Financial Management Problems and Solutions Chapter 4

You are reading a preview.

Create your free account to continue reading.

Like this document? Why not share!

• Email
•  

• 2 Likes
• Statistics
• Notes

• 

• 

1. 1. Solutions Manual FINANCIAL MANAGEMENT Principles and Practice Fourth Edition Timothy J. Gallagher Colorado State University Joseph D. Andrew, Jr. Webster University  2006 Freeload Press, Madison Wisconsin
2. 2. i (Insert publication data on this page)
3. 3. ii Solutions Manual to accompany Financial Management: Principles and Practice 4rd Edition by Timothy J. Gallagher and Joseph D. Andrew, Jr. This solutions manual provides the answers to all the review questions and end-of-chapter problems in Financial Management: Principles and Practice, by Gallagher and Andrew. The answers and the steps taken to obtain the answers are shown. We remind our readers that in finance there is often more than one answer to a question or to a problem, depending on one's viewpoint and assumptions. We provide one answer to each question and show one approach to solving each problem. Other answers and approaches may be equally valid, or judged even better according to each individual's preference.
4. 4. iii TABLE OF CONTENTS Chapter 1 Solutions ...................................................................................................................5 Chapter 2 Solutions ...................................................................................................................9 Chapter 3 Solutions .................................................................................................................13 Chapter 4 Solutions .................................................................................................................16 Chapter 5 Solutions .................................................................................................................24 Chapter 6 Solutions .................................................................................................................34 Chapter 7 Solutions .................................................................................................................41 Chapter 8 Solutions .................................................................................................................53 Chapter 9 Solutions .................................................................................................................61 Chapter 10 Solutions...............................................................................................................67 Chapter 11 Solutions...............................................................................................................79 Chapter 12 Solutions...............................................................................................................93 Chapter 13 Solutions.............................................................................................................103 Chapter 14 Solutions.............................................................................................................113 Chapter 15 Solutions.............................................................................................................120 Chapter 16 Solutions.............................................................................................................124 Chapter 17 Solutions.............................................................................................................131 Chapter 18 Solutions.............................................................................................................138 Chapter 19 Solutions.............................................................................................................147 Chapter 20 Solutions.............................................................................................................163 Chapter 21 Solutions.............................................................................................................167
5. 5. iv
6. 6. 5 Chapter 1 Solutions Answers to Review Questions 1. How is finance related to the disciplines of accounting and economics? Financial management is essentially a combination of accounting and economics. First, financial managers use accounting information—balance sheets, income statements, and so on—to analyze, plan, and allocate financial resources for business firms. Second, financial managers use economic principles to guide them in making financial decisions that are in the best interest of the firm. In other words, finance is an applied area of economics that relies on accounting for input. 2. List and describe the three career opportunities in the field of finance. Finance has three main career paths: financial management, financial markets and institutions, and investments. Financial management involves managing the finances of a business. Financial managers—people who manage a business firm's finances—perform a number of tasks. They analyze and forecast a firm's finances; assess risk, evaluate investment opportunities, decide when and where to find money sources and how much money to raise, and decide how much money to return to the firm's investors. Bankers, stockbrokers, and others who work in financial markets and institutions focus on the flow of money through financial institutions and the markets in which financial assets are exchanged. They track the impact of interest rates on the flow of that money. People who work in the field of investments locate, select, and manage income-producing assets. For instance, security analysts and mutual fund managers both operate in the investment field. 3. Describe the duties of the financial manager in a business firm. Financial managers measure the firm's performance, determine what the financial consequences will be if the firm maintains its present course or changes it, and recommend how the firm should use its assets. Financial managers also locate external financing sources and recommend the most beneficial mix of financing sources, and they determine the financial expectations of the firm's owners. All financial managers must be able to communicate, analyze, and make decisions based on information from many sources. To do this, they need to be able to analyze financial statements, forecast and plan, and determine the effect of size, risk, and timing of cash flows. 4. What is the basic goal of a business? The primary financial goal of the business firm is to maximize the wealth of the firm's owners. Wealth, in turn, refers to value. If a group of people owns a business firm, the contribution that firm makes to that group's wealth is determined by the market value of that firm.
7. 7. 6 5. List and explain the three financial factors that influence the value of a business. The three factors that affect the value of a firm's stock price are cash flow, timing, and risk. The Importance of Cash Flow: In business, cash is what pays the bills. It is also what the firm receives in exchange for its products and services. Cash is therefore of ultimate importance, and the expectation that the firm will generate cash in the future is one of the factors that gives the firm its value. The Effect of Timing on Cash Flows: Owners and potential investors look at when firms can expect to receive cash and when they can expect to pay out cash. All other factors being equal, the sooner companies expect to receive cash and the later they expect to pay out cash, the more valuable the firm and the higher its stock price will be. The Influence of Risk: Risk affects value because the less certain owners and investors are about a firm's expected future cash flows, the lower they will value the company. The more certain owners and investors are about a firm's expected future cash flows, the higher they will value the company. In short, companies whose expected future cash flows are doubtful will have lower values than companies whose expected future cash flows are virtually certain. 6. Explain why accounting profits and cash flows are not the same thing. Stock value depends on future cash flows, their timing, and their riskiness. Profit calculations do not consider these three factors. Profit, as defined in accounting, is simply the difference between sales revenue and expenses. It is true that more profits are generally better than less profits, but when the pursuit of short-term profits adversely affects the size of future cash flows, their timing, or their riskiness, then these profit maximization efforts are detrimental to the firm. 7. What is an agent? What are the responsibilities of an agent? An agent is a person who has the implied or actual authority to act on behalf of another. The owners whom the agents represent are the principals. Agents have a legal and ethical responsibility to make decisions that further the interests of the principals. 8. Describe how society's interests can influence financial managers. Sometimes the interests of a business firm's owners are not the same as the interests of society. For instance, the cost of properly disposing of toxic waste can be so high that companies may be tempted to simply dump their waste in nearby rivers. In so doing, the companies can keep costs low and profits high, and drive their stock prices higher (if they are not caught). However, many people suffer from the polluted environment. This is why we have environmental and other similar laws: So that society's best interests take precedence over the interests of individual company owners. When businesses take a long-term view, the interests of the owners and society often (but not always) coincide. When companies encourage recycling, sponsor programs for disadvantaged young people,
8. 8. 7 run media campaigns promoting the responsible use of alcohol, and contribute money to worthwhile civic causes, the goodwill generated as a result of these activities causes long-term increases in the firm's sales and cash flows, which translate into additional wealth for the firm's owners. 9. Briefly define the terms proprietorship, partnership, and corporation. A proprietorship is a business owned by one person. Two or more people who join together to form a business make up a partnership. This can be done on an informal basis without a written partnership agreement, or a contract can spell out the rights and responsibilities of each partner. A limited liability company is a hybrid between a partnership and a corporation. Profits and losses pass through to the members. Members generally enjoy limited liability. Corporations are legal entities separate from their owners. To form a corporation, the owners specify the governing rules for the running of the business in a contract known as the articles of incorporation. They submit the articles to the government of the state in which the corporation is formed, and the state issues a charter that creates the separate legal entity. 10. Compare and contrast the potential liability of owners of proprietorships, partnerships (general partners), and corporations. The sole proprietor has unlimited liability for matters relating to the business. This means that the sole proprietor is responsible for all the obligations of the business, even if those obligations exceed the amount the proprietor has invested in the business. Each partner in a partnership is usually liable for the activities of the partnership as a whole. Even if there are a hundred partners, each one is technically responsible for all the debts of the partnership. If ninety-nine partners declare personal bankruptcy, the hundredth partner still is responsible for all the partnership's debts. A corporation is a legal entity that is liable for its own activities. Stockholders, the corporation's owners, have limited liability for the corporation's activities. They cannot lose more than the amount they paid to buy the corporation's stock. Answers to End-of-Chapter Problems 1. An accountant prepares financial statements while a financial analyst interprets them. 2. A financial manager's role in a publicly traded company is to make financial decisions so as to best serve the principal stockholders.
9. 9. 8 3. a. The value of the firm would go down due to the increase in the amount of time it takes to receive the cash inflows. b. The value of the firm would go up due to the increase in expected cash inflows. c. If expected future cash flows do not change the value of the firm would go down due to the increased riskiness of the firm. 4. This practice obviously takes advantage of people who are in a difficult financial situation. This transaction is voluntary, however, and high risk loans have high interest rates. 5. LLCs have a small number of members like partnerships and each of these members is likely to have an active voice in the company like a partnership. The LLC is taxed like a partnership. Unlike a partnership, and more like a corporation, the owners generally enjoy limited liability.
10. 10. 9 Chapter 2 Solutions Answers to Review Questions 1. What are financial markets? Why do they exist? Financial markets are where financial securities are bought and sold. They exist primarily to bring deficit economic units (those needing money) and surplus economic units (those having extra money) together. 2. What is a security? Securities are claims on financial assets. They can be described as "claim checks" that give their owners the right to receive funds in the future. Securities are traded in both the money and capital markets. Money market securities include Treasury bills, negotiable certificates of deposit, commercial paper, and banker's acceptances. Capital market securities include bonds and stock. 3. What are the characteristics of an efficient market? The term market efficiency refers to the ease, speed, and cost of trading securities. In an efficient market, securities can be traded easily, quickly, and at low cost. Markets lacking these qualities are considered to be inefficient. 4. How are financial trades made on an organized exchange? Each exchange-listed security is traded at a specified location on the trading floor called the post. The trading is supervised by specialists who act either as brokers (bringing together buyers and sellers) or as dealers (buying or selling the stock themselves). Prominent international securities exchanges include the New York Stock Exchange (NYSE) and major exchanges in Tokyo, London, Amsterdam, Frankfurt, Paris, Hong Kong, and Mexico. 5. How are financial trades made in an over-the-counter market? Discuss the role of a dealer in the OTC market. In contrast to the organized exchanges, which have physical locations, the over-the-counter market has no fixed location,or more correctly, it is everywhere. The over-the-counter market, or OTC, is a network of dealers around the world who maintain inventories of securities for sale. If you wanted to buy a security that is traded OTC, you would call your broker, who would then shop among competing dealers who have the security in their inventory. After locating the dealer with the best price, your broker would buy the security on your behalf.
11. 11. 10 The role of dealers: Dealers make their living buying securities and reselling them to others. They operate just like car dealers who buy cars from manufacturers for resale to others. Dealers make money by buying securities for one price (called the bid price) and selling them for a higher price, (called the ask price). The difference, or spread, between the bid price and the ask price represents the dealer's fee. 6. What is the role of a broker in security transactions? How are brokers compensated? Brokers handle orders to buy or sell securities. Brokers are agents who work on behalf of an investor. When investors call with an order, brokers work on their behalf to find someone to take the other side of the proposed trade. If investors want to buy, brokers find sellers. If investors want to sell, brokers find buyers. Brokers are compensated for their services when the person whom they represent, the investor, pays them a commission on the sale or purchase of securities. 7. What is a Treasury bill? How risky is it? Treasury bills are short-term debt instruments issued by the U.S. Treasury that are sold at a discount and pay face value at maturity. They are very nearly risk-free as they are backed by the U.S. Government which could, if need by, print money to pay their holders at maturity. 8. Would there be positive interest rates on bonds in a world with absolutely no risk (no default risk, maturity risk, and so on)? Why would a lender demand, and a borrower be willing to pay, a positive interest rate in such a no-risk world? Yes, there would be a positive rate of interest in a risk-free world. This is because regardless of risk, lenders of money must postpone spending during the time the money is loaned. Lenders, then, lose the opportunity to invest their money for that period of time. To compensate for the cost of losing investment opportunities while they postpone their spending, lenders demand, and borrowers pay, a basic rate of return, the real rate of interest. Answers to End of Chapter Problems 2-1. a. Surplus economic units have income that exceeds their expenditures. Wealthy families in the household sector and most states (which have balanced budget requirements) are surplus economic units. b. Deficit economic units have expenditures that exceed their incomes. Home buyers and college students are likely to be deficit economic units. 2.2. a. false b. false c. false d. false
12. 12. 11 2-3. a. 2 3 4 1 b. The money market is dominated by large institutional traders and there is much competition. The New York Stock Exchange tends to have larger more actively traded stocks. The over-the-counter market tends to have smaller less actively traded securities. The real estate market has very high transaction costs and trades take months. 2.4. a. A money market security is short term and actively traded. b. Treasury bills and commercial paper are both traded in the money market. 2-5. $66.25/$1,000 = 6 5/8 % coupon rate 2-6. The yield on a Bonds-R-Us bond: Real rate of interest...................... 2% Inflation premium........................ 3% Default risk premium................... 1% Liquidity risk premium................ 1% Maturity risk premium................. 1% Total yield on Bonds-R-Us Bond: 8% (reference figure 2-2) 2-7. Treasury Yield Curve: Given: Treasury Security Yields: Maturity in Years (for Chart) Three-month T-bills 4.50% 0.25 Six-month T-bills 4.75% 0.5 One-year T-notes 5.00% 1 Two-year T-notes 5.25% 2 Three-year T-bonds 5.50% 3 Five-year T-bonds 5.75% 5 Ten-year T-bonds 6.00% 10 Thirty-year T-bonds 6.50% 30 Chart: (see next page)
13. 13. 12 Implications: a. For borrowers: Borrowers tend to look for the low point of the curve, which indicates the least expensive loan maturity. In this case the low point is 3 months, leading the borrower to seek a short- term loan. However, if a firm borrows long-term and obtains the higher interest rate, that rate is locked in for the life of the loan (30 years in this case). If interest rates rise the borrower may be glad he/she locked in the long-term rate. b. Lenders face the opposite situation. Granting short-term-term loans at relatively low interest rates may look unattractive now; but if short-term rates rise, the lenders will be able to roll over investments at higher and higher rates.
