See page 129- 137 on attachment for more details there are five steps to the project.

Step 1: Create the loan amortization schedule for the property.

Step 2: Create the depreciation schedule.

Step 3: Create the schedule that combines interest expenses and depreciation expenses.

Step 4: Create a schedule that converts the interest expense and depreciation expense to aftertax dollars.

Step 5: Create a schedule that shows the aftertax cash outflows.

Study Guide Corporate Finance By A. J. Cataldo II, Ph.D., CPA, CMA About the Author A. J. Cataldo is currently a professor of accounting at West Chester University, in West Chester, Pennsylvania. He holds a bachelor degree in accounting/finance and a master of accounting degree from the University of Arizona. He earned a doctorate from the Virginia Polytechnic Institute and State University. He is a certified public accountant and a certified management accountant. He has worked in public accounting and as a government auditor and controller, and he has provided expert testimony in business litigation engage- ments. His publications include three Elsevier Science monographs, and his articles have appeared in Journal of Accountancy, National Tax Journal, Research in Accounting Regulation, Journal of Forensic Accounting, Accounting Historians Journal, and several others. He has also published in and served on editorial review boards for Institute of Management Accounting association journals, including Management Accounting, Strategic Finance, and Management Accounting Quarterly, since January 1990. All terms mentioned in this text that are known to be trademarks or service marks have been appropriately capitalized. Use of a term in this text should not be regarded as affecting the validity of any trademark or service mark. Copyright 2015 by Penn Foster, Inc. All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner. Requests for permission to make copies of any part of the work should be mailed to Copyright Permissions, Penn Foster, 925 Oak Street, Scranton, Pennsylvania 18515. Printed in the United States of America 10/17/11 1 LESSON ASSIGNMENTS 7 LESSON 1: CORPORATE FINANCE OVERVIEW 9 EXAMINATION 1LESSON 1 33 LESSON 2: FUTURE CASH FLOW VALUATION 37 EXAMINATION 2LESSON 2 67 LESSON 3: CAPITAL BUDGETING 71 EXAMINATION 3LESSON 3 89 LESSON 4: RISK AND RETURN 93 EXAMINATION 4LESSON 4 107 LESSON 5: COST OF CAPITAL AND FINANCIAL POLICY AND OPTIONS 111 EXAMINATION 5LESSON 5 125 GRADED PROJECT 129 SELF-CHECK ANSWERS 139 Contents INSTRUCTIONS TO STUDENTS iii Welcome to Corporate Finance! This course will introduce you to some basic financial management and analysis concepts used in both large and small corporations. One of the most important components of every business operation is financial decision making. All business decisions have some financial implications, either directly or indirectly. Many of the financial concepts addressed in this course arise every day in large companies, and can also be applied to your personal financial and economic decisions. Your course is divided into five major lessons based on your textbook, Fundamentals of Corporate Finance. The purpose of this study guide is to help you understand the key principles addressed in your textbook. To successfully complete your lessons, you must familiarize yourself with the contents of this study guide. You'll be able to test your knowledge of each lesson with self-checks and examinations. OBJECTIVES When you complete this course, you'll be able to Describe the main components of a balance sheet Apply the basic equations used to calculate a firm's working capital and cash flow Read and understand basic balance sheets and income statements Calculate present values and future values Define what a bond is and discuss the different types of bonds Explain the differences between common stocks and preferred stocks Discuss the relative strengths and weaknesses of the various methods for analyzing investments Calculate the break-even point for a project Instructions INTRODUCTION 1 Calculate capital gains, losses, and overall returns in simple stock transactions Define a variety of risk components and explain how they affect investment returns Describe how investment portfolios are assembled and weighted Describe the importance of diversification in an investment portfolio Explain the debt and equity components of a firm's capital structure Discuss the concept of financial leverage Define the basic types of corporate bankruptcy proceedings Explain how options, employee stock options, warrants, and convertible bonds work ABOUT YOUR TEXTBOOK Your textbook, Fundamentals of Corporate Finance, Ninth Edition, by Stephen A. Ross, Randolph W. Westerfield, and Bradford D. Jordan, will instruct you on all aspects of corporate finance. The examinations for this course will be based on material found in the textbook. The textbook is organized in an easy-to-understand format. The preface of the textbook explains the organization of the text and introduces each chapter. Features of the text, such as \"Chapter-Opening Vignettes,\" \"In Their Own Words,\" \"Work the Web,\" and \"Spreadsheet Strategies\" are also introduced. Students often skip the preface and move right into the text. While you won't miss any subject matter that way, you might miss hints that can make your study time more effective. Each chapter in your textbook opens with a vignette, or story taken from real-world events, in the field of corporate finance. Next, the main concepts of the chapter are presented and illustrated with practical examples. Important key terms are 2 Instructions to Students highlighted in bold print and defined in the margins. Other student aids include charts, tables, and mathematical examples. Each chapter concludes with a summary, a review of important concepts, review questions, and Web exercises. Major parts of the textbook correspond with lessons in your study guide, and your self-checks and examination questions are based on the material in the textbook. Also at the end of most chapters, you'll find a feature called \"Minicase,\" in which the operations of a fictional company are outlined. Each case example highlights an important corporate finance topic. You'll find these case studies interesting and valuable, but reading them is optional. At the end of the textbook, you'll find appendices that summarize some important information in an easy-to-find format. Appendix A provides several useful mathematical tables. Appendix B contains a reference list of important equations from each chapter in the textbook. Appendix C contains the answers to selected review questions. The last section of your textbook is a subject index that lists specific page numbers for all the important topics and terms covered in the text. If you need more information, use the subject index to locate the page on which a topic is discussed. COURSE MATERIALS You should have received the following learning materials for this course: 1. Your textbook, Fundamentals of Corporate Finance, Ninth Edition, by Stephen A. Ross, Randolph W. Westerfield, and Bradford D. Jordan, which contains the assigned readings and review questions for selfchecks and examinations Instructions to Students 3 2. Your study guide, which will help you understand major ideas presented and provide background information about specific topics. This study guide also includes Self-checks for each lesson Answers to the self-checks Examinations for the course Graded project assignment Summaries of abbreviations STUDY PLAN To help you understand the information in this course, complete the following steps: 1. Read the introductory material for each assignment. This information, found in the study guide, serves as \"lecture notes\" to help you grasp important concepts presented in your textbook. 