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Solutions to Suggested Homework Problems for Midterm Chapter 1 An Overview of Financial Management and the Financial Environment ANSWERS TO END-OF-CHAPTER QUESTIONS 1-1 a. A proprietorship, or sole proprietorship, is a business owned by one individual. A partnership exists when two or more persons associate to conduct a business. In contrast, a corporation is a legal entity created by a state. The corporation is separate and distinct from its owners and managers. b. In a limited partnership, limited partners' liabilities, investment returns and control are limited, while general partners have unlimited liability and control. A limited liability partnership (LLP), sometimes called a limited liability company (LLC), combines the limited liability advantage of a corporation with the tax advantages of a partnership. A professional corporation (PC), known in some states as a professional association (PA), has most of the benefits of incorporation but the participants are not relieved of professional (malpractice) liability. c. Stockholder wealth maximization is the appropriate goal for management decisions. The risk and timing associated with expected earnings per share and cash flows are considered in order to maximize the price of the firm's common stock. d. A money market is a financial market for debt securities with maturities of less than one year (short-term). The New York money market is the world's largest. Capital markets are the financial markets for long-term debt and corporate stocks. The New York Stock Exchange is an example of a capital market. Primary markets are the markets in which newly issued securities are sold for the first time. Secondary markets are where securities are resold after initial issue in the primary market. The New York Stock Exchange is a secondary market. 1 e. In private markets, transactions are worked out directly between two parties and structured in any manner that appeals to them. Bank loans and private placements of debt with insurance companies are examples of private market transactions. In public markets, standardized contracts are traded on organized exchanges. Securities that are issued in public markets, such as common stock and corporate bonds, are ultimately held by a large number of individuals. Private market securities are more tailor-made but less liquid, whereas public market securities are more liquid but subject to greater standardization. Derivatives are claims whose value depends on what happens to the value of some other asset. Futures and options are two important types of derivatives, and their values depend on what happens to the prices of other assets, say IBM stock, Japanese yen, or pork bellies. Therefore, the value of a derivative security is derived from the value of an underlying real asset. f. An investment banker is a middleman between businesses and savers. Investment banking houses assist in the design of corporate securities and then sell them to savers (investors) in the primary markets. Financial service corporations offer a wide range of financial services such as brokerage operations, insurance, and commercial banking. A financial intermediary buys securities with funds that it obtains by issuing its own securities. An example is a common stock mutual fund that buys common stocks with funds obtained by issuing shares in the mutual fund. g. A mutual fund is a corporation that sells shares in the fund and uses the proceeds to buy stocks, long-term bonds, or short-term debt instruments. The resulting dividends, interest, and capital gains are distributed to the fund's shareholders after the deduction of operating expenses. Different funds are designed to meet different objectives. Money market funds are mutual funds which invest in short-term debt instruments and offer their shareholders check writing privileges; thus, they are essentially interest-bearing checking accounts. h. Physical location exchanges, such as the New York Stock Exchange, facilitate communication between buyers and sellers of securities. Each physical location exchange is a physical entity at a particular location and is governed by an elected board of governors. A computer/telephone network, such as Nasdaq, consists of all the facilities that provide for security transactions not conducted at a physical location exchange. These facilities are, basically, the communications network that links the buyers and sellers. i. An open outcry auction is a method of matching buyers and sellers. In an auction, the buyers and sellers are face-to-face, with each stating the prices and which they will buy or sell. In a dealer market, a dealer holds an inventory of the security and makes a market by offering to buy or sell. Others who wish to buy or sell can see the offers made by the dealers, and can contact the dealer of their choice to arrange a transaction. In an ECN, orders from potential buyers and sellers are automatically matched, and the transaction is automatically completed. 2 j. Production opportunities are the returns available within an economy from investment in productive assets. The higher the production opportunities, the more producers would be willing to pay for required capital. Consumption time preferences refer to the preferred pattern of consumption. Consumer's time preferences for consumption establish how much consumption they are willing to defer, and hence save, at different levels of interest. k. A foreign trade deficit occurs when businesses and individuals in the U. S. import more goods from foreign countries than are exported. Trade deficits must be financed, and the main source of financing is debt. Therefore, as the trade deficit increases, the debt financing increases, driving up interest rates. U. S. interest rates must be competitive with foreign interest rates; if the Federal Reserve attempts to set interest rates lower than foreign rates, foreigners will sell U.S. bonds, decreasing bond prices, resulting in higher U. S. rates. Thus, if the trade deficit is large relative to the size of the overall economy, it may hinder the Fed's ability to combat a recession by lowering interest rates. 1-2 Sole proprietorship, partnership, and corporation are the three principal forms of business organization. The advantages of the first two include the ease and low cost of formation. The advantages of the corporation include limited liability, indefinite life, ease of ownership transfer, and access to capital markets. The disadvantages of a sole proprietorship are (1) difficulty in obtaining large sums of capital; (2) unlimited personal liability for business debts; and (3) limited life. The disadvantages of a partnership are (1) unlimited liability, (2) limited life, (3) difficulty of transferring ownership, and (4) difficulty of raising large amounts of capital. The disadvantages of a corporation are (1) double taxation of earnings and (2) requirements to file state and federal reports for registration, which are expensive, complex and time-consuming. 