14. 14. 13 Chapter 3 Solutions Answers to Review Questions 1. Define intermediation. The financial system makes it possible for surplus and deficit economic units to come together, exchanging funds for securities, to their mutual benefit. When funds flow from surplus economic units to a financial institution to a deficit economic unit, the process is known as intermediation. The financial institution acts as an intermediary between the two economic units. 2. What can a financial institution often do for a surplus economic unit that it would have difficulty doing for itself if the surplus economic unit (SEU) were to deal directly with a deficit economic unit (DEU)? Surplus economic units do not usually have the expertise to determine whether deficit economic units can and will make good on their obligations, so it is difficult for them to predict when a would-be deficit economic unit will fail to pay what it owes. Such a failure is likely to be devastating to a surplus economic unit that has lent a proportionately large amount of money. In contrast, a financial institution is in a better position to predict who will pay and who won't. It is also in a better position, having greater financial resources, to occasionally absorb a loss when someone fails to pay. (This is just one example of the beneficial things financial institutions do for SEUs) 3. What can a financial institution often do for a deficit economic unit (DEU)that it would have difficulty doing for itself if the DEU were to deal directly with an SEU? SEUs typically want to supply a small amount of funds, while DEUs typically want to obtain a large amount of funds. Thus it is often difficult for surplus and deficit economic units to come together on their own to arrange a mutually beneficial exchange of funds for securities. A financial institution can step in and save the day. A bank, savings and loan, or insurance company can take in small amounts of funds from many individuals, form a large pool of funds, and then use that large pool to purchase securities from individual businesses and governments. (This is just one example of the beneficial things financial institutions do for DEUs) 4. What are a bank's primary reserves? When the Fed sets reserve requirements, what is its primary goal? Vault cash and deposits in the bank's account at the Fed are used to satisfy these reserve requirements; they are called primary reserves. These primary reserves are non-interest-earning assets held by financial institutions. The Federal Reserve requires all commercial banks to keep a minimum amount of reserves on hand to meet the withdrawal demands of its depositors and to pay other obligations as they come due.
15. 15. 14 Many would argue, however, that the reserve requirement is set more with monetary policy in mind than to ensure that banks meet their depositors' withdrawal requests. 5. Compare and contrast mutual and stockholder-owned savings and loan associations. Some savings and loan associations are owned by stockholders, just as commercial banks and other corporations are owned by their stockholders. Other S&Ls, called mutuals, are owned by their depositors. When a person deposits money in an account at a mutual S&L, that person becomes a part owner of the firm. The mutual S&L's profits (if any) are put into a special reserve account from which dividends are paid from time to time to the owner/depositors. 6. Who owns a credit union? Explain. Credit unions are owned by their members. When credit union members put money in their credit union, they are not technically "depositing" the money. Instead, they are purchasing shares of the credit union. In general, credit unions exist to pay interest on shares bought by, and collect interest on loans made to, the members. 7. Which type of insurance company generally takes on the greater risks: a life insurance company or a property and casualty insurance company? The risks protected against by property and casualty companies are much less predictable than are the risks insured by life insurance companies. Hurricanes, fires, floods, and trial judgments are all much more difficult to predict than the number of sixty-year-old females who will die this year among a large number in this risk class. This means that property and casualty insurance companies must keep more liquid assets than do life insurance companies. 8. Compare and contrast a defined benefit and a defined contribution pension plan. In a defined benefit plan, retirement benefits are determined by a formula that usually considers the worker's age, salary, and years of service. The employee and/or the firm contribute the amounts necessary to reach the goal. In a defined contribution plan, the contributions to be made by the employee and/or employer are spelled out, but retirement benefits depend on the total accumulation in the individual's account at the retirement date. 9. Special security software is used such that customers who enter their identification and password information can keep sensitive information out of the hands of hackers.
16. 16. 15 Answers to End-of-Chapter Problems 3-1. a) If there were no financial institutions the SEUs and the DEUs would find that the amount of money needed by a given DEU did not match the amount of money available by a given SEU. The money available would not be put to work and the economic activity that would have otherwise taken place would not. b) If financial institutions were available in this society they could position themselves between the SEUs and DEUs. The financial institution could pool the $1,000 available (100 SEUs times $10 each) and pass that money along in $100 increments to the DEUs. This could be done via either a debt or equity claim that the financial institution would accept from the DEU in return for the money. 3-2. a) .10 rate on loans made - .05 rate paid to depositors = .05 = 5% interest rate spread b) (.5 x .10) + (.5 x .12) = .11 = 11% weighted average loan rate (.5 x .05) + (.5 x .07) = .06 = 6% weighted average deposit rate 11% - 6% = 5% interest rate spread 3-3. ($48,300,000 - $7,800,000) x .03) + (($60,000,000 - $48,300,000) x .10) + ($20,000,000 x 0) + ($10,000,000 x 0) = $6,732,000 3-4. a) The FOMC should buy government securities in the open market. This would increase the reserves of the banking system and would put downward pressure on the federal funds rate. b) The Fed's trader at the New York Federal Reserve Bank would contact various government securities dealers and would buy the Treasury securities from them. Payment would be made by crediting the accounts at the Fed of these dealers. This would make more funds available and would tend to put downward pressure on the cost of these funds, the federal funds rate. 3-5. a) ($1,000,000 x .08) – ($1,000,000 x .07) = $10,000 a profit of $10,000 b) ($1,000,000 x .08) – ($1,000,000 x .09) = -$10,000 a loss of $10,000
17. 17. 16 Chapter 4 Solutions Answers to Review Questions 1. Why do total assets equal the sum of total liabilities and equity? Explain. Assets = Liabilities + Equity Assets are the items of value a business owns. Liabilities are claims on the business by non-owners, and equity is the owners' claim on the business. The sum of the liabilities and equity is the total capital contributed to the business, which, by definition, equals the total value of the assets. 2. What are the time dimensions of the income statement, the balance sheet, and the statement of cash flows? Hint: Are they videos or still pictures? Explain. The income statement is like a video: It measures a firm's profitability over a period of time (which can be a week, a month, a year, or any other time period). The balance sheet is like a still photograph. The balance sheet shows the firm's assets, liabilities, and equity at a given point in time. This cash flow statement like the income statement, can be compared to a video: It shows how cash flows into and out of a company over a given period of time. 3. Define depreciation expense as it appears on the income statement. How does depreciation affect cash flow? Accounting depreciation is the allocation of an asset's initial cost over time. Depreciation expense on an income statement is the amount of the asset=s initial cost allocated to the period covered by the income statement. Depreciation expense is not a cash flow. Depreciation as an expense category affects cash flow, however, because it is tax-deductible. Depreciation expense lowers a company's taxable income and, therefore its income tax liability. In this way depreciation reduces cash outflows.. 4. What are retained earnings? Why are they important? Retained earnings represents the sum of all the earnings available to common stockholders of a business during its entire history, minus the sum of all the common stock dividends which it has ever paid. Those earnings that were not paid out were, by definition, retained. Retained earnings are important because they represent amounts reinvested in a company on behalf of the company's owners instead of being paid out in the form of dividends.
18. 18. 17 5. Explain how earnings available to common stockholders and common stock dividends paid from the current income statement affect the balance sheet item retained earnings. The change in the retained earnings account from one balance sheet to the next equals net income less preferred stock dividends (which is the amount of earnings available to common stockholders) less common stock dividends. 6. What is accumulated depreciation? Depreciation is the allocation of an asset's initial cost over time. Accumulated depreciation is the total of all the depreciation expense that has been recognized to date. 7. What are the three major sections of the statement of cash flows? Cash flows from Operations Cash flows from investing activities Cash flows from financing activities Net change in cash balance Cash balance at beginning of period Cash balance at end of period 8. How do financial managers calculate the average tax rate? Average tax rates are calculated by dividing tax dollars paid by earnings before taxes (EBT). 9. Why do financial managers calculate the marginal tax rate? Financial managers use marginal tax rates to estimate the future after-tax cash flows from investments. Since they are interested in how much of the next dollar earned from new investments will have to be paid in taxes, they use the marginal tax rate (rather than the average tax rate) to calculate the tax liability. 10. Identify whether the following items belong on the income statement or the balance sheet. a. Interest Expense IS l. Cash BS b. Preferred Stock Dividends Paid IS m. Capital in Excess of Par BS c. Plant and Equipment BS n. Operating Income IS d. Sales IS o. Depreciation Expense IS e. Notes Payable BS p. Marketable Securities BS f. Common Stock BS q. Accounts Payable BS g. Accounts Receivable BS r. Prepaid Expenses BS h. Accrued Expenses BS s. Inventory BS i. Cost of Goods Sold IS t. Net Income IS j. Preferred Stock BS u. Retained Earnings BS k. Long-Term Debt BS
19. 19. 18 11. Indicate in which section the following balance items belong (current assets, fixed assets, current liabilities, long-term liabilities, or equity). a. Cash CA h. Capital in Excess of Par EQ b. Notes Payable CL i. Marketable Securities CA c. Common Stock EQ j. Accounts Payable CL d. Accounts Receivable CA k. Prepaid Expenses CA e. Accrued Expenses CL l. Inventory CA f. Preferred Stock EQ m. Retained Earnings EQ g. Plant and Equipment FA Answers to End-of-Chapter Problems 4-1. CASE A CASE B Revenues 200,000 110,000 Expenses 160,000 70,000 Net Income 40,000 40,000 Retained Earnings, Jan 1 300,000 100,000 Dividends Declared 70,000 30,000 Retained Earnings, Dec 31 270,000 110,000 Current Assets, Dec 31 80,000 230,000 Non-current Assets, Dec 31 850,000 180,000 Total Assets, Dec 31 930,000 410,000 Current Liabilities, Dec 31 40,000 60,000 Non-current Liabilities, Dec 31 100,000 140,000 Total Liabilities, Dec 31 140,000 200,000 CS & Cap. in Excess of Par, Dec 31 520,000 100,000 Total Stockholders' Equity, Dec 31 790,000 210,000 4-2. CASE A CASE B Sales 500,000 250,000 COGS 200,000 100,000 Gross Profit 300,000 150,000 Operating Expenses 60,000 60,000 Operating Income (EBIT) 240,000 90,000 Interest Expense 10,000 10,000 Earnings Before Taxes (EBT) 230,000 80,000 Tax Expense (40%) 92,000 32,000 Net Income 138,000 48,000 4-3. a) 15%; $48,000 X 0.15 = $7,200 b) $7,200/$48,000 = 0.15 or 15%
