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.
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
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.
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INSTRUCTIONS TO STUDENTS 1
LESSON ASSIGNMENTS 7
LESSON 1: CORPORATE FINANCE OVERVIEW 9
EXAMINATION 1—LESSON 1 33
LESSON 2: FUTURE CASH FLOW VALUATION 37
EXAMINATION 2—LESSON 2 67
LESSON 3: CAPITAL BUDGETING 71
EXAMINATION 3—LESSON 3 89
LESSON 4: RISK AND RETURN 93
EXAMINATION 4—LESSON 4 107
LESSON 5: COST OF CAPITAL AND FINANCIAL POLICY AND OPTIONS 111
EXAMINATION 5—LESSON 5 125
GRADED PROJECT 129
SELF-CHECK ANSWERS 139
INTRODUCTION Welcome to Corporate Finance! This course will introduce you to some basic financial management and analysis con- cepts 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
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� 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 intro- duced. 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
Instructions to Students2
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 inter- esting 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:
Instructions to Students 3
� 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:
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.
Carefully reread the assigned pages in your textbook. Make sure you understand all of the information presented in the reading.
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.
Instructions to Students4
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
Instructions to Students6
Lesson 1: Corporate Finance Overview For: Read in this Read in study guide: the textbook:
Assignment 1 Pages 10–16 Pages 1–45
Assignment 2 Pages 18–26 Pages 46–86
Assignment 3 Pages 27–31 Pages 471–507
Examination 06058401 Material in Lesson 1
Lesson 2: Future Cash Flow Valuation For: Read in this Read in study guide: the textbook:
Assignment 4 Pages 38–42 Pages 119–143
Assignment 5 Pages 44–53 Pages 144–189
Assignment 6 Pages 54–61 Pages 190–230
Assignment 7 Pages 62–64 Pages 231–259
Examination 06058501 Material in Lesson 2
Lesson 3: Capital Budgeting For: Read in this Read in study guide: the textbook:
Assignment 8 Pages 72–76 Pages 260–297
Assignment 9 Pages 77–82 Pages 298–334
Assignment 10 Pages 83–87 Pages 335–364
Examination 06058601 Material in Lesson 3
Lesson 4: Risk and Return For: Read in this Read in study guide: the textbook:
Assignment 11 Pages 94–98 Pages 365–400
Assignment 12 Pages 100–104 Pages 401–436
Examination 06058701 Material in Lesson 4
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Lesson 5: Cost of Capital and Financial Policy and Options For: Read in this Read in study guide: the textbook:
Assignment 13 Pages 112–116 Pages 437–470
Assignment 14 Pages 117–123 Pages 508–545
Examination 06058801 Material in Lesson 5 Graded Project 06058901
Lesson Assignments8
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Corporate Finance Overview
INTRODUCTION 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 busi- ness, 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
Corporate Finance10
� 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 partic- ular 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.
Lesson 1 11
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 long- term 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.
Corporate Finance12
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 corpora- tions that were in effect for the year 2007 are shown in Table 1.
Lesson 1 13
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 � $50,000 = $7,500
Calculate the 25 percent portion of the tax.
25% of ($75,000 – $50,000) = ?
25% of $25,000 = ?
0.25 � $25,000 = $6,250
Calculate the 34 percent portion of the tax.
34% of ($100,000 – $75,000) = ?
34% of $25,000 = ?
0.34 � $25,000 = $8,500
Calculate the 39 percent portion of the tax.
39% of ($300,000 – $100,000) = ?
39% of $200,000 = ?
0.39 � $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
Table 1
MARGINAL TAX RATES FOR CORPORATIONS
Taxable Income
More Than
Taxable Income
Less Than Tax 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%
$183,333,334 35%
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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 � $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.
Lesson 1 15
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 state- ment 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.
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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.
ABBREVIATION MEANING
A 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 Fixed assets
GAAP Generally accepted accounting practices
I/S Income statement
L 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 Operating cash flow
OE Owner’s equity
OTC Over the counter
R Revenues
SEC Securities and Exchange Commission
TI Taxable income
WC Working capital
Lesson 1 17
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.
Corporate Finance18
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 state- ment 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 com- pany’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 1—This illustration shows the relationship between the balance sheet, the income statement,
and the cash flow statement.
Lesson 1 19
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
Assets
Current Assets
Cash $84 $98 +$14
Accounts Receivable $165 $188 +$23
Inventory $393 $422 +$29
Total $642 $708
Fixed Assets
Net Plant and Equipment $2,731 $2,880 +$149
Total Assets $3,373 $3,588
Liabilities and Owners’ Equity
Current Liabilities
Accounts Payable $312 $344 +$32
Notes Payable $231 $196 –$35
Total $543 $540
Long-Term Debt $531 $457 –$74
Owners’ Equity
Common Stock and Paid-In Surplus $500 $550 +$50
Retained Earnings $1,799 $2,041 +$242
Total $2,299 $2,591
Total Liabilities and Owners’ Equity $3,373 $3,588
Net $0
Corporate Finance20
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.
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
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 $242
Total Sources $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 $98
Lesson 1 21
make percentage comparisons for the same firm, from period to period or point to point. It’s also easier to make comparisons between different-sized firms within an industry.
Common-sized balance sheets allow comparisons between the components of assets, liabilities, and owners’ equity (recall that A = L + OE ), where assets are set to equal 100 percent. Common-sized income statements allow comparisons between expenses, where net sales or revenues are set to equal 100 percent.
Example: Shown here is the balance sheet from page 48 of your textbook. Convert it to a common-sized format.
PRUFROCK CORPORATION 2008 and 2009 Balance Sheets
($ in millions)
2006 2007
Assets
Current Assets
Cash $84 $98
Accounts Receivable $165 $188
Inventory $393 $422
Total $642 $708
Fixed Assets
Net Plant and Equipment $2,731 $2,880
Total Assets $3,373 $3,588
Liabilities and Owners’ Equity
Current Liabilities
Accounts Payable $312 $344
Notes Payable $231 $196
Total $543 $540
Long-Term Debt $531 $457
Owners’ Equity
Common Stock and Paid-In Surplus $500 $550
Retained Earnings $1,799 $2,041
Total $2,299 $2,591
Total Liabilities and Owners’ Equity $3,373 $3,588
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Solution: The following is a common-sized balance sheet consistent with the sheet on page 52 of your textbook.
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:
Long-term solvency ratios
Asset management, or turnover, ratios
Profitability ratios
Market value ratios
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%
Inventory 11.7% 11.8% +0.1%
Total 19.1% 19.7% +0.6%
Fixed Assets
Net Plant and Equipment 80.9% 80.3% –0.6%
Total Assets 100.0% 100.0% 0.0%
Liabilities and Owners’ Equity
Current Liabilities
Accounts Payable 9.2% 9.6% +0.4%
Notes Payable 6.8% 5.5% –1.3%
Total 16.0% 15.1% –0.9%
Long-Term Debt 15.7% 12.7% –3.0%
Owners’ Equity
Common Stock and Paid-In Surplus 14.8% 15.3% +0.5%
Retained Earnings 53.3% 56.9% +3.6%
Total 68.1% 72.2% +4.1%
Total Liabilities and Owners’ Equity 100.0% 100.0% 0.0%
Lesson 1 23
Short-term solvency, or liquidity, measures include the following:
� The current ratio
� The quick or acid-test ratio (which excludes a firm’s inven- tory 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 follow- ing:
� 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
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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 � Current Liabilities
Current Ratio = $12,674 � $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.
Lesson 1 25
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 � Equity Multiplier
ROE = 14.28% � 1.29
ROE = 0.1428 � 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 infor- mation 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 capi- tal 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
Corporate Finance26
based on financial statements. However, the news announce- ment 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 abbre- viations you should remember from this assignment.
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.
ABBREVIATION MEANING
NWC Net working capital
PE Ratio Price-earnings ratio
ROA Return on assets
ROE Return on equity
SEC Securities and Exchange Commission
Lesson 1 27
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 entre- preneurs who have ideas but no assets. For people who are seeking financing in the start-up or early stages of a firm’s
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.
Corporate Finance28
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 secu- rities 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.
Lesson 1 29
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:
Other direct expenses, which are direct costs incurred by the issuer that aren’t part of the compensation to under- writers
Indirect expenses, which include the costs of management time working on the new issue and aren’t reported on the prospectus
Abnormal returns, which is the drop in the price of exist- ing stock on the announcement of the issue
Corporate Finance30
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 incor- poration, 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:
Dilution of market value
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 regis- trations 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.
Lesson 1 31
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.
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.
ABBREVIATION MEANING
IPO Initial public offering
LT Long term
VC Venture capital
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)
Corporate Finance32
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.
33
and a use of cash?
A. A decrease in notes payable
B. An increase in long-term debt
C. A decrease in inventory
D. A decrease in common stock
income tax rates never exceeded an average rate of
A. 15%. C. 39%.
B. 35%. D. 34%.
Which of the following is the correct balance of the firm’s
liabilities?
A. $33,000 C. $93,000
B. $27,000 D. $60,000
E x
a m
in a
tio n
E x
a m
in a
tio n
Lesson 1 Corporate Finance Overview
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.
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
Examination, Lesson 134
A. A decrease in notes payable
B. A decrease in long-term debt
C. An increase in inventory
D. An increase in common stock
following is the correct net working capital for the firm?
A. $10,000 C. $3,000
B. $7,000 D. $13,000
$16,500 at the end of 2008, which of the following statements about accounts
receivable is correct?
A. Accounts receivable decreased by $2,300 and represented a use of cash.
B. Accounts receivable increased by $2,300 and represented a source of cash.
C. Accounts receivable decreased by $2,300 and represented a source of cash.
D. Accounts receivable increased by $2,300 and represented a use of cash.
income?
A. $15,090 C. $6,240
B. $8,850 D. $23,940
is correct?
A. IPOs may be either underpriced or overpriced.
B. IPOs are never overpriced.
C. IPOs are never underpriced.
D. IPOs are always correctly priced.
of $2,120, what is the firm’s net income?
A. $8,850 C. $6,240
B. $4,120 D. $8,360
measures is set to equal 100 percent?
A. Total liabilities C. Total owners’ equity
B. Total assets D. Cash
Examination, Lesson 1 35
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
More Than
Taxable Income
Less Than
Tax
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 35%
A. $78,000 C. $39,000
B. $6,250 D. $61,250
average tax rate?
A. 39% C. 34%
B. 30.625% D. 31.625%
marginal tax rate?
A. 39% C. 34%
B. 30.625% D. 31.625%
following except dilution of
A. ownership percentage.
B. market value.
C. the firm’s current ratio.
D. book value per share.
expense, and $2,120 in taxes, what is the firm’s operating cash flow?
A. $4,120 C. $6,240
B. $5,470 D. $9,710
Examination, Lesson 136
over a specified period of time is called the
A. statement of cash flows.
B. income statement.
C. balance sheet.
D. inventory ratio statement.
A. Long-term solvency measures
B. Asset management or turnover measures
C. Short-term solvency or liquidity measures
D. Profitability measures
at the end of 2008, which of the following statements about accounts payable is
correct?
A. Accounts payable decreased by $3,200 and represented a use of cash
B. Accounts payable increased by $3,200 and represented a source of cash
C. Accounts payable decreased by $3,200 and represented a source of cash
D. Accounts payable increased by $3,200 and represented a use of cash
A. Rights offering C. Green Shoe option
B. Abnormal returns D. Gross spread
exceeded a marginal rate of
A. 15%. C. 39%.
B. 35%. D. 34%.
Future Cash Flow Valuation
INTRODUCTION 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 vari- ous 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 com- pound interest rates
37
L e
s s
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2 L
e s
s o
n 2
Corporate Finance38
� 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.
Lesson 2 39
Substitute the known values into the equation and solve:
Future Value = Present Value � (1.0 + Interest Rate )N
FV = $2,000 � (1.0 + 0.10)1
FV = $2,000 � (1.1)1
FV = $2,000 � 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 peri- ods), 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 � (1.0 + Interest Rate )N
FV = $2,000 � (1.0 + 0.10)2
FV = $2,000 � (1.1)2
FV = $2,000 � 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.
Corporate Finance40
Future Value = Present Value � (1.0 + Interest Rate )N
FV = $2,000 � (1.0 + 0.10)3
FV = $2,000 � (1.1)3
FV = $2,000 � 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 � (1.0 + Interest Rate )N
FV = $1,000 � (1.0 + 0.12)4
FV = $1,000 � (1.12)4
FV = $1,000 � 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.
Lesson 2 41
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 � [(1.0 + Interest Rate )N ]
PV = $2,000 � [(1.0 + 0.10)1]
PV = $2,000 � [(1.1)1]
PV = $2,000 � 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 MEANING
FV Future value
PV Present value
Corporate Finance42
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.
Lesson 2 43
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.
Corporate Finance44
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 endeav- ors. 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 peri- ods), 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 � (1.0 + Interest Rate )N
FV = $2,000 � (1 + 0.12)1
FV = $2,000 � (1.12)1
FV = $2,000 � 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).
Lesson 2 45
Future Value = Present Value � (1.0 + Interest Rate )N
FV = $5,240 � (1 + 0.12)1
FV = $5,240 � (1.12)1
FV = $5,240 � 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 � [(1.0 + Interest Rate )N ]
PV = $3,000 � [(1.0 + 0.09)2]
PV = $3,000 � [(1.09)2]
PV = $3,000 � 1.1881
PV = $2,525.04
Next, calculate the present value of $1,000 in one year at 9 percent.
Present Value = Future Value � [(1.0 + Interest Rate )N ]
PV = $2,000 � [(1.0 + 0.09)1]
PV = $2,000 � [(1.09)1]
PV = $2,000 � 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.