1-3 A firm's fundamental, or intrinsic, value is the present value of its free cash flows when discounted at the weighted average cost of capital. If the market price reflects all relevant information, then the observed price is also the intrinsic price. 1-4 Earnings per share in the current year will decline due to the cost of the investment made in the current year and no significant performance impact in the short run. However, the company's stock price should increase due to the significant cost savings expected in the future. 1-6 Financial intermediaries are business organizations that receive funds in one form and repackage them for the use of those who need funds. Through financial intermediation, resources are allocated more effectively, and the real output of the economy is thereby increased. 3 Chapter 2 Financial Statements, Cash Flow, and Taxes ANSWERS TO END-OF-CHAPTER QUESTIONS 2-1 a. The annual report is a report issued annually by a corporation to its stockholders. It contains basic financial statements, as well as management's opinion of the past year's operations and the firm's future prospects. A firm's balance sheet is a statement of the firm's financial position at a specific point in time. It specifically lists the firm's assets on the left-hand side of the balance sheet, while the right-hand side shows its liabilities and equity, or the claims against these assets. An income statement is a statement summarizing the firm's revenues and expenses over an accounting period. Net sales are shown at the top of each statement, after which various costs, including income taxes, are subtracted to obtain the net income available to common stockholders. The bottom of the statement reports earnings and dividends per share. b. Common Stockholders' Equity (Net Worth) is the capital supplied by common stockholders-capital stock, paid-in capital, retained earnings, and, occasionally, certain reserves. Paid-in capital is the difference between the stock's par value and what stockholders paid when they bought newly issued shares. Retained earnings is the portion of the firm's earnings that have been saved rather than paid out as dividends. c. The statement of stockholders' equity shows how much of the firm's earnings were retained in the business rather than paid out in dividends. It also shows the resulting balance of the retained earnings account and the stockholders' equity account. Note that retained earnings represents a claim against assets, not assets per se. Firms retain earnings primarily to expand the business, not to accumulate cash in a bank account. The statement of cash flows reports the impact of a firm's operating, investing, and financing activities on cash flows over an accounting period. d. Depreciation is a non-cash charge against tangible assets, such as buildings or machines. It is taken for the purpose of showing an asset's estimated dollar cost of the capital equipment used up in the production process. Amortization is a non-cash charge against intangible assets, such as goodwill. EBITDA is earnings before interest, taxes, depreciation, and amortization. 4 e. Operating current assets are the current assets used to support operations, such as cash, accounts receivable, and inventory. It does not include short-term investments. Operating current liabilities are the current liabilities that are a natural consequence of the firm's operations, such as accounts payable and accruals. It does not include notes payable or any other short-term debt that charges interest. Net operating working capital is operating current assets minus operating current liabilities. Total net operating capital is sum of net operating working capital and operating long-term assets, such as net plant and equipment. Operating capital also is equal to the net amount of capital raised from investors. This is the amount of interest-bearing debt plus preferred stock plus common equity minus short-term investments. f. Accounting profit is a firm's net income as reported on its income statement. Net cash flow, as opposed to accounting net income, is the sum of net income plus non-cash adjustments. NOPAT, net operating profit after taxes, is the amount of profit a company would generate if it had no debt and no financial assets. Free cash flow is the cash flow actually available for distribution to investors after the company has made all investments in fixed assets and working capital necessary to sustain ongoing operations. Return on invested capital is equal to NOPAT divided by total net operating capital. It shows the rate of return that is generated by assets. g. Market value added is the difference between the market value of the firm (i.e., the sum of the market value of common equity, the market value of debt, and the market value of preferred stock) and the book value of the firm's common equity, debt, and preferred stock. If the book values of debt and preferred stock are equal to their market values, then MVA is also equal to the difference between the market value of equity and the amount of equity capital that investors supplied. Economic value added represents the residual income that remains after the cost of all capital, including equity capital, has been deducted. h. A progressive tax means the higher one's income, the larger the percentage paid in taxes. Taxable income is defined as gross income less a set of exemptions and deductions which are spelled out in the instructions to the tax forms individuals must file. Marginal tax rate is defined as the tax rate on the last unit of income. Average tax rate is calculated by taking the total amount of tax paid divided by taxable income. i. Capital gain (loss) is the profit (loss) from the sale of a capital asset for more (less) than its purchase price. Ordinary corporate operating losses can be carried backward for 2 years or forward for 20 years to offset taxable income in a given year. 5 j. Improper accumulation is the retention of earnings by a business for the purpose of enabling stockholders to avoid personal income taxes on dividends. An S corporation is a small corporation which, under Subchapter S of the Internal Revenue Code, elects to be taxed as a proprietorship or a partnership yet retains limited liability and other benefits of the corporate form of organization. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 2-5 NI = $3,100,000; DEP = $500,000; AMORT = 0; NCF = ? NCF = NI + DEP and AMORT = $3,100,000 + $500,000 = $3,600,000. 2-10 EBIT = $750,000; DEP = $200,000; 100% Equity; T = 40% NI = ?; NCF = ?; OCF = ? First, determine net income by setting up an income statement: EBIT $750,000 Interest EBT Taxes (40%) NI 0 $750,000 300,000 $450,000 NCF = NI + DEP = $450,000 + $200,000 = $650,000. 