20. 20. 19 4-4. a) Tax = $50,000 X 0.15 + $25,000 X 0.25 + $25,000 X 0.34 + $50,000 X 0.39 = $41,750 b) Effective tax rate = $41,750/$150,000 = 0.2783 or 27.83% 4-5. The marginal tax rate is the tax rate applied to the next dollar of income. Therefore, the marginal tax rate is 34%. The average tax rate is 34% 50,000 * .15 = 7,500 25,000 * .25 = 6,250 25,000 * .34 = 8,500 235,000 * .39 = 91,650 2,865,000 * .34 = 974,100 $1,088,000 $1,088,000/$3,200,000 = 34% 4-6. $1 + $400,000/200,000 = $3.00 per share 4-7. Sales $10,000,000 - Operating Costs 5,200,000 - Interest Expense 200,000 = EBT $4,600,000 - Taxes (40%) 1,840,000 Net after-tax income $2,760,000 Simon's net after-tax income was $2,760,000 for the year. 4-8. Depreciation expense in 2006 = $70,000 - $60,000 = $10,000. 4-9 a) Cash + Marketable Securities + Inventory + Accounts Receivable + Prepaid expenses. (11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) = 35,000,000 Current Assets = $35,000,000 b) Fixed assets – depreciation 30,000,000 – 8,000,000 = 22,000,000 Net Fixed Assets = $22,000,000 c) Notes Payable + Accrued Expenses 4,000,000 + 2,000,000 = 6,000,000 Current Liabilities = $6,000,000
21. 21. 20 d) Current Assets – Current Liabilities (11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) – (4,000,000 + 2,000,000) 35,000,000 – 6,000,000 = 29,000,000 Net Working Capital = $29,000,000 4-10. a ) Gross Profit $440,000 - $200,000 = $240,000 b ) Operating Income (EBIT) $240,000 - $40,000 - 85,000 = $115,000 c ) Earning Before Taxes (EBT) $ 115,000 - $40,000 = $75,000 d ) Income Taxes $ 75,000 X 0.4 = $30,000 e ) Net Income $75,000 - $30,000 = $45,000 4-11 $1,500,000 – $200,000 = $1,300,000 Simon and Pieman had a net worth of $1,300,000 at the end of the year. 4-12 a ) 2006 Depreciation Expense for this process line ($131,000 + $12,000) X (0.245) = $35,035 b ) Amount of tax savings due to this investment. $35,035 X 0.4 = $14,014 4-13. Operating Income (EBIT) = $768,000 + Depreciation = $42,000 + Amortization = $15,000 $825,000 Target Telecom's EBITDA = $825,000. 4-14 a ) The company's 2006 taxable income = ($400,000 - $130,000 X 0.2) = $374,000 b ) Income tax = $374,000 X 0.34 = $127,160 4-15. a) Earnings = [($600,000 - 50,000) X (1 - .34) - $63,000] = $300,000 Earnings per share = $300,000 / 100,000 = $3 per share b) Addition to Retained Earnings = $300,000 - 100,000 = $200,000
22. 22. 21 4-16. a ) Current Assets: 2005: $5,534 + 14,745 + 10,733 + 952 + 3,234 = $35,198 2006: $9,037 + 15,943 + 11,574 + 1,801 + 2,357=$40,712 b ) Total Assets: 2005: $35,198+(57,340 - 29,080)+1,010+2,503 = $66,971 2006: $40,712+(60,374 - 32,478)+1,007+4,743 = $74,358 c ) Current Liabilities: 2005: $3,253 + 6,821 = $10,074 2006: $2,450 + 7,330 = $9,780 d ) Total Liabilities: 2005: $10,074 + 2,389 = $12,463 2006: $9,780 + 2,112 = $11,892 e ) Total Stockholders' Equity: 2005: $8,549 + 45,959 = $54,508 2006: $10,879 + 51,587 = $62,466 4-17. 2005: $12,463 TL + $54,508 EQ = $66,971 TA 2006: $11,892 TL + $62,466 EQ = $74,358 TA 4-18. (Dollars) a ) Accumulated Depreciation 3,398 Inflow b ) Accounts Receivable (net) 1,198 Outflow c ) Inventories 841 Outflow d ) Prepaid Expenses 877 Inflow e ) Accounts Payable 803 Outflow f ) Accrued Expenses 509 Inflow g ) Plant and Equipment (gross) 3,034 Outflow h ) Marketable Securities 849 Outflow i ) Land 3 Inflow j ) Long Term Investments 2,240 Outflow k ) Common Stock 2,330 Inflow l ) Bonds Payable 277 Outflow 4-19. Pinewood Company and Subsidiaries Statement of Cash Flows For the year 2006 Operations: Net Income 10,628 Add: Depreciation Exp. 3,398 Decrease in Prepaid Expenses 877 Increase in Accrued Expenses 509 Less: Increase in A/C Receivable (1,198) Increase in Marketable Securities ( 849) Increase in Inventories ( 841) Decrease in A/C Payable ( 803) Total Cash Flow from Operations $11,721 Investments: Add: Decrease in Land 3 Less: Increase in Plant and Equipment (3,034) Increase in Long Term Investment (2,240) Total Cash Flow from Investments ($5,271)
23. 23. 22 Financing: Add: Increase in Common Stock 2,330 Less: Common Stock Dividends (5,000) Decrease in Bonds Payable ( 277) Cash Flow from Financing ($2,947) Net Cash Flow $3,503 4-20. $3,503 = $9,037 end of '02 cash - $5,534 end of '01 cash  Yes, the net cash flow figure from problem #16 gives the same answer as calculating the change in the cash figures from the end of 2005 to the end of 2006 balance sheets. 4-21. Sales 900,000 COGS 300,000 Gross Profit 600,000 Operating Expenses 200,000 Operating Income (EBIT) 400,000 Interest Expense 100,000 Income before taxes (EBT) 300,000 Tax Expense (30%) 90,000 Net Income $210,000 4-22. Retained Earnings end of 2006 $8,700,000 Retained Earnings end of 2005 8,000,000 Addition to retained earnings 2006 700,000 Earnings Available to Common Stockholders $1,500,000 -Addition to Retained Earnings -700,000 Dividends paid to Common Stockholders 2006 = $ 800,000 4-23. Year Deprec. % * Depreciable Base = Depreciation 1 10% $385,000 $38,500 2 18% $385,000 $69,300 3 14.4% $385,000 $55,440 4 11.5% $385,000 $44,275 5 9.2% $385,000 $35,420 6 7.4% $385,000 $28,490 7 6.6% $385,000 $25,410 8 6.6% $385,000 $25,410 9 6.5% $385,000 $25,025 10 6.5% $385,000 $25,025 11 3.3% $385,000 $12,705 4-24. Basis = $1,000,000 + $100,000 + $50,000 = $1,150,000 Year 3 depreciation = $1,150,000 * .148 = $170,200
24. 24. 23 4-25. Year 1 $7,000,000 * .1 = $700,000 Year 2 $7,000,000 * .18 = $1,260,000 Year 3 $7,000,000 * .144 = $1,008,000 Year 4 $7,000,000 * .115 = $805,000 Year 5 $7,000,000 * .092 = $644,000 Year 6 $7,000,000 *.074 = $518,000 Year 7 $7,000,000 * .066 = $462,000 Year 8 $7,000,000 * .066 = $462,000 Year 9 $7,000,000 * .065 = $455,000 Year 10 $7,000,000 * .065 = $455,000 Year 11 $7,000,000 * .033 = $231,000
25. 25. 24 Chapter 5 Solutions Answers to Review Questions 1. What is a financial ratio? A financial ratio is a number that expresses the value of one financial variable relative to another. Put more simply, a financial ratio is the result you get when you divide one financial number by another. Calculating an individual ratio is simple, but each ratio must be analyzed carefully to effectively measure a firm's performance. 2. Why do analysts calculate financial ratios? Ratios are comparative measures. Because the ratios show relative value, they allow financial analysts to compare information that could not be compared in its raw form. For example, ratios may be used to compare one ratio to a related ratio, a firm's performance to management's goals, a firm's past and present performance, or a firm's performance to similar firms 3. Which ratios would a banker be most interested in when considering whether to approve an application for a short-term business loan? Explain. Bankers and other lenders use liquidity ratios to see whether to extend short-term credit to a firm. Liquidity ratios measure the ability of a firm to meet its short-term obligations. These ratios are important because failure to pay such obligations can lead to bankruptcy. Generally, the higher the liquidity ratio, the more able a firm is to pay its short-term obligations. 4. Which ratios would a potential long-term bond investor be most interested in? Explain. Current and potential lenders of long-term funds, such as banks and bondholders, are interested in debt ratios. When a business's debt ratios increase significantly, bondholder and lender risk increases because more creditors compete for that firm's resources if the company runs into financial trouble. 5. Under what circumstances would market to book value ratios be misleading? Explain. The Market to Book ratio is useful, but it is only a rough approximation of how liquidation and going concern values compare. This is because the Market to Book ratio uses accounting-based book values. The actual liquidation value of a firm is likely to be different than the book value. For instance, the assets of a firm may be worth more or less than the value at which they are currently carried on the company's balance sheet. In addition, the current market price of the company's bonds and preferred stock may also differ from the accounting value of these claims.
26. 26. 25 6. Why would an analyst use the Modified Du Pont system to calculate ROE when ROE may be calculated more simply? Explain. Actually, an analyst would not use the Modified Du Pont equation to calculate ROE for precisely the reason stated above. What an analyst would use the Modified Du Pont equation for is to help analyze the factors that contribute to a firm's ROE. In other words, analysts use the Modified Du Pont system to "take apart" ROE to see what factors are influencing it. 7. Why are trend analysis and industry comparison important to financial ratio analysis? Trend analysis helps financial managers and analysts see whether a company's current financial situation is improving or deteriorating. Cross-sectional analysis, or industry comparison, allows analysts to put the value of a firm's ratios in the context of its industry. Answers to End-of-Chapter Problems 5-1. a) Gross Profit Margin = Gross Profit/Sales 20,000,000/35,000,000 = .5714 Gross Profit margin = 57.14% b) Operating Profit Margin = EBIT/Sales 16,000,000/35,000,000 = .4571 Operating Profit Margin = 45.71% c) Net Profit Margin = Net Income/Sales 8,100,000/35,000,000 = .2314 Net Profit Margin = 23.14% 5-2. Current Ratio = Total Current Assets/Total Current Liabilities (5,000) / (500 +850 + 600) = 2.56 Current Ratio = 2.56 Quick Ratio = (Total Current Assets - Inventory)/Total Current Liabilities (5,000 – 900)/(500 + 850 + 600) = 2.10 Quick Ratio = 2.10 5-3. Average Daily Credit Sales = Annual credit sales/365 5,000,000/365 = $13,698.63 Average Collection Period = Accounts Receivable/Average Daily Credit Sales $500,000/13,698.63 = 36.5 Average Collection Period = 36.5 days
27. 27. 26 5-4. Inventory Turnover = Sales/Inventory 35,000,000/2,400,000 = 14.58 Inventory Turnover = 14.58 X Total Asset Turnover = Sales/Total Assets 35,000,000/(15,000,000 + 20,000,000) = 1 Total Asset Turnover = 1 X 5-5. a) Book value per share Book price per share = Common Stock Equity/Number of shares Outstanding $4,500,000/650,000 =$6.92 BPS = $6.92 b) Market to book value ratio Market to book value ratio = Market price per share/Book value per share $25.00/$6.92 = 3.61 Market to book value ratio = 3.61 5-6. a) Gross profit margin: $47,378/$94,001 = 50.40% b) Operating profit margin $12,941/$94,001 = 13.77% c) Net profit margin $8,620/$94,001 = 9.17% d) Return on assets $8,620/$66,971 = 12.87% e) Return on equity $8,620/$54,508 = 15.81% While the Net profit margin is higher than the industry average, the Return on assets is lower. Pinewood may consider increasing its debt to leverage profits. 5-7. a) Current assets = $5,534 + $14,745 + $10,733 + $952 + $3,234 = $35,198 Current ratio = $35,198/$10,074 = 3.494 b) Quick ratio = ($35,198 - $10,733)/$10,074 = 2.429 Pinewood seems highly capable of paying off short-term debts. 5-8. a) Total debt = $3,253 + $6,821 + $2,389 = $12,463 Debt to total assets = $12,463/$66,971 = 18.61% b) Times interest earned = $12,941/$48 = 270 times Yes. The Pinewood has very low debt and its earnings are extremely high compared to its interest expense. 5-9. a. Average collection period $14,745/($94,001 / 365) = 57.25 days b. Inventory turnover $94,001/$10,733 = 8.76 c. Total asset turnover $94,001/$66,971 = 1.404 We would need to know the industry averages for these figures, and also know about Pinewood's credit and inventory management practices to comment meaningfully on the above figures.