Corporate Finance46
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 � (1.0 + I )1] + [FV � (1.0 + I )2] + [FV � (1.0 + I )3] + [FV � (1.0 + I )4]
PV = [$100 � (1.0 + 0.10)1] + [$100 � (1.0 + 0.10)2] + [$100 � (1.0 + 0.10)3] + [$100 � (1.0 + 0.10)4]
PV = [$100 � (1.10)1] + [$100 � (1.10)2] + [$100 � (1.10)3] + [$100 � (1.10)4]
PV = [$100 � 1.10] + [$100 � 1.21] + [$100 � 1.331] + [$100 � 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.
Lesson 2 47
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 � (1.0 + I )1] + [FV � (1.0 + I )2] + [FV � (1.0 + I )3]
PV = $100 + [$100 � (1.0 + 0.10)1] + [$100 � (1.0 + 0.10)2] + [$100 � (1.0 + 0.10)3]
PV = $100 + [$100 � (1.10)1] + [$100 � (1.10)2] + [$100 � (1.10)3]
PV = $100 + [$100 � 1.10] + [$100 � 1.21] + [$100 � 1.331]
PV = $100 + $90.91 + $82.64 + $75.14
PV = $348.69
Answer: The present value of this annuity due is $348.69.
FIGURE 2—This figure illustrates an ordinary annuity.
Corporate Finance48
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.
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 � (1.0 + r )
PV = $316.99 � (1.0 + 0.10)
PV = $316.99 � 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.
FIGURE 3—This figure illustrates an annuity due.
Lesson 2 49
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 com- pounded 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 � (1.0 + Interest Rate )N
FV = $1,000 � (1 + 0.12)1
FV = $1,000 � (1.12)1
FV = $1,000 � 1.12
FV = $1,120
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
Total $316.99 $348.69 $31.70
Corporate Finance50
Second, calculate the future value of the investment at 12 percent per year, compounded semiannually for one year.
Future Value = Present Value � (1.0 + Interest Rate )N
FV = $1,000 � (1 + 0.06)2
FV = $1,000 � (1.06)2
FV = $1,000 � 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
Lesson 2 51
balance, the payments of $1,285.46, the interest component of the payment, the principal component of the payment, and the ending principal balance.
Solution: The following is the loan amortization schedule. (Note that some of the amounts in this schedule are rounded. This is why the sum of the “Interest Paid” column and the “Principal Paid” column differs slightly from the total payment.)
Note that, while the payment amount is fixed at $1,285.46 for each period, the portion of the payment used to reduce the principal amount of the loan increases with each payment, and therefore, the amount of interest expense decreases with each payment. This is typical for automobile loans, home mortgages, and so on. Figure 4 illustrates this relationship for a hypothetical 30-year mortgage.
There are some exceptions to the type of loan described. One example is the adjustable rate loan or ARM. These loans are sometimes made to individuals who aren’t creditworthy, and often offer low introductory interest rates (called “teaser rates”) that are scheduled to readjust to much higher rates after a few years. When these interest rate adjustments occur, they can lead to much higher required loan payments, which the borrower may be unable to pay. In the case of
LOAN AMORTIZATION SCHEDULE
For a Loan of $5,000 at 9% Interest, Over 5 Years
Year Beginning
Balance
Total
Payment
Interest
Paid
Principal
Paid
Ending
Balance
1 $5,000 $1,285.46 $450 $835.46 $4,164.54
2 $4,164.54 $1,285.46 $374.81 $910.65 $3,253.89
3 $3,253.89 $1,285.46 $292.85 $992.61 $2,261.28
4 $2,261.28 $1,285.46 $203.52 $1,081.95 $1,179.33
5 $1,179.33 $1,285.46 $106.14 $1,179.32 $0
Total $6,427.30 $1,427.32 $5,000.00
Corporate Finance52
home mortgage loans, the increase in required monthly payments can result in loan defaults and home foreclosures. In some cases, these loans result in negative amortization, in which the monthly payment isn’t large enough to pay the interest due on the loan.
So, using the loan amortization schedule from the previous example problem, imagine that the Year 1 payment was only $400. This amount isn’t sufficient to pay the interest ($450), so the additional $50 of interest is added to the principal. The principal then increases to $5,050 ($5,000 plus $50). If a similar pattern is repeated for the second and third periods, the payment will increase in Period 4 to an amount greater than $1,285.46. Eventually, the borrower may be unable to pay the monthly payments.
FIGURE 4—This figure shows the relationship between the interest component and the principal
component of a mortgage loan.
Lesson 2 53
After you’ve carefully read pages 144–189 in the Fundamentals of Corporate Finance textbook, complete Self-Check 5. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from Assignment 5, move on to Assignment 6.
Self-Check 5 Indicate whether each of the following statements is True or False.
______ 1. A perpetuity is an annuity in which the cash flows continue forever.
______ 2. An ordinary annuity includes a payment in time period zero.
______ 3. An annuity due includes a payment in time period zero.
______ 4. In general terms, an annuity due will always have a lower present value as compared
to an ordinary annuity.
______ 5. A loan that has a fixed payment per period would provide for a decreasing principal
component with each periodic payment.
______ 6. A loan amortization schedule provides the breakdown of a payment into principal and
interest components.
In the “Questions and Problems” section on pages 179–183 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 6, 22, and 42.
Check your answers with those on page 141.
Corporate Finance54
ASSIGNMENT 6 Read this introduction to Assignment 6. Then, read Chapter 7, pages 190–230, in your Fundamentals of Corporate Finance textbook.
Bonds and Bond Valuation When corporations want to borrow money on a long-term basis, they usually do so by issuing or selling debt securities called bonds. A bond is an interest-only loan in which the final interest and principal payment are made at maturity, which is the end of the bond term.
The amount that will be repaid at the end of the loan is referred to as the bond’s face value or par value. The number of years until the face value is paid is called the bond’s time to maturity.
Example: Assume that a corporation wants to borrow $1,000 for 30 years by issuing bonds. The interest rate required for similar bonds from similar corporations is 12 percent. What is the bond’s maturity? If the corporation makes annual interest payments, how much will they pay each year for the first 29 years? What is the bond’s face value? What is the bond’s par value? How much will the corporation pay at the end of 30 years?
Solution: If the corporation makes annual interest payments, they will pay 12 percent of $1,000 at the end of each year for the first 29 years. You can calculate the interest pay- ments as follows:
Interest Payment = $1,000 � 12%
Interest Payment = $1,000 � 0.12
Interest Payment = $120
Answer: The bond’s maturity is 30 years. The interest payments will be $120 per year for the first 29 years. The bond’s face value is $1,000. The bond’s par value is $1,000. The corporation will pay their final interest payment of $120 plus the principal amount of $1,000, for a total of $1,120, at the end of the 30th year.
Lesson 2 55
Example: Illustrate the cash flows for the last five payments for the previous example.
Solution: The last five payments would result in cash outflows of $120 for years 26 through 29, and $1,120 for Year 30, as shown in the following illustration.
More about Bond Features The securities issued by corporations may be classified as equity securities or debt securities. In the case of debt, the individual or corporate entity making the loan is referred to as a creditor or lender and the individual or corporate entity borrowing the money is referred to as a debtor or borrower. The main differences between debt and equity are the following:
The corporation’s payments of interest on debt are tax deductible. Dividends paid to stockholders aren’t tax deductible.
Unpaid debt is a liability of the firm. If the debt isn’t paid, the creditors can claim the assets of the firm, which may lead to corporate bankruptcy (liquidation or reorganization). This doesn’t occur when equity is issued.
An indenture is the written agreement between the corpora- tion (borrower) and its creditors. It’s sometimes referred to as the deed of trust. It usually includes the following provisions:
� The terms of the bond
� The total amount of bonds issued
Year 26 27 28 29 30
Interest $120 $120 $120 $120 $120
Principal $0 $0 $0 $0 $1,000
Total $120 $120 $120 $120 $1,120
Corporate Finance56
� A description of the property used as security for the bond
� The repayment arrangements
� The call provisions
� Details of any applicable protective covenants
Corporate bonds usually have a face value of $1,000. Corporate bonds are usually in registered form, in which the company registrar records the ownership of each bond. However, some bonds are issued in bearer form, which means that the bond is issued without a record of the owner’s name. Thus, payment is made to whomever holds the bond.
A debenture is an unsecured bond, for which no specific pledge of property is made. Some bonds are secured by specific assets or collateral, just as mortgage securities are secured by real property.
It’s common for bonds and other debt instruments to have different levels of seniority, which becomes relevant in the event of a corporate liquidation or bankruptcy. If a company defaults or fails to make timely interest and principal payments, senior debt securities are paid first, followed by junior or subordinated debt instruments.
Bonds are usually repaid at maturity. On this date, the bondholder usually receives the face value of the bond, or the bondholder may be repaid in part or in entirety before the maturity date. Some corporations use a sinking fund to plan and account for the repayment of the principal portion of these bonds. The company often retains a trustee and makes annual payments to the trustee; the trustee then manages the retirement of the bonds. This may occur prior to the maturity date, if the bonds are callable.
A call provision allows the corporation to repurchase or “call” part or all of the bonds at some stated price over a specific period.
Some bonds are issued with a protective covenant, which is a part of the loan agreement that limits certain actions the company can take during the term of the loan. A negative
Lesson 2 57
covenant specifies actions that the company may not take. In contrast, a positive covenant describes the actions the company must take or conditions that it must abide by.
Bond Ratings Firms often pay to have their bonds rated. Bond ratings are an assessment of the credit-worthiness of the corporation that issues the bonds. This rating is similar to the credit rating or FICO score that an individual might receive on his or her credit report.
The two leading bond-rating firms are Moody’s and Standard and Poor’s (S&P). These firms rate corporate and government bonds based on the creditworthiness of the firm, or how likely the firm or entity is to default on the bonds. For example, the most creditworthy firm would receive an “Aaa” rating from Moody’s and an “AAA” rating from S&P. The highest possible rating reflects the entities’ ability to pay the interest and principal on their debt instruments. A high rating by one or both of these bond-rating firms suggests a lower default risk, and will enable the issuing entity to successfully place or sell the debt while paying a lower interest rate. The same concept applies to individual credit scores. A person who has a favorable credit report will find it easier to borrow money at a lower rate of interest.
Some Different Types of Bonds A variety of different bonds are available, including government bonds, zero coupon bonds, and floating rate bonds.
Government bonds are those issued by the U.S. Treasury to finance the national debt. Most government bonds are in the form of Treasury notes and bonds. Most of these U.S. bonds are coupon bonds, issued with maturities between 2 and 30 years, and have no default risk. Also, the interest received by the taxpayer for these bonds is tax-exempt for state income tax purposes. Bonds may also be issued by states, local governments, and municipalities (these bonds are often called “munis”), with varying degrees of default risk. Municipal bonds are exempt from federal income taxes.
Corporate Finance58
Zero coupon bonds (often called “zeroes”) pay no coupon, but are issued at a discount. Over the life of the bond, the bond value increases until the bond’s stated value is achieved at maturity.
Floating-rate bonds (often called “floaters”) have adjustable- rate coupon payments. Adjustments are often tied to an interest rate index, such as the Treasury bill interest rate or the 30-year Treasury bond rate.
Example: Suppose that a firm issues a five-year, zero coupon bond with a $1,000 face value. The initial price is established at $497, and the bond yields (or earns) 15 percent to matu- rity. Prepare a schedule to show the beginning value, ending value, implicit interest expense, and straight-line interest expense for each of the five years, and in total.
Solution: The following illustration shows the schedule for the bond.
Bond Markets Most bond trading occurs over the counter (OTC). Bonds (like stocks) have bid prices and ask prices. The bid price is the amount that a buyer is willing to pay for the bond. The ask price is the amount that a seller is willing to accept for a bond. The difference between the two prices, at any point in time, is referred to as the bid-ask spread (or simply, the spread ).
Year Beginning
Value
Ending
Value
Implicit
Interest
Expense
Straight-Line
Interest
Expense
1 $497.00 $572.00 $75.00 $100.60
2 $572.00 $658.00 $86.00 $100.60
3 $658.00 $756.00 $98.00 $100.60
4 $756.00 $870.00 $114.00 $100.60
5 $870.00 $1000.00 $130.00 $100.60
Total $503.00 $503.00
Lesson 2 59
Bond prices may change over the life of the bond. For example, suppose that a bond provides for semiannual interest payments on January 1 and July 1 of each year. What if you wanted to sell your corporate bond to someone on a date other than January 1 or July 1? In such a situation, the price paid and received would have to reflect the accrued interest for the period. So, if the exchange took place on April 1, halfway between the two interest payment dates, the buyer would expect to receive (and the seller would expect to pay) one-half of the interest payable in three more months on July 1. Recall that the interest to be paid on a bond is “stated” at the time of the bond issuance.
Example: Suppose that you buy a $1,000 bond with a 12 percent annual coupon, payable semiannually on January 1 and July 1. On both January 1 and July 1, the bondholder will receive $60, for a total annual interest payment of $120 ($60 + $60). Based on the principal and accrued interest only, how much would you expect to pay to purchase this bond on April 1?
Solution: At $120 per year, this bond pays interest of $10 per month. On April 1, the bond would have accrued three month’s worth of interest, or $30.
Answer: To buy the bond on April 1, you would expect to pay the $1,000 face value plus $30 in accrued interest for a total of $1,030.
Inflation and Interest Rates Nominal interest rates are the stated interest rates you pay on a credit card or home mortgage. In contrast, a real interest rate is an interest rate adjusted for inflation. The rates of interest on corporate bonds are stated in nominal terms. Nominal interest rates include a real rate component and an inflation rate component (or an anticipated inflation rate component).
The relationship between nominal and real rates of interest can be illustrated with the following equation:
Real Interest Rate + Inflation Rate (or Anticipated Inflation Rate) = Nominal Interest Rate
Corporate Finance60
This information can also be illustrated as shown here:
While some people might argue the validity of these nominal rates, focus on the components of the nominal rates. A home mortgage interest rate is usually lower than a credit card rate, because the home mortgage is secured by real property. In other words, if the borrower defaults on the home mort- gage loan, the property can be foreclosed upon. A credit card, on the other hand, represents unsecured debt. For example, if you take a trip to Hawaii and finance the cost on your credit card, the trip can’t be repossessed. The inflation rate or anticipated inflation rate is held constant in each case, and the real rate of interest is held constant in each case. The different nominal rates for the home mortgage and credit card reflect the risk or default rate components of the debt.