2-12 a. EBIT $1,260 x (1-Tax rate) 60.0% Net operating profit after taxes (NOPAT) $756 6 b. 2013 2012 $550 $500 + Accounts receivable 2,750 2,500 + Inventories 1,650 1,500 Operating current assets $4,950 $4,500 Accounts payable $1,100 $1,000 550 500 Operating current liabilities $1,650 $1,500 Operating current assets $4,950 $4,500 1,650 1,500 $3,300 $3,000 Cash + Accruals - Operating current liabilities Net operating working capital (NOWC) c. 2011 $3,300 Total net operating capital 3,500 $7,150 + Net plant and equipment $3,000 3,850 Net operating working capital (NOWC) 2010 $6,500 d. 2013 NOPAT $756 - Investment in total net operating capital 650 7 Free cash flow $106 e. 2013 NOPAT $756 Total net operating capital 7,150 Return on invested capital (ROIC) 10.57% Chapter 3 Analysis of Financial Statements ANSWERS TO END-OF-CHAPTER QUESTONS 3-1 a. A liquidity ratio is a ratio that shows the relationship of a firm's cash and other current assets to its current liabilities. The current ratio is found by dividing current assets by current liabilities. It indicates the extent to which current liabilities are covered by those assets expected to be converted to cash in the near future. The quick, or acid test, ratio is found by taking current assets less inventories and then dividing by current liabilities. b. Asset management ratios are a set of ratios that measure how effectively a firm is managing its assets. The inventory turnover ratio is COGS divided by inventories. Days sales outstanding is used to appraise accounts receivable and indicates the length of time the firm must wait after making a sale before receiving cash. It is found by dividing receivables by average sales per day. The fixed assets turnover ratio measures how effectively the firm uses its plant and equipment. It is the ratio of sales to net fixed assets. Total assets turnover ratio measures the turnover of all the firm's assets; it is calculated by dividing sales by total assets. c. Financial leverage ratios measure the use of debt financing. The debt ratio is the ratio of total debt, which usually is the sum of notes payable and long-term bonds, to total assets, it measures the percentage of assets financed by debtholders. The debt-to-equity ratio is the total debt divided by the total common equity. The times-interest-earned ratio is determined by dividing earnings before interest and taxes by the interest charges. This ratio measures the extent to which operating income can decline before the firm is unable to meet its annual 8 interest costs. The EBITDA coverage ratio is similar to the times-interest-earned ratio, but it recognizes that many firms lease assets and also must make sinking fund payments. It is found by adding EBITDA and lease payments then dividing this total by interest charges, lease payments, and sinking fund payments over one minus the tax rate. d. Profitability ratios are a group of ratios, which show the combined effects of liquidity, asset management, and debt on operations. The profit margin on sales, calculated by dividing net income by sales, gives the profit per dollar of sales. Basic earning power is calculated by dividing EBIT by total assets. This ratio shows the raw earning power of the firm's assets, before the influence of taxes and leverage. Return on total assets is the ratio of net income to total assets. Return on common equity is found by dividing net income by common equity. e. Market value ratios relate the firm's stock price to its earnings and book value per share. The price/earnings ratio is calculated by dividing price per share by earnings per share--this shows how much investors are willing to pay per dollar of reported profits. The price/cash flow is calculated by dividing price per share by cash flow per share. This shows how much investors are willing to pay per dollar of cash flow. Market-to-book ratio is simply the market price per share divided by the book value per share. Book value per share is common equity divided by the number of shares outstanding. f. Trend analysis is an analysis of a firm's financial ratios over time. It is used to estimate the likelihood of improvement or deterioration in its financial situation. Comparative ratio analysis is when a firm compares its ratios to other leading companies in the same industry. This technique is also known as benchmarking. g. The Du Pont equation is a formula, which shows that the rate of return on assets can be found as the product of the profit margin times the total assets turnover. Window dressing is a technique employed by firms to make their financial statements look better than they really are. Seasonal factors can distort ratio analysis. At certain times of the year a firm may have excessive inventories in preparation of a \"season\" of high demand. Therefore an inventory turnover ratio taken at this time as opposed to after the season will be radically distorted. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 3-6 ROA = 12%; PM = 5%; ROE = 20%; S/TA = ?; A/E = ? ROA = NI/A; PM = NI/S; ROE = NI/E 9 ROA = PM S/TA NI/A = NI/S S/TA 12% = 5% S/TA S/TA = 2.40. ROE = PM S/TA TA/E NI/E = NI/S S/TA TA/E 20% = 5% 2.4 TA/E 20% = 12% TA/E TA/E = 1.67. 10 3-13 a. (Dollar amounts in thousands.) Industry Firm = Accounts receivable Sales/ 365 COGS Inventory Sales Fixed assets Sales Total assets Net income Sales = = = = = $2,925,000 $1,453,500 $1,575,000 $20,548 $6,375,000 $1,125,000 $7,500,000 $1,350,000 $7,500,000 $4,275,000 $113,022 $7,500,000 11 Average = 2.01 2.0 = 77 days 35 days = 5.67 6.7 = 5.56 12.1 = 1.75 3.0 = 1.5% 1.2% Net income Total assets Net income Common equity = = = = $113,022 $4,275,000 $113,022 $1,752,750 $1,395,384 $4,275,000 $2,522,250 $4,275,000 = 2.6% 3.6% = 6.4% 9.0% = 33% 30% = 59% 60.0% b. For the firm, ROE = PM T.A. turnover EM = 1.51% 1.75 $4,275,000 $1,752,750 = 6.45%. For the industry, ROE = 1.2% 3 2.5 = 9%. Note: To find the industry ratio of assets to common equity, recognize that 1 minus the Liabilities-to-assets ratio = common equity/total assets. So, common equity/total assets = 1 - 60% = 40%, and 1/0.40 = 2.5 = total assets/common equity. c. The firm's days sales outstanding is more than twice as long as the industry average, indicating that the firm should tighten credit or enforce a more stringent collection policy. The total assets turnover ratio is well below the industry average so sales should be increased, 12 assets decreased, or both. While the company's profit margin is higher than the industry average, its other profitability ratios are low compared to the industry--net income should be higher given the amount of equity and assets. However, the company seems to be in an average liquidity position and financial leverage is similar to others in the industry. Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest. PV is also the beginning amount that will grow to some future value. The parameter i is the periodic interest rate that an account pays. The parameter INT is the dollars of interest earned each period. FV n (future value) is the ending amount in an account, where n is the number of periods the money is left in the account. PVAn is the value today of a future stream of equal payments (an annuity) and FVA n is the ending value of a stream of equal payments, where n is the number of payments of the annuity. PMT is equal to the dollar amount of an equal, or constant cash flow (an annuity). In the EAR equation, m is used to denote the number of compounding periods per year, while iNom is the nominal, or quoted, interest rate. b. The opportunity cost rate (i) of an investment is the rate of return available on the best alternative investment of similar risk. c. An annuity is a series of payments of a fixed amount for a specified number of periods. A single sum, or lump sum payment, as opposed to an annuity, consists of one payment occurring now or at some future time. A cash flow can be an inflow (a receipt) or an outflow (a deposit, a cost, or an amount paid). We distinguish between the terms cash flow and PMT. We use the term cash flow for uneven streams, while we use the term PMT for annuities, or constant payment amounts. An uneven cash flow stream is a series of cash flows in which the amount varies from one period to the next. The PV (or FV n) of an uneven payment stream is merely the sum of the present values (or future values) of each individual payment. 13 d. An ordinary annuity has payments occurring at the end of each period. A deferred annuity is just another name for an ordinary annuity. An annuity due has payments occurring at the beginning of each period. Most financial calculators will accommodate either type of annuity. The payment period must be equal to the compounding period. e. A perpetuity is a series of payments of a fixed amount that last indefinitely. In other words, a perpetuity is an annuity where n equals infinity. Consol is another term for perpetuity. Consols were originally bonds issued by England in 1815 to consolidate past debt. f. An outflow is a deposit, a cost, or an amount paid, while an inflow is a receipt. A time line is an important tool used in time value of money analysis; it is a graphical representation which is used to show the timing of cash flows. The terminal value is the future value of an uneven cash flow stream. g. Compounding is the process of finding the future value of a single payment or series of payments. Discounting is the process of finding the present value of a single payment or series of payments; it is the reverse of compounding. h. Annual compounding means that interest is paid once a year. In semiannual, quarterly, monthly, and daily compounding, interest is paid 2, 4, 12, and 365 times per year respectively. When compounding occurs more frequently than once a year, you earn interest on interest more often, thus increasing the future value. The more frequent the compounding, the higher the future value. i. The effective annual rate is the rate that, under annual compounding, would have produced the same future value at the end of 1 year as was produced by more frequent compounding, say quarterly. The nominal (quoted) interest rate, i Nom, is the rate of interest stated in a contract. If the compounding occurs annually, the effective annual rate and the nominal rate are the same. If compounding occurs more frequently, the effective annual rate is greater than the nominal rate. The nominal annual interest rate is also called the annual percentage rate, or APR. The periodic rate, i PER, is the rate charged by a lender or paid by a borrower each period. It can be a rate per year, per 6-month period, per quarter, per month, per day, or per any other time interval (usually one year or less). j. An amortization schedule is a table that breaks down the periodic fixed payment of an installment loan into its principal and interest components. The principal component of each 14 payment reduces the remaining principal balance. The interest component is the interest payment on the beginning-of-period principal balance. An amortized loan is one that is repaid in equal periodic amounts (or "killed off" over time). 4-2 The opportunity cost rate is the rate of interest one could earn on an alternative investment with a risk equal to the risk of the investment in question. This is the value of i in the TVM equations, and it is shown on the top of a time line, between the first and second tick marks. It is not a single rate--the opportunity cost rate varies depending on the riskiness and maturity of an investment, and it also varies from year to year depending on inflationary expectations. 4-3 True. The second series is an uneven payment stream, but it contains an annuity of $400 for 8 years. The series could also be thought of as a $100 annuity for 10 years plus an additional payment of $100 in Year 2, plus additional payments of $300 in Years 3 through 10. 4-4 True, because of compounding effects--growth on growth. The following example demonstrates the point. The annual growth rate is I in the following equation: $1(1 + I)10 = $2. The term (1 + I)10 is the FVIF for I percent, 10 years. We can find I in one of two ways: 1. Using a financial calculator input N = 10, PV = -1, PMT = 0, FV = 2, and I/YR = ?. Solving for I/YR you obtain 7.18%. 2. Using a financial calculator, input N = 10, I/YR = 10, PV = -1, PMT = 0, and FV = ?. Solving for FV you obtain $2.59. This formulation recognizes the "interest on interest" phenomenon. 4-5 For the same stated rate, daily compounding is best. You would earn more "interest on interest." SOLUTIONS TO END-OF-CHAPTER PROBLEMS 15 4-10 a. 0 1 2 3 4 5 6 7 8 9 10 $500(1.06)10 = $895.42. | | | | | | | | | | | -500 FV = ? 12% b. 0 1 2 3 4 5 6 7 8 9 10 | | | | | | | | | | | -500 FV = ? 6% c. 0 1 2 3 4 5 6 7 8 9 10 | | | | | | | | | | | $500(1/1.06)10 = $279.20 PV = ? 500 12% d. 0 1 2 3 4 5 6 7 8 9 | | | | | | | | | | | $500(1/1.12)10 = $160.99 PV = ? 500 16 10 $500(1.12)10 = $1,552.92. 4-26 0 12% | | 1 | 1,250 2 | | 1,250 3 | 4 5 6 | 1,250 1,250 1,250 ? FV = 10,000 With a financial calculator, get a "ballpark" estimate of the years by entering I/YR = 12, PV = 0, PMT = -1250, and FV = 10000, and then pressing the N key to find N = 5.94 years. This answer assumes that a payment of $1,250 will be made 94/100th of the way through Year 5. Now find the FV of $1,250 for 5 years at 12%; N = 5, I/YR = 12, PV = 0, and PMT = -1250. Press FV to get FV = $7,941.06. Compound this value for 1 year at 12% to obtain the value in the account after 6 years and before the last payment is made; it is $7,941.06(1.12) = $8,893.99. Thus, you will have to make a payment of $10,000 - $8,893.99 = $1,106.01 at Year 6, so the answer is: it will take 6 years, and $1,106.01 is the amount of the last payment. Chapter 5 Bonds, Bond Valuation, and Interest Rates ANSWERS TO END-OF-CHAPTER QUESTIONS 5-1 a. A bond is a promissory note issued by a business or a governmental unit. Treasury bonds, sometimes referred to as government bonds, are issued by the Federal government and are not exposed to default risk. Corporate bonds are issued by corporations and are exposed to default risk. Different corporate bonds have different levels of default risk, depending on the issuing company's characteristics and on the