28. 28. 27 5-10. Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity = 0.0917 X 1.404 X $66,971/$54,508 = 15.82% 5-11. a) EVA = EBIT (1- tax rate) – (invested capital * investor's required rate of return) EVA = $12,941,000 * (1 - 0.35) – ($77,389,000 * 0.10) = $672,750 b) Pinewood has a true economic profit of $672,750. This is the amount by which its earnings exceed the returned expected by the firm's investors. c) MVA = Total market value – invested capital MVA = ($75,000,000 + $2,389,000) – ($54,508,000 + $2,389,000) = $20,492,000 d) Pinewood has a total market value that is $20,492,000 greater that the amount of capital invested in the firm. 5-12. a) EVA = EBIT (1 – Tax Rate) – (invested capital * investors required rate of return) EVA = $8,000 (.65) – ($33,000 * .12) = $5,200 – $3,960 EVA = $1,240 b) The economic value is positive; therefore, Eversharp earned a sufficient amount during the year to provide more than the expected rate of return from the investors and lenders who contributed to the capital of the company. c) MVA = Total market value – invested capital MVA = $33,000 - $21,000 = $12,000 d) Eversharp's total market value exceeds its invested capital by $12,000. 5-13. EVA & MVA Calculation: Income tax rate 35% Cost of Capital 12% Ka Stock Price (ref) $9 Number of shares outstanding (ref) 3,000 Market Value of Common Equity (ref) $27,000 Book Value of Common Equity $15,210 Debt Capital (ref) $6,630 (Notes payable + Long-Term Debt ) Total Invested Capital (ref) $33,630 (Debt + Common) EVA MVA a. EVA $189 EBIT(1-Tr) - (Invested Capital * Ka) b. Comment on EVA: This year T & J earned enough to exceed the return expected by the contributors of the firm's capital by $189.
29. 29. 28 5-14. a. Du Pont: ROA = Net Profit Margin X Total Asset Turnover = (80/1,000) X (1,000/500) = 16% Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity = ($80/$1,000) X ($1,000/$500) X (1/(1-0.5) = 32% b. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.7) = 53.3% c. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.9) = 160% d. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.1) = 17.78% 5-15. Assets Liabilities + Equity Cash $6,000 Accounts Payable $6,000 Accounts Receivable 15,068 Notes Payable 2,739 Inventory 6,667 Accrued Expenses 600 Prepaid Expenses 282 Total Current Liabilities 9,339 Total Current Assets 28,017 Bonds Payable 15,661 Fixed Assets 34,483 Common Stock 16,000 Retained Earnings 21,500 Total Assets $62,500 Total Liabilities + Equity $62,500 Total Assets = Sales / Total Asset Turnover = $100,000/1.6 = $62,500 Fixed Assets = Sales / Fixed Asset Turnover = $100,000/2.9 = $34,483 Total Current Assets = $62,500 - $34,483 = $28,017 Accounts Receivable = Sales/day X Ave. Collection Period = ($100,000/365) X 55 = $15,068 Inventory = Sales / Inventory Turnover = $100,000/15 = $6,667 Prepaid Expenses = $28,017 - ($15,068 + $6,667 + $6,000) = $282 Total Debt = Total Assets X Debt to Asset Ratio = $62,500 X 0.4 = $25,000 Total Current Liabilities = Total Current Assets / Current Ratio = $28,017/3 = $9,339 Bonds Payable = Total Debt - Total Current Liabilities = $25,000 - $9,339 = $15,661 Retained Earnings = $62,500 - ($16,000 + $25,000) = $21,500 Notes Payable = $9,339 - ($600 + $6,000) = $2,739 5-16. NI/$5,000 = 0.10 NI = $500 TE = TA - TL = $10,000 - $6,000 = $4,000 ROE = $500/$4,000 = .125 = 12.5% 5-17. Current Liability = $20,000 - $18,000 = $2,000 Current Ratio = $5,000/$2,000 = 2.5 times 5-18. Return on Assets = Net Profit Margin X Total Asset Turnover 0.12 = 0.04 X Total Asset Turnover Total Asset Turnover = 0.12/0.04 = 3
30. 30. 29 5-19. Gross Profit = 0.50 X $5,000,000 = $2,500,000 5-20. EBIT = $2,500,000 - $200,000 - $50,000 = $2,250,000 Operating Profit Margin = $2,250,000/$5,000,000 = .45 = 45% 5-21. Net Income = 0.20 X $5,000,000 = $1,000,000 5-22. Net Income = 0.20 X $5,000,000 = $1,000,000 ROA = $1,000,000/$20,000,000 = .05 = 5% 5-23. Net Income = 0.10 X $15,000,000 = $1,500,000 5-24. Current Ratio = (20,000,000 - 2,000,000)/4,000,000 = 4.5 5-25. Quick Ratio = ($20,000,000 - $2,000,000 - $3,000,000)/$4,000,000 = 3.75 times 5-26. Total Debt = 0.30 X $20,000,000 = $6,000,000 Debt to Equity ratio = $6,000,000/$14,000,000 = 0.43 5-27. Inventory Turnover = 5,000,000/3,000,000 = 1.67 5-28. Return on Assets = 0.20 X 0.25 = 0.05 = 5% 5-29. a) Du Pont: ROA = Net Profit Margin X Total Asset Turnover = ($200/$2,000) X ($2,000/$1,000) = .20 = 20% Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.6)) = .50 = 50% b) ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.8)) = 100% c) ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.2)) = 25% 5-30. Notoriously Niagara Niagara's Notions a) NPM = $100,000/$500,000 = 0.20 NPM = $10,000/$500,000 = 0.02 b) TATO = $500,000/$500,0000 = 0.10 TATO = $500,000/$500,000 = 1.0 c) ROA = 0.20 X 0.10 = 0.02 ROA = 0.02 X 1.0 = 0.02
31. 31. 30 d) Notoriously Niagara must have a higher net profit margin because their asset turnover is low compared to that of Niagara's Notions even though they have the same ROA. Niagra's Notions has a high asset turnover but a low net profit margin. 5-31. a ) $2,250,000/1,750,000=$1.29 b ) $40/$1.29 = 31 c ) $15,000,000/1,750,000 = $8.57 d ) $40/$8.57 = 4.67 e ) Yes, the market seems to believe that the company has going-concern value as evidenced by the market to book ratio greater than 1. 5-32. Net Profit Margin Current Ratio Total Asset Turnover Year NI/Sales CA/CL Sales/TA 2004 10.00% .94 1.05 2005 9.44% 1.02 1.15 2006 9.36% 1.08 1.18 Golden Products Industry averages: 9.42% 1.13 2.00 The NPM is about average, although it is deteriorating. The liquidity, as measured by the current ratio, is below average but improving. Asset utilization, as measured by the total asset turnover is way below average. 5-33. The Industry averages are: Fixed Asset Turnover Return on Assets Debt to Assets Ratio Return on equity 1.33 11.00% 0.60 26% YEAR PM CR TATO FATO ROA D/A ROE 2004 10.00% 0.94 1.05 1.21 10.53% 0.68 33.33% 2005 9.44% 1.02 1.15 1.33 10.90% 0.64 30.36% 2006 9.36% 1.08 1.18 1.36 11.00% 0.60 27.50% Golden Products has an improving ROA that now equals that of the industry norm. The ROE has slipped a little, but is still above the industry norm in spite of the fact that Golden has a little less debt in its capital structure in 2006. Overall, Johnny should be pleased. 5-34. ( Figures in $ '000) Mining Smelting Rolling Extrusion Whole Company NPM 3.3% 8.7% 11.7% 10.0% 9.7% ROA 4.2% 10.4% 17.9% 13.9% 13.4%
32. 32. 31 5-35. National Glass Company Income Statement (in $ 000's) Ratios: 2006 ACP 48.7 days Sales $45,000 Inventory Turnover 9 X Cost of Goods Sold 23,000 Debt to Assets 40% Gross Profit 22,000 Current Ratio 1.6250 Selling and Admin Expenses 13,000 Total Asset turnover 1.50 Depreciation 3,000 Fixed Asset Turnover 2.6471 Operating Income 6,000 Return on Equity 19.33% Interest Expense 200 Return on Assets 11.6% Earnings Before Tax 5,800 Operating Profit Margin 13.33% Income Taxes 2,320 Gross Profit Margin 48.89% Net Income $3,480 Preferred Dividends $0 Earnings Available to Common $3,480 Balance Sheet (in $ 000's) As of Dec 31 2006 Assets Current Assets: Cash $2,000 Accounts Receivable 6,000 Inventory 5,000 Total Current Assets 13,000 Plant & Equipment, Net 16,000 Land 1,000 Total Assets $30,000 Liabilities & Equity Current Liabilities: Accounts Payable $2,000 Notes Payable 3,000 Accrued Expenses 3,000 Total Current Liabilities 8,000 Bonds Payable 4,000 Total Liabilities 12,000 Common Stock 4,000 Retained Earnings 14,000 Total Stockholders' Equity 18,000 Total Liabilities & Equity $30,000 5-36. a.) (Industry) Kingston, 2006 Kingston, 2007 i. Gross Profit Margin (50%) 48.9% 48.9% ii. Operating Profit Margin (15%) 15.1% 13.3% iii. Net Profit Margin (8%) 8.5% 7.5% iv. Return on Assets (10%) 11.56% 9.97% v. Return on Equity (20%) 19.3% 16.3% vi. Current Ratio (1.5) 1.63 1.62 vii. Quick Ratio (1.0) 1.00 1.04 viii. Debt to Total Asset (0.5) .4 .39 ix. Times Interest Earned (25) 15.5X 14.6X
33. 33. 32 x. Average Collection Period (45 days) 53.5days 61.6days xi. Inventory Turnover (8) 8.18X 8.62X xii. Total Asset Turnover (1.6) 1.4X 1.3X b.) Kingston has about the same net profit margin and return on equity as the industry norm. The return on assets ratio for Kingston is about the same as than the industry norm. c.) Determine the sources and uses of funds and prepare a statement of cash flows for 2007. (1) Sources and Uses of Funds: Change, 2006 to 2007 Balance SheetSources Uses Net Income $3,353 Dividends paid $733 Depreciation $3,000 Cash ($200) $200 Accounts Receivable, Net $1,600 $1,600 Inventory $220 $220 Property, Plant & Equipment, Gross $5,000 $5,000 Land $0 Accounts Payable $600 $600 Notes Payable $300 $300 Accrued expenses $100 $100 Bonds Payable $0 Common Stock $0 Totals $7,553$7,553 (2) Statement of Cash Flows: Kingston Tool Company Statement of Cash Flows for the year 2007 ( in $ 000s) Cash Flows from Operations: Net Income $3,353 Depreciation 3,000 Decrease(Increase) in Accounts Receivable (1,600) Decrease(Increase) in Inventory (220) Increase(Decrease) in Accounts Payable 600 Increase(Decrease) in Notes Payable 300 Increase(Decrease) in Accrued Expenses 100 Total Cash Flows from Operations $5,533 Cash Flows from Investments: New Property, Plant, & Equipment($5,000) Total Cash Flows from Investments ($5,000) Cash Flows from Financing: Dividends Paid ($733) Total Cash Flows from Financing (733) - Net Cash Flow ($200) Beginning Cash Balance $2,000 Ending Cash Balance $1,800
34. 34. 33 d.) Profit margins are eroding and generally a little below the industry norm. Liquidity is about average. Debt is low, but interest coverage is below the industry norm in spite of the low debt load. Inventory turnover is way below average. The negative cash flow of $200,000 came mainly from the buildup of accounts receivable and plant & equipment. e.) The current ratio, quick ratio, and times interest earned would get the most scrutiny from loan officers. 5-36b. EVA = EBIT * (1 – tax rate) – (invested capital * investor's required rate of return) EVA = ($4,000 * 0.60) – ($60,000 * 0.10) = -$3,600 EVA = -$3,600 MVA = Total market value – invested capital MVA = $50,000 - $60,000 = -$10,000 MVA = -$10,000 5.37. a) Accounts Receivable/Average Daily Credit Sales $564,000.00 / ($3,814,000 / 365)= 53.71 = 54 days b) Super Dot Com was more profitable in 2006 than it was in 2004. 2004 2006_________ $519,000/$2,100,000 $1,115,000/$3,814,000 Net Profit Margin 24.71% 29.23% $519,000/$2,859,000 $1,115,000/$5,316,000 Return on Assets 18.15% 20.97% Both the NPM and ROA ratios were better in 2006. c) Super Dot Com was less liquid at the end of 2006 than it was at the end of 2004. 2004 2006_________ $981,000/$245,000 $1,720,000/$623,000 Current Ratio 4.00 2.76 ($981,000 - $307,000)/$245,000 ($1,720,000 - $960,000)/$623,000 Quick Ratio 2.75 1.22
35. 35. 34 Chapter 6 Solutions Answers to Review Questions 1. Why do businesses spend time, effort, and money to produce forecasts? Explain. Businesses succeed or fail depending on how well prepared they are to deal with the situations they confront in the future. Therefore they expend considerable sums making estimates (forecasts) of what the future situation is likely to be. Businesses develop new products, set production quotas, and select financing sources based on forecasts about the future economic environment and the firm's condition. If economists predict interest rates will be relatively high, for example, firms may plan to limit borrowing and defer expansion plans. 2. What is the primary assumption behind the experience approach to forecasting? The experience approach to forecasting is based on the assumption that things will happen a certain way in the future because they happened that way in the past. For instance, if it has always taken you fifteen minutes to drive to the grocery store, then you will probably assume that it will take you about fifteen minutes the next time you drive to the store. Similarly, financial managers often assume sales, expenses, or earnings will grow at certain rates in the future because they grew at that rate in the past. 3. Describe the sales forecasting process. Sales forecasting is a group effort. Sales and marketing personnel usually provide assessments of demand and the competition. Production personnel usually provide estimates of manufacturing capacity and other production constraints. Top management will make strategic decisions affecting the firm as a whole. Financial managers coordinate, collect, and analyze the sales forecasting information. Figure 6-1 in the text shows a diagram of the process. 4. Explain how the cash budget and the capital budget relate to pro forma financial statements. The cash budget shows the projected flow of cash in and out of the firm for specified time periods. The capital budget shows planned expenditures for major asset acquisitions. Forecasters incorporate data from these budgets into pro forma financial statements under the assumption that the budget figures will, in fact, occur. 5. Explain how management goals are incorporated into pro forma financial statements. Management sets a target goal, and forecasters produce pro forma financial statements under the assumption that the goal will be reached. For example, if management's goal is to pay off all short- term notes during the coming year, forecasters would incorporate this into the pro forma balance sheet by setting Notes Payable to zero.
