TABLE OF CONTENTS Part 1: INTRODUCTION AND OVERVIEW OF FINANCIAL MARKETS Chapter 1: Introduction Chapter 2: Determinants of Interest Rates Chapter 3: Interest Rates and Security Valuation Chapter 4: The Federal Reserve System, Monetary Policy, and InterestRates Part 2: SECURITIES MARKETS Chapter 5: Money Markets Chapter 6: Bond Markets Chapter 7: Mortgage Markets Chapter 8: Stock Markets Chapter 9: Foreign Exchange Markets Chapter 10: Derivative Securities Markets Part 3: COMMERCIAL BANKS Chapter 11: Commercial Banks Chapter 12: Commercial Banks’ Financial Statements and Analysis Chapter 13: Regulation of Commercial Banks Part 4: OTHER FINANCIAL INSTITUTIONS Chapter 14: Other Lending Institutions Chapter 15: Insurance Companies
Chapter 16: Securities Firms and Investment Banks Chapter 17: Investment Companies Chapter 18: Pension Funds Chapter 19: Fintech Companies Part 5: RISK MANAGEMENT IN FINANCIAL INSTITUTIONS Chapter 20: Types of Risks Incurred by Financial Institutions Chapter 21: Managing Credit Risk on the Balance Sheet Chapter 22: Managing Liquidity Risk on the Balance Sheet Chapter 23: Managing Interest Rate Risk and Insolvency Risk on the Balance Sheet Chapter 24: Managing Risk off the Balance Sheet with Derivative Securities Chapter 25: Managing Risk off the Balance Sheet with Loan Sales and Securitization
Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Answers to Chapter 1 Questions: 1.
a. primary b. primary c. secondary d. secondary e. secondary
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a. money market b. money market c. capital market d. capital market e. capital market f. money market g. money market h. money market i. capital market j. money market
3. The capital markets are more likely to be characterized by actual physical locations such as the New York Stock Exchange. Money market transactions are more likely to occur via telephone, wire transfers, and computer trading. 4. According to Figure 1-4, federal funds and repurchase agreements, followed by Treasury bills, negotiable CDs, and commercial paper, had the largest amounts outstanding in 2019. 5. The major instruments traded in capital markets are corporate stocks, mortgages, corporate bonds, Treasury notes and bonds, state and local government bonds, U.S. government owned and sponsored agencies, and bank and consumer loans. 6. According to Figure 1-4, corporate stocks represent the largest capital market instrument in 2019, followed by mortgages, Treasury securities, and corporate bonds. 7. The bank would be most concerned about a depreciation of the yen against the dollar. 8. Financial institutions consist of: Commercial banks - depository institutions whose major assets are loans and major liabilities are deposits. Commercial banks’ loans are broader in range, including consumer, commercial, and real estate loans, than other depository institutions. Commercial banks’ liabilities include more nondeposit sources of funds, such as subordinate notes and debentures, than other depository institutions. Thrifts - depository institutions in the form of savings and loans, savings banks, and credit unions. Thrifts generally perform services similar to commercial banks, but they tend to concentrate their loans in one segment, such as real estate loans or consumer loans. Insurance companies - financial institutions that protect individuals and corporations (policyholders) from adverse events. Life insurance companies provide protection in the event of untimely death, illness, and retirement. Property casualty insurance protects against personal injury and liability due to accidents, theft, fire, etc. Securities firms and investment banks - financial institutions that underwrite securities and engage in related activities such as securities brokerage, securities trading, and making a market in which securities can trade. Finance companies - financial intermediaries that make loans to both individual and businesses. Unlike depository institutions, finance companies do not accept deposits but instead rely on short- and long-term debt for funding. Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Mutual funds and hedge funds - financial institutions that pool financial resources of individuals and companies and invest those resources in diversified portfolios of asset. Pension funds - financial institutions that offer savings plans through which fund participants accumulated savings during their working years before withdrawing them during their retirement years. Funds originally invested in and accumulated in pension funds are exempt from current taxation. 9. If there were no FIs then the users of funds, such as corporations in the economy, would have to approach the savers of funds, such as households, directly in order to fund their investment projects and fill their borrowing needs. This would be extremely costly because of the up-front information costs faced by potential lenders. These include costs associated with identifying potential borrowers, pooling small savings into loans of sufficient size to finance corporate activities, and assessing risk and investment opportunities. Moreover, lenders would have to monitor the activities of borrowers over each loan's life span, which is compounded by the free rider problem. The net result is an imperfect allocation of resources in an economy. 10. There are at least three reasons for this. First, once they have lent money in exchange for financial claims, suppliers of funds need to monitor or check the use of their funds. They must be sure that the user of funds neither absconds with nor wastes the funds on projects that have low or negative returns. Such monitoring actions are often extremely costly for any given fund supplier because they require considerable time, expense, and effort to collect this information relative to the size of the average fund supplier’s investment. Second, the relatively long-term nature of some financial claims (e.g., mortgages, corporate stock, and bonds) creates a second disincentive for suppliers of funds to hold the direct financial claims issued by users of funds. Specifically, given the choice between holding cash and long-term securities, fund suppliers may well choose to hold cash for liquidity reasons, especially if they plan to use savings to finance consumption expenditures in the near future and financial markets are not very deep in terms of active buyers and sellers. Third, even though real-world financial markets provide some liquidity services, by allowing fund suppliers to trade financial securities among themselves, fund suppliers face a price risk upon the sale of securities. That is, the price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE) may well differ from the price they initially paid for the security either because investors change their valuation of the security between the time it was bought and when it was sold and/or because dealers, acting as intermediaries between buyers and sellers, charge transaction costs for completing a trade. 