terms of the specific bond. Municipal bonds are issued by state and local governments. The interest earned on most municipal bonds is exempt from federal taxes, and also from state taxes if the holder is a resident of the issuing state. Foreign bonds are issued by foreign governments or foreign corporations. These bonds are not only exposed to default risk, but are also exposed to an additional risk if the bonds are denominated in a currency other than that of the investor's home currency. b. The par value is the nominal or face value of a stock or bond. The par value of a bond generally represents the amount of money that the firm borrows and promises to repay at some future date. The par value of a bond is often $1,000, but can be $5,000 or more. The maturity date is the date when the bond's par value is repaid to the bondholder. Maturity dates generally range from 10 to 40 years from the time of issue. A call provision may be written into a bond contract, giving the issuer the right to redeem the bonds under specific conditions 17 prior to the normal maturity date. A bond's coupon, or coupon payment, is the dollar amount of interest paid to each bondholder on the interest payment dates. The coupon is so named because bonds used to have dated coupons attached to them which investors could tear off and redeem on the interest payment dates. The coupon interest rate is the stated rate of interest on a bond. c. In some cases, a bond's coupon payment may vary over time. These bonds are called floating rate bonds. Floating rate debt is popular with investors because the market value of the debt is stabilized. It is advantageous to corporations because firms can issue long-term debt without committing themselves to paying a historically high interest rate for the entire life of the loan. Zero coupon bonds pay no coupons at all, but are offered at a substantial discount below their par values and hence provide capital appreciation rather than interest income. In general, any bond originally offered at a price significantly below its par value is called an original issue discount bond (OID). d. Most bonds contain a call provision, which gives the issuing corporation the right to call the bonds for redemption. The call provision generally states that if the bonds are called, the company must pay the bondholders an amount greater than the par value, a call premium. Redeemable bonds give investors the right to sell the bonds back to the corporation at a price that is usually close to the par value. If interest rates rise, investors can redeem the bonds and reinvest at the higher rates. A sinking fund provision facilitates the orderly retirement of a bond issue. This can be achieved in one of two ways: The company can call in for redemption (at par value) a certain percentage of bonds each year. The company may buy the required amount of bonds on the open market. e. Convertible bonds are securities that are convertible into shares of common stock, at a fixed price, at the option of the bondholder. Bonds issued with warrants are similar to convertibles. Warrants are options which permit the holder to buy stock for a stated price, thereby providing a capital gain if the stock price rises. Income bonds pay interest only if the interest is earned. These securities cannot bankrupt a company, but from an investor's standpoint they are riskier than "regular" bonds. The interest rate of an indexed, or purchasing power, bond is based on an inflation index such as the consumer price index (CPI), so the interest paid rises automatically when the inflation rate rises, thus protecting the bondholders against inflation. f. Bond prices and interest rates are inversely related; that is, they tend to move in the opposite direction from one another. A fixed-rate bond will sell at par when its coupon interest rate is equal to the going rate of interest, r d. When the going rate of interest is above the coupon rate, a fixed-rate bond will sell at a "discount" below its par value. If current interest rates are below the coupon rate, a fixed-rate bond will sell at a "premium" above its par value. 18 g. The current yield on a bond is the annual coupon payment divided by the current market price. YTM, or yield to maturity, is the rate of interest earned on a bond if it is held to maturity. Yield to call (YTC) is the rate of interest earned on a bond if it is called. If current interest rates are well below an outstanding callable bond's coupon rate, the YTC may be a more relevant estimate of expected return than the YTM, since the bond is likely to be called. h. Corporations can influence the default risk of their bonds by changing the type of bonds they issue. Under a mortgage bond, the corporation pledges certain assets as security for the bond. All such bonds are written subject to an indenture, which is a legal document that spells out in detail the rights of both the bondholders and the corporation. A debenture is an unsecured bond, and as such, it provides no lien against specific property as security for the obligation. Debenture holders are, therefore, general creditors whose claims are protected by property not otherwise pledged. Subordinated debentures have claims on assets, in the event of bankruptcy, only after senior debt as named in the subordinated debt's indenture has been paid off. Subordinated debentures may be subordinated to designated notes payable or to all other debt. i. A development bond is a tax-exempt bond sold by state and local governments whose proceeds are made available to corporations for specific uses deemed (by Congress) to be in the public interest. Municipalities can insure their bonds, in which an insurance company guarantees to pay the coupon and principal payments should the issuer default. This reduces the risk to investors who are willing to accept a lower coupon rate for an insured bond issue vis-a-vis an uninsured issue. Bond issues are normally assigned quality ratings by major rating agencies, such as Moody's Investors Service and Standard & Poor's Corporation. These ratings reflect the probability that a bond will go into default. Aaa (Moody's) and AAA (S&P) are the highest ratings. Rating assignments are based on qualitative and quantitative factors including the firm's debt/assets ratio, current ratio, and coverage ratios. Because a bond's rating is an indicator of its default risk, the rating has a direct, measurable influence on the bond's interest rate and the firm's cost of debt capital. Junk bonds are high-risk, high-yield bonds issued to finance leveraged buyouts, mergers, or troubled companies. Most bonds are purchased by institutional investors rather than individuals, and many institutions are restricted to investment grade bonds, securities with ratings of Baa/BBB or above. j. The real risk-free rate is that interest rate which equalizes the aggregate supply of, and demand for, riskless securities in an economy with zero inflation. The real risk-free rate could also be called the pure rate of interest