Example: Generally, would you expect to pay a higher nominal interest rate for a home mortgage (secured debt) or a credit card (unsecured debt)?
Answer: You should expect to pay a higher nominal interest rate for an unsecured credit card.
Example: If the inflation rate is 5 percent, would you expect to pay more or less than 5 percent, in nominal terms, for a home mortgage?
Answer: The inflation rate is a component of the nominal interest rate charged by a lender. You should expect the lender to charge a nominal interest rate that’s higher than the inflation rate. Thus, at a time when the inflation rate is 5 percent, you should expect to pay more than 5 percent for a home mortgage.
COMPARISON OF INTEREST RATES
Home Mortgage Credit Card
Real Interest Rate 2% 2%
Plus: Risk or Default Risk Rate 2% 12%
Plus: Inflation Rate (or Anticipated Inflation Rate) 4% 4%
Equals: Nominal Interest Rate 8% 18%
Lesson 2 61
Interest rates, discount rates, and rates of return are almost always stated in nominal terms. Therefore, the discount rate that’s used to calculate the present value of an investment alternative is stated in nominal terms, and includes an inflation (or anticipated inflation) component.
Determinants of Bond Yields Short-term and long-term interest rates change over time. The relationship between short-term and long-term interest rates are called the term structure of interest rates. The term structure of interest rates tells us what the nominal interest rates are on default-free, pure discount bonds. Because the term default-free suggests zero risk of default, these rates represent pure interest rates.
After you’ve carefully read pages 190–230 in the Fundamentals of Corporate Finance textbook, complete Self-Check 6. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from Assignment 6, move on to Assignment 7.
Self-Check 6 Indicate whether each of the following statements is True or False.
______ 1. A bond is an interest-only loan in which the final interest and principal payment are
made at maturity, which is the end of the bond term.
______ 2. In the case of debt, the individual or corporate entity making the loan is referred to as
a debtor or borrower.
______ 3. The most creditworthy firm would receive an “Aaa” rating from Moody’s and an “AAA”
rating from S&P.
(Continued)
Corporate Finance62
ASSIGNMENT 7 Read this introduction to Assignment 7. Then, read Chapter 8, pages 231–259, in your Fundamentals of Corporate Finance textbook.
Common Stock Valuation Shares of stock are priced to be sold in the public market- place. There are several ways in which stock prices may be established for the marketplace. None of these methods are perfect and all are theoretical. The important point to understand is that a stock’s price reflects the present value of all future cash flows that the stock market, as a whole, anticipates will be generated by the firm. For this reason, positive news reports about increased anticipated earnings (and cash flows) result in increases in stock prices, and negative news reports about decreased anticipated earnings (and cash flows) result in decreases in stock prices.
Self-Check 6 ______ 4. Most bond trading occurs on the New York Stock Exchange (NYSE).
______ 5. Real interest rates are the stated rates that you pay on your credit card or home
mortgage.
______ 6. On a home mortgage or credit card debt, the real interest rate plus the inflation rate is
equal to the nominal interest rate.
In the “Questions and Problems” section on pages 226–229 of the Fundamentals of
Corporate Finance textbook, answer questions 4, 8, 12, 26 (a and b only), and 28.
Check your answers with those on page 142.
Lesson 2 63
Some Features of Common and Preferred Stocks Common stock (C/S) is a type of company stock that has no special preference or priority for shareholders, either in receiving dividends or in bankruptcy. In contrast, preferred stock (P/S) is company stock that provides some sort of “preferential” treatment to the preferred stockholders, relative to the rights held by common stockholders. Usually, preferred stocks provide shareholders with a preference over dividends, as well as in the distribution of company assets in the event of liquidation or bankruptcy. Some preferred stocks may also come with special voting rights for their shareholders. For example, a class of preferred stock may come with the right to vote 10-to-1 as compared to the voting rights of a common shareholder.
Usually, preferred stocks deliver better dividends to stock- holders than common stocks. Sometimes the dividends are cumulative, which means that the preferred shareholders must receive some minimal or stated dividend before any dividends are paid to the common shareholders. It’s the dividend pref- erence that makes some investors view preferred stocks to be more like debt securities than equity securities.
If a firm has only one class of stock, it will be common stock. If a firm has two or more classes of stock, only one class of stock may be appropriately called common stock.
The Stock Markets The stock market consists of a primary market and a second- ary market. In the primary market, new stock issues are brought to market and sold to investors. In the secondary market, existing shares are traded among investors.
Most stock sales involve dealers and brokers. The dealers maintain an inventory of stocks and stand by, ready to buy or sell at any time. The brokers bring buyers and sellers together and charge each a commission to arrange for the purchase and sale of a security. In many cases, a seller is
Corporate Finance64
both a broker and a dealer, arranging for purchases and sales between buyers and sellers, and also buying and selling their own inventory of securities.
The New York Stock Exchange (NYSE) is the largest stock mar- ket in the world. The NYSE is a publicly traded corporation, and exchange members must purchase a special license that entitles them to buy and sell shares in the exchange.
The second largest stock market in the United States is the National Association of Securities Dealers Automated Quotations (NASDAQ) system. The NASDAQ is a computer network of securities dealers. The NASDAQ is often referred to as an over-the-counter (OTC) market, which is a market characterized by dealers who buy and sell securities for their own inventory. In the late 1990s, the NASDAQ system was opened to electronic communications networks (ECNs), which allow investors to trade directly with one another by using Web sites.
Review of Abbreviations Throughout Assignment 7, 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.
After you’ve carefully read pages 231–259 in the Fundamentals of Corporate Finance textbook, complete Self-Check 7. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from these four assignments, complete the examination for Lesson 2.
ABBREVIATION MEANING
C/S Common stock
ECN Electronic communications network
NASDAQ National Association of Securities Dealers Automated Quotations
NYSE New York Stock Exchange
P/S Preferred stock
Lesson 2 65
Self-Check 7 Indicate whether each of the following statements is True or False.
______ 1. Common stock comes with special priorities for shareholders in receiving dividends.
______ 2. Preferred stocks may provide shareholders with a preference in the distribution
of company assets in the event of liquidation or bankruptcy, relative to the rights
held by common stockholders.
______ 3. In the secondary market, new stock issues are brought to market and sold to
investors.
______ 4. The New York Stock Exchange (NYSE) is the second largest stock market in the world.
______ 5. The NASDAQ is often referred to as an over-the-counter market, which is a market
characterized by dealers who buy and sell securities for their own inventory.
______ 6. In the late 1990s, the NYSE was opened to electronic communications networks,
which allow investors to trade directly with one another by using Web sites.
In the “Questions and Problems” section on pages 255–257 of the Fundamentals of
Corporate Finance textbook, complete questions 2, 6, 10, 14, 18, and 20.
Check your answers with those on page 142.
Corporate Finance66
NOTES
67
interest per period, for two periods? (Round your answer to
the nearest cent.)
A. $2,777.78 C. $3,499.20
B. $2,572.02 D. $3,240.00
A. yield to maturity. C. face value.
B. maturity. D. coupon.
of 8 percent per period for 3 periods, has a present value of
$1,288.55. If this same annuity was an annuity due, what
would its present value be? (Round your answer to the
nearest cent.)
A. $1,288.55 C. $1,391.63
B. $1,500.00 D. $1,788.55
E x
a m
in a
tio n
E x
a m
in a
tio n
Lesson 2 Future Cash Flow Valuation
When you feel confident that you have mastered the material in
Lesson 2, 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.
EXAMINATION NUMBER
06058501
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
Examination, Lesson 268
referred to as the
A. dirty price. C. Treasury yield curve.
B. Fisher effect. D. bid-ask spread.
semiannually. What is the future value of this investment after one year?
A. $2,205 C. $2,420
B. $2,100 D. $4,500
per period, after three periods? (Round your answer to the nearest cent.)
A. $7,117.80 C. $12,544.00
B. $11,200.00 D. $14,049.28
A. At the corporate headquarters of Moody’s
B. In the New York Stock Exchange (NYSE)
C. Electronically, over the counter
D. At the corporate headquarters of Standard and Poor’s
semiannually on January 1 and July 1. On both January 1 and July 1, the bondholder
will receive $300, for a total annual interest payment of $600 ($300 + $300).
Based on the principal and accrued interest only, how much would you expect
to pay to purchase this bond on May 1?
A. $5,200 C. $5,300
B. $5,000 D. $5,600
How much will you have in the account after 4 years? (Round your answer to the
nearest cent.)
A. $635.52 C. $1,120.00
B. $1,254.40 D. $1,573.52
to a specified schedule, is called a(n)
A. annuity due. C. amortizing loan.
B. debenture. D. corporate bond.
Examination, Lesson 2 69
annuity) of $500 per period, discounted at a rate of 10 percent per period? (Round
your answer to the nearest cent.)
A. $341.51 C. $1,584.94
B. $454.55 D. $732.05
compounded annually, or 12 percent interest per year compounded semiannually.
Which of the following statements is correct?
A. 12 percent per year, compounded annually, is the better interest rate for
the investment.
B. 12 percent per year, compounded semiannually, is the better interest rate
for the investment.
C. There’s no difference between the two interest rates; both rates will produce
the same future value.
D. It isn’t possible to determine the future value of this investment based on
the information provided.
are called
A. dividends. C. cash flows.
B. capital gains. D. bond yields.
per period, after two periods? (Round your answer to the nearest cent.)
A. $1,650.00 C. $1,815.00
B. $1,363.63 D. $1,239.67
A. dividend yield. C. constant growth.
B. capital gains yield. D. ask price.
year, you’ll deposit another $4,000 in the account. How much will you have in the
account after two years?
A. $10,600 C. $10,000
B. $11,660 D. $11,000
for one period? (Round your answer to the nearest cent.)
A. $2,420.00 C. $1,818.18
B. $2,000.00 D. $1,980.00
Examination, Lesson 270
A. The NASDAQ is a computer network, with no physical location for trading.
B. The number of NYSE exchange members is unlimited.
C. The NASDAQ uses a specialist system for actively traded stocks.
D. The NYSE does not have a physical location for stock trading activities.
annually. How much would you need to invest today to reach a future goal of $5,000?
(Round your answer to the nearest cent.)
A. $4,650.00 C. $4,762.90
B. $6,125.22 D. $4,081.49
of $1,000 per period, discounted at a rate of 10 percent per period? (Round your
answer to the nearest cent.)
A. $1,909.09 C. $1,464.10
B. $3,486.85 D. $2,486.85
Capital Budgeting
INTRODUCTION Lesson 3 contains three assignments that review the basic concepts of capital budgeting. In Assignment 8, the material from Chapter 9 in your textbook is discussed. The assignment focuses on the variety of capital budgeting techniques used to evaluate investment decisions. You’ll learn about net present value, the payback rule, the average accounting return, the internal rate of return, and the profitability index.
Assignment 9 covers the material from Chapter 10, which focuses on project cash flows, particularly the conversion of pretax cash flows to aftertax cash flows. Aftertax cash flows are used when making net present value calculations, and in other discounted cash flow techniques. You’ll also learn about pro forma statements and cash flow analysis.
In Assignment 10, you’ll review the topics from Chapter 11. You’ll learn how to calculate a firm’s break-even point, and you’ll be introduced to the concept of operating leverage, which is associated with risk.
OBJECTIVES When you complete this lesson, you’ll be able to
� Discuss the relative strengths and weaknesses of the various methods for analyzing investments
� Define the terms net present value, profitability index, internal rate of return, discounted payback, payback, and accounting rate of return
� Convert pretax cash flows to aftertax cash flows
� Calculate the break-even point for a project
� Explain the concept of operating leverage
71
L e
s s
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3 L
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s o
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Corporate Finance72
ASSIGNMENT 8 Read this introduction to Assignment 8. Then, read Chapter 9, pages 260–297, in your Fundamentals of Corporate Finance textbook.
Net Present Value The net present value (NPV) approach is a procedure used to determine whether an investment, project, or undertaking creates value in excess of its cost. The net present value, therefore, is the difference between an investment’s market value and its cost. The net present value is calculated by subtracting the present value of aftertax cash outflows from the present value of aftertax cash inflows. The following formula can be used to calculate NPV:
NPV (Aftertax Cash Flows) = PV (Aftertax Cash Inflows) – PV (Aftertax Cash Outflows)
Example: A project requires an initial investment of $30,000 today. The present value of the cash inflows likely to result from this initial investment is $27,578. What is the net present value of this investment? Is the value positive or negative? Should the firm proceed with this investment?
Solution: In this example, the present value of the anticipated cash inflow from the investment is $27,578, and the present value of the cash outflow from the initial investment is $30,000. Substitute these values into the following formula and cal- culate the net present value.
NPV = PV (Cash Inflows) – PV (Cash Outflows)
NPV = $27,578 – $30,000
NPV = –$2,422
Answer: The net present value is negative $2,422. Because the NPV is a negative value, the firm shouldn’t proceed with this investment.
Lesson 3 73
The Payback Rule When a project is under consideration, the payback is the length of time it takes to recover the initial investment for the project. When the payback is calculated using the payback rule, the time value of money for the project or period is ignored. Thus, the payback rule is popularly used for short- term projects and during periods of relatively low rates of inflation, where time value of money considerations are less relevant.
Example: An investment project that requires an initial ash outlay of $1,000 will generate positive cash flows of $200 in Year 1, $400 in Year 2, and $1,000 in Year 3. What is the payback period?
Solution: The payback occurs between years 2 and 3, as follows:
Answer: The payback period for this investment is about two years and five months.
Three advantages of the payback rule are
It adjusts for the uncertainty of later cash flows.