2. Quickly skim the textbook pages mentioned in the assignment. Note any key terms that appear in boldface type, and write down these words for future reference. Some students choose to use index cards as study tools. You may write the key term on one side of the card and write the definition of the term on the reverse side. You can also write important financial equations on index cards. If a concept is confusing to you, place a question mark next to it. 3. Carefully reread the assigned pages in your textbook. Make sure you understand all of the information presented in the reading. 4. At the conclusion of each reading, review the summary and questions found in the textbook. If your schedule permits, complete the review exercises and Internet activities so that you may apply the concepts you've learned to real-life situations. 4 Instructions to Students 5. Complete the self-check at the conclusion of each assignment. Check your answers against those found at the end of the study guide. Be sure to review any questions you answered incorrectly. The self-checks are provided to help you prepare for the examination, but the school doesn't grade them. Thus, do not submit your answers to these self-checks for grading. 6. When you feel you understand all of the material presented in the lesson assignments, you may take the examination for that lesson. Remember, you may e-mail your instructor whenever you need help. The instructor can provide answers to any questions you may have about the course or your study materials. Good luck with your course! Instructions to Students 5 NOTES 6 Instructions to Students For: Read in this study guide: Read in the textbook: Pages 18-26 Pages 46-86 Assignment 1 Pages 10-16 Assignment 3 Pages 27-31 Assignment 2 Examination 06058401 Pages 1-45 Pages 471-507 Material in Lesson 1 Lesson 2: Future Cash Flow Valuation For: Read in this study guide: Read in the textbook: Pages 44-53 Pages 144-189 Assignment 4 Pages 38-42 Assignment 6 Pages 54-61 Assignment 5 Assignment 7 Pages 62-64 Examination 06058501 Lesson 3: Capital Budgeting For: Pages 298-334 Pages 83-87 Examination 06058601 Lesson 4: Risk and Return Assignment 12 Material in Lesson 2 Pages 77-82 Assignment 10 Assignment 11 Pages 231-259 Read in the textbook: Pages 72-76 For: Pages 190-230 Read in this study guide: Assignment 8 Assignment 9 Pages 119-143 Pages 260-297 Pages 335-364 Material in Lesson 3 Read in this study guide: Read in the textbook: Pages 100-104 Pages 401-436 Pages 94-98 Examination 06058701 Pages 365-400 Material in Lesson 4 Assignments Lesson 1: Corporate Finance Overview 7 Lesson 5: Cost of Capital and Financial Policy and Options For: Assignment 13 Assignment 14 Read in this study guide: Pages 112-116 Pages 117-123 Examination 06058801 Read in the textbook: Pages 437-470 Pages 508-545 Material in Lesson 5 Graded Project 06058901 8 Lesson Assignments INTRODUCTION Lesson 1 Corporate Finance Overview In Lesson 1, you'll learn some important fundamentals of corporate finance. Much of the material in this lesson (and in others to follow later) will require you to perform mathematical calculations. You can use a regular calculator, a financial calculator, or a computer program such as Excel to assist you when you encounter example problems. In Assignment 1, you'll cover Chapters 1 and 2 in your textbook. Chapter 1 includes an introduction to corporate finance, and discusses the importance of the financial manager in the corporate environment. You'll review the basic forms of business organization, and learn how financial management operates in each type of business. Then, you'll be introduced to financial markets, and learn how cash flows affect business operations. Chapter 2 covers the basics of financial statements, including the balance sheet and income statement. You'll learn about corporate taxes and how they're calculated. You'll also learn more about cash flow in a business, and how the various types of cash flows are calculated. Assignment 2 includes the material from Chapter 3. This chapter is a more in-depth look at financial statements and long-term financial planning. Assignment 3 covers Chapter 15. This assignment focuses on long-term financial planning and growth, and is designed to give you a broad understanding of capital markets. Your textbook identifies some useful Web sites that can help familiarize you with these concepts. OBJECTIVES When you complete this lesson, you'll be able to Describe the main components of a balance sheet Apply the basic equations used to calculate a firm's working capital and cash flow 9 Read and understand basic balance sheets and income statements Discuss the differences between a firm's average and marginal income tax rates Use the common-sized financial statement approach to analyze a firm's balance sheet and income statement ASSIGNMENT 1 Read this introduction to Assignment 1. Then, read Chapters 1-2, pages 1-45, in your Fundamentals of Corporate Finance textbook. The Balance Sheet The balance sheet is a snapshot of a firm's financial position, as represented by its assets, liabilities, and equity at a particular point in time. The relationship between assets, liabilities, and owner's equity can be shown with the following formula: Assets = Liabilities + Owner's Equity or A = L + OE Example: Suppose a firm has assets of $10,000 and owner's equity of $4,700. What are the firm's total liabilities? Solution: Substitute the known values ($10,000 and $4,700) into the equation and solve. Assets = Liabilities + Owner's Equity $10,000 = L + $4,700 Solve for L by subtracting $4,700 from both sides of the equation. $10,000 - $4,700 = L + $4,700 - $4,700 $5,300 = L Answer: The firm's total liabilities are $5,300. 10 Corporate Finance Assets are classified as either current or fixed, and liabilities are classified as either current or long-term. Current assets and current liabilities both have a life span of less than one year, which means that they will convert to cash in less than 12 months. A fixed asset has a longer life span, and may be either tangible or intangible. Tangible assets are real objects held by the company (such as equipment), while intangible assets are items such as patents and trademarks. A longterm liability is a debt that's not due within the coming year (such as a five-year loan). The difference between a firm's current assets and current liabilities is called working capital (or net working capital ). The net working capital can be calculated with the following formula: Net Working Capital = Current Assets - Current Liabilities or NWC = CA - CL Example: If your current assets are $2,500 and your current liabilities are $400, what is your net working capital? Is your net working capital a positive or negative amount? Solution: Substitute the known values ($2,500 and $400) into the equation and solve. Net Working Capital = Current Assets - Current Liabilities NWC = $2,500 - $400 NWC = $2,100 Answer: Your net working capital is $2,100, which is a positive amount. Three particularly important measures derived from a firm's balance sheet include liquidity, debt versus equity, and market value versus book value. Lesson 1 11 The Income Statement The income statement provides a measure of a firm's operating performance over a period of time, usually one quarter or one year. The relationship between revenues, expenses, and income can be illustrated with the following formula: Revenues - Expenses = Income or R-E=I In this equation, the income amount represents taxable income (TI) or net income before tax (NIBT). Example: If your revenues are $1,509 and your expenses are $885, what is your income (or taxable income or net income before tax)? Solution: Substitute the known values ($1,509 and $885) into the equation and solve. Revenues - Expenses = Income $1,509 - $885 = I $624 = I Answer: Your income is $624. Taxes Taxes often represent the single largest cash outflow for a firm. Federal marginal tax rates for corporations vary from 15 percent to 39 percent (depending on the amount of a firm's income), but never exceed an average tax rate of 35 percent. The average tax rate is a firm's tax bill divided by its taxable income. The marginal tax rate is the amount of tax payable on the next dollar earned. The marginal tax rates for corporations that were in effect for the year 2007 are shown in Table 1. 