since it is the rate of interest that would exist on very short-term, default-free U.S. Treasury securities if the expected rate of inflation were zero. It has been estimated that this rate of interest, denoted by r*, has fluctuated in recent 19 years in the United States in the range of 2 to 4 percent. The nominal risk-free rate of interest, denoted by rRF, is the real risk-free rate plus a premium for expected inflation. The short-term nominal risk-free rate is usually approximated by the U.S. Treasury bill rate, while the long-term nominal risk-free rate is approximated by the rate on U.S. Treasury bonds. Note that while T-bonds are free of default and liquidity risks, they are subject to risks due to changes in the general level of interest rates. k. The inflation premium is the premium added to the real risk-free rate of interest to compensate for the expected loss of purchasing power. The inflation premium is the average rate of inflation expected over the life of the security. Default risk is the risk that a borrower will not pay the interest and/or principal on a loan as they become due. Thus, a default risk premium (DRP) is added to the real risk-free rate to compensate investors for bearing default risk. Liquidity refers to a firm's cash and marketable securities position, and to its ability to meet maturing obligations. A liquid asset is any asset that can be quickly sold and converted to cash at its \"fair\" value. Active markets provide liquidity. A liquidity premium is added to the real risk-free rate of interest, in addition to other premiums, if a security is not liquid. l. Interest rate risk arises from the fact that bond prices decline when interest rates rise. Under these circumstances, selling a bond prior to maturity will result in a capital loss, and the longer the term to maturity, the larger the loss. Thus, a maturity risk premium must be added to the real risk-free rate of interest to compensate for interest rate risk. Reinvestment rate risk occurs when a short-term debt security must be \"rolled over.\" If interest rates have fallen, the reinvestment of principal will be at a lower rate, with correspondingly lower interest payments and ending value. Note that long-term debt securities also have some reinvestment rate risk because their interest payments have to be reinvested at prevailing rates. m. The term structure of interest rates is the relationship between yield to maturity and term to maturity for bonds of a single risk class. The yield curve is the curve that results when yield to maturity is plotted on the Y-axis with term to maturity on the X-axis. n. When the yield curve slopes upward, it is said to be \"normal,\" because it is like this most of the time. Conversely, a downward-sloping yield curve is termed \"abnormal\" or \"inverted.\" 5-2 False. Short-term bond prices are less sensitive than long-term bond prices to interest rate changes because funds invested in short-term bonds can be reinvested at the new interest rate sooner than funds tied up in long-term bonds. 20 5-3 The price of the bond will fall and its YTM will rise if interest rates rise. If the bond still has a long term to maturity, its YTM will reflect long-term rates. Of course, the bond's price will be less affected by a change in interest rates if it has been outstanding a long time and matures shortly. While this is true, it should be noted that the YTM will increase only for buyers who purchase the bond after the change in interest rates and not for buyers who purchased previous to the change. If the bond is purchased and held to maturity, the bondholder's YTM will not change, regardless of what happens to interest rates. 5-4 If interest rates decline significantly, the values of callable bonds will not rise by as much as those of bonds without the call provision. It is likely that the bonds would be called by the issuer before maturity, so that the issuer can take advantage of the new, lower rates. 5-5 From the corporation's viewpoint, one important factor in establishing a sinking fund is that its own bonds generally have a higher yield than do government bonds; hence, the company saves more interest by retiring its own bonds than it could earn by buying government bonds. This factor causes firms to favor the second procedure. Investors also would prefer the annual retirement procedure if they thought that interest rates were more likely to rise than to fall, but they would prefer the government bond purchases program if they thought rates were likely to fall. In addition, bondholders recognize that, under the government bond purchase scheme, each bondholder would be entitled to a given amount of cash from the liquidation of the sinking fund if the firm should go into default, whereas under the annual retirement plan, some of the holders would receive a cash benefit while others would benefit only indirectly from the fact that there would be fewer bonds outstanding. On balance, investors seem to have little reason for choosing one method over the other, while the annual retirement method is clearly more beneficial to the firm. The consequence has been a pronounced trend toward annual retirement and away from the accumulation scheme. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 5-6 r* = 3%; IP = 3%; rT-2 = 6.3%; MRP2 = ? rT-2 = r* + IP + MRP = 6.3% rT-2 = 3% + 3% + MRP = 6.3% MRP = 0.3%. 21 5-9 a. 1. 5%: Bond L: Input N = 15, I/YR = 5, PMT = 100, FV = 1000, PV = ?, PV = $1,518.98. Bond S:Change N = 1, PV = ? PV = $1,047.62. 2. 8%: Bond L: From Bond S inputs, change N = 15 and I/YR = 8, PV = ?, PV = $1,171.19. Bond S:Change N = 1, PV = ? PV = $1,018.52. 3. 12%: Bond L: From Bond S inputs, change N = 15 and I/YR = 12, PV = ? PV = $863.78. Bond S:Change N = 1, PV = ? PV = $982.14. b. Think about a bond that matures in one month. Its present value is influenced primarily by the maturity value, which will be received in only one month. Even if interest rates double, the price of the bond will still be close to $1,000. A one-year bond's value would fluctuate more than the one-month bond's value because of the difference in the timing of receipts. However, its value would still be fairly close to $1,000 even if interest rates doubled. A longterm bond paying semiannual coupons, on the other hand, will be dominated by distant receipts, receipts which are multiplied by 1/(1 + r d/2)t, and if rd increases, these multipliers will decrease significantly. Another way to view this problem is from an opportunity point of view. A one-month bond can be reinvested at the new rate very quickly, and hence the opportunity to invest at this new rate is not lost; however, the long-term bond locks in subnormal returns for a long period of time. 22 5-10 a. Calculator solution: 1. Input N = 5, PV = -829, PMT = 90, FV = 1000, I/YR = ? I/YR = 13.98%. 2. Change PV = -1104, I/YR = ? I/YR = 6.50%. b. Yes. At a price of $829, the yield to maturity, 13.98 percent, is greater than your required rate of return of 12 percent. If your required rate of return were 12 percent, you should be willing to buy the bond at any price below $891.86. 