36. 36. 35 6. Explain the significance of the term additional funds needed. When the pro forma balance sheet is completed, total assets and total liabilities and equity will rarely match. The discrepancy between forecasted assets and forecasted liabilities and equity results when either too little or too much financing is projected for the amount of asset growth expected. The discrepancy is called additional funds needed (AFN) when forecast assets exceed forecast liabilities and equity, and excess financing when forecast liabilities and equity exceed forecast assets. 7. What do financial managers look for when they analyze pro forma financial statements? After the pro forma financial statements are complete, financial managers analyze the forecast to determine (1) what current trends suggest what will happen to the firm in the future, (2) what effect management's current plans and budgets will have on the firm, and (3) what actions to take to avoid problems revealed in the pro forma statements 8. What action(s) should be taken if analysis of pro forma financial statements reveals positive trends? Negative trends? When analyzing the pro forma statements, managers often see signs of emerging positive or negative conditions. If forecasters discover positive indicators, they will recommend that current plans be continued. If forecasters see negative indicators, they will recommend corrective action. Answers to End-of-Chapter Problems 6-1. Sales Record for The Miniver Corporation Sales in 2007 is expected to be approximately $215,000 following the trend of the last six years as shown above. $0 $50,000 $100,000 $150,000 $200,000 $250,000 1997 1998 1999 2000 2001 2002 2003
37. 37. 36 6-2. This year Next Year Forecasting Assumption Sales 100 120 Sales will grow 20%(100 X 1.2) - Variable Costs 50 60 Constant % of sales(120 X 0.5) - Fixed Costs 40 40 Remains same = Net Income 10 20 (120 - 60 - 40) Dividends 5 10 Keep 50% Payout Ratio(20 X 0.5) Current Assets 60 72 Constant % of sales(120 X 0.6) Fixed Assets 100 100 Remains same Total Assets 160 172 (100 + 72) Current Liabs. 20 24 Constant % of sales (120 X 0.2) Long-term Debt 20 20 Remains same Common Stock 20 20 Remains same Retained Earns. 100 110 (100+20-10) Tot Liabs & Eq 160 174 AFN = 172-174= -2 (Negative AFN means there are excess funds.) 6-3. Jolly Joe's Pizza, Inc. Financial Status and Forecast 2006 Est. for 2007 Sales $10,000 20,000 COGS 4,000 8,000 Gross Profit 6,000 12,000 Fixed Expenses 3,000 3,000 Before-Tax Profit 3,000 9,000 Tax @ 33.33% 1,000 3,000 Net Profit $2,000 6,000 Dividends $0 0 Current Assets $25,000 50,000 Net Fixed Assets 15,000 15,000 Total Assets $40,000 65,000 Current Liabilities $17,000 34,000 Long-term debt 3,000 3,000 Common Stock 7,000 7,000 Retained Earnings 13,000 19,000 Total Liabs & Eq $40,000 63,000 Joe will need $2,000 in additional funds in 2007 ($65,000 - $63,000).
38. 38. 37 6-4. Sugar Cane Alley Financial Status and Forecast 2006 Est. for 2007 Sales $90,000 110,000 COGS 48,000 58,667 Gross Profit 42,000 51,333 Selling and marketing expenses 13,000 15,889 General and admini- strative expenses 5,000 5,000 Depreciation Expense 2,000 2,000 Operating Income 22,000 28,444 Interest Expense 800 EBT 27,644 Tax @ 30% 8,293 Net Profit 19,351 Dividends 10,000 Addition to RE 9,351 6-5. a ) Cash .111111 X $110,000 = $12,222 Accounts Receivable .024667 X $110,000 = $2,713 Inventory .088889 X $110,000 = $9,778 b ) Property and Equipment, gross $25,000 Accumulated Depreciation $6,000 Property and Equipment, net $19,000 Total Assets $19,000 + $12,222 + $2,713 + $9,778 = $43,713 c ) Accounts Payable .015333 X $110,000 = $1,687 d ) Total Liabilities = $8,000 + $1,687 = $9,687 e ) Total Liabilities and Equity = $9,687 + $9,351 + $5,000 + $26,840 = $50,878 f ) Total Assets = $12,222 + $2,713 + $9,778 + $19,000 = $43,713 AFN = $43,713 - $50,878 = -$7,165 There are excess funds of $7,165. g ) 2006: Net Profit Margin = $14,840/$90,000 = 16.49% 2007: Net Profit Margin = $19,351/$110,000 = 17.6%
39. 39. 38 6-6. Assets 2006 2007 Liabilities 2006 2007 Cash $10,000 $12,500 Accounts Payable $10,500 $13,125 Acct Rec. 25,000 31,250 Notes Payable 10,000 12,500 Inventory 20,000 25,000 Accrued Expenses 11,000 13,750 Prepaid Exp 2,000 2,500 Long Term Debt 15,000 15,000 Total Current Common Equity 38,500 38,500 Assets 57,000 71,250 Total Liabilities Fixed Assets 32,000 32,000 Equity 85,000 $92,875 Depreciation 4,000 4,000 Total Assets 85,000 $99,250 *Net Sales for 2007 = $150 million * 1.25 = $187.5 million Additional funds needed = $99,250 - $92,875 = $6,375 6-7. 2006 2007 Sales 1,000 1,250 Variable Costs 500 562.50 Fixed Costs 160 160 Net Income 340 527.50 Dividends 136 290.13 6-8. Pro Forma Balance Sheets End of Year Assets 2006 2007 Liabilities + Equity 2006 2007 Cash $4,000 4,400 Accounts Payable $4,400 4,840 Accounts Rec 10,000 11,000 Notes Payable 4,000 4,400 Inventory 13,000 14,300 Accrued Expenses 5,000 5,500 Prepaid Exp 400 440 Tot.Current Liabilities13,400 14,740 Current Assets27,400 30,140 Bonds Payable 6,000 6,000 Fixed Assets 11,000 11,000 Common Equity 19,000 21,468 Total Assets $38,400 $41,140 Tot.Liab. + Equity $38,400 $42,208 In 2007 there would be $1,068 ($42,208-$41,140) in excess funds. This assumes, as the problem states, that notes payable would increase by 10% along with other current liabilities. Notes payable usually does not increase with sales. Year Total Sales PBT NI Addition to RE 2007 $85,000 X 1.1 $93,500 X .11 $10,285 X .6 $6,171 X .40 = $93,500 = $10,285 = $6,171 = $2,468
40. 40. 39 6-9. Compute the following ratios for 2006 and 2007: 2006 2007 Current Ratio 3 3 Debt to Assets Ratio 25% 25.3% Sales to Assets Ratio 62.5% 66.27% Net Profit Margin 10% 13.64% Return on Assets 6.25% 9.04% Return on Equity 8.33% 12.10% Liquidity seems strong and stable. Debt is modest and stable. Asset utilization is improving slightly while all the profit margins calculated show marked improvement. 6-10. BRIGHT FUTURE CORPORATION Historical and Projected Income Statements Historical Projected 2006 2007 Sales $10,000,000 $12,000,000 Cost of goods Sold $4,000,000 $4,800,000 Gross Profit $6,000,000 $7,200,000 Selling & Admin. Expenses $800,000 $960,000 Depreciation Expense $2,000,000 $2,000,000 Operating Income (EBIT) $3,200,000 $4,240,000 Interest Expenses $1,350,000 $1,350,000 Earnings Before Tax (EBT) $1,850,000 $2,890,000 Income Tax (40%) $740,000 $1,156,000 Net Income (NI) $1,110,000 $1,734,000 Common Stock Dividends paid $400,000 $400,000 Addition to Retained earnings $710,000 $1,334,000 Earnings per Share (1,000,000 shares) $1.11 $1.73 BRIGHT FUTURE CORPORATION Historical and Projected Balance Sheets Projection with AFN Historical Projected Excess Financing Dec 31, 2006 Dec 31, 2007 Incorporated ASSETS Current Assets: Cash $9,000,000 $10,800,000 $10,800,000 Marketable Securities $8,000,000 $9,600,000 $9,600,000 Accounts Receivable (gross) $1,200,000 $1,440,000 $1,440,000 Less: Allowance for bad Debts $200,000 $240,000 $240,000 Accounts Receivable (Net) $1,000,000 $1,200,000 $1,200,000 Inventory $20,000,000 $24,000,000 $24,000,000 Prepaid Expenses $1,000,000 $1,200,000 $1,200,000 Total Current Assets $39,000,000 $46,800,000 $46,800,000 Plant and Equipment (gross) $20,000,000 $20,000,000 $20,000,000 Less: Accumulated Depreciation $9,000,000 $11,000,000 $11,000,000 Plant and equipment (net) $11,000,000 $9,000,000 $9,000,000 TOTAL ASSETS $50,000,000 $55,800,000 $55,800,000 LIABILITIES AND EQUITY Current Liabilities: Accounts payable $12,000,000 $14,400,000 $14,400,000 Notes Payable $5,000,000 $5,000,000 $5,000,000
41. 41. 40 Accrued Expenses $3,000,000 $3,600,000 $3,600,000 Total Current Liabilities $20,000,000 $23,000,000 $23,000,000 L-T Debt (Bonds Payable, 5%, due 2015) $20,000,000 $20,000,000 $21,466,000 Total Liabilities $40,000,000 $43,000,000 $44,576,000 Common Stock (1,000,000 shares, $1 par) $1,000,000 $1,000,000 $1,000,000 Capital in Excess of Par $4,000,000 $4,000,000 $4,000,000 Retained Earnings $5,000,000 $6,334,000 $6,334,000 Total Equity $10,000,000 $11,224,000 $11,224,000 TOTAL LIABILITIES AND EQUITY $50,000,000 $54,224,000 $55,800,000 Question 2a. Excess Financing (Additional Funds Needed) $1,466,000 AFN is incorporated in L-T debt. If $1,466,000 of new L-T debt is issued the financing need will be met. Other financing sources could be used but we chose new L-T debt in this illustration. Question 2, Ratios: 2006 2007 b. Current Ratio 1.95 2.03 c. Total Asset Turnover 0.20 0.22 Inventory Turnover 0.50 0.50 d. Total Debt to Assets 0.80 0.77 e. Net Profit Margin 11.10% 14.45% Return on Assets 2.22% 3.11% Return on Equity 11.10% 15.30% Question 3, Comments on liquidity, asset productivity, debt management, and profitability: Liquidity is improving. Debt is high but stable. Inventory and overall asset utilization are stable. The net profit margin appears healthy. The return on assets ratio is much lower than the net profit margin because of the low asset turnover. The return on equity ratio is much higher than the return on assets because of the high debt load. Question 4, Recommendations: A 20% projected increase in sales is quite impressive. Management should prepare now, however, to raise the $1,466,000 that will be needed in 2007 to support the necessary new investments if the projected sales increase is to be achieved.