12 Corporate Finance Table 1 MARGINAL TAX RATES FOR CORPORATIONS Taxable Income Taxable Income More Than Less Than $0 $50,000 15% $50,001 $75,000 25% $75,001 $100,000 34% $100,001 $335,000 39% $335,001 $10,000,000 34% $10,000,001 $15,000,000 35% $15,000,001 $183,333,334 38% $183,333,334 Tax Rate 35% Example: Suppose a corporation has a taxable income of $300,000. What is the firm's corporate income tax? Solution: First, calculate the 15 percent portion of the tax. 15% of $50,000 = ? 0.15 \u0001 $50,000 = $7,500 Calculate the 25 percent portion of the tax. 25% of ($75,000 - $50,000) = ? 25% of $25,000 = ? 0.25 \u0001 $25,000 = $6,250 Calculate the 34 percent portion of the tax. 34% of ($100,000 - $75,000) = ? 34% of $25,000 = ? 0.34 \u0001 $25,000 = $8,500 Calculate the 39 percent portion of the tax. 39% of ($300,000 - $100,000) = ? 39% of $200,000 = ? 0.39 \u0001 $200,000 = $78,000 Add all of the tax amounts together to find the total tax. $7,500 + $6,250 + $8,500 = $78,000 = $100,250 Lesson 1 13 Answer: The firm's corporate income tax is $100,250. Example: For the same corporation described in the previous example, what is the firm's marginal tax rate? Solution: The firm earned $300,000. If it earned one additional dollar over that amount, the tax on that dollar would be 39 cents. Answer: Therefore, the firm's marginal tax rate is 39%. Example: For the same corporation, find the firm's average tax rate. Solution: To calculate the firm's average tax rate, divide the total corporate tax ($100,250) by the taxable income ($300,000). $100,250 \u0002 $300,000 = 0.33417, or 33.417% Answer: The average tax rate is 33.417 percent. Taxes represent an expense, as shown by the following formulas: Revenues - Expenses = Income Before Taxes Income Before Taxes - Tax Expense = Net Income After Taxes Example: Again, assume that your revenues are $1,509, your expenses (other than taxes) are $885, and your tax expense is $212. What is your net income? Solution: Substitute the known values into the equations and solve. Revenues - Expenses = Income Before Taxes $1,509 - $885 = Income Before Taxes $624 = Income Before Taxes Income Before Taxes - Tax Expense = Net Income After Taxes $624 - $212 = Net Income After Taxes $412 = Net Income After Taxes Answer: Your income before taxes is $624. Your net income after taxes is $412. State corporate tax rates may also apply. 14 Corporate Finance Cash Flow Perhaps the most important piece of financial information that can be obtained from financial statements is cash flow (CF), as reported on the statement of cash flows. The statement of cash flows is covered in more detail in Lesson 2. Operating cash flow (OCF) is the amount of cash generated from a firm's normal business activities. The OCF can be calculated by using the following equation: OCF = Earnings Before Interest and Taxes (EBIT) + Depreciation - Taxes Example: Assume that a firm has $5,296 in earnings before interest and taxes, $923 in depreciation expense, and $419 in taxes. What is the firm's operating cash flow? Solution: Substitute the known values into the equation and solve. OCF = EBIT + Depreciation - Taxes OCF = $5,296 + $923 - $419 OCF = $5,800 Answer: The firm's operating cash flow is $5,800. Review of Abbreviations Throughout Assignment 1 of this first lesson, you've been exposed to a variety of abbreviations commonly used by financial professionals. The following table lists some of the important abbreviations that you should remember. Lesson 1 15 ABBREVIATION A MEANING Assets AD Accumulated depreciation B/S Balance sheet CA Current assets CF Cash flow CEO Chief executive officer CFO Chief financial officer CL Current liabilities D Depreciation E Expenses EBIT Earnings before interest and taxes EPS Earnings per share FA GAAP I/S L Fixed assets Generally accepted accounting practices Income statement Liabilities LLC Limited liability company NFA Net fixed assets NI Net income NIBT Net income before tax NWC Net working capital NYSE New York Stock Exchange OCF OE OTC R SEC Operating cash flow Owner's equity Over the counter Revenues Securities and Exchange Commission TI Taxable income WC Working capital After you've carefully read pages 1-45 in the Fundamentals of Corporate Finance textbook, complete Self-Check 1. Check your answers with those provided at the back of this study guide. When you're sure you understand the material from Assignment 1, move on to Assignment 2. 16 Corporate Finance Self-Check 1 At the end of each section of Corporate Finance, you'll be asked to pause and check your understanding of what you've just read by completing a \"Self-Check\" exercise. Answering these questions will help you review what you've studied so far. Please complete Self-Check 1 now. Indicate whether each of the following statements is True or False. ______ 1. The basic equation used on a firm's balance sheet is Assets + Liabilities = Owner's Equity. ______ 2. Working capital (or net working capital) is calculated with the equation Current Assets - Current Liabilities = Working Capital. ______ 3. The basic equation used on a firm's income statement is Revenues - Expenses = Income. ______ 4. A firm's marginal tax rate and average income tax rate are always the same. ______ 5. The basic equation used to calculate a firm's net income is Revenues - (Nontax) Expenses - Tax Expense = Net Income. ______ 6. The basic equation used to calculate a firm's operating cash flow is Earnings Before Interest and Taxes + Depreciation Expense + Tax Expense = Operating Cash Flow. In the \"Questions and Problems\" section on pages 41-42 of the Fundamentals of Corporate Finance textbook, answer questions 1, 2, 6, 7, and 10. Check your answers with those on page 139. Lesson 1 17 ASSIGNMENT 2 Read this introduction to Assignment 2. Then, read Chapter 3, pages 46-86, in your Fundamentals of Corporate Finance textbook. Cash Flow and Financial Statements Business activities that increase the flow of cash represent sources of cash. Activities that spend, consume, or decrease cash represent uses of (or applications of ) cash. The statement of cash flows provides a summary of both sources and uses of cash flow. Cash flow, including both sources of cash and uses of cash, can be evaluated by looking at a company's balance sheet. Compare the balance from the end of a period to the balance at the beginning of the next period. Recall that a balance sheet represents the financial position for a firm at a point in time. Additional cash flow can be evaluated by reviewing the company's income statement for a particular period. Remember that an income statement summarizes the results of business operations for a period of time. Therefore, a statement of cash flow is a financial statement that summarizes the cash flows for a period of time. Figure 1 summarizes what you've just learned. FIGURE 1This illustration shows the relationship between the balance sheet, the income statement, and the cash flow statement. 