11. A suppler of funds who directly invests in a fund user’s financial claims faces a high cost of monitoring the fund user’s actions in a timely and complete fashion after purchasing securities. One solution to this problem is for a large number of small investors to place their funds with a single FI serving as a broker between the two parties. The FI groups the fund suppliers’ funds together and invests them in the direct or primary financial claims issued by fund users. This aggregation of funds resolves a number of problems. First, the “large” FI now has a much greater incentive to hire employees with superior skills and training in monitoring. This expertise can be used to collect information and monitor the ultimate fund user’s actions because the FI has far more at stake than any small individual fund supplier. Second, the monitoring function performed by the FI alleviates the “free-rider” problem that exists when small fund suppliers leave it to each other to collect information and monitor a fund user. In an economic sense, fund suppliers have appointed the financial institution as a delegated monitor to act on their behalf. For example, full-service securities firms such as Morgan Stanley carry out investment research on new issues and make investment recommendations for their retail clients (or investors), while commercial banks collect deposits from fund suppliers and lend these funds to ultimate users such as corporations. 12. In addition to information costs, FIs help small savers alleviate liquidity and price risk. Often claims issued by financial institutions have liquidity attributes that are superior to those of primary securities. For example, banks and thrift institutions (e.g., savings associations) issue transaction account deposit contracts with a fixed principal value and often a guaranteed interest rate that can be withdrawn immediately, on demand, by investors. Money market mutual funds issue shares to household savers that allow them to enjoy almost fixed principal (depositlike) contracts while earning higher interest rates than on bank deposits, and that can be withdrawn immediately. Even life Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e insurance companies allow policyholders to borrow against their policies held with the company at very short notice. Notice that in reducing the liquidity risk of investing funds for fund suppliers, the FI transfers this risk to its own balance sheet. That is, FIs such as depository institutions offer highly liquid, low price-risk securities to fund suppliers on the liability side of their balance sheets, while investing in relatively less liquid and higher price-risk securities—such as the debt and equity—issued by fund users on the asset side. 13. As long as the returns on different investments are not perfectly positively correlated, by spreading their investments across a number of assets, FIs can diversify away significant amounts of their portfolio risk. Thus, FIs can exploit the law of large numbers in making their investment decisions, whereas due to their smaller wealth size, individual fund suppliers are constrained to holding relatively undiversified portfolios. As a result, diversification allows an FI to predict more accurately its expected return and risk on its investment portfolio so that it can credibly fulfill its promises to the suppliers of funds to provide highly liquid claims with little price risk. As long as an FI is sufficiently large, to gain from diversification and monitoring on the asset side of its balance sheet, its financial claims (it issues as liabilities) are likely to be viewed as liquid and attractive to small savers, especially when compared to direct investments in the capital market. A mutual fund invested in a diverse group of stocks and fixed income securities will best provide diversification for an investor. 14. If net borrowers and net lenders have different optimal time horizons, FIs can service both sectors by mismatching their asset and liability maturities. That is, by maturity mismatching, FIs can produce long-term contracts such as long-term, fixed-rate mortgage loans to households, while still raising funds with short-term liability contracts such as deposits. In addition, although such mismatches can subject an FI to interest rate, a large FI is better able than a small investor to manage this risk through its superior access to markets and instruments for hedging the risks of such loans. 15. Because they are sold in very large denominations, many assets are either out of reach of individual savers or would result in savers holding highly undiversified asset portfolios. For example, the minimum size of a negotiable CD is $100,000; commercial paper (short-term corporate debt) is often sold in minimum packages of $250,000 or more. Individual savers may be unable to purchase such instruments directly. However, by buying shares in a mutual fund with other small investors, household savers overcome the constraints to buying assets imposed by large minimum denomination sizes. Such indirect access to these markets may allow small savers to generate higher returns on their portfolios as well. 16. Other services provided by FIs that benefit the overall economy include: Money Supply Transmission - Depository institutions are the conduit through which monetary policy actions impact the rest of the financial system and the economy in general. Credit Allocation - FIs are often viewed as the major, and sometimes only, source of financing for a particular sector of the economy, such as farming and residential real estate. Intergenerational Wealth Transfers - FIs, especially life insurance companies and pension funds, provide savers the ability to transfer wealth from one generation to the next. Payment Services - The efficiency with which depository institutions provide payment services directly benefits the economy. 