5-12 a. Using a financial calculator, input the following: N = 20, PV = -1100, PMT = 60, FV = 1000, and solve for I/YR = 5.1849%. However, this is a periodic rate. The nominal annual rate = 5.1849%(2) = 10.3699% 10.37%. b. The current yield = $120/$1,100 = 10.91%. c. YTM = Current Yield + Capital Gains (Loss) Yield 10.37% = 10.91% + Capital Loss Yield -0.54% = Capital Loss Yield. d. Using a financial calculator, input the following: N = 8, PV = -1100, PMT = 60, FV = 1060, and solve for I/YR = 5.0748%. However, this is a periodic rate. The nominal annual rate = 5.0748%(2) = 10.1495% 10.15%. 23 5-13 The problem asks you to solve for the YTM, given the following facts: N = 5, PMT = 80, and FV = 1000. In order to solve for I/YR we need PV. However, you are also given that the current yield is equal to 8.21%. Given this information, we can find PV. Current yield 0.0821 PV = Annual interest/Current price = $80/PV = $80/0.0821 = $974.42. Now, solve for the YTM with a financial calculator: N = 5, PV = -974.42, PMT = 80, and FV = 1000. Solve for I/YR = YTM = 8.65%. 5-16 Price at 8% 10-year, 10% annual coupon $1,134.20 Price at 7% $1,210.71 Pctge. change 6.75% 10-year zero 463.19 508.35 9.75 5-year zero 680.58 712.99 4.76 30-year zero 99.38 131.37 32.19 $100 perpetuity 1,250.00 24 1,428.57 14.29 5-17 t Price of Bond C Price of Bond Z 0 $1,012.79 $ 693.04 1 1,010.02 759.57 2 1,006.98 832.49 3 1,003.65 912.41 4 1,000.00 1,000.00 Chapter 6 Risk and Return ANSWERS TO END-OF-CHAPTER QUESTIONS 6-1 a. Stand-alone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset. Risk is the chance that some unfavorable event will occur. For instance, the risk of an asset is essentially the chance that the asset's cash flows will be unfavorable or less than expected. A probability distribution is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome. When in graph form, the tighter the probability distribution, the less uncertain the outcome. b. The expected rate of return (^ ) is the expected value of a probability distribution of expected returns. c. A continuous probability distribution contains an infinite number of outcomes and is graphed from - and +. d. The standard deviation () is a statistical measure of the variability of a set of observations. The variance (2) of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation. 25 e. A risk averse investor dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their expected return. f. A risk premium is the difference between the rate of return on a risk-free asset and the expected return on Stock i which has higher risk. The market risk premium is the difference between the expected return on the market and the risk-free rate. g. CAPM is a model based upon the proposition that any stock's required rate of return is equal to the risk free rate of return plus a risk premium reflecting only the risk remaining after diversification. h. The expected return on a portfolio. , is simply the weighted-average expected return of the p r individual stocks in the portfolio, with the weights being the fraction of total portfolio value invested in each stock. The market portfolio is a portfolio consisting of all stocks. i. Correlation is the tendency of two variables to move together. A correlation coefficient () of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions. A correlation coefficient of zero suggests that the two variables are not related to one another; that is, they are independent. j. Market risk is that part of a security's total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. Diversifiable risk is also known as company specific risk, that part of a security's total risk associated with random events not affecting the market as a whole. This risk can be eliminated by proper diversification. The relevant risk of a stock is its contribution to the riskiness of a well-diversified portfolio. k. The beta coefficient is a measure of a stock's market risk, A stock with a beta greater than 1 has stock returns that tend to be higher than the market when the market is up but tend to be below the market when the market is down. The opposite is true for a stock with a beta less than 1.. 26 l. The security market line (SML) represents in a graphical form, the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities. The SML equation is essentially the CAPM, r i = rRF + bi(RPM). It can also be written in terms of the required market return: ri = rRF + bi(rM - rRF). m. The slope of the SML equation is (r M - rRF), the market risk premium. The slope of the SML reflects the degree of risk aversion in the economy. The greater the average investors aversion to risk, then the steeper the slope, the higher the risk premium for all stocks, and the higher the required return. n. Equilibrium is the condition under which the expected return on a security is just equal to its required return, = r, and the market price is equal to the intrinsic value. The Efficient r Markets Hypothesis (EMH) states (1) that stocks are always in equilibrium and (2) that it is impossible for an investor to consistently \"beat the market.\" In essence, the theory holds that the price of a stock will adjust almost immediately in response to any new developments. In other words, the EMH assumes that all important information regarding a stock is reflected in the price of that stock. Financial theorists generally define three forms of market efficiency: weak-form, semistrong-form, and strong-form. Weak-form efficiency assumes that all information contained in past price movements is fully reflected in current market prices. Thus, information about recent trends in a stock's price is of no use in selecting a stock. Semistrong-form efficiency states that current market prices reflect all publicly available information. Therefore, the only way to gain abnormal returns on a stock is to possess inside information about the company's stock. Strong-form efficiency assumes that all information pertaining to a stock, whether public or inside information, is reflected in current market prices. Thus, no investors would be able to earn abnormal returns in the stock market. o. The Fama-French 3-factor model has one factor for the excess market return (the market return minus the risk free rate), a second factor for size (defined as the return on a portfolio of small firms minus the return on a portfolio of big firms), and a third factor for the book-tomarket effect (defined as the return on a portfolio of firms with a high book-to-market ratio minus the return on a portfolio of firms with a low book-to-market ratio). p. Most people don't behave rationally in all aspects of their personal lives, and behavioral finance assumes that investors have the same types of psychological behaviors in their financial lives as in their personal lives. 