42. 42. 41 Chapter 7 Solutions Answers to Review Questions 1. What is risk aversion? If common stockholders are risk averse, how do you explain the fact that they often invest in very risky companies? Risk aversion is the tendency to avoid additional risk. Risk-averse people will avoid risk if they can, unless they receive additional compensation for assuming that risk. In finance, the added compensation is a higher expected rate of return. People are not all are equally risk averse. For example, some people are willing to buy risky stocks, while others are not. The ones that do, however, almost always demand an appropriately high expected rate of return for taking on the additional risk. 2. Explain the risk–return relationship. The relationship between risk and required rate of return is known as the risk–return relationship. It is a positive relationship because the more risk assumed, the higher the required rate of return most people will demand. Risk aversion explains the positive risk–return relationship. It explains why risky junk bonds carry a higher market interest rate than essentially risk-free U.S. Treasury bonds. 3. Why is the coefficient of variation often a better risk measure when comparing different projects than the standard deviation? Whenever we want to compare the risk of investments that have different means, we use the coefficient of variation (CV). The CV represents the standard deviation's percentage of the mean. Because the CV is a ratio, it adjusts for differences in means, while the standard deviation does not. therefore the CV provides a standardized measure of the degree of risk that can be used to compare alternatives. 4. What is the difference between business risk and financial risk? Business risk refers to the uncertainty a company has with regard to its operating income (also known as earnings before interest and taxes or EBIT). Business risk is brought on by sales volatility and intensified by the presence of fixed operating costs. Financial risk is the additional volatility of net income caused by the presence of interest expense. Firms that have only equity financing have no financial risk because they have no debt on which to make fixed interest payments. Conversely, firms that operate primarily on borrowed money are exposed to a high degree of financial risk.
43. 43. 42 5. Why does the riskiness of portfolios have to be looked at differently than the riskiness of individual assets? The riskiness of portfolios has to be looked at differently than the riskiness of individual assets because the weighted average of the standard deviations of returns of individual assets does not result in the standard deviation of a portfolio containing the assets. There is a reduction in the fluctuations of the returns of portfolios which is called the diversification effect. 6. What happens to the riskiness of a portfolio if assets with very low correlations (even negative correlations) are combined? How successfully diversification reduces risk depends on the degree of correlation between the two variables in question. When assets with very low or negative correlations are combined in portfolios, the riskiness of the portfolios (as measured by the coefficient of variation) is greatly reduced. 7. What does it mean when we say that the correlation coefficient for two variables is -1? What does it mean if this value were zero? What does it mean if it were +1? Correlation is measured by the correlation coefficient, represented by the letter r. The correlation coefficient can take on values between +1.0 (perfect positive correlation) to -1.0 (perfect negative correlation). The closer r is to +1.0, the more the two variables will tend to move with each other at the same time. The closer r is to -1.0, the more the two variables will tend to move opposite each other at the same time. An r value of zero indicates that the variables' values aren't related at all. This is known as statistical independence. 8. What is nondiversifiable risk? How is it measured? Unless the returns of one-half the assets in a portfolio are perfectly negatively correlated with the other half—which is extremely unlikely—some risk will remain after assets are combined into a portfolio. The degree of risk that remains is nondiversifiable risk, the part of a portfolio's total risk that can't be eliminated by diversifying. Nondiversifiable risk is measured by a term called beta (). The ultimate group of diversified assets, the market, has a beta of 1.0. The betas of portfolios, and individual assets, relate their returns to those of the overall stock market. Portfolios with betas higher than 1.0 are relatively more risky than the market. Portfolios with betas less than 1.0 are relatively less risky than the market. (Risk-free portfolios have a beta of zero.) 9. Compare diversifiable and nondiversifiable risk. Which do you think is more important to financial managers in business firms? Diversifiable risk can be dealt with by, of course, diversifying. Nondiversifiable risk is generally compensated for by raising one's required rate of return. Both types of risk are important to financial managers.
44. 44. 43 10. How do risk-averse investors compensate for risk when they take on investment projects? Because of risk aversion, people demand higher rates of return for taking on higher-risk projects. 11. Given that risk-averse investors demand more return for taking on more risk when they invest, how much more return is appropriate for, say, a share of common stock, than is appropriate for a Treasury bill? Although we know that the risk–return relationship is positive, the question of much return is appropriate for a given degree of risk is especially difficult. Unfortunately, no one knows the answer for sure. One well-known model used to calculate the required rate of return of an investment, given its degree of risk, is the Capital Asset Pricing Model (CAPM). 12. Discuss risk from the perspective of the Capital Asset Pricing Model (CAPM). The Capital Asset Pricing Model, or CAPM, can be used to calculate the appropriate required rate of return for an investment project given its degree of risk as measured by beta (). A project's beta represents its degree of risk relative to the overall stock market. In the CAPM, when the beta term is multiplied by the market risk premium term, the result is the additional return over the risk-free rate that investors demand from that individual project. High-risk (high-beta) projects have high required rates of return, and low-risk (low-beta) projects have low required rates of return. Answers to End-of-Chapter Problems 7-1. Cash Flow Probability Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 P x (CF - mean)2 $10,000 5.00% $500 ($9,000) $81,000,000 $4,050,000 $13,000 10.00% $1,300 ($6,000) $36,000,000 $3,600,000 $16,000 20.00% $3,200 ($3,000) $9,000,000 $1,800,000 $19,000 30.00% $5,700 $0 $0 $0 $22,000 20.00% $4,400 $3,000 $9,000,000 $1,800,000 $25,000 10.00% $2,500 $6,000 $36,000,000 $3,600,000 $28,000 5.00% $1,400 $9,000 $81,000,000 $4,050,000 Sum of (R x P) = mean: $19,000 Sum of P x (CF- mean)2 = variance: $18,900,000 Square root of variance = standard deviation of the variance: $4,347 Coefficient of Variation = std.dev./mean = 22.88%
45. 45. 44 7-2. EXPECTED VALUE, STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF OPERATING INCOME Operating Sales Variable Fixed Income Prob. Estimate Expenses Expenses Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 Px(CF - mean2 $500 $250 $250 $0 2.00% $0 ($350) $122,500 $2,450 $700 $350 $250 $100 8.00% $8 ($250) $62,500 $5,000 $1,200 $600 $250 $350 80.00% $280 $0 $0 $0 $1,700 $850 $250 $600 8.00% $48 $250 $62,500 $5,000 $1,900 $950 $250 $700 2.00% $14 $350 $122,500 $2,450 a. Sum of (R x P) = mean: $350 Sum of (CF- mean)2 x P= variance $14,900 b. Square root of variance = standard deviation: $122 c. Coeff. of Variation = std.dev/mean: 34.88% d. New expected value, standard deviation, and coefficient of variation based on revised sales forecast: Operating Sales Variable Fixed Income Probability Estimate Expenses Expenses Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 Px(CF - mean)2 $500 $250 $250 $0 10.00% $0 ($350) $122,500 $12,250 $700 $350 $250 $100 15.00% $15 ($250) $62,500 $9,375 $1,200 $600 $250 $350 50.00% $175 $0 $0 $0 $1,700 $850 $250 $600 15.00% $90 $250 $62,500 $9,375 $1,900 $950 $250 $700 10.00% $70 $350 $122,500 $12,250 a. Sum of (R x P) = mean: $350 Sum of P x (CF - mean)2 = variance: $43,250 b. Square root of variance = standard deviation: $208 c. Coeff. of Variation = std. dev./mean: 59.43% e. Comments: Note how the increased possibilities that sales will be other than $1,200 caused the standard deviation and coefficient of variation of operating income to nearly double. 7-3. Mean: .10(1,000) + .2(5,000) + .45(10,000) + .15(15,000) + .10(20,000) = 100 + 1,000 + 4,500 + 2,250 + 2,000 Mean = $9,850 Standard Deviation: ơ 2 = .1(1,000 – 9,850)2 + .2(5,000 – 9,850)2 + .45(10,000 – 9,850)2 + .15(15,000 – 9,850)2 + .1(20,000 – 9,850)2 ơ 2 = 7,832,250 + 4,704,500 + 10,125 + 3,978,375 + 10,302,250 ơ 2 = 26,827,500 ơ = √ 26,827,500 ơ = 5,179.53 Standard deviation = 5,179.53
46. 46. 45 7-4. I. EQUITY EDDIE'S COMPANY: Operating Income Interest Before-Tax Net Probability Estimate Expense Income Taxes Income of Occurrence CF P CF x P CF - mean (CF - mean)2 Px(CF - mean)2 $100 $0 $100 $28 $72 5.00% $4 ($216) $46,656 $2,333 $200 $0 $200 $56 $144 10.00% $14 ($144) $20,736 $2,074 $400 $0 $400 $112 $288 70.00% $202 $0 $0 $0 $600 $0 $600 $168 $432 10.00% $43 $144 $20,736 $2,074 $700 $0 $700 $196 $504 5.00% $25 $216 $46,656 $2,333 a. Sum of (R x P) = mean: $288 Sum of P x (CF - mean)2 = variance: $8,813 b. Square root of variance = standard deviation: $94 c. Coeff. of Variation = std. dev./mean: 32.60% II. BARRY BORROWER'S COMPANY: Operating Income Interest Before-Tax Net Probability Estimate Expense Income Taxes Income of Occurrence CF P CF x P CF - mean (CF - mean)2 Px(CF - mean)2 $110 $40 $70 $19.6 $50.4 5.00% $2.52 ($237.60) $56,453.76 $2,822.69 $220 $40 $180 $50.4 $129.6 10.00% $12.96 ($158.40) $25,090.56 $2,509.06 $440 $40 $400 $112.0 $288.0 70.00% $201.60 $0.00 $0.00 $0.00 $660 $40 $620 $173.6 $446.4 10.00% $44.64 $158.40 $25,090.56 $2,509.06 $770 $40 $730 $204.4 $525.6 5.00% $26.28 $237.60 $56,453.76 $2,822.69 a. Sum of (R x P) = mean: $288.00 Sum of P x (CF - mean)2 = variance: $10,663.49 b. Square root of variance = standard deviation= $103.26 c. Coeff. of Variation = std. dev./ mean: 35.86% e. Comments: Note how Barry Borrower's use of debt financing causes his company to have a higher standard deviation and coefficient of variation of net income than Equity Eddie's. 7-5. STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF CASH FLOWS FOR THE GO-RILLA PROJECT Cash Flow Probability Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 P x (CF - mean)2 $20,000 1.00% $200 ($6,000) $36,000,000 $360,000 $22,000 12.00% $2,640 ($4,000) $16,000,000 $1,920,000 $24,000 23.00% $5,520 ($2,000) $4,000,000 $920,000 $26,000 28.00% $7,280 $0 $0 $0 $28,000 23.00% $6,440 $2,000 $4,000,000 $920,000