17. As financial institutions perform the various services described above, they face many types of risk. Specifically, all FIs hold some assets that are potentially subject to default or credit risk (such as loans, stocks, and bonds). As FIs expand their services to non-U.S. customers or even domestic customers with business outside the United States, they are exposed to both foreign exchange risk and country or sovereign risk as well. Further, FIs tend to mismatch the maturities of their balance sheet assets and liabilities to a greater or lesser extent and are thus exposed to interest rate risk. If FIs actively trade these assets and liabilities rather than hold them for longer-term investments, they are further exposed to market risk or asset price risk. Increasingly, FIs hold contingent assets and liabilities off the balance sheet, which presents an additional risk called off-balance-sheet risk. Moreover, all FIs are exposed to some degree of liability withdrawal or liquidity risk, depending on the type of claims they have sold to Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e liability holders. All FIs are exposed to technology risk and operational risk because the production of financial services requires the use of real resources and back-office support systems (labor and technology combined to provide services). Finally, the risk that an FI may not have enough capital reserves to offset a sudden loss incurred as a result of one or more of the risks it faces creates insolvency risk for the FI. 18. FIs provide various services to sectors of the economy. Failure to provide these services, or a breakdown in their efficient provision, can be costly to both the ultimate suppliers (households) and users (firms) of funds as well as the overall economy. For example, bank failures may destroy household savings and at the same time restrict a firm’s access to credit. Insurance company failures may leave households totally exposed in old age to catastrophic illnesses and sudden drops in income on retirement. In addition, individual FI failures may create doubts in savers’ minds regarding the stability and solvency of FIs in general and cause panics and even runs on sound institutions. FIs are regulated in an attempt to prevent these types of market failures. 19. A major event that changed and reshaped the financial services industry was the financial crisis of the late 2000s. As FIs adjusted to regulatory changes brought about by the likes of the FSM Act, one result was a dramatic increase in systemic risk of the financial system, caused in large part by a shift in the banking model from that of “originate and hold” to “originate to distribute.” In the traditional model, banks take short term deposits and other sources of funds and use them to fund longer term loans to businesses and consumers. Banks typically hold these loans to maturity, and thus have an incentive to screen and monitor borrower activities even after a loan is made. However, the traditional banking model exposes the institution to potential liquidity, interest rate, and credit risk. In attempts to avoid these risk exposures and generate improved return-risk tradeoffs, banks have shifted to an underwriting model in which they originated or warehouse loans, and then quickly sell them. When loans trade, the secondary market produces information that can substitute for the information and monitoring of banks. Further, banks may have lower incentives to collect information and monitor borrowers if they sell loans rather than keep them as part of the bank’s portfolio of assets. Indeed, most large banks are organized as financial service holding companies to facilitate these new activities. More recently activities of shadow banks, non-bank financial service firms that perform banking services, have facilitated the change from the originate and hold model of commercial banking to the originate and distribute banking model. In the shadow banking system savers place their funds with money market mutual7 and similar funds, which invest these funds in the liabilities of shadow banks. Borrowers get loans and leases from shadow banks rather than from banks. Like the traditional banking system, the shadow banking system intermediates the flow of funds between net savers and net borrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, or shadow bank, that intermediates. Further, unlike the traditional banking system, where the complete credit intermediation is performed by a single bank, in the shadow banking system it is performed through a series of steps involving many nonbank financial service firms. These innovations remove risk from the balance sheet of financial institutions and shift risk off the balance sheet and to other parts of the financial system. Since the FIs, acting as underwriters, are not exposed to the credit, liquidity, and interest rate risks of traditional banking, they have little incentive to screen and monitor activities of borrowers to whom they originate loans. Thus, FIs role as specialists in risk measurement and management has been reduced. 20. The boom (“bubble”) in the housing markets began building in 2001, particularly after the terrorist attacks of 9/11. The immediate response by regulators to the terrorist attacks was to create stability in the financial markets by providing liquidity to FIs. For example, the Federal Reserve lowered the short-term interest rate that banks and other financial institutions pay in the Federal funds market and even made lender of last resort funds available to non-bank FIs such as investment banks. Perhaps not surprisingly, low interest rates and the increased liquidity provided by Central banks resulted in a rapid expansion in consumer, mortgage, and corporate debt financing. Demand for residential mortgages and credit card debt rose dramatically. As the demand for mortgage debt grew, especially among those who had previously been excluded from participating in the market because of their poor credit ratings, FIs began lowering their credit quality cut-off points. Moreover, to boost their earnings, in the market now popularly known as the “subprime market,” banks and other mortgage-supplying institutions often offered relatively low “teaser” rates on adjustable rate mortgages (ARMs) at exceptionally low initial interest rates, but with substantial step-up in rates after the initial rate period expired two or three year later and if market rates rose in the future. Under the traditional banking structure, banks might have been reluctant to so aggressively pursue low credit quality Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e borrowers for fear that the loans would default. However, under the originate-to-distribute model of banking, asset securitization and loan syndication allowed banks to retain little or no part of the loans, and hence the default risk on loans that they originated. Thus, as long as the borrower did not default within the first months after a loan’s issuance and the loans were sold or securitized without recourse back to the bank, the issuing bank could ignore longer term credit risk concerns. The result was deterioration in credit quality, at the same time as there was a dramatic increase in consumer and corporate leverage. 21. Measured as more than $1 trillion in international debt outstanding as of 2019 the biggest issuers are France, Germany, the Netherlands, the United Kingdom, and the United States. 22. China, France, Japan, the United Kingdom, and the United States have the biggest banks (in terms of total assets held in 2019).