It’s biased toward liquidity.
Four disadvantages of the payback rule are
It requires an arbitrary cutoff point.
It ignores cash flows beyond the cutoff date.
It’s biased against long-term and new projects, including research and development.
Cash
Outflow
Cash
Inflow
Net Cash
Flow
Cumulative
Cash Flow
Year 1 –$1,000 $200 –$800 –$800
Year 2 $0 $400 $400 $400
Year 3 $0 $1,000 $1,000 $600
Total –$1,000 $1,600 $600
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The Discounted Payback A discounted payback period is the length of time required for an investment’s discounted cash flows to equal its initial cost. Thus, the discounted payback has been discounted or adjusted for present value.
Example: Suppose that you require a 12.5 percent return on an investment of $300, and the investment produces cash flows of $100 for each of the first five years. What are the undiscounted and discounted cash flows? When are the pay- back and discounted payback?
Solution: The values are shown in the following illustration:
Answer: The undiscounted cash flow is $500, and the dis- counted cash flow is $355. The payback is in three years, and the discounted payback is in four years.
The Average Accounting Return The average accounting return (AAR) represents an investment’s average net income divided by its average book value, and can be calculated by using the following formula:
AAR = Average Net Income � Average Book Value
Example: Assume that a firm has an average net income of $50,000 and an average book value of $250,000. What is the firm’s average accounting return?
Cash Flow,
Undiscounted
Cash Flow,
Discounted
Accumulated Cash
Flow, Undiscounted
Accumulated Cash
Flow, Discounted
Year 1 $100 $89 $100 $89
Year 2 $100 $79 $200 $168
Year 3 $100 $70 $300 $238
Year 4 $100 $62 $400 $300
Year 5 $100 $55 $500 $355
Total $500 $355
Lesson 3 75
Solution: Substitute the values into the formula and solve.
AAR = Average Net Income � Average Book Value
AAR = $50,000 � $200,000
AAR = 0.25, or 25%
Answer: The firm’s average accounting return is 25%.
The Internal Rate of Return The most important (and popular) alternative to the net present value approach is the internal rate of return (IRR). In the case of NPV, a project with an NPV of zero or greater is acceptable. In the case of IRR, projects with an IRR that exceeds some specified level is acceptable. The IRR on a project or investment is the required rate of return that would result in an NPV of zero, when the IRR is used as the discount rate. Therefore, the advantages associated with the IRR method are the following:
The method is easy to understand and communicate.
Disadvantages with the IRR method are
It may result in incorrect decisions when comparing mutually exclusive investment or project alternatives.
The Profitability Index The profitability index (PI) is the present value of an invest- ment’s future cash flows divided by its initial cost. The PI represents an extension of the NPV technique, in which the index ranks projects in terms of relative NPVs.
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The Practice of Capital Budgeting All financial projections that result from capital budgets are subject to error or risk. For this reason, a variety of techniques may be used to evaluate a project or projects.
Review of Abbreviations Throughout Assignment 8, 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.
After you’ve carefully read pages 260–297 in the Fundamentals of Corporate Finance textbook, complete Self-Check 8. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from Assignment 8, move on to Assignment 9.
ABBREVIATION MEANING
AAR Average accounting return
IRR Internal rate of return
NPV Net present value
PI Profitability index
Lesson 3 77
ASSIGNMENT 9 Read this introduction to Assignment 9. Then, read Chapter 10, pages 298–334, in your Fundamentals of Corporate Finance textbook.
Project Cash Flows: A First Look A relevant cash flow for a project is a change in the firm’s overall future cash flow that comes about as a direct conse- quence of the decision to take that project.
Self-Check 8 Indicate whether each of the following statements is True or False.
______ 1. A project with a negative net present value (NPV) is usually acceptable to investors.
______ 2. The net present value (NPV) technique takes the time value of money into
consideration.
______ 3. The payback technique takes the time value of money into consideration.
______ 4. The discounted payback technique takes the time value of money into consideration.
______ 5. The internal rate of return (IRR) on a project or investment is the required rate of
return that would result in a net present value of zero, when the IRR is used as the
discount rate.
______ 6. The accounting rate of return (ARR) takes the time value of money into consideration.
In the “Questions and Problems” section on pages 292–296 of the Fundamentals of
Corporate Finance textbook, answer questions 4, 8, 12, 16, and 22.
Check your answers with those on page 143.
Corporate Finance78
Example: Suppose you’re considering the purchase or lease of a piece of equipment for your firm. Your firm rents its facility at a cost of $2,000 per month. How does the monthly rental fee of $2,000 enter into the decision?
Solution: The $2,000 monthly rent for the facility isn’t relevant to the decision to purchase or lease the piece of equipment.
Incremental Cash Flows The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct result of taking the project. Incremental cash flows are the focus of most financial projections used to decide whether to proceed with or reject a capital investment project.
Sunk costs are costs that have already been incurred and can’t be removed, and therefore shouldn’t be considered in an investment decision. Sunk costs don’t change, in the short- term. For example, a mortgage payment for real property results in a cash outflow that’s fixed, periodic and sunk, in the short-term. In the long-term, the property may be sold and the mortgage paid from the proceeds of the sale.
An opportunity cost is the value of an investment that’s forgone (given up) to undertake another investment. For example, once you decide to spend your money on a particular investment, you’ll be missing out on other investment opportunities. The opportunity cost is the cost of the best alternative investment you could have made. The opportunity cost must be consid- ered when you’re evaluating investments to make the best choice of where to place your money.
Lesson 3 79
Pro Forma Financial Statements and Project Cash Flows Pro forma financial statements are financial statements that project future years’ operations. Most often, project cash flows are used to gauge the desirability of a project.
More about Project Cash Flow There are several components to project cash flows. Working capital is frequently required to initiate a capital investment project. When the project’s life is completed, this working capital is released for use elsewhere (for other projects). Working capital is already in aftertax terms, as Table 5 illustrates.
Table 5 lists some components of working capital or net working capital. Remember that working capital is equal to current assets less current liabilities. Note that cash is already in aftertax dollars, as the accrual for corporate (income) taxes payable is matched with other balance sheet items. Therefore, the working capital used to finance a proj- ect at the beginning of the project’s life (and released for use elsewhere, at the end of the project’s life) is presumed to be in aftertax terms.
Revenues, operating expenses, and depreciation are all adjusted to convert from accrual-based net income to aftertax cash flows. Your textbook uses a corporate tax rate of 34 percent. Some texts use a 40 percent tax rate, which would include an average state corporate tax rate (for purely domestic corpora- tions). In the following examples, we’ll use 34 percent for T to be consistent with your textbook.
Table 5
WORKING CAPITAL
Current Assets Current Liabilities
Cash Corporate Taxes Payable
Accounts Receivable Accounts Payable
Inventory
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Generally, increased revenues result in increased cash flows at 1 minus the tax rate, as follows:
Revenues increase cash flows at (1 – T ).
Generally, operating expenses result in decreased cash flows at 1 minus the tax rate, as follows:
Operating expenses decrease cash flows at (1 – T ).
Therefore, revenues minus operating expenses results in net cash flows, when the difference is multiplied by (1 – T ).
Unlike revenues and expenses, the values of depreciation, amortization, and depletion represent noncash charges. For example, no one writes a check to pay for depreciation; however, the depreciation expense is an expense on a firm’s income statement and a deductible expense on the firm’s corporate income tax return. For this reason, depreciation expenses generate cash flows by reducing corporate income tax expenses, as follows:
Depreciation expenses increase cash flows at (T).
Table 6 is adapted from your textbook. It will be used to illustrate the conversion from accrual-based income state- ment measures to cash flows. To achieve this objective, the components have been separated into revenues and expenses, or operating cash flows and depreciation-related cash flows.
Table 6
PROJECTED INCOME STATEMENT
Operating
Cash Flows
Depreciation
Cash Flows
Unit price $120
Unit sales 3,000
Revenues $360,000 $360,000
Variable costs –$180,000 –$180,000
Fixed costs –$25,000 –$25,000
Depreciation –$114,320 $0 –$114,320
EBIT $40,680 $155,000 $114,320
Taxes (34%) –$13,831 –$52,700 $38,869
Net income $26,849 $102,300 –$75,451
Lesson 3 81
Our focus is on aftertax cash flows, so it wouldn’t be appro- priate to use a generally accepted accounting principle that’s based on the depreciation technique. Instead, we’ll use the technique required under the current tax law, which is called the modified accelerated cost recovery system (MACRS). This method allows for the accelerated write-off of property under various classifications. The MACRS schedules are based on a 200 percent or double-declining balance technique (or 150 percent for longer-lived assets) that has been adjusted for a first year modifying convention. These techniques differ from the straight-line approach to calculating depreciation expenses. The MACRS depreciation schedules are determined by law, so the depreciable life and depreciation technique is prescribed by tax law.
Alternative Definitions of Operating Cash Flow In the bottom-up approach, a crude approximation of operating cash flow may be determined by simply adding depreciation expenses and other noncash charges to net income. This can be illustrated with the following equation:
OCF = Net Income + Depreciation
Some Special Cases of Discounted Cash Flow Analysis Discounted cash flow (DCF) techniques are used for a variety of decisions. Sometimes, these techniques are used to evaluate cost-cutting proposals. At other times, they may be used to make projections for new-product launches. There are no restrictions on the applications for discounted cash flow analysis.
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Review of Abbreviations Throughout Assignment 9, 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.
After you’ve carefully read pages 298–334 in the Fundamentals of Corporate Finance textbook, complete Self-Check 9. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from Assignment 9, move on to Assignment 10.
ABBREVIATION MEANING
DCF Discounted cash flow
GAAP Generally accepted accounting principles
MACRS Modified accelerated cost recovery system
Self-Check 9 Indicate whether each of the following statements is True or False.
______ 1. Sunk costs are costs that can change in the short-term.
______ 2. An opportunity cost is the value of an investment that’s forgone to undertake another
investment.
______ 3. Working capital is already in aftertax terms.
______ 4. Revenues result in decreased cash flows at 1 minus the tax rate.
(Continued)
Lesson 3 83
ASSIGNMENT 10 Read this introduction to Assignment 10. Then, read Chapter 11, pages 335–364, in your Fundamentals of Corporate Finance textbook.
Evaluating NPV Estimates As you learned earlier, an investment has a positive net pres- ent value (NPV) if its market value exceeds its cost. Generally, NPV estimates are based on assumptions and projections. Therefore, the estimates are only as accurate as the underly- ing assumptions.
Scenario and Other What-If Analyses When you’re evaluating cash flow and NPV estimates, you’ll need to perform an organized analysis in which you ask what-if questions. The goal in performing this type of analysis is to assess the degree of forecasting risk and to identify the most important components of the success or failure of the investment.
Self-Check 9 ______ 5. Operating expenses result in decreased cash flows at 1 minus the tax rate.
______ 6. Depreciation generates cash flows by reducing corporate income tax expenses.
In the “Questions and Problems” section on pages 327–330 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 8, 12, 16, and 22.
Check your answers with those on page 143.
Corporate Finance84
One basic type of what-if analysis is the scenario analysis. Using this method, you can determine what changes occur in your NPV estimates when various business scenarios are applied. Another type of what-if analysis is the sensitivity analysis. In this method, you can determine what happens to NPV estimates when only one variable is changed. Finally, a method called simulation analysis can be used, and it combines elements of both scenario analysis and sensitivity analysis.
Break-Even Analysis When you’re making a new product or entering a new market, how much of the product can you sell? When a new business venture begins, the sales volume is often the most important variable, but is often the hardest to predict.
Break-even (B/E) analysis is a popular and commonly used tool for analyzing the relationship between sales volume and profitability. It involves the use of fixed costs (FC), variable costs per unit (VC), and sales revenues per unit to calculate the sales volume at which break-even is achieved. The accounting break-even point is the sales level that results in zero project net income.
The difference between the unit sales price and the unit variable cost is called the unit contribution margin.
Unit Contribution Margin = Unit Sales Price – Unit Variable Cost
The break-even point can be calculated by dividing the fixed cost by the unit contribution margin.
Break-Even Point = Fixed Costs � Unit Contribution Margin
Example: Assume that an item costs $3 per unit to manu- facture, and sells for $5 per unit. The firm has fixed costs of $900 per year. What is the unit contribution margin? What is the firm’s break-even point, in units?
Solution: Calculate the unit contribution margin.
Unit Contribution Margin = Unit Sales Price – Unit Variable Cost
Unit Contribution Margin = $5 – $3
Unit Contribution Margin = $2
Lesson 3 85
Then, calculate the break-even point.
Break-Even Point = Fixed Costs � Unit Contribution Margin
Break-Even Point = $900 � $2
Break-Even Point = 450 units
Answer: The contribution margin per unit is $2 per unit. The break-even point is 450 units.
Operating Cash Flow, Sales Volume, and Break-Even Break-even may be calculated in terms of aftertax cash flows. The cash break-even point is the sales level that results in a zero operating cash flow. Table 11.1 on page 353 of your textbook summarizes the definitions and provides formulas to calculate several different break-even points.
Operating Leverage Operating leverage is the degree to which a firm or project relies on fixed costs. Operating leverage is a measure of risk, and is comparable to financial leverage (from financial accounting). Remember that all assets are financed with debt or equity:
Assets = Liabilities + Owner’s Equity
Also, the total costs are either fixed costs or variable costs.
Total Costs = Fixed Costs + Variable Costs
Now, let’s consider both of these formulas together using Firm A and Firm B as examples.
Assets = Liabilities + Owner’s Equity
Firm A 100% = 50% + 50% Firm B 100% = 70% + 30%
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Given this illustration, would you prefer to loan money to Firm A or Firm B? Firm A has less debt (liabilities) than Firm B, and Firm B is more financially leveraged, or at greater risk. Therefore, all other things being equal, it would be better to loan money to Firm A.