47. 47. 46 $30,000 12.00% $3,600 $4,000 $16,000,000 $1,920,000 $32,000 1.00% $320 $6,000 $36,000,000 $360,000 Sum of (R x P) = mean: $26,000 Sum of P x (CF - mean)2 = variance: $6,400,000 a. Square root of variance = standard deviation: $2,530 b. Coefficient of Variation = std. dev./mean: 9.73% c. Comment: Given that the average coefficient of variation of George's other product lines is 12%, we would say that the Go-Rilla project is LESS risky than average 7-6. Effect of Adding Asset B to Existing Portfolio A Correlation coefficient r between existing portfolio A and new asset B: 0 Amount invested in Portfolio A: $700,000 Amount invested in Asset B: $200,000 Total value of combined portfolio: $900,000 Weight of existing assets in combined portfolio: 77.8% Weight of new asset B in combined portfolio: 22.2% Expected Return of existing portfolio A: 9.00% Standard deviation of existing portfolio A: 3.00% Coefficient of variation of existing portfolio A: 33.33% Expected Return of new asset B: 12.00% Standard deviation of new asset B: 4.00% Coefficient of variation of new asset B: 33.33% Expected Return of combined portfolio per equation 7-1: 9.67% Standard deviation of combined portfolio per equation 7-5: 2.50% Coefficient of Variation of combined portfolio: 25.83% a. Comparison of standard deviations of existing portfolio A and the new combined portfolio: Standard deviation of existing portfolio A: 3.00% Standard deviation of combined portfolio: 2.50% a. Comparison of coefficients of variation of existing portfolio A and the new combined portfolio: Coefficient of variation of existing portfolio A: 33.33% Coefficient of variation of combined portfolio: 25.83%
48. 48. 47 7-7. Coefficient of variation (CV) = Standard Deviation/Mean 288/1,200 = .24 CVzazzle = 24% 7-8. Total Portfolio = $10,000 Weights: Stock A: 4,000/10,000 = .4 Stock B: 6,000/10,000 = .6 .4(13) + .6(9) = 10.6% Expected Rate of Return = 10.6% 7-9. ơp = √ (0.3)2 * (0.05)2 + (0.7)2 * (0.02)2 + ( 2 * 0.3 * 0.7 * 0.6 * 0.05 * 0.02) ơp = √0.000673 ơp = 0.0259 ơp = 2.59% 7-10. Effect of Adding PROJ1 to Existing Portfolio Expected Return of existing portfolio: 11.00% Standard deviation of existing portfolio: 4.00% a. Coefficient of variation of existing portfolio: 36.36% Expected Return of new PROJ1: 13.00% Standard deviation of new PROJ1: 5.00% b. Coefficient of variation of new PROJ1: 38.46% Amount invested in existing portfolio: $820,000 Amount invested in PROJ1: $194,000 Total value of combined portfolio: $1,014,000 c. Weight of existing assets in combined portfolio: 80.9% d. Weight of new PROJ1 in combined portfolio: 19.1% Correlation coefficient r between existing portfolio and new PROJ1: 0 e. Standard deviation of combined portfolio: 3.37% (lower than existing portfolio) : Expected Return of combined portfolio per equation 7-1 11.38% f.: Coefficient of Variation of combined portfolio 29.63% (lower than existing portfolio) g. Firm's risk decreases with the addition of PROJ1 to the portfolio
49. 49. 48 7-11. Required Rate of Return per the CAPM Risk free rate (kRF) 5.0% Expected rate of return on the market (km) 15.0% Beta 1.2 Required rate of return on stock per the CAPM: 17.0% (equation 7-6) 7-12. kl = 4.5 + .5(12.5) = 10.75% ka = 4.5 + 1.0(12.5) = 17% kh = 4.5 + 1.6(12.5) = 24.5% 7-13. Effect on CAPM Required Rate of Return of Adding a New Project Risk free rate (kRF) 5.0% Expected rate of return on the market (km) 15.0% Existing firm's Beta 1.5 New Project's Beta 0.8 a. Required rate of return on company per the CAPM: 20.0% b. Required rate of return on new project per the CAPM: 13.0% Weight of new project in firm's portfolio: 20.0% Weight of firm's other assets: 80.0% c. Beta of firm with new project 1.36 7-14. STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF PSC SALES REVENUE Sales Probability Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 P x (CF - mean)2 $800 2.00% $16 ($1,200) $1,440,000 $28,800 $1,000 8.00% $80 ($1,000) $1,000,000 $80,000 $1,400 20.00% $280 ($600) $360,000 $72,000 $2,000 40.00% $800 $0 $0 $0 $2,600 20.00% $520 $600 $360,000 $72,000 $3,000 8.00% $240 $1,000 $1,000,000 $80,000 $3,200 2.00% $64 $1,200 $1,440,000 $28,800 Sum of (R x P) = exp val: $2,000
50. 50. 49 Sum of P x (CF - mean)2 = variance: $361,600 Square root of variance = standard deviation: $601 Coefficient of Variation = std. dev./mean: 30.07% 7-15. COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME Operating Sales Variable Fixed Income Probability Estimate Expenses Expenses Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 Px(CF - mean)2 $800 $480 $0 $320 2.00% $6 ($480) $230,400 $4,608 $1,000 $600 $0 $400 8.00% $32 ($400) $160,000 $12,800 $1,400 $840 $0 $560 20.00% $112 ($240) $57,600 $11,520 $2,000 $1,200 $0 $800 40.00% $320 $0 $0 $0 $2,600 $1,560 $0 $1,040 20.00% $208 $240 $57,600 $11,520 $3,000 $1,800 $0 $1,200 8.00% $96 $400 $160,000 $12,800 $3,200 $1,920 $0 $1,280 2.00% $26 $480 $230,400 $4,608 Sum of (R x P) = mean: $800 Sum of P x (CF - mean)2 = variance: $57,856 Square root of variance = standard deviation: $241 Coefficient of Variation = std. dev./mean: 30.07% 7-16. COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME Operating Sales Variable Fixed Income Probability Estimate Expenses Expenses Estimate of Occurrence CF P CF x P CF - mean (CF - mean)2 Px(CF - mean)2 $800 $480 $400 ($80) 2.00% ($2) ($480) $230,400 $4,608 $1,000 $600 $400 $0 8.00% $0 ($400) $160,000 $12,800 $1,400 $840 $400 $160 20.00% $32 ($240) $57,600 $11,520 $2,000 $1,200 $400 $400 40.00% $160 $0 $0 $0 $2,600 $1,560 $400 $640 20.00% $128 $240 $57,600 $11,520 $3,000 $1,800 $400 $800 8.00% $64 $400 $160,000 $12,800 $3,200 $1,920 $400 $880 2.00% $18 $480 $230,400 $4,608 Sum of (R x P) = mean: $400
51. 51. 50 Sum of P x (CF - mean)2 = variance: $57,856 Square root of variance = standard deviation: $241 Coefficient of Variation = std. dev./mean: 60.13% Comment: Note how the addition of fixed costs caused the coefficient of variation of PSC's operating income to double from what it was in problem 7-10 7-17. MEASURING PSC'S FINANCIAL RISK I. Expected value, standard deviation, and coefficient of variation of PSC's net income when no interest expense is present Sales Variable Fixed Operating Interest Before- Tax Probability of Estimate Expenses Expenses Income Expense Income Taxes Net Income Occurrence NI P NI X P NI - mean (NI - mean)2 P X (NI - mean)2 $800 $480 $400 -$80 $0 -$80 -$56 -$24 2% $0 -$144 $20,736 $415 $1,000 $600 $400 $0 $0 $0 $0 $0 8% $0 -$120 $14,400 $1,152 $1,400 $840 $400 $160 $0 $160 $112 $48 20% $10 -$72 $5,184 $1,037 $2,000 $1,200 $400 $400 $0 $400 $280 $120 40% $48 $0 $0 $0 $2,600 $1,560 $400 $640 $0 $640 $448 $192 20% $38 $72 $5,184 $1,037 $3,000 $1,800 $400 $800 $0 $800 $560 $240 8% $19 $120 $14,400 $1,152 $3,200 $1,920 $400 $880 $0 $880 $616 $264 2% $5 $144 $20,736 $415 Sum of (NI X P) = mean $ 120 Sum of P X (CF - mean)2 = variance: $5,207 Square root of variance = standard deviation: $72 Coefficient of Variation = std. dev./mean: 60.1% II. Expected value, standard deviation, and coefficient of variation of PSC's net income when interest expense is present Sales Variable Fixed Operating Interest Before- Tax Probability of Estimate Expenses Expenses Income Expense Income Taxes Net Income Occurrence NI P NI X P NI - mean (NI - mean)2 P X (NI - mean)2 $800 $480 $400 ($80) $60 ($140) ($42) ($98) 2% ($2) ($336) $112,896 $2,258 $1,000 $600 $400 $0 $60 ($60) ($18) ($42) 8% ($3) ($280) $78,400 $6,272 $1,400 $840 $400 $160 $60 $100 $30 $70 20% $14 ($168) $28,224 $5,645 $2,000 $1,200 $400 $400 $60 $340 $102 $238 40% $95 $0 $0 $0 $2,600 $1,560 $400 $640 $60 $580 $174 $406 20% $81 $168 $28,224 $5,645 $3,000 $1,800 $400 $800 $60 $740 $222 $518 8% $41 $280 $78,400 $6,272 $3,200 $1,920 $400 $880 $60 $820 $246 $574 2% $11 $336 $112,896 $2,258 Sum of (R X P) = mean = $ 238 Sum of P X (CF - mean)2 = variance = $28,349 Square root of variance = standard deviation = $168 Coefficient of variation equals std. dev./mean = 70.7%
52. 52. 51 7-18. I. New coefficient of variation of PSC's operating income: Operating Sales Variable Fixed Income Probability of Estimate Expenses Expenses Estimate Occurrence EBIT P EBIT X P EBIT - mean (EBIT - mean)2 P X (EBIT - mean)2 $800 $480 $250 $70 1% $0.70 ($480) $230,400 $2,304 $1,000 $600 $250 $150 6% $9.00 ($400) $160,000 $9,600 $1,400 $840 $250 $310 13% $40.30 ($240) $57,600 $7,488 $2,000 $1,200 $250 $550 60% $330.00 $0 $0 $0 $2,600 $1,560 $250 $790 13% $102.70 $240 $57,600 $7,488 $3,000 $1,800 $250 $950 6% $57.00 $400 $160,000 $9,600 $3,200 $1,920 $250 $1,030 1% $10.30 $480 $230,400 $2,304 Sum of (EBIT X P) = mean = $550.00 Sum of P X (CF - mean)2 = variance = $38,784 Square root of variance = standard deviation = $197 Coefficient of Variation = std. dev./mean = 35.8% II. New coefficient of variation of PSC's net income when no interest expense is present Sales Variable Fixed Operating Interest Before- Tax Net Probability of Estimate Expenses Expenses Income Expense Income Taxes Income Occurrence NI P NI X P (NI - mean)2 P X (NI - mean)2 $800 $480 $250 $70 $0 $70 $21 $49 1% $0 $112,896 $1,129 $1,000 $600 $250 $150 $0 $150 $45 $105 6% $6 $78,400 $4,704 $1,400 $840 $250 $310 $0 $310 $93 $217 13% $28 $28,224 $3,669 $2,000 $1,200 $250 $550 $0 $550 $165 $385 60% $231 $0 $0 $2,600 $1,560 $250 $790 $0 $790 $237 $553 13% $72 $28,224 $3,669 $3,000 $1,800 $250 $950 $0 $950 $285 $665 6% $40 $78,400 $4,704 $3,200 $1,920 $250 $1,030 $0 $1,030 $309 $721 1% $7 $112,896 $1,129 Sum of (NI X P) = mean = $385 Sum of P X (CF - mean)2 = variance = $19,004 Square root of variance = standard deviation = $138 Coefficient of Variation = std. dev./mean = 35.8% III. New coefficient of variation of PSC's net income when interest expense is present Sales Variable Fixed Operating Interest B-T Net Probability of Estimate Expenses Expenses Income Expense Income Taxes Income Occurrence NI P NI X P (NI - mean)2 P X (NI - mean)2 $800 $480 $250 $70 $40 $30 $9 $21 1% $0 $112,896 $1,129 $1,000 $600 $250 $150 $40 $110 $33 $77 6% $5 $78,400 $4,704 $1,400 $840 $250 $310 $40 $270 $81 $189 13% $25 $28,224 $3,669 $2,000 $1,200 $250 $550 $40 $510 $153 $357 60% $214 $0 $0 $2,600 $1,560 $250 $790 $40 $750 $225 $525 13% $68 $28,224 $3,669 $3,000 $1,800 $250 $950 $40 $910 $273 $637 6% $38 $78,400 $4,704 $3,200 $1,920 $250 $1,030 $40 $990 $297 $693 1% $7 $112,896 $1,129 Sum of (NI X P) = mean = $357
53. 53. 52 Sum of P X (CF - mean)2 = variance = $19,004 Square root of variance = standard deviation = $138 Coefficient of Variation = std. dev./mean = 38.62% Summary: Old Coefficient of variation of operating income (business risk) 60.13% New coefficient of variation of operating income (business risk) 35.81% Old difference between the coefficient of variation of net income with and without interest expense (financial risk) -10.6% New difference between the coefficient of variation of net income with and without interest expense (financial risk) -2.8% Comments: The effect of PSC's risk reduction measures was to lower business risk substantially, but financial risk increased slightly. Managers must evaluate this trade-off and proceed accordingly.