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Answers to Chapter 2 Questions: 1. The household sector (consumers) is one of the largest supplier of loanable funds. Households supply funds when they have excess income or want to reinvest a part of their wealth. For example, during times of high growth households may replace part of their cash holdings with earning assets. As the total wealth of the consumer increases, the total supply of funds from that household will also generally increase. Households determine their supply of funds not only on the basis of the general level of interest rates and their total wealth, but also on the risk on financial securities change. The greater a security’s risk, the less households are willing to invest at each interest rate. Further, the supply of funds provided from households will depend on the future spending needs. For example, near term educational or medical expenditures will reduce the supply of funds from a given household. Higher interest rates will also result in higher supplies of funds from the business sector. When businesses mismatch inflows and outflows of cash to the firm they have excess cash that they can invest for a short period of time in financial markets. In addition to interest rates on these investments, the expected risk on financial securities and the business’ future investment needs will affect the supply of funds from businesses. Loanable funds are also supplied by some government units that temporarily generate more cash inflows (e.g., taxes) than they have budgeted to spend. These funds are invested until they are needed by the governmental agency. Additionally, the federal government (i.e., the Federal Reserve) implements monetary policy by influencing the availability of credit and the growth in the money supply. Monetary policy implementation in the form of increases the money supply will increase the amount of loanable funds available. Finally, foreign investors increasingly view U.S. financial markets as alternatives to their domestic financial markets. When interest rates are higher on U.S. financial securities than on comparable securities in their home countries, foreign investors increase the supply of funds to U.S. markets. Indeed, the high savings rates of foreign households combined with relatively high U.S. interest rates compared to foreign rates, has resulted in foreign market participants as major suppliers of funds in U.S. financial markets. Similar to domestic suppliers of loanable funds, foreign suppliers assess not only the interest rate offered on financial securities, but also their total wealth, the risk on the security, and their future spending needs. Additionally, foreign investors alter their investment decisions as financial conditions in their home countries change relative to the U.S. economy. 2. Households (although they are net suppliers of funds) borrow funds in financial markets. The demand for loanable funds by households comes from their purchases of homes, durable goods (e.g., cars, appliances), and nondurable goods (e.g., education expenses, medical expenses). In addition to the interest rate on borrowed funds, the greater the utility the household receives from the purchased good, the higher the demand for funds. Additionally, nonprice conditions and requirements (discussed below) affect a households demand for funds at every level of interest rates. Businesses often finance investments in long-term (fixed) assets (e.g., plant and equipment) and in shortterm assets (e.g., inventory and accounts receivable) with debt and other financial instruments. When interest rates are high (i.e., the cost of loanable funds is high), businesses prefer to finance investments with internally generated funds (e.g., retained earnings) rather than through borrowed funds. Further, the greater the number of profitable projects available to businesses, or the better the overall economic conditions, the greater the demand for loanable funds. Governments also borrow heavily in financial markets. State and local governments often issue debt to finance temporary imbalances between operating revenues (e.g., taxes) and budgeted expenditures (e.g., road improvements, school construction). Higher interest rates cause state and local governments to postpone such capital expenditures. Similar to households and businesses, state and local governments’ demand for funds vary with general economic conditions. The federal government is also a large borrower partly to finance current budget deficits (expenditures greater than taxes) and partly to finance past deficits. In contrast to other demanders of funds, the federal government’s borrowing is not influenced by the level of interest rates. Expenditures in the federal government’s budget are spent regardless of the interest cost. Finally, foreign participants might also borrow in U.S. financial markets. Foreign borrowers look for the cheapest source of funds globally. Most foreign borrowing in U.S. financial markets comes from the business sector. In addition to interest costs, foreign borrowers consider nonprice terms on loanable funds as well as economic conditions in the home country. 3. Factors that affect the supply of funds include total wealth, risk of the financial security, future spending needs, monetary policy objectives, and economic conditions.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Wealth. As the total wealth of financial market participants (households, business, etc.) increases the absolute dollar value available for investment purposes increases. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the supply of funds due to an increase in the total wealth of market participants results in a decrease in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. Conversely, as the total wealth of financial market participants decreases the absolute dollar value available for investment purposes decreases. Accordingly, at every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the supply of funds due to a decrease in the total wealth of market participants results in an increase in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Risk. As the risk of a financial security decreases, it becomes more attractive to supplier of funds. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the supply of funds due to a decrease in the risk of the financial security results in a decrease in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. Conversely, as the risk of a financial security increases, it becomes less attractive to supplier of funds. Accordingly, at every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the supply of funds due to an increase in the financial security’s risk results in an increase in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Near-term Spending Needs. When financial market participants have few near-term spending needs, the absolute dollar value of funds available to invest increases. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The financial market, holding all other factors constant, reacts to this increased supply of funds by decreasing the equilibrium interest rate, and increasing the equilibrium quantity of funds traded. Conversely, when financial market participants have near-term spending needs, the absolute dollar value of funds available to invest decreases. At every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in this financial market that, when corrected results in an increase in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Monetary Expansion. One method used by the Federal Reserve to implement monetary policy is to alter the availability of credit and thus, the growth in the money supply. When monetary policy objectives are to enhance growth in the economy, the Federal Reserve increases the supply of funds available in the financial markets. At every interest rate the supply of loanable funds increases, the supply curve shifts down and to the right, and the equilibrium interest rate falls, while the equilibrium quantity of funds traded increases. Conversely, when monetary policy objectives are to contract economic growth, the Federal Reserve decreases the supply of funds available in the financial markets. At every interest rate the supply of loanable funds decreases, the supply curve shifts up and to the left, and the equilibrium interest rate rises, while the equilibrium quantity of funds traded decreases. Economic Conditions. Finally, as economic conditions improve in a country relative to other countries, the flow of funds to that country increases. The inflow of foreign funds to U.S. financial markets increases the supply of loanable funds at every interest rate and the supply curve shifts down and to the right. Accordingly, the equilibrium interest rate falls, and the equilibrium quantity of funds traded increases. Conversely, when economic conditions in foreign countries improve, domestic and foreign investors take their funds out of domestic financial markets (e.g., the United States) and invest abroad. Thus, the supply of funds available in the financial markets decreases and the equilibrium interest rate rises, while the equilibrium quantity of funds traded decreases. 4. Factors that affect the demand for funds utility derived from the asset purchased with borrowed funds, restrictiveness of nonprice conditions of borrowing, domestic economic conditions, and foreign economic conditions. Utility Derived from Asset Purchased With Borrowed Funds. As the utility derived from an asset purchased with