However, financial leverage can be beneficial. During a period of growth, financial leverage can generate higher returns for a firm. Suppose that Firm A and Firm B have these costs:
Now, given this illustration, would you prefer to have a cost structure like that of Firm A or Firm B? Firm A has a lower proportion of fixed costs as compared to Firm B. Firm B, with its higher proportion of fixed costs, has more operating leverage. Like financial leverage, operating leverage isn’t neces- sarily a bad thing, but it represents greater risk, particularly in the event of a period of slow growth (or no growth).
Capital Rationing Firms, like individuals, don’t have unlimited resources for investment. Capital rationing is the situation that exists if a firm has positive NPV projects but can’t find the necessary funding. Generally, investment alternatives are ranked accord- ing to returns, and the project or investment with the highest return is selected first, the project with the second highest return is selected second, and so on.
Review of Abbreviations Throughout Assignment 10, 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.
Total Costs = Fixed Costs + Variable Costs
Firm A 100% = 50% + 50% Firm B 100% = 70% + 30%
Lesson 3 87
After you’ve carefully read pages 335–364 in the Fundamentals of Corporate Finance textbook, complete Self-Check 10. 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 3.
ABBREVIATION MEANING
B/E Break-even
CM Contribution margin
FC Fixed cost
VC Variable cost
Self-Check 10 Indicate whether each of the following statements is True or False.
______ 1. Business forecasts that use point estimates are at risk for error.
______ 2. Break-even analysis is used to analyze the relationship between sales
volume and profitability.
______ 3. Operating leverage is a measure of risk.
______ 4. The unit contribution margin is the same as the gross margin.
______ 5. The break-even point may be calculated by dividing fixed costs by the
unit contribution margin.
______ 6. Rent is an example of a variable cost.
In the “Questions and Problems” section on pages 360–364 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 8, 12, 18, 22, and 30.
Check your answers with those on page 144.
Corporate Finance88
NOTES
89
cash flows sufficient to recover its initial cost is called the
A. net present value.
B. average accounting return.
C. internal rate of return.
D. payback period.
A. divide fixed costs by variable costs.
B. add fixed costs to variable costs, and divide the total
by the unit contribution margin.
C. divide fixed costs by the unit contribution margin.
D. divide the unit contribution margin by variable costs.
divided by its initial cost is called the
A. profitability index.
B. average accounting return.
C. net present value.
D. discounted payback.
E x
a m
in a
tio n
E x
a m
in a
tio n
Lesson 3 Capital Budgeting
When you feel confident that you have mastered the material in
Lesson 3, 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.
EXAMINATION NUMBER
06058601
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
Examination, Lesson 390
value of $500,000. What is the firm’s average accounting return?
A. 25 percent C. 40 percent
B. 65 percent D. 12.5 percent
in an investment decision is called a(n)
A. pro forma. C. erosion.
B. sunk cost. D. opportunity cost.
circumstances is called
A. simulation analysis. C. operating leverage.
B. hard rationing. D. forecasting risk.
cash inflows likely to result from this initial investment is $98,293. What is the net
present value of this investment?
A. –$23,293 C. $51,707
B. $75,000 D. $23,293
A. average accounting return. C. project cash flow.
B. internal rate of return. D. crossover rate.
What is the unit contribution margin?
A. $23 C. $15
B. 21 percent D. 4.75 percent
A. discounted cash flow. C. net present value.
B. average accounting return. D. probability index.
by the average book value equals the
A. average accounting return. C. net present value.
B. internal rate of return. D. project cash flow.
Examination, Lesson 3 91
is called a(n)
A. stand-alone investment.
B. opportunity cost.
C. marginal revenue investment.
D. mutually exclusive investment decision.
depreciation deduction, calculated as the depreciation multiplied by the corporate
tax rate is called the
A. discounted cash flow.
B. accelerated cost recovery system.
C. depreciation tax shield.
D. net working capital.
of property under certain classifications is called the
A. modified depreciation allowance.
B. accelerated cost recovery system.
C. bottom-up approach.
D. depreciation tax shield.
A. pro forma statement.
B. modified depreciation statement.
C. discounted cash flow analysis.
D. project cash flow statement.
has fixed costs of $3,600 per year. What is the break-even point, in units?
A. 27 units C. 32,400 units
B. 400 units D. 200 units
A. operating cash flow. C. opportunity cost.
B. accounting break-even point. D. internal rate of return.
A. Operating leverage is a measure of risk.
B. Operating leverage increases as fixed costs increase.
C. Operating leverage decreases as variable costs decrease.
D. Operating leverage is a combination of scenario and sensitivity analysis.
Examination, Lesson 392
A. operating leverage. C. capital rationing.
B. accelerated cost recovery. D. sunk cost.
from existing products. This negative effect is known as
A. opportunity cost. C. erosion.
B. incremental cash flow. D. MACRS depreciation.
Risk and Return
INTRODUCTION In Lesson 4, you’ll continue to develop your understanding of the components of risk and return measures. This lesson includes two assignments.
In Assignment 11, you’ll review the material from Chapter 12 in your textbook. This assignment reviews the importance of capital market history and shows you how you can extract useful information from historical market data. You’ll learn some basic computations for capital gains and losses, and you’ll be introduced to the efficient markets hypothesis.
Assignment 12 covers the concepts from Chapter 13. This assignment more fully develops the concepts of risk and introduces the capital asset pricing model, which is used to calculate a firm’s cost of capital. You’ll learn about system- atic and unsystematic risk and how they affect investment returns. You’ll also review how investment portfolios are assembled, and the affect that diversification has on risk.
OBJECTIVES When you complete this lesson, you’ll be able to
� Calculate capital gains, losses, and overall returns in simple stock transactions
� Describe the efficient markets hypothesis
� 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 invest- ment portfolio
� Explain the capital asset pricing model and how it relates to the firm’s cost of capital
93
L e
s s
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4 L
e s
s o
n 4
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ASSIGNMENT 11 Read this introduction to Assignment 11. Then, read Chapter 12, pages 365–400, in your Fundamentals of Corporate Finance textbook.
Returns If you buy an asset, your gain (or loss) from that investment is called the return on your investment. In the case of a stock, this would include both dividends and capital gains (or losses).
Example: Suppose you purchased 100 shares of a stock at $37 per share (ignore all commissions). Assume the stock paid a dividend of $1.85 per share for the year. The stock price rose to $40.33 per share, and was then sold at that price. What was the total cost of the stock? What was the total amount of dividends received? What was the total amount of the capital gain (or loss)? What was the total dollar return?
Solution: Calculate the total cost of the stock.
Total Cost = Stock Price � Number of Shares
Total Cost = $37 � 100 shares
Total Cost = $3,700
Calculate the total amount of dividends received.
Total Dividends = Dividend � Number of Shares
Total Dividends = $1.85 � 100 shares
Total Dividends = $185
Calculate the total amount of the capital gain (or loss).
Capital Gain or Loss = (Ending Stock Price – Beginning Stock Price) � Number of Shares
Capital Gain or Loss = ($40.33 – $37) � 100 shares
Capital Gain or Loss = $3.33 � 100
Capital Gain = $333
Lesson 4 95
Calculate the total dollar return.
Total Dollar Return = Dividends Earned + Capital Gain
Total Dollar Return = $185 + $333
Total Dollar Return = $518
Answer: The total cost of the stock was $3,700. The total amount of dividends received was $185. The capital gain was $333, and the total dollar return was $518.
Example: Using the same stock purchase from the previous example problem, assume the sale price was $34.78 per share instead of $40.33. At this price, what was the total amount of the capital gain (or loss)? What was the total dollar return?
Solution: Calculate the total amount of the capital gain (or loss).
Capital Gain or Loss = (Ending Stock Price – Beginning Stock Price) � Number of Shares
Capital Gain or Loss = ($34.78 – $37) � 100 shares
Capital Gain or Loss = –$2.22 � 100
Capital Loss = –$222
Calculate the total dollar return.
Total Dollar Return = Dividends Earned + Capital Loss
Total Dollar Return = $185 + (–$222)
Total Dollar Return = –$37
Answer: The capital loss was –$222. The total dollar return was –$37.
The Historical Record A famous study by Roger Ibbotson and Rex Sinquefield examined rates of return in U.S. financial markets. Their study examined the year-to-year historical rates of return on portfolios consisting of the following five items:
� Large-company stocks
� Small-company stocks
Corporate Finance96
� Long-term corporate bonds
� Long-term corporate bonds
� U.S. Treasury bills
Using a starting year of 1925, the study calculated the returns on an investment made in each of these five categories, over an 80-year period that ended in 2005. The nominal, pretax returns were highest for the small-company stocks. However, these returns weren’t steadily achieved over the 80-year period. There was quite a lot of variability, and these results don’t suggest that small-company stocks will generate the highest returns for future years.
Average Returns: The First Lesson A risk premium is the excess return required from an invest- ment in a risky asset over that required from a risk-free investment. Table 7 summarizes the average annual returns and related risk premiums for different investments, over the years 1926 through 2005.
The first thing to note is that the risk premium for U.S. Treasury bills is zero. This is because the U.S. Government has never defaulted on a debt (that is, failed to pay). Therefore, a zero historical default rate suggests a future default risk of zero, which is often called a risk-free return. This concept of a zero default risk or risk-free return is frequently used by those in the finance industry.
Table 7
AVERAGE ANNUAL RETURNS AND RISK PREMIUMS
Average
Return
Risk
Premium
Large-Company Stocks 12.3% 8.5%
Small-Company Stocks 17.4% 13.6%
Long-Term Corporate Bonds 6.2% 2.4%
Long-Term Government Bonds 5.8% 2.0%
U.S. Treasury Bills 3.8% 0.0%
Lesson 4 97
The Variability of Returns: The Second Lesson The variability of returns from various investments is associ- ated with lower levels of certainty and therefore, higher levels of risk. Let’s consider an example.
As people age and approach retirement age, they have less time to recover from personal investment losses. To protect their savings, therefore, they often want to reduce the risk in their investment portfolios. Typically, they do this by increas- ing the amount of their personal portfolio invested in bonds, and reducing the amount invested in stocks. However, they may retain certain stocks that have provided many years of quarterly dividend payouts. These stocks are viewed as less risky than others, and the steady history of quarterly dividend payouts tends to make the price of these stocks less volatile (relative to others in the stock market as a whole). The upside of keeping these stocks is that there’s little risk of stock price volatility. The downside, of course, is that the price of these stocks isn’t likely to suddenly increase. In other words, these stocks aren’t likely to jump in price and make the investor wealthy overnight.
In terms of stock prices, a lot of variability equals volatility. To help with stock price calculations and predictions, statisti- cians have found ways to quantify these measures in terms of variance and the standard deviation. The variance is the average squared difference between an investment’s actual return and its average return. The standard deviation is the positive square root of the variance.
A high degree of uncertainty about a firm’s future will usually lead to greater variability in the firm’s stock price. The return on this type of stock (including both increases in the stock price per share and dividends) will usually be more volatile than average, and have a higher variance and standard deviation.
Corporate Finance98
Alternatively, a low degree of uncertainty about a firm’s future will usually lead to lesser variability in the firm’s stock price. The return on this type of stock will generally be less volatile than average, and will have a lower variance and standard deviation.
More about Average Returns Stock returns may be calculated either geometrically or arithmetically. The geometric average return for a stock is defined as the average compound return earned per year over a multiyear period. The arithmetic average return is defined as the return earned in an average year over a multiyear period.
Capital Market Efficiency In the fields of finance, economics, and accounting, an efficient capital market is defined as a market in which security prices reflect available information. This means that in an efficient capital market, based on the available information, there’s generally no reason to believe current security prices are either too low or too high. The efficient markets hypothesis (EMH) asserts that well-organized capital markets (such as the NYSE) are efficient.
Of course, there are exceptional cases in which market failures have occurred, even in a so-called efficient market. Two examples of famous market failures can be seen in the Enron and WorldCom corporations. In these examples, both the financial auditors and the capital markets failed to quickly and efficiently investigate these firm’s financial statements, and thus failed to detect the intentional deceit or fraud that occurred.
After you’ve carefully read pages 365–400 in the Fundamentals of Corporate Finance textbook, complete Self-Check 11. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from Assignment 11, move on to Assignment 12.
Lesson 4 99
Self-Check 11 Indicate whether each of the following statements is True or False.
______ 1. The risk premium for U.S. Treasury bills is zero.
______ 2. The gain or loss from an investment is called the return on the investment.
______ 3. The excess return required from an investment in a risky asset over that
required from a risk-free investment is called the variance.
______ 4. A market in which security prices accurately reflect available information
is called an efficient capital market.
______ 5. A low degree of uncertainty about a firm’s future usually leads to greater
levels of variability in the firm’s stock price.
______ 6. Imagine that you purchased 25 shares of a stock at $28 per share. The stock
paid a dividend of $1.45 per share for the year. Given this information, you can
calculate that the total cost of the stock was $736.25.
In the “Questions and Problems” section on pages 396–398 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 6, 16, and 20.
Check your answers with those on page 145.
Corporate Finance100
ASSIGNMENT 12 Read this introduction to Assignment 12. Then, read Chapter 13, pages 401–436, in your Fundamentals of Corporate Finance textbook.
Expected Returns and Variances In this chapter, you’ll learn how to analyze returns and variances when the information you have concerns future possible returns and their probabilities.
The expected return is defined as the return on a risky asset expected in the future. The risk premium is the difference between the return on a risky investment and the return on a risk-free investment. The following formula can be used to calculate the risk premium:
Risk Premium = Expected Return – Risk-Free Rate
The expected return may, of course, vary from any point estimate. The range of this variation can be used to calculate a variance and a standard deviation.
Portfolios A portfolio is a group of assets (such as stocks and bonds) held by an investor. Portfolios may be assembled for individuals, other entities (such as pension funds), or for mutual funds. Any type of portfolio may be designed to include a specified level of risk or risk premium. Assembling a portfolio is com- plex, and investors need to make many decisions about how to invest their money. However, speaking in very general terms, investment advisors usually recommend that younger persons invest their money in higher-risk securities, because these may generate higher returns over the long term. In con- trast, older individuals who are closer to the age of retirement are usually advised to participate in lower-risk portfolios.