18 Corporate Finance It's very important that you understand the purpose of the balance sheet and the income statement before you proceed to study the cash flow statement. Example: Assume that a firm provides the following balance sheet information. You then use this information to develop an Excel spreadsheet, where you show the net result of debits and credits. Table 2 PRUFROCK CORPORATION 2008 and 2009 Balance Sheets ($ in millions) 2008 2009 Change $84 $98 +$14 Accounts Receivable $165 $188 +$23 Inventory $393 $422 +$29 $642 $708 $2,731 $2,880 $3,373 $3,588 Assets Current Assets Cash Total Fixed Assets Net Plant and Equipment Total Assets +$149 Liabilities and Owners' Equity Current Liabilities Accounts Payable $312 $344 +$32 Notes Payable $231 $196 -$35 $543 $540 $531 $457 -$74 $500 $550 +$50 $1,799 $2,041 +$242 $2,299 $2,591 $3,373 $3,588 Total Long-Term Debt Owners' Equity Common Stock and Paid-In Surplus Retained Earnings Total Total Liabilities and Owners' Equity Net Lesson 1 $0 19 Solution: This example uses the same information developed and provided on page 48 of your textbook, but in a slightly modified form. In Table 2, for example, note that debits equal credits in the balance sheet for each year. This same relation has been retained in the change column, so that changes net out to zero. Also, note that the subtotals that would otherwise result in double-counting haven't been extended to the change column. Table 3 summarizes the sources and uses of cash from the firm's balance sheet. Table 3 SUMMARY OF USES AND SOURCES OF CASH Sources of Cash: Increase in Accounts Payable $32 Increase in Common Stock $50 Increase in Retained Earnings Total Sources $242 $324 Uses of cash: Increase in Accounts Receivable $23 Increase in Inventory $29 Decrease in Notes Payable $35 Decrease in Long-Term Debt $74 Net Fixed Asset Acquisitions $149 Total Uses $310 Net Addition to/Source of Cash $14 Add: Beginning Cash $84 Equals: Ending Cash $98 Standardized Financial Statements Standardized financial statements are also referred to as common-sized financial statements. This standardized approach can be applied to a firm's balance sheet, income statement, and/or statement of cash flows. When these financial statements are standardized, it becomes easier to 20 Corporate Finance make percentage comparisons for the same firm, from period to period or point to point. It's also easier to make comparisons between different-sized firms within an industry. Common-sized balance sheets allow comparisons between the components of assets, liabilities, and owners' equity (recall that A = L + OE ), where assets are set to equal 100 percent. Common-sized income statements allow comparisons between expenses, where net sales or revenues are set to equal 100 percent. Example: Shown here is the balance sheet from page 48 of your textbook. Convert it to a common-sized format. PRUFROCK CORPORATION 2008 and 2009 Balance Sheets ($ in millions) 2006 2007 $84 $98 Accounts Receivable $165 $188 Inventory $393 $422 $642 $708 $2,731 $2,880 $3,373 $3,588 Assets Current Assets Cash Total Fixed Assets Net Plant and Equipment Total Assets Liabilities and Owners' Equity Current Liabilities Accounts Payable $312 $344 Notes Payable $231 $196 $543 $540 $531 $457 $500 $550 $1,799 $2,041 $2,299 $2,591 $3,373 $3,588 Total Long-Term Debt Owners' Equity Common Stock and Paid-In Surplus Retained Earnings Total Total Liabilities and Owners' Equity Lesson 1 21 Solution: The following is a common-sized balance sheet consistent with the sheet on page 52 of your textbook. PRUFROCK CORPORATION Common-Size Balance Sheets 2008 and 2009 2008 2009 Change Assets Current Assets Cash 2.5% 2.7% +0.2% Accounts Receivable 4.9% 5.2% +0.3% 11.7% 11.8% +0.1% 19.1% 19.7% +0.6% 80.9% 80.3% -0.6% 100.0% 100.0% 0.0% Inventory Total Fixed Assets Net Plant and Equipment Total Assets Liabilities and Owners' Equity Current Liabilities Accounts Payable 9.2% 9.6% +0.4% Notes Payable 6.8% 5.5% -1.3% 16.0% 15.1% -0.9% 15.7% 12.7% -3.0% Common Stock and Paid-In Surplus 14.8% 15.3% +0.5% Retained Earnings 53.3% 56.9% +3.6% 68.1% 72.2% +4.1% 100.0% 100.0% 0.0% Total Long-Term Debt Owners' Equity Total Total Liabilities and Owners' Equity Ratio Analysis Ratio analysis is used to examine and compare a firm's various financial characteristics. Financial ratios are usually classified in the following categories: 1. Short-term solvency, or liquidity, ratios 2. Long-term solvency ratios 3. Asset management, or turnover, ratios 4. Profitability ratios 5. Market value ratios 22 Corporate Finance Short-term solvency, or liquidity, measures include the following: The current ratio The quick or acid-test ratio (which excludes a firm's inventory in the numerator, as it's the least liquid of the current assets) The cash ratio The net working capital to total assets ratio The interval measure ratio Long-term solvency measures include the following: The total debt ratio The debt-equity ratio The equity multiplier ratio The long-term debt ratio The times interest earned ratio The cash coverage ratio Asset management, or turnover, measures include the following: The inventory turnover ratio The days' sales in inventory ratio The inventory turnover ratio The days' sales in receivables ratio The net working capital turnover ratio The fixed asset turnover ratio The total asset turnover ratio Lesson 1 23 Profitability measures include the following: The profit margin ratio The return on assets ratio The return on equity ratio Market value measures include the following: The price-earnings ratio The price-sales ratio The market-to-book ratio Example: Assume that a firm has current assets of $12,674 and current liabilities of $9,260. What is the firm's current ratio? Solution: To find the firm's current ratio, divide current assets by current liabilities. Current Ratio = Current Assets \u0002 Current Liabilities Current Ratio = $12,674 \u0002 $9,260 Current Ratio = 1.37 Answer: The firm's current ratio is 1.37. The DuPont Identity The DuPont Corporation popularized an equation, called the DuPont identity, that can be used to examine return on assets (ROA) and return on equity (ROE). In the DuPont identity, the difference represents a reflection on the use of debt financing. The identity decomposes ROE into three components: operating efficiency, asset use efficiency, and financial leverage. Figure 3.1 on page 68 of your textbook provides an excellent flowchart of this information. While you should familiarize yourself with the DuPont identity, it isn't necessary for you to commit it to memory. 24 Corporate Finance Example: If a firm has a return on assets of 14.28% and an equity multiplier of 1.29, what is this firm's return on equity? Solution: To find the ROE, multiply the ROA by the equity multiplier. ROE = ROA \u0001 Equity Multiplier ROE = 14.28% \u0001 1.29 ROE = 0.1428 \u0001 1.29 ROE = 0.1842, or 18% Answer: The firm's ROE is 18%. Using Financial Statement Information Market information about a firm's activities, whether it's good news or bad news, will often have a significant and timely effect on a firm's stock price. Good news may include information about a new contract that will increase revenues, or a buyout offer. Bad news may reveal that the Securities and Exchange Commission (SEC) is investigating the firm's financial statements. News of this type may have more effect on a firm's stock price than actual accounting information. However, the evaluation of historical financial statement information provides the foundation for use by both internal and external users. For example, when a firm's current ratio or net working capital position is improving over time, or if the firm's financial ratios are improving (as compared to other firms in the same industry), the fact will be viewed favorably by observers. Example: Assume that Firm A has a negative working-capital position. The firm's current liabilities are higher than its current assets. This represents a negative working-capital position and has led to a decline in the firm's stock price. However, while the firm's stock price has declined from $10 per share to $2 per share, a buyout offer has just been announced at $5 per share. The information contained in the firm's financial statements, the negative working-capital position, and the poor current ratio is information that's Lesson 1 25 based on financial statements. However, the news announcement that Firm B is willing to pay $5 per share for Firm A results in an increase in Firm A's stock price to $4.90 per share. Which information is more relevant or reliable? Solution: The negative working-capital position, where current liabilities exceeded current assets, probably led to a decline in the firm's stock price. The fact that Firm B is willing to pay $5 per share led to the increase in the firm's stock price. Answer: In this example, the offer for a buyout (market information) is more relevant than the financial statement information. Review of Abbreviations Throughout Assignment 2, you've been exposed to a variety of abbreviations commonly used by financial professionals. The following table summarizes some of the important abbreviations you should remember from this assignment. ABBREVIATION MEANING NWC Net working capital PE Ratio Price-earnings ratio ROA Return on assets ROE Return on equity SEC Securities and Exchange Commission After you've carefully read pages 46-86 in the Fundamentals of Corporate Finance textbook, complete Self-Check 2. Check your answers with those provided at the back of this study guide. When you're sure you understand the material from Assignment 2, move on to Assignment 3. 