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e borrowed funds increases the willingness of market participants (households, business, etc.) to borrow increases and the absolute dollar value borrowed increases. Accordingly, at every interest rate the demand for loanable funds increases, or the demand curve shifts up and to the right. The shift in the demand curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the demand for funds due to an increase in the utility from the purchased asset results in an increase in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. Conversely, as the utility derived from an asset purchased with borrowed funds decreases the willingness of market participants (households, business, etc.) to borrow decreases and the absolute dollar value borrowed decreases. Accordingly, at every interest rate the demand of loanable funds decreases, or the demand curve shifts down and to the left. The shift in the demand curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the demand for funds due to a decrease in the utility from the purchased asset results in a decrease in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. Restrictiveness on Nonprice Conditions on Borrowed Funds. As the nonprice restrictions put on borrowers as a condition of borrowing decrease the willingness of market participants to borrow increases and the absolute dollar value borrowed increases. Accordingly, at every interest rate the demand of loanable funds increases, or the demand curve shifts up and to the right. The shift in the demand curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the demand for funds due to a decrease in the restrictive conditions on the borrowed funds results in an increase in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. Conversely, as the nonprice restrictions put on borrowers as a condition of borrowing increase market participants willingness to borrow decreases and the absolute dollar value borrowed decreases. Accordingly, at every interest rate the demand for loanable funds decreases, or the demand curve shifts down and to the left. The shift in the demand curve results in a decrease in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded.
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Economic Conditions. When the domestic economy is experiencing a period of growth, market participants are willing to borrow more heavily. Accordingly, at every interest rate the demand of loanable funds increases, or the demand curve shifts up and to the right. As competitive forces adjust, and holding all other factors constant, the increase in the demand for funds due to economic growth results in an increase in the equilibrium interest rate, and an increase in the equilibrium quantity of funds traded. Conversely, when economic growth is stagnant market participants reduce their borrowings increases. Accordingly, at every interest rate the demand for loanable funds decreases, or the demand curve shifts down and to the left. The shift in the demand curve results in a decrease in the equilibrium interest rate, and a decrease in the equilibrium quantity of funds traded. 5. Specific factors that affect the nominal interest rate on any particular security include: inflation, the real risk-free rate, default risk, liquidity risk, special features regarding the use of funds raised by a particular security issuer, and the security’s term to maturity. 6. The nominal interest rate on a security reflects its relative liquidity, with highly liquid assets carrying the lowest interest rates (all other characteristics remaining the same). Likewise, if a security is illiquid, investors add a liquidity risk premium (LRP) to the interest rate on the security. 7. Explanations for the yield curve’s shape fall predominantly into three categories: the unbiased expectations theory, the liquidity premium theory, and the market segmentation theory. According to the unbiased expectations theory of the term structure of interest rates, at any given point in time, the yield curve reflects the market's current expectations of future short-term rates. The second popular explanation―the liquidity premium theory of the term structure of interest rates—builds on the unbiased expectations theory. The liquidity premium idea is as follows: investors will hold long-term maturities only if these securities with longer term maturities are offered at a premium to compensate for future uncertainty in the security’s value. The liquidity premium theory states that long-term rates are equal to geometric averages of current and expected short-term rates (like the unbiased expectations theory), plus liquidity risk premiums that increase with the security’s maturity (this is the extension of the liquidity premium added to the unbiased expectations theory). The market segmentation theory does not build on the unbiased expectations theory or the liquidity premium theory, but rather argues that individual investors and FIs have specific maturity preferences, and convincing them to hold securities with maturities other than their most preferred requires a higher interest rate (maturity premium). The main thrust of the market segmentation theory is that investors do not consider securities with different maturities as perfect substitutes. Rather, individual investors and FIs have distinctly preferred investment horizons dictated by the dates when their liabilities will come due. 8. According to the unbiased expectations theory, the one-year interest rate one year from now is expected to be less than the one-year interest rate today. 9. The liquidity premium theory is an extension of the unbiased expectations theory. It based on the idea that investors will hold long-term maturities only if they are offered at a premium to compensate for future uncertainty in a security’s value, which increases with an asset’s maturity. Specifically, in a world of uncertainty, short-term securities provide greater marketability (due to their more active secondary market) and have less price risk (due to smaller price fluctuations for a given change in interest rates) than long-term securities. As a result, investors prefer to hold shorter term securities because they can be converted into cash with little risk of a loss of capital, i.e., short-term securities are more liquid. Thus, investors must be offered a liquidity premium to get them to but longer term securities. The liquidity premium theory states that long-term rates are equal to geometric averages of current and expected short-term rates (as under the unbiased expectations theory), plus liquidity risk premiums that increase with the maturity of the security. For example, according to the liquidity premium theory, an upward-sloping yield curve may reflect investor’ expectations that future short-term rates will be flat, but because liquidity premiums increase with maturity, the yield curve will nevertheless be upward sloping. 10. A forward rate is an expected or implied rate on a short-term security that will originate at some point in the future. 11. The present value of an investment decreases as interest rates increase. Also as interest rates increase, present
values decrease at a decreasing rate. This is because as interest rates increase, fewer funds need to be invested at the beginning of an investment horizon to receive a stated amount at the end of the investment horizon. This inverse relationship between the value of a financial instrument—for example, a bond—and interest rates is one of the most fundamental relationships in finance and is evident in the swings that occur in financial asset prices whenever major changes in interest rates arise. Further, because of the compounding of interest rates, the inverse relationship between interest rates and the present value of security investments is neither linear nor proportional.
