inputs that reflect quoted market prices for identical assets or liabilities in active markets. (Least subjective)
Level 2: Inputs other than quoted prices included in Level 1 that are observable for the asset or liability either directly or through corroboration with observable data. Rely on evaluating similar assets or liabilities in active markets. (More subjective)
Level 3: Unobservable inputs. Much judgement is needed, based on the best information available to arrive at a relevant and representationally faithful fair value measurement. Measures may be developed using expected cash flows and present value techniques (SFAC #7).
2. Revenue Recognition Principle. Revenue is recognized at the time in which the performance obligation is satisfied.
3. Expense Recognition Principle. (AKA the Matching Principle). Recognition of expenses is related to net changes in assets and earning revenues. The expense recognition principle is implemented in accordance with the definition of expense by matching efforts (expenses) with
accomplishment (revenues).
An expense is defined as outflows or other “using up” of assets or incurring of liabilities during a period as a result of delivering products or producing goods and/or performing services (i.e. .. generating revenues)
Costs are generally classified into two groups: Product Cost and Period Cost
Product costs, such as material, labor, and overhead, attach to the product, and are recognized in the same period the products are sold.
Period costs, such as officers’ salaries and other administrative expenses, attach to the period, and are recognized in the period incurred.
4. Full Disclosure Principle. In the preparation of financial statements, the accountant should include sufficient information to influence the judgment and decision of an informed user. A series of judgmental tradeoffs must occur.
These trade-offs strive for:
(1) sufficient detail to disclose matters that make a difference to users.
Yet
(2) Sufficient condensation to make the information understandable, keeping in mine costs of preparing and using it.
Notes to financial statements generally amplify or explain the items presented in the main body of the statements. Examples: descriptions of accounting policies and methods used in measuring elements reported in the statement, explanations of uncertainties or contingencies, and statistics and details to voluminous for inclusion in the statements.
Supplementary Information may include details and amounts that present a different perspective from that adopted in the financial statements. It may be quantifiable information that is high in relevance but low in faithful representation. (Example: Oil and gas companies providing information on proven reserves as well as the related discounted cash flows.) Supplementary information may also include management’s explanation of the financial information and its discussion of the significance of that information.
C Cost Constraint
Although accounting theory is based upon certain assumptions and the application of basic principles, there are some exceptions to these assumptions. One exception is often called a constraint, and sometimes justifies departures from basic accounting theory.
Cost Constraint. The cost constraint (or cost-benefit relationship) relates to the notion that the benefits to be derived from providing certain accounting information should exceed the costs of providing that information.
The difficulty in cost-benefit analysis is that the costs and especially the benefits are not always evident or measurable.
Topic 8
Time Value of Money
I. Basic Time Value Concepts.
A. Time value of money indicates a relationship between time and money. A dollar received today is worth more than a dollar promised sometime in the future.
1. For example, $1,000 loaned today is worth more to you than $1,000 to be received in 1 year.
2. The time value of money provides the lender compensation for delayed consumption, expected inflation, and risk.
B. Interest and the time value of money impacts the decision making related to operating, investing, and financing activities of a business.
C. Various discounting and compounding techniques can be used to measure either the present value or the future value of different assets and liabilities and various types of transactions.
1. The conversion of future cash flow amounts to the present value is known as discounting.
2. The conversion of current-period cash flows to future value is known as compounding.
D. Accounting applications of time value concepts:
1. Long-term assets
a. Evaluating alternative investment by discounting future cash flows.
b. Determine the value of assets purchased under deferred payment contracts.
c. Measuring impairments of assets.
2. Long-term notes - Valuing noncurrent receivables and payables that do not have a stated interest rate or a below market interest rate.
3. Stock-based compensation - Determining the fair value of employee services in compensatory stock-option plans.
4. Business combinations
a. Determining the fair value of assets and liabilities acquired.
b. Determining the present value of a stream of fture earnings.
c. Valuing goodwill.
5. Others include: Long-term leases, Pensions, and Disclosures.
E. Personal applications of time value concepts:
1. Purchasing a home.
2. Planning for retirement.
3. Evaluating alternative investments.
II. Nature of Interest
A. Interest is payment for the use of money. It represents compensation for delayed consumption, expected inflation, and risk.
B. It is the excess cash received or repaid over and above the principal (amount loaned or borrowed).
C. Interest rates are stated on an annual basis unless indicated otherwise.
D. Simple Interest vs Compound Interest
1. Simple Interest
a. Simple interest is computed on the amount of the principal only.
b. Simple interest = p × i × n
where:
p = principal.
i = rate of interest for a single period.
n = number of periods.
c. Example: Compute the amount of interest earned if you invest 10,000 at 12% interest compounded annually for three years.