Lesson 4 101
Announcements, Surprises, and Expected Returns The total annual return on any stock investment consists of two parts—expected returns and unexpected returns. The expected return is the normal return shareholders and the market expect to receive from the investment. The unexpected return is any additional return (either positive or negative) that results from unexpected information revealed during the year. This information may come from various sources, and may include good or bad news about the company, a sudden drop in interest rates, or a government announcement.
The total return can be expressed with the following formula:
Total Returns = Expected Returns + Unexpected Returns
Information that comes from news announcements tends to have more significant and faster effects on stock prices than information from other sources. It’s often difficult to predict the effects of a news announcement on stock prices, particu- larly if the news is surprising.
For example, suppose a small biotech firm has developed a new cancer drug. The drug is effective, but causes many dangerous side effects. For this reason, many people in the drug industry anticipate that the Food and Drug Administration (FDA) will refuse to approve the drug. However, the drug does in fact receive approval from the FDA. When the news of the FDA approval is announced, the news is likely to have an imme- diate and significant positive effect on the biotech firm’s stock price.
Risk: Systematic and Unsystematic In the world of investments, risk can be classified as being either systematic or unsystematic. Systematic risk affects a large number of assets, while unsystematic risk affects only a small number of assets, or just one unique asset.
Corporate Finance102
The unexpected components of returns may be classified as systematic or unsystematic, and can be represented with the following formula:
Unexpected Returns = Systematic Portion + Unsystematic Portion
Also, total returns on an investment can be calculated with the following formula:
Total Returns = Expected Returns + Systematic Portion + Unsystematic Portion
Diversification and Portfolio Risk In the process of diversification, an investment is spread across assets to form a portfolio. The process of diversifica- tion will eliminate some (but not all) of the risk.
Some of the variability associated with individual assets is eliminated by diversification. When assets are combined in a portfolio, the unsystematic risk tends to be eliminated. A portfolio with many assets has almost no unsystematic risk. Therefore, the terms diversifiable risk and unsystematic risk are often used interchangeably, as shown here:
Diversifiable Risk = Unsystematic Risk
Diversification is recommended by the financial community as a way to remain invested in securities during economic downturns and upturns while reducing unsystematic risk.
Systematic Risk and Beta Unlike unsystematic risk, the systematic risk in an investment can’t be eliminated by diversification. According to the systemic risk principle, the estimated return on a risky asset depends only on that asset’s systemic risk. Therefore, no matter how much total risk an asset has, only the systemic portion is relevant in determining the expected return.
Lesson 4 103
The amount of systemic risk present in a particular risky asset relative to that in an average asset is defined as the beta coefficient. In calculations and formulas, the beta coefficient is represented by the Greek symbol β.
An average asset is defined as having a beta coefficient of 1.0. This means that an asset with a beta coefficient of less than 1.0 has less systemic risk than an average asset. An asset with a beta coefficient of greater than 1.0 has more systemic risk than an average asset. So, for example, an asset that has a beta coefficient of 0.5 has half as much systemic risk as an average asset. An asset with a beta coefficient of 2.0 has twice as much systemic risk as an average asset.
The Security Market Line The security market line (SML) is a positively sloped straight line that illustrates the relationship between expected return and the beta coefficient. Perhaps the most practical applica- tion of the SML is the capital asset pricing model (CAPM), which is an equation that shows the relationship between expected return and beta. The CAPM equation is shown here:
E (Ri ) = Rf + [E (RM ) – Rf ] � βi In this formula, E (Ri ) stands for the expected return; Rf is the risk-free rate of return (that is, the rate of return on treasury securities, which is calculated for you or available through research); E (RM ) is the market rate of return for a comparable investment vehicle or security, and β is the beta coefficient (calculated for you or available through research). The only value you must project or estimate is E (RM ). Other measures are available through a variety of sources and can be researched on the Internet. Of course, the measures available are histori- cal (not projected), and your projection of these measures may differ from historical rates.
Corporate Finance104
The SML and the Cost of Capital: A Preview The CAPM-based application of the SML, for our purposes, is very helpful toward explaining how one calculates a firm’s cost of capital. The cost of capital is the minimum required return on a new investment.
Review of Abbreviations Throughout Assignment 12, 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.
After you’ve carefully read pages 401–436 in the Fundamentals of Corporate Finance textbook, complete Self-Check 12. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from these two assignments, complete the examination for Lesson 4.
ABBREVIATION MEANING
CAPM Capital asset pricing model
FDA Food and Drug Administration
SML Security market line
Lesson 4 105
Self-Check 12 Indicate whether each of the following statements is True or False.
______ 1. When calculating the risk premium for an investment, you would subtract the
risk-free rate from the expected return.
______ 2. The total return on an investment can be calculated by adding the expected
returns to the unexpected returns.
______ 3. The terms diversifiable risk and unsystematic risk are often used interchangeably.
______ 4. An average asset is defined as having a beta coefficient of 0.0.
______ 5. An asset that has a beta coefficient of less than 1.0 has more systemic risk
than an average asset.
______ 6. In general terms, older persons are usually advised to invest their money in
higher-risk securities, because these may generate higher returns over the long term.
In the “Questions and Problems” section on pages 432–435 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 6, 10, 14, 18, 24, and 26.
Check your answers with those on page 145.
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107
between the expected return on a market portfolio and the
risk-free rate, is called the
A. market risk premium.
B. portfolio variance.
C. arithmetic average return.
D. cost of capital.
A. one-tenth of the risk of an average asset.
B. the same systemic risk as an average asset.
C. one-half the systemic risk of an average asset.
D. twice as much systemic risk as an average asset.
in stock prices, the market is said to be
A. weak form efficient.
B. geometrically efficient.
C. strong form efficient.
D. average return efficient.
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Lesson 4 Risk and Return
When you feel confident that you have mastered the material in
Lesson 4, 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.
EXAMINATION NUMBER
06058701
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
Examination, Lesson 4108
commissions). Assume the stock paid a dividend of $1.20 per share for the year.
The stock price rose to $52.78 per share, and was then sold at that price. What
was the total amount of dividends received?
A. $120 C. $9,200
B. $240 D. $1,356
A. Risk premium C. Systematic risk
B. Unsystematic risk D. Total risk
A. arithmetic average return. C. geometric average return.
B. normal distribution. D. standard deviation.
A. risk premium = expected return + projected return
B. total returns = expected return + unexpected return
C. unexpected returns = systematic portion + unsystematic portion
D. risk premium = expected return – risk-free rate
commissions). Assume the stock paid a dividend of $1.45 per share for the year.
The stock price rose to $42.50 per share, and was then sold at that price. What
was the total dollar return?
A. $12,750 C. $2,250
B. $2,685 D. $435
are efficient is called the
A. geometric average return. C. efficient markets hypothesis.
B. normal distribution. D. standard deviation.
A. portfolio weight. C. portfolio variance.
B. beta coefficient. D. systematic risk.
Examination, Lesson 4 109
and the beta coefficient is called the
A. frequency distribution. C. geometric average return.
B. bell curve. D. security market line.
The stock paid a dividend of $0.75 per share for the year. What is the total cost of
the stock?
A. $112.50 C. $1,800
B. $2,812.50 D. $2,700
A. greater variability in the firm’s stock price.
B. lower variability in the firm’s stock price.
C. a lower variance and standard deviation.
D. less volatile returns on the stock.
return and beta is called the
A. security market beta line.
B. unsystematic risk equation.
C. principle of diversification.
D. capital asset pricing model (CAPM).
A. average return. C. beta coefficient.
B. cost of capital. D. risk premium.
A. normal distribution. C. arithmetic average return.
B. geometric average return. D. standard deviation.
A. Total Return = Expected Return + Unexpected Return
B. Total Return = Unexpected Return + Stock Price
C. Total Return = Stock Price � Number of Shares
D. Total Return = Dividend � Number of Shares
Examination, Lesson 4110
(but not all) of the risk is called the
A. systematic component of return. C. principle of diversification.
B. portfolio variance. D. beta coefficient.
commissions). Assume that the stock paid a dividend of $1.40 per share for the
year. The stock price rose to $34.65 per share, and was then sold at that price.
What was the total amount of the capital gain (or loss)?
A. $2,800 C. $140
B. $665 D. $3,465
required on the risky investment is called a
A. risk premium. C. frequency distribution.
B. portfolio weight. D. portfolio variance.
Cost of Capital and Financial Policy and Options
INTRODUCTION Lesson 5 focuses on the cost of capital, financial leverage, and capital structure policy. The lesson contains three assignments.
Assignment 13 covers the material in Chapter 14 of your text- book. The main topic of this assignment is the cost of capital. You’ll learn about the weighted average cost of capital, which represents the discount rate used by a firm to calculate the net present value of investment alternatives. The separate components of debt and equity will be examined.
Assignment 14 includes the topics from Chapter 16. This assignment more fully develops the concepts associated with financial leverage, and the debt and equity components of a firm’s capital structure. You’ll also learn about the cost of bankruptcy and the proceedings that a firm uses to declare bankruptcy.
OBJECTIVES When you complete this lesson, you’ll be able to
� Calculate the weighted average cost of capital and its components, the weighted average cost of debt and equity
� Explain the debt and equity components of a firm’s capital structure
� Discuss the concept of financial leverage
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� Define the basic types of corporate bankruptcy proceedings
� Describe the costs associated with the bankruptcy process
ASSIGNMENT 13 Read this introduction to Assignment 13. Then, read Chapter 14, pages 437–470, in your Fundamentals of Corporate Finance textbook.
The Cost of Capital: Some Preliminaries Remember that all assets are financed with debt or equity, as illustrated in the following basic equation:
Assets = Liabilities + Owner’s Equity
Any bondholder or financial institution will require a profit (a rate of return) on money loaned to a firm, typically in the form of interest. In the same way, it’s reasonable for a firm’s shareholders to expect a rate of return, typically in the form of dividends or capital appreciation (an increase in value) of the firm’s stock price per share.
Combined, debt and equity are used to finance the assets a firm uses to generate revenues and profits, and both debt and equity holders expect some rate of return. Therefore, a cost is associated with the financing of a firm’s assets. This cost is called the cost of capital.
The most important point to remember is that the cost of capital associated with an investment depends on the risk of that investment. Therefore, the cost of capital depends primarily on the use of the funds, not the source.
Lesson 5 113
The Cost of Equity The cost of equity is the return equity investors require on their investment in a firm. This amount can be difficult to determine because it can’t be directly observed. Instead, the cost of equity must be estimated. There are two approaches to estimating a firm’s cost of equity:
The security market line (SML) approach
The dividend growth model approach uses the following formula for calculations:
RE = D1/P0 + g
In this formula, RE is the return shareholders require on the stock (or the firm’s cost of equity capital), D1 is the next period’s projected dividend, P0 is the stock price per share, and g is the constant rate at which the firm’s dividend is projected to grow.
The second method used to calculate a firm’s cost of equity is the security market line (SML) approach, which uses the following formula:
E(Ri ) = Rf + [E(RM ) – Rf ] � βi Remember that in this formula, E(Ri ) stands for the return shareholders require on the stock (or the firm’s cost of equity capital); Rf stands for the risk-free rate of return; E(RM ) is the market rate of return for a comparable investment, and β is the beta coefficient.
The dividend growth model is ideally suited for use in a firm that pays all or most of its earnings to shareholders in the form of dividends. In contrast, the SML approach is ideally suited for use in a growth firm. A growth firm is defined as a firm that pays few or no dividends and instead retains profits in the corporation for growth, providing shareholders with capital gains appreciation through an increase in stock values.
Corporate Finance114
The Costs of Debt and Preferred Stock The cost of debt is the return lenders require on a firm’s debt. The cost of debt is the interest rate a firm must pay on new borrowing, and can generally be directly observed.
Remember that a preferred stock has a fixed dividend paid every period forever, so a share of a preferred stock is basically a perpetuity. The cost of preferred stock can be calculated by using the following formula:
RP = D/P0 In this formula, RP stands for the return the shareholders require on the preferred stock, D stands for the next period’s projected dividend, and P0 stands for the current price per share for the preferred stock.
The Weighted Average Cost of Capital The weighted average cost of capital (WACC) is the overall return a company must earn on its existing assets to main- tain the value of its stock and to satisfy its owners, creditors, and providers of capital. The WACC is equal to the weighted average of the cost of equity and the aftertax cost of debt. Again, consider the following formula:
Assets = Liabilities + Owner’s Equity
In this formula, we can say that the WACC is the cost of the debt (liabilities) and equity used to finance assets. The WACC is the aftertax cost.
You should also remember the information you learned in an earlier lesson: operating expenses result in decreased cash flows at 1 minus the tax rate (1 – T ).
The following formula can be used to calculate the weighted average cost of capital (WACC):
WACC = (E/V) � RE + (D/V) � RD � (1 – TC )
In this formula, E stands for equity; V stands for the combined market value of debt and equity; D stands for debt; RE stands for return on equity; and RD � (1 – TC ) stands for the aftertax interest rate.
Lesson 5 115
Remember that the return on equity can be calculated using the following formula:
E (Ri ) = Rf + [E (RM ) – Rf ] � βi There are a number of practical difficulties involved in calcu- lating the return on equity (as well as the relative fair market values of debt and equity), but each firm chooses to resolve these issues in its own way. Our focus is on the application of the WACC, which is the discount rate used by firms to calculate the net present value (NPV) of projects.
As you learned in an earlier lesson, the net present value (NPV) approach is used to determine whether an investment, project or undertaking creates value in excess of its cost. The NPV is calculated as follows:
PV (Aftertax Cash Inflows) – PV (Aftertax Cash Outflows) = NPV (Aftertax Cash Flows)
A project with an NPV of zero or greater is acceptable. Therefore, an NPV of zero (using the WACC) must include a profit com- ponent. This makes sense, because the owner’s equity includes retained earnings (net income less dividends paid to share- holders). The growth in retained earnings increases the owner’s equity, resulting in the inclusion of a profit component in the WACC.