Problems: 1. The fair interest rate on a financial security is calculated as i* = IP + RFR + DRP + LRP + SCP + MP 8% = 1.75% + 3.5% + DRP + 0.25% + 0% + 0.85% Thus, DRP = 8% - 1.75% - 3.5% - 0.25% - 0% - 0.85% = 1.65% 2. a. IP = i* – RFR = 3.25% - 2.25% = 1.00% b. ij* = 1.00% + 2.25% + 1.15% + 0.50% + 1.75% = 6.65% 3. 8.00% = 1.75% + 3.50% + DRP + 0.25% + 0.85% => DRP = 8.00% - (1.75% + 3.50% + 0.25% + 0.85%) = 1.65% 4. 1.94% = 0.50% + 1.00% + 0.00% + 0.00% + MP => MP = 1.94% - (0.50% + 1.00% + 0.00% + 0.00%) = 0.44% 5. 8.25% = 2.25% + 3.50% + 0.80 + LRP + (0.75% + (0.04% × 10)) => LRP = 8.25% - (2.25% + 3.50% + 0.80% + (0.75% + (0.04% × 10))) = 0.55% 6.
6.05% = 1.00% + 2.10% + DRP + 0.25% + (0.10% + (0.05% × 8)) => DRP = 6.05% - (1.00% + 2.10% + 0.25% + (0.10% + (0.05% × 8))) = 2.20%
7. 1R2 = [(1 + 0.052)(1 + 0.058)]1/2 - 1 = 5.50% 8.
R1 = 6% R2 = [(1 + 0.06)(1 + 0.07)]1/2 - 1 = 6.499% 1/3 - 1 = 6.832% 1R3 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)] 1/4 - 1 = 7.085% 1R4 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)(1 + 0.0785)] 1 1
yield to maturity 7.085% 6.832% 6.499%
6.00%
_____________________________ term to maturity 0 1 2 3 4 (in years) 9. 10.
R2 = [(1 + 0.0345)(1 + 0.0365)]1/2 - 1 = 3.55%
1
1 + 1R2 = {(1 + 1R1)(1 + E(2r1))}1/2 1.10 = {1.08(1 + E(2r1))}1/2 1.21= 1.08 (1 + E(2r1)) 1.21/1.08 = 1 + E(2r1) 1 + E(2r1) = 1.1204
E(2r1) = 0.1204 = 12.04% 11.
1.12 = {(1 + 1R1)(1 + E(2r1))(1 + E(3r1))}1/3 1.12 = {(1 + 1R1)(1.08)(1.10)}1/3 1.4049 = (1 + 1R1 )(1.08)(1.10) 1 + 1R1 = 1.4049/{(1.08)(1.10)} 1R1 = 0.1826 = 18.26%
12.
1 + 1R5 = {(1 + 1R4)4(1 + E(5r1))}1/5 1.0615 = {(1.056)4(1 + E(5r1))}1/5 (1.0615)5 = (1.056)4 (1 + E(5r1)) (1.0615)5/(1.056)4 = 1 + E(5r1) 1 + E(5r1) = 1.08379 E(5r1) = 8.379%
13.
1 + 1R4 = {(1 + 1R3)3(1 + E(4r1))}1/4 1.026 = {(1.0225)3(1 + E(4r1))}1/4 (1.026)4 = (1.0225)3(1 + E(4r1)) (1.026)4/(1.0225)3 = 1 + E(4r1) 1 + E(4r1) = 1.03657 E(4r1) = 3.657% 1 + 1R5 = {(1 + 1R4)4(1 + E(5r1))}1/5 1.0298 = {(1.026)4(1 + E(5r1))}1/5 (1.0298)5 = (1.026)4 (1 + E(5r1)) (1.0298)5/(1.026)4 = 1 + E(5r1) 1 + E(5r1) = 1.04514 E(5r1) = 4.514% 1 + 1R6 = {(1 + 1R5)5(1 + E(6r1))}1/6 1.0325 = {(1.0298)5(1 + E(6r1))}1/6 (1.0325)6 = (1.0298)5(1 + E(6r1)) (1.0325)6/(1.0298)5 = 1 + E(6r1) 1 + E(6r1) = 1.04611 E(6r1) = 4.611%
14.
R1 = 5.65% R2 = [(1 + 0.0565)(1 + 0.0675 + 0.0005)]1/2 - 1 = 6.223% 1/3 - 1 = 6.465% 1R3 = [(1 + 0.0565)(1 + 0.0675 + 0.0005)(1 + 0.0685 + 0.0010)] R = [(1 + 0.0565)(1 + 0.0675 + 0.0005)(1 + 0.0685 + 0.0010)(1 + 0.0715 + 0.0012)]1/4 - 1 = 6.666% 1 4 1 1
yield to maturity 6.666% 6.465% 6.223%
5.65%
_____________________________ term to maturity
0
1
2
3
4
(in years)
15.