26 Corporate Finance Self-Check 2 Indicate whether each of the following statements is True or False. ______ 1. The balance sheet presents a firm's financial position at a point in time. ______ 2. The income statement presents a firm's results of operation for a point in time. ______ 3. The statement of cash flows presents a firm's sources and uses of cash for a period of time. ______ 4. Standardized financial statements provide a means for comparing a firm's balance sheet, from period to period, by setting total assets at 100 percent and presenting the components of the balance sheet as a percentage of total assets. ______ 5. The current and quick ratios are examples of short-term solvency or liquidity measures. ______ 6. Financial statement information and financial ratios are always more useful than market information or recent good or bad news releases about a firm. In the \"Questions and Problems\" section on pages 81-85 of the Fundamentals of Corporate Finance textbook, answer questions 1, 2, and 26. Check your answers with those on page 139. ASSIGNMENT 3 Read this introduction to Assignment 3. Then, read Chapter 15, pages 471-507, in your Fundamentals of Corporate Finance textbook. The Financing Life Cycle of a Firm Banks and financial institutions rarely make loans to entrepreneurs who have ideas but no assets. For people who are seeking financing in the start-up or early stages of a firm's Lesson 1 27 life cycle, venture capital (VC) may be the only available means of financing. Venture capitalists may require a high rate of return, due to the high risk associated with a start-up enterprise led by those without a successful track record. Selling Securities to the Public Firms that have publicly traded securities listed on a national exchange must file documents and financial statements with the Securities and Exchange Commission (SEC). You can access a significant amount of information about securities, as well as registrations and financial statements for publicly traded firms, on the SEC Web site: http://www.sec.gov Alternative Issue Methods When a company decides to issue a new security, the first public offering made by the company is called an initial public offering or IPO. For equity sales, the public issue may be made by way of a general cash offer or a rights offer (also called a rights offering). You can learn more about initial public offerings of stock at the following Web site: http://www.ipohome.com Underwriters Underwriters are investment firms that act as intermediaries between a company that's selling securities and public investors. Underwriters are usually involved in public offerings of securities for cash, and facilitate the pricing and sale of new securities. Often, because of the risk involved in underwriting, the underwriters will combine to form a group of brokers and dealers called a syndicate. These brokers and dealers work to stimulate interest in the firm and its securities. 28 Corporate Finance IPOs and Underpricing It's often difficult for underwriters to determine the correct price for an initial public offering of a new stock. For this reason, IPOs are sometimes overpriced or underpriced as compared to their true market value. If an IPO is overpriced, it may be unsuccessful and have to be withdrawn from the market. In contrast, if the IPO is underpriced, the existing shareholders will have an opportunity loss when they sell their shares. New Equity Sales and the Value of the Firm Seasoned offerings represent additional offerings of securities by firms that already have outstanding securities. Seasoned offerings tend to result in a decline in a firm's already existing equity security. The reasons for this may include managerial information, the use of debt, and/or new equity security issuance costs. The Costs of Issuing Securities The costs of issuing securities can be classified in the following six categories: 1. Gross spread, which consists of the direct fees paid by the issuer to the underwriters 2. Other direct expenses, which are direct costs incurred by the issuer that aren't part of the compensation to underwriters 3. Indirect expenses, which include the costs of management time working on the new issue and aren't reported on the prospectus 4. Abnormal returns, which is the drop in the price of existing stock on the announcement of the issue Lesson 1 29 5. Underpricing, which includes losses that arise from selling the stock below the true market value 6. The Green Shoe option, which gives the underwriters the opportunity to buy additional shares at the offer price Rights A preemptive right, when included in a firm's articles of incorporation, requires that existing shareholders be provided the first right to purchase additional shares during a new issue of common stock. This right helps the existing shareholders to avoid dilution of their ownership interests. Dilution Dilution refers to the loss of existing shareholder value. There are several kinds of dilution, as follows: 1. Dilution of percentage ownership 2. Dilution of market value 3. Dilution of book value and earnings per share Issuing Long-Term Debt More than 50 percent of all long-term debt is issued privately. The two basic forms of direct long-term financing include term loans (loans that have maturities of one to five years) and private placements (loans that have longer maturities as compared to term loans). Shelf Registration Shelf registration is a type of registration permitted by the SEC, and it's available for both debt and equity issues. Shelf registrations permit corporations to register offerings that are reasonably expected to sell within the next two years, and to sell the securities at any time within a two-year window. 30 Corporate Finance Review of Abbreviations Throughout Assignment 3, you've been exposed to a variety of abbreviations commonly used by financial professionals. The following table lists some of the important abbreviations you should remember from this assignment. ABBREVIATION IPO MEANING Initial public offering LT Long term VC Venture capital After you've carefully read pages 471-507 in the Fundamentals of Corporate Finance textbook, complete Self-Check 3. Check your answers with those provided at the back of this study guide. When you're sure you understand the material from these three assignments, complete the examination for Lesson 1. Self-Check 3 Indicate whether each of the following statements is True or False. ______ 1. For people who are seeking financing in the start-up stages of a firm's life cycle, venture capital may provide the only available means of financing. ______ 2. For firms that have publicly traded securities on national exchanges, it's optional to file documents and financial statements with the Securities and Exchange Commission (SEC). ______ 3. Underwriters are usually involved in a public offering of securities for cash. (Continued) Lesson 1 31 Self-Check 3 ______ 4. Preemptive rights, if provided for in the firm's articles of incorporation, prevent existing shareholders from being provided the first right of refusal to purchase any additional shares to avoid dilution of their ownership interests. ______ 5. The abbreviation IPO stands for internal public offering. ______ 6. Shelf registrations permit corporations to register an offering that's reasonably expected to sell within the next two years; however, the firm may sell the security at any time within the two-year window. In the \"Questions and Problems\" section on pages 505-507 of the Fundamentals of Corporate Finance textbook, answer questions 2 (a, b, and c only), 6, 8, and 14. Check your answers with those on page 140. 