If the WACC didn’t contain a profit component, a project with an NPV of zero would be a break-even or unprofitable project, and no rational person would take the risk of investing in a project with zero profit potential. Instead, they would invest in low-risk or no-risk investments (such as U.S. Treasury securities).
Divisional and Project Costs of Capital It’s appropriate to use the WACC as a discount rate for future cash flows only when the proposed investment is similar to a firm’s existing activities. Therefore, in a corporation that has more than one line of business, problems can arise when using the WACC. The divisional cost of capital is the cost of capital in each division of a corporation. Together, the divisional costs of capital add up to the firm’s overall cost of capital.
Corporate Finance116
Problems can arise if you try to use the WACC inappropriately with a firm that has several different divisions. One solution is to use the pure play approach to estimate the required return on an investment. The pure play approach uses a WACC unique to a particular project, based on companies in similar lines of business. This approach allows the costs of capital to be calculated for the firm overall, or at the divisional level.
Flotation Costs and the Weighted Average Cost of Capital As new projects are selected for investment, a firm may decide to borrow additional funds to finance these additional projects. The firm may raise money by issuing, or floating, new stocks or bonds. The costs associated with the new stock or bond issues are called flotation costs.
As this process of project investment leads to borrowing, the cost of borrowing increases. Increasing levels of financial leverage increase the risk to the lender, as debt-to-equity ratios increase. At some point, the increased cost of borrow- ing will prohibit the financing of additional projects. At that point, the incremental WACC becomes so high that an NPV of zero or greater can’t be achieved.
After you’ve carefully read pages 437–470 in the Fundamentals of Corporate Finance textbook, complete Self-Check 13. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from Assignment 13, move on to Assignment 14.
Lesson 5 117
ASSIGNMENT 14 Read this introduction to Assignment 14. Then, read Chapter 16, pages 508–545, in your Fundamentals of Corporate Finance textbook.
The Capital Structure Question The types of debt and equity a firm uses to finance its assets determine the firm’s capital structure. Financial managers attempt to identify the capital structure that maximizes the
Self-Check 13 Indicate whether each of the following statements is True or False.
______ 1. Together, the divisional costs of capital add up to the firm’s overall cost of capital.
______ 2. As the process of project investment leads to borrowing, the cost of borrowing
increases.
______ 3. The cost of capital depends primarily on the source of funds, not the use.
______ 4. The WACC is equal to the weighted average of the cost of equity and the aftertax
cost of debt.
______ 5. An NPV of zero, using the WACC, excludes a profit component.
______ 6. Owner’s equity excludes retained earnings or profits.
In the “Questions and Problems” section on pages 465–467 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 4, 8, 12 (a and b only), 16, and 20.
Check your answers with those on page 146.
Corporate Finance118
value of the firm. To do this, they vary the amount of debt and equity financing to minimize the firm’s weighted average cost of capital (WACC).
The Effect of Financial Leverage Financial leverage refers to the extent to which a firm relies on debt. Higher levels of debt indicate the use of more financial leverage in a firm’s capital structure. Higher levels of debt (and financial leverage) may at first suggest increased earnings per share (EPS) and increased return on equity (ROE). However, the interest expense associated with these higher levels of debt reduces both EPS and ROE.
To illustrate the effects of financial leverage, a comparison of a firm’s capital structure under no debt and under 50 percent debt is shown in Table 8. The table illustrates the effect on EPS, ROE, and (because financial leverage results in interest expense) earnings before interest and taxes (EBIT). The table
Table 8
IMPACT OF CAPITAL LEVERAGE
NO DEBT 50% DEBT
Assets $8,000,000 $8,000,000
Debt $0 $4,000,000
Equity $8,000,000 $4,000,000
Debt-to-Equity Ratio 0 1.0
Shares Outstanding 400,000 200,000
Interest Rate 10% 10%
EBIT $1,000,000 $1,000,000
Interest Expense $0 $400,000
Net Income $1,000,000 $600,000
ROE 12.5% 15.0%
EPS $2.50 $3.00
Lesson 5 119
ignores corporate income taxes to simplify the coverage of financial leverage. In the “50% Debt” column, note that the end result is an increase in both ROE and EPS. In this case, the use of financial leverage appears to have been beneficial to equity or shareholders.
Using a modern example, perhaps you’ve seen a “get rich with real estate” infomercial on late-night cable television. Some of these programs suggest they can teach you how to purchase real estate properties with little or no money down. These programs recommend using the highest possible levels of financial leverage when purchasing real estate, in anticipation of appreciating property values. This business model tends to work very well during a period of fast-rising real estate values and high prices. However, in periods of economic downturn, real estate values go down and the numbers of residential property foreclosures increase. These foreclosures illustrate the downside of the use of excessive levels of financial leverage. Financial leverage, therefore, can be beneficial in a “boom” economy or economic upturn, but devastating in a “bust” economy or recession.
Capital Structure and the Cost of Equity Capital The cost of equity capital (without corporate income taxes) can be illustrated by the following formula:
RE = RA + (RA – RD ) � (D/E)
In this formula, RE stands for the return on the equity com- ponent of the firm’s capital structure; RA stands for the required rate of return on the firm’s assets; RD stands for the firm’s cost of debt; and D/E is the firm’s debt-to-equity ratio. Therefore, the firm’s cost of equity is dependent on RA, RD, and D/E.
The cost of equity can be viewed as the combination of two risk components: business risk and financial risk. Business risk is the equity risk that comes from the nature of a firm’s operations. Financial risk is the equity risk that comes from a firm’s financial policy (that is, its capital structure).
Corporate Finance120
Again, using the equation for the cost of equity capital, business risk and financial risk can be associated with its components, as follows:
RE = RA + (RA – RD ) � (D/E)
Total Risk = Business Risk + Financial Risk
M&M Propositions I and II with Corporate Taxes Two Nobel prize-winners for economics, Franco Modigliani and Merton Miller, developed the Modigliani-Miller theorem for corporate finance. This theorem proposed that under certain conditions, the value of a company isn’t affected by how it chooses to arrange its finances. In other words, the company’s value isn’t affected whether it’s financed by equity or debt.
In your textbook, the concepts from the Modigliani-Miller theorem are presented as M&M Propositions I and II. According to M&M Proposition I, the value of a firm is independent of the firm’s capital structure. Then, M&M Proposition II states that a firm’s cost of equity capital is a positive linear function of the firm’s capital structure.
Remember that the corporate interest expense paid on debt financing is tax deductible, but the dividends paid to com- pensate shareholders for the use of equity is taxed (not tax deductible). The cost of equity capital, with corporate income taxes, can be calculated by using the following formula:
RE = RU + (RU – RD ) � (D/E) � (1 – TC )
In this formula, RE stands for the return on the equity component of the firm’s capital structure. RU stands for the unlevered cost of capital. (The unlevered cost of capital is the cost of capital for a firm that has no debt.) RD represents the firm’s cost of debt, D/E represents the firm’s debt-to-equity ratio, and TC is the firm’s marginal corporate income tax rate. Therefore, the firm’s cost of equity is dependent on RU, RD, D/E, and TC.
Lesson 5 121
Bankruptcy Costs As a firm’s debt-to-equity ratio rises, the increased level of financial leverage can be viewed as an increase in the level of risk (and default risk) associated with the firm’s capital structure. As debt rises, so do the payments required to service the debt (that is, cash outflows for interest expenses). Just as an individual can become overextended in his or her use of personal debt (home mortgages and credit cards), a corporation might use too much financial leverage and find itself unable to make corporate debt interest payments. If this happens, the firm may be forced into bankruptcy, and thereby incur both direct and indirect bankruptcy costs.
Optimal Capital Structure Firms borrow money because the interest expenses from these debts are tax deductible, and this tax deductibility feature has economic value. At low levels of debt, the risk of bankruptcy is low, and the benefits from debt exceed the costs. The static theory of capital structure suggests that firms will borrow debt up to the point where the benefit from the last dollar of debt is equal to the cost associated with the increased probability of financial distress.
The Pie Again The extended pie theory holds that all claims are paid from the cash flows of the firm, and include payments to the following:
� Stockholders
� Creditors
� The government
� Bankruptcy courts and lawyers
� All other claimants to the cash flows of the firm
In this model, the value of all claims against the firm’s cash flows isn’t affected by capital structure, but the relative values of claims change as the amount of debt financing is increased.
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The Pecking-Order Theory The pecking-order theory provides an alternative to the static trade-off theory. It suggests that firms prefer to use internal financing when possible. Under the pecking-order theory, there are several important points:
� There’s no optimal debt-equity ratio. Instead, a firm’s capital structure is determined by its need for external financing.
� Profitable firms will need less external financing and will therefore have less debt.
� To avoid selling new equity, companies will want to stockpile internally generated cash in a reserve called financial slack.
Observed Capital Structures Capital structure is influenced by industry, but there’s no fully satisfactory theory that explains these regularities. Most U.S. corporations tend to have low debt-equity ratios.
A Quick Look at the Bankruptcy Process One possibility of using debt is the possibility of financial distress, which may be defined as one of the following:
Legal bankruptcy, in which a failing firm brings a petition to court for bankruptcy
Technical insolvency, which occurs when a firm is unable to meet its financial obligations
Accounting insolvency, which occurs when a firm’s total book liabilities exceed the book value of the total assets
Lesson 5 123
After you’ve carefully read pages 508–545 in the Fundamentals of Corporate Finance textbook, complete Self-Check 14. Check your answers with those provided at the back of this study guide. When you’re sure you understand the material from these two assignments, complete the examination for Lesson 5.
Self-Check 14 Indicate whether each of the following statements is True or False.
______ 1. Financial managers will attempt to maximize the value of a firm by varying the amount
of debt and equity financing to minimize the firm’s weighted average cost of capital
(WACC).
______ 2. Financial leverage refers to the extent to which a firm relies on debt.
______ 3. When a firm has a high level of debt, the interest expense associated with the
debt will reduce both EPS and ROE.
______ 4. The cost of equity can be viewed as the combination of business risk and financial risk.
______ 5. An increase in financial leverage reduces the level of risk (and default risk)
associated with a firm’s capital structure.
______ 6. Bankruptcy proceedings can take the form of either liquidation or reorganization.
In the “Questions and Problems” section on pages 541–544 of the Fundamentals of
Corporate Finance textbook, answer questions 2, 6, 10, 12, and 16.
Check your answers with those on page 147.
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needs to earn to satisfy all its investors?
A. NPV C. BASF 2015
B. RE D. WACC
A. cost of a bond.
B. cost of preferred stock.
C. cost of common stock.
D. dividend resulting from one share of stock.
A. the financial leverage and the cost of capital.
B. corporate taxes and shareholder claims.
C. business risk and financial risk.
D. the weighted average cost of capital and the capital
structure.
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Lesson 5 Cost of Capital and Financial Policy
and Options
When you feel confident that you have mastered the material in
Lesson 5, 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.
EXAMINATION NUMBER
06058801
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
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Examination, Lesson 5126
A. financial leverage. C. warrant.
B. cost of debt. D. cost of equity.
A. internal financing. C. flotation.
B. financial leveraging. D. bankruptcy.
adjustment factors to or from the WACC, the firm is using the _______ approach.
A. basic C. objective
B. subjective D. pure play
A. cost of equity. C. conversion value.
B. financial leverage. D. beta coefficient.
capital gains through an increase in stock values is called a
A. business failure. C. leveraged firm.
B. pure play. D. growth firm.
outstanding debt, the company rate is
A. critical. C. low.
B. (E/V) � RE. D. irrelevant.
A. weighted average cost of capital.
B. financial leverage.
C. interest tax shield.
D. unlevered cost of capital.
to continue operations is called
A. liquidation. C. reorganization.
B. tax shielding. D. capital structuring.
A. restructures. C. prepares for bankruptcy.
B. refinances. D. prepares for its IPO.
Examination, Lesson 5 127
is called a(n)
A. pure play. C. growth firm.
B. unlevered company. D. internally financed firm.
value of its stock and to satisfy its owners, creditors, and providers of capital is
called the
A. reorganization value.
B. flotation cost.
C. weighted average cost of capital.
D. capital structure.
A. the court assigns an unbiased individual to run the company in the interim.
B. the judge prepares a reorganization plan the company must follow.
C. payments to creditors and shareholders are suspended.
D. the “debtor in possession” runs the business.
A. cost of equity.
B. weighted average cost of capital.
C. capital structure weight.
D. project cost of capital.
with the new stock or bond issues are called the
A. intrinsic value. C. strike costs.
B. floor value. D. flotation costs.
A. reorganization priority list. C. absolute priority rule.
B. bankruptcy proceeding rule. D. prepack claims petition.
A. floor value. C. capital appreciation.
B. divisional cost of capital. D. option cost.
A. technical insolvency. C. reorganization.
B. liquidation. D. accounting insolvency.
Examination, Lesson 5128
NOTES
OVERVIEW This project integrates quite a few components of your course. The most important thing to keep in mind, as you progress through this project, is to take one step at a time.
Do not rush through this project. After completing each step, pause, take a break, and give some thought to the task you’ve just completed. If necessary, refer back to the relevant lesson, assignments, and textbook chapters each step refers to. This will reinforce the learning process.
INSTRUCTIONS In this project, you’ll create a loan amortization schedule for an example mortgage loan. Imagine the mortgage is for a nonresidential real property your company has purchased. The property includes land and a building. Once you’ve created the amortization schedule, you can use it to prepare other financial documents. Your project is divided into sev- eral steps for you to follow. Each step includes figures that illustrate the concepts.