(1 + 1R2) = {(1 + 1R1)(1 + E(2r1) + L2)}1/2 1.14 = {1.10 × (1 + 0.18 + L2)}1/2 1.2996 = 1.10 × (1 + 0.18 + L2) 1.2996/1.10 = 1 + 0.18 + L2 1.18145 = 1 + 0.18 + L2 L2 = 0.00145 = 0.145%
16.
1 + 1R4 = {(1 + 1R3)(1 + E(4r1) + L4)}1/4 1.0550 = {(1.0525)3(1 + 0.0610 + L4)}1/4 (1.0550) 4 = (1.0525)3(1 + 0.0610 + L4) (1.0550) 4/(1.0525)3 = 1 + 0.0610 + L4 (1.0550) 4/(1.0525)3 – 1.0610 = L4 = .001536 = 0.1536% R2 = 0.065 = [(1 + 0.055)(1 + 2f1)]1/2 - 1 => [(1.065)2/(1.055)] - 1 = 2f1 = 7.51%
17.
1
18.
1
19.
R3 = 0.09 = [(1 + 0.065)2(1 + 3f1)]1/3 - 1 => [(1.09)3/(1.065)2)] - 1 = 3f1 = 14.18% f = [(1 + 1R2)2/(1 + 1R1)] - 1 = [(1 + 0.0495)2/(1 + 0.0475)] - 1 = 5.15% 3 2 3 2 3f1 = [(1 + 1R3) /(1 + 1R2) ] - 1 = [(1 + 0.0525) /(1 + 0.0495) ] - 1 = 5.85% 4 3 4 3 4f1 = [(1 + 1R4) /(1 + 1R3) ] - 1 = [(1 + 0.0565) /(1 + 0.0525) ] - 1 = 6.86% 2 1
f = [(1 + 1R4)4/(1 + 1R3)3] - 1 = [(1 + 0.0635)4/(1 + 0.06)3] - 1 = 7.41% 5 4 5 4 5f1 = [(1 + 1R5) /(1 + 1R4) ] - 1 = [(1 + 0.0665) /(1 + 0.0635) ] - 1 = 7.86% 6 5 6 5 6f1 = [(1 + 1R6) /(1 + 1R5) ] - 1 = [(1 + 0.0675) /(1 + 0.0665) ] - 1 = 7.25%
20.
4 1
21.
1
R1 = 4.5% R2 = 5.25% = [(1 + 0.045)(1 + 2f1)]1/2 - 1 => 2f1 = 6.01% 1/3 - 1 => 3f1 = 9.04% 1R3 = 6.50% = [(1 + 0.045)(1 + 0.0601)(1 + 3f1)] 1
22. a. PV = $5,000/(1+0.06)5 = $5,000 (0.747258) = $3,736.29 b. PV = $5,000/(1+0.08)5 = $5,000 (0.680583) = $3,402.92 c. PV = $5,000/(1+0.10)5 = $5,000 (0.620921) = $3,104.61 d. PV = $5,000/(1+0.05)10 = $5,000 (0.613913) = $3,069.57 e. PV = $5,000/(1+0.025)20 = $5,000 (0.610271) = $3,051.35 From these answers we see that the present values of a security investment decrease as interest rates increase. As rates rose from 6 percent to 8 percent, the (present) value of the security investment fell $333.37 (from $3,736.29 to $3,402.92). As interest rates rose from 8 percent to 10 percent, the value of the investment fell $298.31 (from $3,402.92 to $3,104.61). This is because as interest rates increase, fewer funds need to be invested at the beginning of an investment horizon to receive a stated amount at the end of the investment horizon. Also, as interest rates increase, the present values of the investment decrease at a decreasing rate. The fall in present value is greater when interest rates rise from 6 percent to 8 percent compared to when they rise from 8 percent to 10 percent. The inverse relationship between interest rates and the present value of security investments is neither linear nor proportional. From the above answers, we also see that the greater the number of compounding periods per year, the smaller the present value of a future amount. This is because, the greater the number of compounding periods the more frequently interest is paid and thus, a greater amount of interest that is paid. Thus, to get to a stated amount at the end of an investment horizon, the greater the amount that will come from interest and the less the amount the investor must pay up front.