10,000 12% = $1,200 per year 3 years = $3,600
2. Compound Interest.
a. Compound interest is computed on the principal and on any interest earned that has not been paid or withdrawn.
b. Compound interest is common in business where capital is financed over long periods of time.
c. Compound Interest = (p + ai) x i x n
where:
p = principal.
ai = accumulated interest
i = rate of interest for a single period.
n = number of periods.
d. Using the examples above, compounding would result in the following:
10,000 * 12% = 1,200
11,200 * 12% = 1,344
12,544 * 12% =. 1,505
4,049
E. The term period should be used instead of years.
1. Interest may be compounded more than once a year:
If interest is Number of compounding
compounded periods per year
Annually 1
Semiannually 2
Quarterly 4
Monthly 12
2. Adjustments must be made when interest is compounded more than once a year.
a. Compute the compounding period interest rate:
annual interest rate / the number of compounding periods per year
Example: 12% compounded semi-annually = .12/2 = 6%
b. Compute the total number of compounding periods:
number of years * number of compounding periods per year
Example 12% compounded semi-annually for 1 year = 1 * 2 = 2 periods
F. Variables in Compound Interest Problem
1. Rate of interest. An annual rate, adjusted to reflect the length of the compounding period.
2. Number of time periods. The number of compounding periods.
3. Future value. The value at a future date of a given sum(s) invested assuming compound interest.
4. Present value. The value now of a future sum(s) discounted assuming compound interest.
III. Financial Calculator
A. Business professionals, after mastering the above concepts, will often use a financial (business) calculator to solve time value of money problems.
B. When using financial calculators, the five most common keys used to solve time value of money problems are:
 |
where:
N = number of periods.
I/Y = interest rate per period (some calculators use I/YR or i).
PV = present value (occurs at the beginning of the first period).
PMT = payment (all payments are equal in amount, and the time between each payment is the same).
FV = future value (occurs at the end of the last period).
When entering PV, PMT, and FV outflows of cash will be negative and inflows of cash will be positive.
IV. Present Value
A. May be described as the amount that must be invested now to produce a known future value.
B. Calculating Present Value – Computing the unknown present value of a known amount of money in the future that is discounted for a certain number of periods at a certain interest rate.
1. Discounting all cash flows from the future to the present.
2. Discounting reduces the amounts or values, so that the present value is less than the future value.
C. Calculate the Present Values of a Single Sum or Lump Sum. What is the present value of $73,466 to be received in 5 years discounted at 8% interest compounded annually?
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5 8 ? 0 73,466
CPT PV = $49,999.72
V. Future Value
A. May be described as the future value of a known amount today.
B. Calculating Future Value – Computing the unknown future value of a known amount of money that is invested now for a certain number of periods at a certain interest rate.
1. Accumulate all cash flows to a future point.
2. Interest increases the amounts or values over time so that the future value exceeds the present value.
C. Calculate the Future Values of a Single Sum or Lump Sum. What is the future value of $50,000 at the end of 5 years invested at 8% compounded annually?
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5 8 50,000 0 ?
CPT FV = $73,466
VI. What is an annuity?
A. An annuity is a series of equal cash flows (deposits, receipts, payments, withdrawals) occurring at regular intervals with interest compounded at a specified rate.
B. An annuity requires:
1. The periodic cash flows (PMTs) are equal in amount
2. The time periods between the cash flows are the same length.
3. The interest rate is constant for each time period.
4. The interest is compounded at the end of each time period.
C. The cash flows (rents) may occur at either the beginning or the end of the periods.
1. Ordinary Annuity – Rents occur at the end of each period.
2. Annuity Due – Rents occur at the beginning of each period.
a. An annuity due has one additional time period.
b. Annuity Due = Ordinary Annuity * (1+ i)
D. Example: Ordinary Annuity: What is the future value of 5 equal investments of $5,000 made at the end of each year, earning interest at 6%.
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5 6 0 -5,000 ?
CPT FV = $28,185.46
E. Example: Ordinary Annuity: What is the future value of 5 equal investments of $5,000 made at the beginning of each year, earning interest at 6%.
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5 6 0 -5,000 ?
CPT FV = $28,185.46. * 1.06 =$29,876.59
F. Example: Ordinary Annuity: What is the present value of receipts of $5,000 each to be received at the end of each of the next 5 years discounted at 6%?
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5 6 ? -5000 0
CPT PV = $21,061.82
VII. Bond Valuation
A. A long-term bond produces two cash flows:
1. Annuity – periodic interest payments during the life of a bond.
2. Single Sum – the principal (face value) paid at maturity.
B. At the time of issue, bond buyers determine the present value of these two cash flows using the market rate of interest.
C. The current market value of the bonds is the sum of the present value of the annuity and the single sum discounted at the current market rate.
D. Example: On 1/1/2020, A Corp issues $100,000 of 5% bonds. The bonds mature on 1/1/2025. At the date of issuance, the market rate of interest for similar bonds is 6%. What amount will the bonds sell for on 1/1/2020?
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5 6 ? 100,000 * 5% -100,000
-5,000
CPT PV = $95,787.64