32 Corporate Finance EXAMINATION NUMBER 06058401 Whichever method you use in submitting your exam answers to the school, you must use the number above. For the quickest test results, go to http://www.www.pennfoster.edu When you feel confident that you have mastered the material in Lesson 1, go to http://www.www.pennfoster.edu and submit your answers online. If you don't have access to the Internet, you can phone in or mail in your exam. Submit your answers for this examination as soon as you complete it. Do not wait until another examination is ready. Questions 1-20: Select the one best answer to each question. 1. Which of the following would result in a decrease in cash flow and a use of cash? A. B. C. D. A decrease in notes payable An increase in long-term debt A decrease in inventory A decrease in common stock 2. In the United States, for the 2007 tax year, federal corporate income tax rates never exceeded an average rate of A. 15%. B. 35%. C. 39%. D. 34%. 3. A firm has assets of $60,000 and owners' equity of $33,000. Which of the following is the correct balance of the firm's liabilities? A. $33,000 B. $27,000 C. $93,000 D. $60,000 Examination Lesson 1 Corporate Finance Overview 33 4. Which of the following would result in an increase in cash flow and a source of cash? A. B. C. D. A decrease in notes payable A decrease in long-term debt An increase in inventory An increase in common stock 5. A firm has current assets of $10,000 and current liabilities of $7,000. Which of the following is the correct net working capital for the firm? A. $10,000 B. $7,000 C. $3,000 D. $13,000 6. If a firm has an accounts receivable balance of $18,800 at the end of 2007 and $16,500 at the end of 2008, which of the following statements about accounts receivable is correct? A. B. C. D. Accounts Accounts Accounts Accounts receivable receivable receivable receivable decreased by $2,300 and represented a use of cash. increased by $2,300 and represented a source of cash. decreased by $2,300 and represented a source of cash. increased by $2,300 and represented a use of cash. 7. If a firm has revenues of $15,090 and expenses of $8,850, what is the firm's taxable income? A. $15,090 B. $8,850 C. $6,240 D. $23,940 8. Which of the following statements about the issuance of an initial public offering (IPO) is correct? A. B. C. D. IPOs IPOs IPOs IPOs may be either underpriced or overpriced. are never overpriced. are never underpriced. are always correctly priced. 9. If a firm has revenues of $15,090, operating expenses of $8,850, and a tax expense of $2,120, what is the firm's net income? A. $8,850 B. $4,120 C. $6,240 D. $8,360 10. When you're preparing a common-sized balance sheet, which of the following measures is set to equal 100 percent? A. Total liabilities B. Total assets 34 C. Total owners' equity D. Cash Examination, Lesson 1 11. Suppose that a corporation has a taxable income of $200,000. What is the firm's corporate income tax for the current tax year? (You can use the following table to calculate the firm's U.S. federal corporate tax.) Taxable Income Taxable Income Tax More Than Less Than Rate $0 $50,000 15% $50,001 $75,000 25% $75,001 $100,000 34% $100,001 $335,000 39% $335,001 $10,000,000 34% $10,000,001 $15,000,000 35% $15,000,001 $183,333,334 38% $18,333,334 A. $78,000 B. $6,250 35% C. $39,000 D. $61,250 12. Using the same table and information provided in Question 11, what is the firm's average tax rate? A. 39% B. 30.625% C. 34% D. 31.625% 13. Using the same table and information provided in Question 11, what is the firm's marginal tax rate? A. 39% B. 30.625% C. 34% D. 31.625% 14. Dilution refers to the loss of shareholder value, and may be represented by all of the following except dilution of A. B. C. D. ownership percentage. market value. the firm's current ratio. book value per share. 15. If a firm has $6,940 in earnings before interest and taxes, $650 in depreciation expense, and $2,120 in taxes, what is the firm's operating cash flow? A. $4,120 B. $5,470 Examination, Lesson 1 C. $6,240 D. $9,710 35 16. The type of financial statement that summarizes the sources and uses of cash over a specified period of time is called the A. B. C. D. statement of cash flows. income statement. balance sheet. inventory ratio statement. 17. The current ratio falls within which of the following classifications of financial ratios? A. B. C. D. Long-term solvency measures Asset management or turnover measures Short-term solvency or liquidity measures Profitability measures 18. If a firm has an accounts payable balance of $34,400 at the end of 2007 and $31,200 at the end of 2008, which of the following statements about accounts payable is correct? A. B. C. D. Accounts Accounts Accounts Accounts payable payable payable payable decreased by $3,200 and represented a use of cash increased by $3,200 and represented a source of cash decreased by $3,200 and represented a source of cash increased by $3,200 and represented a use of cash 19. Which of the following is not one of the six costs of issuing securities? A. Rights offering B. Abnormal returns C. Green Shoe option D. Gross spread 20. In the United States, for the 2007 tax year, federal corporate income tax rates never exceeded a marginal rate of A. 15%. B. 35%. 36 C. 39%. D. 34%. Examination, Lesson 1 INTRODUCTION Lesson 2 Future Cash Flow Valuation In Lesson 2, you'll learn how present values and future values are calculated, and some basics related to corporate stocks and bonds. This lesson includes four assignments. In Assignment 4, you'll cover the material in Chapter 5 of your textbook. This chapter discusses the time value of money, and you'll learn how to calculate interest on various types of investments. Assignment 5 includes the topics from Chapter 6. You'll learn about annuities and perpetuities, and about the effect of compounding interest. You'll also learn about various types of loans and how loans are amortized. In Assignment 6, you'll review the concepts from Chapter 7. The main focus of this chapter is bonds. Bonds form the debt component of a company's capital structure. You'll learn about different types of bonds, their valuation, features, ratings, and yields. Assignment 7 covers the material in Chapter 8. This chapter is an in-depth look at stocks and stock markets. Stocks are the equity component of a firm's capital structure. You'll learn how common stocks and preferred stocks differ, and how various stocks are valued. OBJECTIVES When you complete this lesson, you'll be able to Calculate present values and future values Explain the concepts of discounting and compounding Discuss the differences between an ordinary annuity and an annuity due Describe how returns are generated by simple and compound interest rates 37 Explain how debt and equity securities work Define what a bond is and discuss the different types of bonds Explain the differences between common stocks and preferred stocks Summarize the basic differences between debt and equity financing alternatives ASSIGNMENT 4 Read this introduction to Assignment 4. Then, read Chapter 5, pages 119-143, in your Fundamentals of Corporate Finance textbook. Future Value and Compounding The future value (FV) is the amount of money an investment will grow to over a period of time at a particular interest rate (or rate of return). Compounding is the process of accumulating interest on an investment over time, for more than one period. Compounding also includes the interest on interest or compound interest, which is the interest earned on the reinvestment of previous interest payments. This differs from simple interest, where the interest isn't reinvested. Simple interest is earned each period, but only on the original principal. Let's look at an example problem. Example: Suppose that today, you deposit $2,000 in an account that pays 10 percent interest annually. How much will you have in the account after one year? Solution: This calculation is relatively simple. In this example, you've been provided with three variables. The present value is the amount you begin with, which is $2,000. The number of (compounding) time periods is one year. The interest rate is 10 percent annually. The missing variable that you need to calculate is the future value, which is the value of the investment at the end of one year. 38 Corporate Finance Substitute the known values into the equation and solve: Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $2,000 \u0001 (1.0 + 0.10)1 FV = $2,000 \u0001 (1.1)1 FV = $2,000 \u0001 1.1 FV = $2,200 Answer: The future value of a $2,000 investment invested at 10 percent per year for 1 year is $2,200. Now, consider what happens to the same investment when it's deposited for a 2-year period. Example: Today, you deposit $2,000 into an account that pays 10 percent interest annually. How much will you have in the account after 2 years? Solution: In this problem, the present value is $2,000, the number of time periods is 2 years (two compounding periods), and the interest rate is 10 percent per year. Substitute the values into the equation and solve to calculate the future value of the investment. Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $2,000 \u0001 (1.0 + 0.10)2 FV = $2,000 \u0001 (1.1)2 FV = $2,000 \u0001 1.21 FV = $2,420 Answer: The future value of $2,000 invested at 10 percent per year for 2 years is $2,420. Now, consider what happens to the same investment when it's deposited for a 3-year period. Example: Today, you deposit $2,000 into an account that pays 10 percent annually. How much will you have in the account after 3 years? Solution: In this problem, the present value is $2,000, the number of time periods is 3 years (three compounding periods), and the interest rate is 10 percent per year. Substitute the values into the equation and solve to calculate the future value of the investment. Lesson 2 39 Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $2,000 \u0001 (1.0 + 0.10)3 FV = $2,000 \u0001 (1.1)3 FV = $2,000 \u0001 1.331 FV = $2,662 Answer: The future value of $2,000 invested at 10 percent per year for 3 years is $2,662. The future value of an investment will be higher with higher interest rates and lower with lower interest rates. Example: Today, you deposit $1,000 into an account that pays 12 percent annually. How much will you have in the account after 4 years? Solution: In this problem, the present value is $1,000, the number of time periods is 4 years (four compounding periods), and the interest rate is 12 percent per year. Substitute the values into the equation and solve to calculate the future value of the investment. Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $1,000 \u0001 (1.0 + 0.12)4 FV = $1,000 \u0001 (1.12)4 FV = $1,000 \u0001 1.573519 FV = $1,573.52 Answer: The future value of $1,000 invested at 12 percent per year for 4 years is $1,573.52. Present Value and Discounting Finding the present value (PV) of an investment is the opposite of calculating the future value. The present value is the current value of a future investment discounted at the appropriate discount rate. You would calculate the present value when you need to determine how much money to invest today to obtain some future goal. This is a useful tool in a variety of cases, including retirement planning. Discounting is the process of finding the present value of some future amount. Let's look at another example problem. 40 Corporate Finance Example: Suppose you want to know how much money to invest today to reach a future goal of $2,000. You want to invest money for one year in an account that pays 10 percent interest annually. Solution: For this problem, the future value of the investment is $2,000, the number of time periods is one year, and the interest rate is 10 percent per year. The missing variable that you need to calculate is the present value, which is the amount of money you'll need to invest today to reach your future goal. Substitute the values into the following equation and solve to calculate PV: Present Value = Future Value \u0002 [(1.0 + Interest Rate )N ] PV = $2,000 \u0002 [(1.0 + 0.10)1] PV = $2,000 \u0002 [(1.1)1] PV = $2,000 \u0002 1.1 PV = $1,818.18 Answer: You'll need to invest $1,818.18 today, at an interest rate of 10 percent per year, to have $2,000 after one year. We've discounted the desired future value to arrive at the present value. The present value of an investment will be higher with lower interest (or discount) rates and lower with higher interest (or discount) rates. More about Present and Future Values The present value factor is the reciprocal of the future value factor. This means that the present value factor is equal to 1 divided by the future value factor, as shown here: Future Value Factor = (1 + I )N Present Value Factor = 1/(1 + I )N ABBREVIATION Lesson 2 MEANING FV Future value PV Present value 41 Review of Abbreviations Throughout Assignment 4, you've been exposed to a variety of abbreviations commonly used by financial professionals. The following table summarizes the important abbreviations you should remember from this assignment. After you've carefully read pages 119-143 in the Fundamentals of Corporate Finance textbook, complete Self-Check 4. Check your answers with those provided at the back of this study guide. When you're sure you understand the material from Assignment 4, move on to Assignment 5. 42 Corporate Finance Self-Check 4 Indicate whether each of the following statements is True or False. ______ 1. Compounding involves earning interest for only one time period, and includes interest on interest or compound interest. ______ 2. In the case of simple interest, the interest earned on the investment isn't reinvested, so interest is earned for each period only on the original principal. ______ 3. Discounting is the process of finding the present value of some future investment amount. ______ 4. The future value of an investment will be higher with higher interest rates and lower with lower interest rates. ______ 5. The present value of an investment will be higher with lower interest rates and lower with higher interest rates. ______ 6. The future value factor is the reciprocal of the present value factor. In the \"Questions and Problems\" section on page 141 of the Fundamentals of Corporate Finance textbook, answer questions 1, 2, and 3. Check your answers with those on page 140. Lesson 2 43 ASSIGNMENT 5 Read this introduction to Assignment 5. Then, read Chapter 6, pages 144-189, in your Fundamentals of Corporate Finance textbook. Future and Present Values of Multiple Cash Flows In the last assignment, you learned about future value, with a focus on single deposits. Now, you'll learn about multiple cash flows. As you work through this assignment, review the examples carefully, preferably using a computer program such as Excel. This practice will benefit you, both in your work on this course and in your personal financial planning endeavors. For example, once you've mastered the problems in this assignment, you'll be able to understand how payments are calculated for your home mortgage, automobile loan, cell phone, or lease payments. Example: Today, you deposit $2,000 into an account that pays 12 percent annually. In one year, you'll deposit another $3,000 in the account. How much will you have in the account after 2 years? Solution: In this problem, the present value is $2,000, the number of time periods is 2 years (two compounding periods), and the interest rate is 12 percent per year. Substitute the values into the following equation and solve to calculate the future value of the investment at the end of the first year: Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $2,000 \u0001 (1 + 0.12)1 FV = $2,000 \u0001 (1.12)1 FV = $2,000 \u0001 1.12 FV = $2,240 At the end of the first year, add the second deposit of $3,000. $2,240 + $3,000 = $5,240 The value at the end of the first year is $5,240. Now, calculate the value at the end of the second year (with interest). 