27 Anchoring bias is the human tendency to \"anchor\" too closely on recent events when predicting future events. Herding is the tendency of investors to follow the crowd. When combined with overconfidence, anchoring and herding can contribute to market bubbles. 6-3 Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because A > B and CVA > CVB. 6-5 According to the Security Market Line (SML) equation, an increase in beta will increase a company's expected return by an amount equal to the market risk premium times the change in beta. For example, assume that the risk-free rate is 6 percent, and the market risk premium is 5 percent. If the company's beta doubles from 0.8 to 1.6 its expected return increases from 10 percent to 14 percent. Therefore, in general, a company's expected return will not double when its beta doubles. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 6-1 Investment $20,000 0.7 35,000 Total Beta 1.3 $55,000 ($20,000/$55,000)(0.7) + ($35,000/$55,000)(1.3) = 1.08. 6-2 rRF = 4%; rM = 12%; b = 0.8; rs = ? rs = rRF + (rM - rRF)b = 4% + (12% - 4%)0.8 = 10.4%. 28 6-9 Old portfolio beta = $70,000 $75,000 (b) + $5,000 $75,000 (0.8) 1.2 = 0.9333b + 0.0533 1.1467 = 0.9333b 1.229 = b. New portfolio beta = 0.9333(1.229) + 0.0667(1.6) = 1.25. Alternative Solutions: 1. Old portfolio beta = 1.2 = (0.0667)b1 + (0.0667)b2 +...+ (0.0667)b20 1.2 = (bi)(0.0667) bi = 1.2/0.0667 = 18.0. New portfolio beta = (18.0 - 0.8 + 1.6)(0.0667) = 1.253 = 1.25. 2. bi excluding the stock with the beta equal to 0.8 is 18.0 - 0.8 = 17.2, so the beta of the portfolio excluding this stock is b = 17.2/14 = 1.2286. The beta of the new portfolio is: 1.2286(0.9333) + 1.6(0.0667) = 1.1575 = 1.253. 29 6-10 Portfolio beta = $400,000 $4,000,000 + (1.50) + $1,000,000 $4,000,000 $600,000 $4,000,000 (1.25) + (-0.50) $2,000,000 $4,000,000 (0.75) = 0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 - 0.075 + 0.3125 + 0.375 = 0.7625. rp = rRF + (rM - rRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%. Alternative solution: First compute the return for each stock using the CAPM equation [r RF + (rM - rRF)b], and then compute the weighted average of these returns. rRF = 6% and rM - rRF = 8%. Stock A Investment $ 400,000 B C D Total 600,000 1,000,000 2,000,000 Beta r = rRF + (rM - rRF)b 1.50 18% (0.50) 0.10 2 1.25 0.15 16 0.75 Weight 0.25 12 0.50 $4,000,000 1.00 rp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%. 6-13 The answers to a, b, and c are given below: A 2009 B (20.00%) Portfolio (5.00%) 30 (12.50%) 2010 42.00 2011 20.00 2012 2013 15.00 28.50 3.50 (8.00) 50.00 21.00 25.00 12.00 18.50 11.80 Mean (13.00) 11.80 11.80 Std Dev 25.28 24.32 16.34 d. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated ( AB = -0.13). Chapter 25 Portfolio Theory and Asset Pricing Models ANSWERS TO END-OF-CHAPTER QUESTIONS 25-1 a. A portfolio is made up of a group of individual assets held in combination. An asset that would be relatively risky if held in isolation may have little, or even no risk if held in a well-diversified portfolio. The feasible, or attainable, set represents all portfolios that can be constructed from a given set of stocks. This set is only efficient for part of its combinations. An efficient portfolio is that portfolio which provides the highest expected return for any degree of risk. Alternatively, the efficient portfolio is that which provides the lowest degree of risk for any expected return. The efficient frontier is the set of efficient portfolios out of the full set of potential portfolios. On a graph, the efficient frontier constitutes the boundary line of the set of potential portfolios. 31 b. An indifference curve is the risk/return trade-off function for a particular investor and reflects that investor's attitude toward risk. The indifference curve specifies an investor's required rate of return for a given level of risk. The greater the slope of the indifference curve, the greater is the investor's risk aversion. The optimal portfolio for an investor is the point at which the efficient set of portfolios--the efficient frontier--is just tangent to the investor's indifference curve. This point marks the highest level of satisfaction an investor can attain given the set of potential portfolios. c. The Capital Asset Pricing Model (CAPM) is a general equilibrium market model developed to analyze the relationship between risk and required rates of return on assets when they are held in well-diversified portfolios. The SML is part of the CAPM. The Capital Market Line (CML) specifies the efficient set of portfolios an investor can attain by combining a risk-free asset and the risky market portfolio M. The CML states that the expected return on any efficient portfolio is equal to the riskless rate plus a risk premium, and thus describes a linear relationship between expected return and risk. d. The characteristic line for a particular stock is obtained by regressing the historical returns on that stock against the historical returns on the general stock market. The slope of the characteristic line is the stock's beta, which measures the amount by which the stock's expected return increases for a given increase in the expected return on the market. The beta coefficient (b) is a measure of a stock's market risk. It measures the stock's volatility relative to an average stock, which has a beta of 1.0. e. Arbitrage Pricing Theory (APT) is an approach to measuring the equilibrium risk/return relationship for a given stock as a function of multiple factors, rather than the single factor (the market return) used by the CAPM. The APT is based on complex mathematical and statistical theory, but can account for several factors (such as GNP and the level of inflation) in determining the required return for a particular stock. 32 25-2 Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because A > B and CVA > CVB. SOLUTIONS TO END-OF-CHAPTER PROBLEMS 25-1 bi = iM (i / M) = 0.70(0.40/0.20) = 1.4. 25-3 rp = wArA + (1 wA) rB = 0.30(12%) + 0.70(18%) = 16.20% p = = = = = 0.459 = 45.9% Chapter 7 Stocks, Stock Valuation, and Stock Market Equilibrium ANSWERS TO END-OF-CHAPTER QUESTIONS 7-1 a. A proxy is a document giving one person the authority to act for another, typically the power to vote shares of common stock. If earnings are poor and stockholders are dissatisfied, an outside group may solicit the proxies in an effort to overthrow management and take control of the business, known as a proxy fight. The preemptive right gives the current shareholders the right to purchase any new shares issued in proportion to their current holdings. The preemptive right may or may not be required by state law. When granted, the preemptive right enables current owners to maintain their proportionate share of ownership and control of the business. It also prevents the sale of shares at low prices to new stockholders which would dilute the value of the previously issued shares. Classified stock is sometimes created by a firm to meet special needs and circumstances. Generally, when special classifications of stock are used, one type is designated \"Class A\