54. 54. 53 Chapter 8 Solutions Answers to Review Questions 1. What is the time value of money? The time value of money means that money you hold in your hand today is worth more than money you expect to receive in the future. Similarly, money you must pay out today is a greater burden than the same amount paid in the future. 2. Why does money have time value? Positive interest rates indicate that money has time value. When one person lets another borrow money, the first person requires compensation in exchange for reducing current consumption. The person who borrows the money is willing to pay to increase current consumption. The required rate of return on an investment reflects the pure time value of money, an adjustment for expected inflation, and any risk premiums present. 3. What is compound interest? Compare compound interest to discounting. Compound interest occurs when interest is earned on interest and on the original principal of an investment. Discounting is the inverse of compounding. Compound interest causes the value of a beginning amount to increase at an increasing rate. Discounting causes the present value of a future amount to decrease at an increasing rate. 4. How is present value affected by a change in the discount rate? Present value is inversely related to the discount rate. In other words, present value moves in the opposite direction of the discount rate. If the discount rate increases, present value decreases. If the discount rate decreases, present value increases. 5. What is an annuity? An annuity is a series of equal cash flows, spaced evenly over time. 6. Suppose you are planning to make regular contributions in equal payments to an investment fund for your retirement. Which formula would you use to figure out how much your investments will be worth at retirement time, given an assumed rate of return on your investments? To figure out how much your investments will be worth at retirement time, given an assumed rate of return on your investments, you would use the future value of an annuity formula:
55. 55. 54 Future Value of an Annuity Formula         k k PMTFVA n 1)1( where: FVA = Future Value of an Annuity PMT = Amount of each annuity payment k = Interest rate per time period n = Number of annuity payments 7. How does continuous compounding benefit an investor? The effect of increasing the number of compounding periods per year is to increase the future value of the investment. The more frequently interest is compounded, the greater the future value. The smallest compounding period is used when we do continuous compounding--compounding that occurs every tiny unit of time (the smallest unit of time imaginable). 8. If you are doing PVA and FVA problems, what difference does it make if the annuities are "ordinary annuities" or "annuities due"? In FVA or a PVA of annuity due problems, annuity payments earning interest one period sooner than in ordinary annuity problems. So, higher FVA and PVA values result with an annuity due. The first payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due problems, each annuity payment occurs one period sooner, so the payments are discounted less severely. 9. Which formula would you use to solve for the payment required for a car loan if you know the interest rate, length of the loan, and the borrowed amount? Explain. To solve for k when the known values are PVA, n, and PMT, start with the present value of an annuity formula, Equation 8-3b, as follows: Present Value of an Annuity Formula, Table Method PVA = PMT(PVIFA k, n) Next, rearrange terms and solve for (PVIFA k, n) as follows PVA / PMT = (PVIFA k, n) Now refer to the PVIFA values in the text, Table IV. You know n, so find the n row corresponding to the number of periods in your problem on the left hand side of the table. You have also determined the PVIFA, so move across the n row until you find (or come close to) the value of PVIFA that you have solved for. The percent column in which the value is located is the interest rate.
56. 56. 55 Answers to End-of-Chapter Problems 8-1. $1,000 X (1 + 0.07)5 = $1,402.55 8-2. a) 0% $50,000 X (1 + 0.00)10 = $50,000.00 b) 5% $50,000 X (1 + 0.05)10 = $81,444.73 c) 10% $50,000 X (1 + 0.10)10 = $129,687.12 d) 20% $50,000 X (1 + 0.20)10 = $309,586.82 8-3. $5,000 * (1 + 0.08)10 = $10,794.62 8-4. a) 3% $100,000 * (1 + 0.03)15 = $155,796.74 b) 6% $100,000 * (1 + 0.06)15 = $239,655.82 c) 9% $100,000 * (1 + 0.09)15 = $364,248.25 d) 12% $100,000 * (1 + 0.12)15 = $547,356.58 8-5 a) 50,000 $50,000 * (1 + 0.10)25 = $541,735.30 b) 75,000 $75,000 * (1 + 0.10)25 = $812,602.95 c) 100,000 $100,000 * (1 + 0.10)25 = $1,083,470.59 d) 125,000 $125,000 * (1 + 0.10)25 = $1,354,338.24 8-6 a) 5 years $60,000 * (1 + 0.12)5 = $105,740.50 b) 10 years $60,000 * (1 + 0.12)10 = $186,350.89 c) 15 years $60,000 * (1 + 0.12)15 = $328,413.95 d) 20 years $60,000 * (1 + 0.12)20 = $578,777.59 8-7. PV = $20,000 X [1/(1 + .12)10 ] = $6,439.46 8-8. a) 0% $60,000 X [1/(1+0.00)20 ] = $60,000.00 b) 5% $60,000 X [1/(1+0.05)20 ] = $22,613.37 c) 10% $60,000 X [1/(1+0.10)20 ] = $8,918.62 d) 20% $60,000 X [1/(1+0.20)20 ] = $1,565.04 8-9 $9,000 * [1/(1+0.08)4 ] = $6,615.27 8-10 a) 3% $25,000 * [1/(1 + 0.03)10 ] = $18,602.35 b) 6% $25,000 * [1/(1 + 0.06)10 ] = $13,959.87 c) 9% $25,000 * [1/(1 + 0.09)10 ] = $10,560.27 d) 12% $25,000 * [1/(1 + 0.12)10 ] = $8,049.33
57. 57. 56 8-11. a)$50,000 $50,000 * [1/(1 + 0.06)15 = $20,863.25 b)$75,000 $75,000 * [1/(1 + 0.06)15 = $31,294.88 c)$100,000 $100,000 * [1/(1 + 0.06)15 = $41,726.51 d)$125,000 $125,000 * [1/(1 + 0.06)15 = $52,158.13 8-12. a) 5 years $80,000 * [1/(1 + 0.09)5 ] = $51,994.51 b) 10 years $80,000 * [1/(1 + 0.09)10 ] = $33,792.86 c) 15 years $80,000 * [1/(1 + 0.09)15 ] = $21,963.04 d) 20 years $80,000 * [1/(1 + 0.09)20 ] = $14,274.47 8-13. PVA = $500 X [(1-1/1.0610 )/0.06] = $3,680.04 8-14. a) 0% $10,000 X 30 = $300,000 b) 10% $10,000 X [(1-1/1.1030 )/0.10] = $94,269.14 c) 20% $10,000 X [(1-1/1.2030 )/0.20] = $49,789.36 d) 50% $10,000 X [(1-1/1.5030 )/0.50] = $19,999.90 8-15. $20,000 * [(1-1/1.0710 )/0.07] = $140,471.63 8-16. a) 9 % $10,000 * [(1-1/1.095 )/0.09] = $38,896.51 b) 13% $10,000 * [(1-1/1.135 )/0.13] = $35,173.31 c) 15%$10,000 * [(1-1/1.155 )/0.15] = $33,521.55 d) 21% $10,000 * [(1-1/1.215 )/0.21] = $29,259.84 8-17. FVA = $500 X [(1.095 -1)/.09] = $2,992.36 8-18. a) 0% $6,000 X 12 = $72,000.00 b) 2% $6,000 X [(1.0212 -1)/0.02] = $80,472.54 c) 10% $6,000 X [(1.1012 -1)/0.10] = $128,305.70 d) 20% $6,000 X [(1.2012 -1)/0.20] = $237,483.01 8-19. $5,000 * [(1.0610 – 1)/0.06] = $65,903.97 8-20. $5,000 * [(1.118 – 1)/0.11] = $59,297.17 8-21. a) $1,000 $1,000 * [(1.105 – 1)/0.10] = $6,105.10 b) $10,000 $10,000 * [(1.105 – 1)/0.10] = $61,051.00 c) $75,000 $75,000 * [(1.105 – 1)/0.10] = $457,882.50 d) $125,000 $125,000 * [(1.105 – 1)/0.10] = $763,137.50
58. 58. 57 8-22. $1,200 X [(1.1240 – 1)/.12] X 1.12 = $1,030,970.87 8-23. $500 * [(1.085 – 1)/0.08] * 1.08 = $3,167.96 8-24. $56,370.93 * 1.06 = $59,753.19 8-25. $80 X [(1-1/1.1220 )/.12] X 1.12 = $669.26 8-26. $30,000 * [1-1/1.0925 )/0.09] * 1.09 = $321,198.35 8-27. $1,300 * [1-1/1.00583333180 )/0.00583333] * 1.00583 = $144,632.74 8-28. $185,361 = FVIF10,k% X $50,000 FVIF10,k% = 3.7072; from Table I, k = 14% 8-29. $1,000 X (1 + k)5 = $773.78 (1 + k)5 = $773.78/$1,000 (1 + k)5 = .77378 1 + k = .95 k = -.05 = -5% 8-30. $50,000 * (1 + k)10 = $246,795 (1 + k)10 = $246,795/$50,000 (1 + k)10 = 4.9359 1 + k = 1.173104 k = .1731 = 17.31% 8-31. PV = $50/0.08 = $625 8-32. $80/0.09 = $888.89 8-33. $65/0.085 = $764.71 8-34. FV = $10 X (1.08)200 = $48,389,496 8-35. PVA = PMT X PVIFA k,n $24,000 = $4,247.62 X PVIFA k,10
59. 59. 58 5.6502 = PVIFA k,10 k = 12% 8-36 PVA = PMT X PVIFA k,n $200,000 = $1,330.61 X PVIFA k,360 150.3070 = PVIFA k,360 k = .5833% per month X 12 = 7% annual rate 8-37. a ) 5 years? 10,000/(1+.07)5 = 7130 b ) 10 years? 10,000/(1+.07)10 = 5083 c ) 20 years? 10,000/(1+.07)20 = 2584 8-38. PV = $16,850.58 X [1/(1+.11)5 ] PV = $10,000 8-39. a ) FV = $20,000 X (1 + .05)7 = $28,142.01 b ) FV = $20,000 X (1 + .07)10 = $39,343.03 8-40. $55.00 = $67.73 X [PVIFk%, 12 years ] .8120 = PVIFk%, 12 years; k = 1.75% 8-41. 1,000 = 2653.3 X [PVIF5%, ?]; .3769 = PVIF5%,?; ? = 20 semi-annual periods, so it will take 10 years. 8-42. PV = 20,000 X [(1-1/1.0615 )/0.06] = $194,244.98 8-43. $4,000 * [(1.0920 –1)/0.09] * 1.09 = $223,058.12 8-44. $100 * [(1.0220 –1)/0.02] = $2,429.74 8-45. $2,000 X [((1+.08)10 - 1)/.08] = $2,000 X 14.4866 = $28,973 8-46. a ) $300 X [((1+.02)120 - 1)/.02] = $146,477 b ) $146,477 = $6,000 X [PVIFA2%, n quarters ] PVIFA2%, n quarters = 24.4128; n = 34 quarters or 8.5 years
60. 60. 59 8-47. $30,000 = PMT X [(1-1/(1+0.1)7 )/0.1]; $30,000 = PMT X 4.86841882; PMT = $6,162.16 8-48. $10,000/.12 = $83,333.33 8-49. FV = $500 X e.05 x 23 = $1,579.10 8-50. FVIF k=8%, n=? = 2 n = 9 years 8-51. PVA = PMT X PVIFA k,n $4,000 = $200 X PVIFA k=.195/12, n=? 20 = PVIFA k=.01625, n=? n = 24.39 months 8-52. $14,568.50 = $5,000 X [PVIFAk%,4 years], assuming payments start one year from the date of borrowing [PVIFAk%,4 years] = 2.9137; k = 14% 8-53. a) FVA = $1,000 X [[(1+.02)60 - 1]/.02] = $114,051.54 b) $114,051.54 = $6,000 X PVIFA.02, n quarters PVIFA.02, n quarters = 19.00859; n = 24 quarters = 6 years 8-54. Option 1) PV = $5,650 Option 2) PV = $6,750 X [1/1.028 ] = $5,761.06 Option 3) PV = $800 X [(1-(1/(1+.02)8 )/.02] = $5,860.39 Option 4) PV = $1,000 + $5,250 X (1/(1+.02)8 ) = $5,480.82 Option 4) is the one with lowest cost to Jack. 8-55. n = 30 X 12 = 360 k = .09/12 =0 .0075 or 0.75% $120,000 = PMT X [(1-1/1.0075360 )/0.0075] PMT = $120,000/124.28186568 = $965.55 8-56. PVA = PMT [(1-1/1.005 180 )/.005] $250,000 = PMT X 118.5035147 PMT = $2,109.64 8-57. a) n = 4 X 12 = 48 k = .06/12 =0 .005 or 0.5%
61. 61. 60 $18,000 = PMT X [(1-1/1.00548 )/0.005] PMT = $18,000/42.58031778 = $422.73 b) n = 6 X 12 = 72 k = .06/12 =0 .005 or 0.5% $18,000 = PMT X [(1-1/1.00572 )/0.005] PMT = $18,000/60.33951394 = $298.31 8-58, Missing Cash Flow Problem I. Given Information: Discount Rate 10% Known Cash Flows Time 0 Time 1 $100 Time 2 $150 Time 3 Time 4 $100 Total Present Value of all Cash Flows, including the missing cash flow $320.74 II. Solution: The value of the missing cash flow at Time 3: Known Cash Flows Present Value of Known Cash Flows Time 0 Time 1 $100 $90.9091 Time 2 $150 $123.9669 Time 3 Time 4 $100 $68.3013 Total Present Value of all Cash Flows, including the missing cash flow $320.74 (given) Total present value of known cash flows only $283.1774 Difference (Present Value of missing cash flow) $37.5657 Future Value of Missing Cash Flow at Time 3 $50 8-59. a) n = 5*12 = 60 k = .08/12 = .0066666 $22,000 = PMT * [1-1/1.00666666760 )/0.006666667] PMT = $22,000/118.5035147 = $446.0806 = $446.08

Financial Management Problems and Solutions Chapter 4

Source: https://www.slideshare.net/indrahayuni/1-45399114

Share this post