44 Corporate Finance Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $5,240 \u0001 (1 + 0.12)1 FV = $5,240 \u0001 (1.12)1 FV = $5,240 \u0001 1.12 FV = $5,868.80 Answer: The final value of the investment at the end of the second year is $5,868.80. Now, let's look at a problem that involves the present value of an investment with multiple cash flows. Example: Suppose you need $2,000 in one year and $3,000 more in two years. If you can get an interest rate of 9 percent on your money, how much do you need to invest today to obtain those amounts in the future? Solution: The problem is asking you to determine the present value of the two cash flows at 9 percent. First, calculate the present value of $3,000 in two years at 9 percent. Present Value = Future Value \u0002 [(1.0 + Interest Rate )N ] PV = $3,000 \u0002 [(1.0 + 0.09)2] PV = $3,000 \u0002 [(1.09)2] PV = $3,000 \u0002 1.1881 PV = $2,525.04 Next, calculate the present value of $1,000 in one year at 9 percent. Present Value = Future Value \u0002 [(1.0 + Interest Rate )N ] PV = $2,000 \u0002 [(1.0 + 0.09)1] PV = $2,000 \u0002 [(1.09)1] PV = $2,000 \u0002 1.09 PV = $1,834.86 Finally, add the two values together to determine the total present value. $2,525.04 + $1,834.86 = $4,359.90 Answer: You'll need to invest $4,359.90 today to obtain the desired amounts in the future. Lesson 2 45 Valuing Level Cash Flows: Annuities and Perpetuities An annuity is a fixed, periodic payment that occurs on an investment for a fixed period of time. An ordinary annuity is a series of constant cash flows that occur at the end of each period for a fixed number of periods. An annuity due is an annuity in which the cash flows occur at the beginning of the period. A perpetuity is an annuity in which the cash flows continue forever. Example: An ordinary annuity promises to pay $100 at the end of each of the next four years. If you want to earn 10 percent on your money, how much should you offer for this annuity? Solution: The problem is asking you to determine the present value of this ordinary annuity. In this example, the future value is $100, the interest rate is 10 percent, and the number of compounding periods is four. Substitute these values into the following equation, and calculate the present value. Note that the formula you used previously has been modified to reflect the four separate payments. Present Value = [FV \u0002 (1.0 + I )1] + [FV \u0002 (1.0 + I )2] + [FV \u0002 (1.0 + I )3] + [FV \u0002 (1.0 + I )4] PV = [$100 \u0002 (1.0 + 0.10)1] + [$100 \u0002 (1.0 + 0.10)2] + [$100 \u0002 (1.0 + 0.10)3] + [$100 \u0002 (1.0 + 0.10)4] PV = [$100 \u0002 (1.10)1] + [$100 \u0002 (1.10)2] + [$100 \u0002 (1.10)3] + [$100 \u0002 (1.10)4] PV = [$100 \u0002 1.10] + [$100 \u0002 1.21] + [$100 \u0002 1.331] + [$100 \u0002 1.4641] PV = $90.91 + $82.64 + $75.14 + $68.30 PV = $316.99 Answer: The present value is $316.99, so this is the amount you should offer for the annuity. This information can also be displayed in table form. Figure 2 illustrates an ordinary annuity of $100 per period for four periods, with a discount rate of 10 percent per period. 46 Corporate Finance FIGURE 2This figure illustrates an ordinary annuity. Example: Calculate the present value of an annuity due of $100 per period for four periods, discounted at a rate of 10 percent per period. Solution: In this example, the future value is $100 and the interest rate is 10 percent. You start with a value of $100 and then add the discounted value of $100 paid for each of three compounding periods. Substitute these values into the following equation, and calculate the present value. Note that the formula you used previously has been modified to reflect the separate payments. Present Value = $100 + [FV \u0002 (1.0 + I )1] + [FV \u0002 (1.0 + I )2] + [FV \u0002 (1.0 + I )3] PV = $100 + [$100 \u0002 (1.0 + 0.10)1] + [$100 \u0002 (1.0 + 0.10)2] + [$100 \u0002 (1.0 + 0.10)3] PV = $100 + [$100 \u0002 (1.10)1] + [$100 \u0002 (1.10)2] + [$100 \u0002 (1.10)3] PV = $100 + [$100 \u0002 1.10] + [$100 \u0002 1.21] + [$100 \u0002 1.331] PV = $100 + $90.91 + $82.64 + $75.14 PV = $348.69 Answer: The present value of this annuity due is $348.69. Lesson 2 47 Again, this information can be displayed in the form of a table. Figure 3 illustrates an annuity due of $100 per period for four periods, with a discount rate of 10 percent per period. FIGURE 3This figure illustrates an annuity due. There's another, easier method that can be used to calculate the value of an annuity due. Let's look at this example again. Example: Calculate the present value of an annuity due of $100 per period, discounted at a rate of 10 percent per period. Solution: To find the present value of this annuity due, multiply the ordinary annuity value by (1 + r ), where r is the discount rate. You already calculated the ordinary annuity value of $316.99 in the preceding example problem. PV of Annuity Due = Ordinary Annuity Value \u0001 (1.0 + r ) PV = $316.99 \u0001 (1.0 + 0.10) PV = $316.99 \u0001 1.1 PV = $348.69 Answer: The present value of this annuity due is $348.69. Now, compare the last two example problems, where you calculated the value of the ordinary annuity and the annuity due. The comparison is illustrated in Table 4. 48 Corporate Finance Table 4 COMPARISON OF ORDINARY ANNUITY AND ANNUITY DUE Ordinary Annuity Annuity Due Difference Time Period 0 $0.00 $100 -$100 Time Period 1 $90.91 $90.91 $0.00 Time Period 2 $82.64 $82.64 $0.00 Time Period 3 $75.14 $75.14 $0.00 Time Period 4 $68.30 $0.00 $68.30 $316.99 $348.69 $31.70 Total Notice that, given the same interest rate and number of time periods, an annuity due will always have a higher present value when compared to an ordinary annuity. Comparing Rates: The Effect of Compounding Would you prefer to earn 12 percent interest per year on an investment, compounded annually, or 12 percent interest per year compounded semiannually? To illustrate the power of compounding, let's look at a simple example. Assume that your initial investment is $1,000. Example: You can earn 12 percent interest per year compounded annually, or 12 percent interest per year compounded semiannually. Calculate the principal and interest for each case for one year, based on an initial investment of $1,000. Which interest rate is better? Solution: First, calculate the future value of the investment at 12 percent per year, compounded annually for one year. Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $1,000 \u0001 (1 + 0.12)1 FV = $1,000 \u0001 (1.12)1 FV = $1,000 \u0001 1.12 FV = $1,120 Lesson 2 49 Second, calculate the future value of the investment at 12 percent per year, compounded semiannually for one year. Future Value = Present Value \u0001 (1.0 + Interest Rate )N FV = $1,000 \u0001 (1 + 0.06)2 FV = $1,000 \u0001 (1.06)2 FV = $1,000 \u0001 1.1236 FV = $1,123.60 Answer: The interest that's compounded semiannually produces a future value of $1,123.60, which is slightly higher than the future value compounded annually. Notice that the larger number of compounding periods results in the larger present value, despite the fact that both cases represent annual returns of 12 percent per year. This will always be the case. The greater the number of compounding periods, the greater the future value of the investment. Loan Types and Loan Amortization There are several types of loans available, in which the borrower receives money from a lender today and agrees to repay the money in the future. The type of repayment schedule varies with the type of loan. For example, in a pure discount loan, the borrower receives money today and repays a single lump sum at some time in the future. An interest-only loan requires the borrower to pay interest each period and repay the entire original loan amount at some point in the future. With an amortized loan, the borrower repays parts of the loan amount over time. Most consumer loans (such as mortgages and car loans) are amortized loans. Example: Suppose that you borrow $5,000 at an interest rate of 9 percent per year for five years, and agree to make interest and principal payments in the amount of $1,285.46 at the end of each year. Prepare a loan amortization schedule for each of the five years, showing the beginning principal 50