Step 1: Create a Loan Amortization Schedule In this first step of your project, you’ll need to create a loan amortization schedule. The following table illustrates the pay- ments and interest amounts for a fixed-rate, 30-year mortgage loan. The total amount of the mortgage is $300,000, and the interest rate is 6 percent. This mortgage requires monthly payments of $1,798.65, with a final payment of $1,800.23. The table was created in Excel.
The following is an explanation of the columns in the table:
� The first column in the table, with the heading “Payment Number,” shows the 360 payments required to pay off the mortgage loan (30 years, with 12 monthly payments per year).
129
G ra
d e
d P
ro je
c t
G ra
d e
d P
ro je
c t
� The second column, with the heading “Payment Amount,” shows the monthly payment amount.
� The third and fourth columns show the portion of the monthly payment paid for interest, and the portion paid towards the principal.
� The fifth column, headed “Balance,” shows the starting balance of $300,000, and the remaining balance each month after the principal is subtracted.
� The sixth column, headed “Current,” reflects the current portion of the principal (12 months).
� The amounts in the “Non-Current” column are calculated by subtracting the current portion of the principal from the total balance.
� The “Annual Interest Expense” column provides a run- ning total of the interest expense on the mortgage for the entire 12-month period.
� The “Totals” under the “6% Interest Expense” and “Principal” columns show the final totals for the 30-year life of the mortgage.
Graded Project130
Payment Number
Payment Amount
6% Interest Expense
Principal Balance Current Non-
Current
Annual Interest Expense
0 $300,000.00 $3,684.02 $296,315.98 $0
1 $1,798.65 $1,500.00 $298.65 $299,701.35 $3,702.44 $295,998.91
2 $1,798.65 $1,498.51 $300.14 $299,401.21 $3,720.95 $295,680.26
————————————-Break in Sequence————————————-
359 $1,798.65 $17.86 $1,780.79 $1,791.28 $1,791.27 $0
360 $1,800.23 $8.96 $1,791.27 $0 $0 $0 $685.50
Totals $347,515.58 $300,000.00
Once you’ve determined how each of the amounts in the table are obtained, you can calculate them and fill them in for all 360 payments.
Note that the table shows only the figures for the first two payments and the last two payments; you’ll need to calculate the amounts for the remaining payments and fill them in.
Once this loan amortization schedule is completely filled in, it can be printed out and used to prepare other financial state- ments. For example, when the first payment of $1,798.65 is made, the following accounting journal entry would be made:
Notice that the amounts of principal and interest in this journal entry would change for each and every payment.
When originated, the journal for the loan was created as shown here:
Graded Project 131
Debit Credit
Mortgage Payable $298.65 Interest Expense $1,500.00 Cash $1,798.65
Debit Credit
Fixed Asset–Real Property $300,000 Mortgage Payable $300,000
The balance of this mortgage, after the first payment, is $299,701.35. If a classified balance sheet were prepared on this date, the current portion of the mortgage would be $3,702.44, and the noncurrent portion of the mortgage would be $295,998.91.
If you were to create a chart of the interest and principal components of each mortgage payment, over the life of the mortgage, it would look like the following illustration:
Once you’ve completed the amortization schedule for this loan, you’ll be able to create loan amortization schedules for your own home mortgage, automobile loan, personal loans, and so on. You can even create a pro forma report that shows the effects of additional principal payments on the life of your loan (this assumes you don’t have a prepayment penalty, which is typically the case). You may be surprised at the effects a modest additional principal payment has on the life of a loan.
Graded Project132
Once the monthly schedule is completed, generate an annual- ized version, using the following preferred format:
Step 2: Create a Depreciation Schedule The next step in your project is to create a depreciation schedule for the (fictional) property purchased with this loan. When the property was purchased, an appraisal was performed. The property included separate components of land and improvements (the building), and also included some fixtures (appliances, such as a refrigerator). You paid a slightly higher appraisal fee than usual, and instructed the appraiser to provide you with the following breakdown of values:
Graded Project 133
Year Payment Number
Balance Current Non-Current Annual Interest Expense
0 $300,000.00 $3,684.02 $296,315.98 $0
1 12 $296,315.98 $3,911.24 $292,404.75 $17,899.78
2 24 $292,404.75 $4,152.47 $288,252.27 $17,672.56
————————————-Break in Sequence————————————-
28 336 $40,584.10 $19,684.22 $20,899.88 $3,043.13
29 348 $20,899.88 $20,899.88 $0 $1,899.58
30 360 $0 $0 $0 $685.50
Total $347,515.58
Appraised Values
Percentage
Land $45,000 14.29%
Improvements $260,000 82.54%
Fixtures $10,000 3.17%
Total $315,000 100.00%
Your mortgage loan cost of $300,000 must be allocated between these different asset classes, so you can use the appropriate depreciable life to prepare a depreciation schedule, as shown in the following illustration:
Now, you’ll need to use the MACRS tables to determine the amount of depreciation expense. Assume that the “improve- ments” represent 39-year, nonresidential rental property and the “fixtures” represent 7-year property. Create a depreciation schedule using the MACRS tables on pages 308–309 of your textbook. Create annual measures and a source document for annual financial statement preparation. Your textbook didn’t provide a depreciation schedule for the 39-year, non- residential real property, so we’ve provided one below. The measures in the table represent the percentage by which the improvements to the real property may be depreciated, per year, based on the month placed in service, which in this case was January:
The amounts in this table are carried out to the third decimal place, so some rounding errors will prevent the improvements from being fully depreciated through year 39. You should prepare the depreciation schedule only through year 30, to match the loan amortization schedule you prepared in Step 1 of the project. To check your work, you can use the following figure, which shows part of the completed depreciation schedule:
Graded Project134
Appraised Values
Percentage Cost
Allocation
Land $45,000 14.29% $42,857
Improvements $260,000 82.54% $247,619
Fixtures $10,000 3.17% $9,524
Total $315,000 100.00% $300,000
Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1 2.461 2.247 2.033 1.819 1.695 1.391 1.177 0.963 0.749 0.535 0.321 0.107
2 thru 39
2.564 2.564 2.564 2.564 2.564 2.564 2.564 2.564 2.564 2.564 2.564 2.564
Step 3: Create a Schedule Combining Interest Expenses and Depreciation Expenses In this step, you’ll need to create a schedule that combines interest expenses and depreciation expenses, but only for the first 10 years of the life of the asset. Here is how the completed schedule should appear:
Step 4: Convert the Interest Expense and Depreciation Expense In this step of your project, you’ll need to convert the interest expense and depreciation expense from pretax to aftertax dol- lars. Assume the firm is subject to a 34 percent marginal tax rate, and convert the 10-year schedule of interest expense and depreciation expense to aftertax terms. Review Lesson 3, Assignment 9, to obtain the applicable formulas.
Graded Project 135
Year Land Improvements Fixtures Total
1 $0 $6,094 $1,361 $7,455
2 $0 $6,349 $2,332 $8,681
————————————-Break in Sequence————————————-
29 $0 $6,349 $0 $6,349
30 $0 $6,349 $0 $6,349
Total $0 $190,213 $9,524 $199,737
Year Annual
Interest Expense
Annual Depreciation
Expense
1 $17,899.78 $7,455
—————Break in Sequence—————
10 $15,270.50 $6,349
Remember from your lessons that operating and interest expense results in a cash outflow, and depreciation expense results in a cash inflow, from the depreciation tax shield. Therefore, in this step, you’re computing a net cash outflow.
The following illustration shows how the completed schedule should appear, with the combined annual interest expense and depreciation expense, both converted to aftertax terms.
Step 5: Calculate the Aftertax Cash Outflows In this step of your project, you’ll need to calculate the present values and net present values of the aftertax cash flows or expenses for the project. In this case, this is the present value, aftertax cash outflow.
You’ve calculated the aftertax cash flows for the interest expense and the depreciation expense associated with the purchase of this piece of non-residential real property. Now, the final step requires you to calculate the present value of these ATCFs for each year, and the NPV for these expenses, in aggregate.
Using a discount rate of 10 percent, extend the table completed in Step 4 by adding a column for the present value of ATCFs. You’ll find a “present value of $1” table on pages A-4 and A-5 of your textbook (near the back of the book). The following illustration shows how the completed table should appear.
Graded Project136
Year
Pretax Annual Interest Expense
Pretax Annual
Depreciation Expense
(a) AT CF
or Posttax (1 – T) Interest Expense
(b) AT CF
or Posttax
(T) Depreciation
Expense
(a) – (b) AT CF
or Posttax
Combined Interest &
Depreciation Expense
1 $17,900 $7,455 $11,814 $2,535 $9,279
————————————-Break in Sequence————————————-
10 $15,271 $6,349 $10,079 $2,159 $7,920
Evaluation Criteria Your instructor will use the following criteria to evaluate your project:
Step 1: Create the loan amortization schedule for the property. (20 points)
Step 2: Create the depreciation schedule. (20 points)
Step 3: Create the schedule that combines interest expenses and depreciation expenses. (20 points)
Step 4: Create a schedule that converts the interest expense and depreciation expense to aftertax dollars. (20 points)
Step 5: Create a schedule that shows the aftertax cash out- flows. (20 points)
Graded Project 137
Year
Pretax Annual Interest Expense
Pretax Annual
Depreciation Expense
(a) AT CF
or Posttax (1 – T) Interest Expense
(b) AT CF
or Posttax
(T) Depreciation
Expense
(a) – (b) AT CF
or Posttax
Combined Interest &
Depreciation Expense
10% PV
Factor
PV ATCFs
1 $17,900 $7,455 $11,814 $2,535 $9,279 0.9091 $8,436
————————————-Break in Sequence————————————-
10 $15,271 $6,349 $10,079 $2,159 $7,920 0.3855 $3,053
Total $166,896 $72,757
NPV $53,068
SUBMITTING YOUR FILES Your documents should be created using a computer program such as Excel, and using a standard font in 12-point size. To submit your project, make sure you include the following:
� Your completed amortization schedule
� Depreciation schedule
� Interest and depreciation schedule
� Aftertax interest and depreciation schedule
� Aftertax cash outflow schedule
You’ll submit your project online. To send the files via an e-mail attachment,
Go to student portal.
Click on Take Exam next to the graded project number 06058901.
Enter your e-mail address in the box provided. (Note: This information is required for online submission.)
Attach your file or files as follows:
a. Click on the Browse box.
b. Locate the file you wish to attach.
c. Double-click on the file.
d. Click on Upload File.
Graded Project138
139
A n
s w
e r
s A
n s
w e
r s
Self-Check 1 1. False
True
False
True
False
Answers to Textbook Problems
$171,600
$75,290
Average rate = 31.90% Marginal rate = 39%
–$180
Self-Check 2 1. True
True
True
True
False
Answers to Textbook Problems
Net income = $2.32 million ROA = 13.26% ROE = 20.71%
Self-Check Answers140
Self-Check 3 1. True
True
False
False
True
Answers to Textbook Problems
3,186,813
no change; declines by $0.69; declines by $1.55
$38,467.41
Self-Check 4 1. False
True
Self-Check Answers 141
True
True
Answers to Textbook Problems
$6,419.51 $14,999.39 $687,764.17 $315,795.75
$10,300.67 $21,939.15 $43,520.28 $116,560.17
Self-Check 5 1. True
True
False
False
True
Answers to Textbook Problems
$411,660.36
EAR = 313,916,515.69% APR = 1,733.33%
$386,936.54
Self-Check 6 1. True
True
False
False
True
Answers to Textbook Problems
5.97%
6.30%
a. 30,000 coupon bonds; 315,589 zeroes b. $32,400,000; $315,588,822
$7,367.76
Self-Check 7 1. False
False
False
True
False
Answers to Textbook Problems
$2.45
$63.47
$48.70
$96.15
$69.55
Self-Check Answers142
Self-Check 8 1. False
False
True
True
False
Answers to Textbook Problems
At 11%: NPV = $5,991.49 At 30%: NPV = –$4,213.93
a. IRRA = 20.44% b. IRRB = 18.84% c. Crossover rate = 15.30%
a. PII = 1.267 PIII = 1.414
b. NPVI = $14,145.00 NPVII = $6,630.35
Self-Check 9 1. False
True
False
True
True
Self-Check Answers 143
Self-Check Answers144
Answers to Textbook Problems
$1,387,792
CF0 = –$4,200,000 CF1 = $1,631,455 CF2 = $1,738,243 CF3 = $1,916,303 NPV = $42,232.43
–$117,803.98
$0.03163
Self-Check 10 1. True
True
False
True
False
Answers to Textbook Problems
D = $420,800 P = $69.36 VC = $37.57
OCF = $34,333 DOL = 4.786
DOL = 1.2480 DOLA = 2.7143
∆NPV/∆P = $148,973.62 ∆NPV/∆Q = $1,226.84
DOL = 1.0381 ∆OCF = 2.97%
Self-Check Answers 145
Self-Check 11 1. True
False
True
False
False (The total stock price was $700.)
Answers to Textbook Problems
2.62%; 3.01%
RA = 11.83% RG = 10.58%
14.95%; 14.52%; 13.64%
Self-Check 12 1. True
True
False
False
False
Answers to Textbook Problems
12.50%
a. 7.64% b. σ 2P = 0.02436
σP =15.61%
0.0792
Self-Check Answers146
βI = 2.06 σI = 8.53% βII = 0.63 σII = 33.96%
Self-Check 13 1. True
False
True
False
False
Answers to Textbook Problems
RA = 11.47% RG = 11.46%
Book value = $115,000,000 Market value = $97,350,000 Aftertax cost = 5.34%
a. E/V = 0.3455 D/V = 0.6545
b.E/V = 0.8595 D/V = 0.1405
b. 12.80%
Self-Check Answers 147
Self-Check 14 1. True
True
True
False
True
Answers to Textbook Problems
a. $3.29; $3.00; $3.55 b. $44,000 c. $44,000 d. $44,000
$2,070,000
a. 18.18% b. 12.66% c. 20.01%; 16.34%; 12.66%
$310,583.33