23. a. FV = $5,000 (1+0.06)5 = $5,000 (1.338226) = $6,691.13 b. FV = $5,000 (1+0.08)5 = $5,000 (1.469328) = $7,346.64 c. FV = $5,000 (1+0.10)5 = $5,000 (1.610510) = $8,052.55 d. FV = $5,000 (1+0.05)10 = $5,000 (1.628895) = $8,144.47 e. FV = $5,000 (1+0.025)20 = $5,000 (1.638616) = $8,193.08 From these answers we see that the future values of a security investment increase as interest rates increase. As rates rose from 6 percent to 8 percent, the (future) value of the security investment rose to $655.51 (from $6,691.13 to $7,346.). As interest rates rose from 8 percent to 10 percent, the value of the investment rose to $705.91 (from $7,346.64 to $8,052.55). This is because as interest rates increase, a stated amount of funds invested at the beginning of an investment horizon accumulates to a larger amount at the end of the investment horizon. Also as interest rates increase, the future values of the investment increase at an increasing rate. The rise in present value is greater when interest rates rise from 8 percent to 10 percent compared to when they rise from 6 percent to 8 percent. The positive relationship between interest rates and the future value of security investments is neither linear nor proportional. From the above answers, we also see that the greater the number of compounding periods per year, the greater the future value of a future amount. This is because, the greater the number of compounding periods the more frequently interest is paid and thus, a greater amount of interest that is paid. The greater the amount of interest paid and the greater the future value of a present amount. 24. a. PV = $5,000{[1 - (1/(1 + 0.06)5)]/0.06} = $5,000 (4.212364) = $21,061.82 b. PV = $5,000{[1 - (1/(1 + 0.015)20)]/0.015} = $5,000 (17.168639) = $85,843.19 c. PV = $5,000{[1 - (1/(1 + 0.06)5)]/0.06}(1 + .06) = $5,000 (4.212364)(1 + .06) = $22,325.53 d. PV = $5,000{[1 - (1/(1 + 0.015)20)]/0.015}(1 + .015) = $5,000 (17.168639)(1.015) = $87,130.84 25. a. FV = $5,000{[(1 + 0.06)5 -1]/0.06} = $5,000 (5.637092) = $28,185.46 b. FV = $5,000{[(1 + 0.015)20 -1]/0.015} = $5,000 (23.123667) = $115,618.34 c. FV = $5,000{[(1 + 0.06)5 -1]/0.06}(1 + 0.06) = $5,000 (5.637092)(1 + .06) = $29,876.59 d. FV = $5,000{[(1 + 0.015)20 -1]/0.015}(1 + 0.015) = $5,000 (23.123667)(1.015) = $117,352.61 26. FV = $123{[(1 + 0.13)13 -1]/0.13} = $3,688.12 FV = $123{[(1 + 0.13)13 -1]/0.13} (1 + 0.13/1) = $4,167.57 FV = $4,555{[(1 + 0.08)8 - 1]/0.08} = $48,449.84 FV = $4,555{[(1 + 0.08)8 - 1]/0.08}(1 + 0.08/1) = $52,325.83 FV = $74,484{[(1+0.10)5-1]/0.10} = $454,732.27 FV = $74,484{[(1+0.10)5-1]/0.10(1 + 0.10/1) = $500,205.50 FV = $167,332{[(1 + 0.01)9 - 1]/0.01} = $1,567,654.40 FV = $167,332{[(1 + 0.01)9 - 1]/0.01}(1 + 0.01/1) = $1,583,330.95 27. PV = $678.09{[1 - (1/(1 + 0.13)7)]/0.13} = $2,998.93 PV = $678.09{[1 - (1/(1 + 0.13)7)]/0.13}(1 + 0.13/1) = $3,388.79 PV = $7,968.26{[1 - (1/(1 + 0.06)13)]/0.06} = $70,540.48 PV = $7,968.26{[1 - (1/(1 + 0.06)13)]/0.06}(1 + 0.06/1) = $74,772.91 PV = $20,322.93{[1 - (1/(1 + 0.04)23)]/0.04} = $301,934.55 PV = $20,322.93{[1 - (1/(1 + 0.04)23)]/0.04}(1 + 0.04/1) = $314,011.94 PV = $69,712.54{[1 - (1/(1 + 0.31)4)]/0.31} = $148,519.49 PV = $69,712.54{[1 - (1/(1 + 0.31)4)]/0.31}(1 + 0.31/1) = $194,560.54 28. FV = $500 (1.06)3 = $595.51. So, the interest portion is $95.51 = $595.51 − $500.
29. PV = $2,000/(1.08)4 = $1,470.06 30. PV = -$1,200 = $2,000/(1.075)t => Using a financial calculator, I = 7.5, PV= -1,200, PMT = 0, FV = 2,000, then compute N = 7.06 years 31. FV = $1,000{[(1 + 0.10)6 - 1]/0.10}(1 + 0.10) = $8,487.17 or using a financial calculator, N = 6, I = 10, PV = 0, PMT = -1,000, then compute FV = $7,715.61, then multiply $7,715.61 × (1+0.10) = $8,487.17. 32. PV = $180,000 = PMT{[1 - (1/(1 + 0.08/12)15x12)]/(0.08/12)} = $1,720.17 or using a financial calculator, N = 15x12 = 180, I = 8÷12 = .66667, PV = -180,000, FV = 0, then compute PMT = $1,720.17
Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Answers to Chapter 3 Questions: 1. The required rate of return is the interest rate an investor should receive on a security given its risk. Required rate of return is used to calculate the fair present value on a security. The expected rate of return is the interest rate an investor expects to receive on a security if he or she buys the security at its current market price, receives all expected payments, and sells the security at the end of his or her investment horizon. 2. Once an expected rate of return, E(r), on a financial security is calculated, the market participant compares this expected rate of return to its required rate of return (r). If the expected rate of return is greater than the required rate of return, the projected cash flows on the security are greater than is required to compensate for the risk incurred from investing in the security and the current market price is less than the fair market price of the security. Thus, the market participant would want to buy more of this security. If the expected rate of return is less than the required rate of return, the projected cash flows from the security are less than those required to compensate for the risk involved and the current market price is greater than the fair market price of the security. Thus, the market participant would not want to invest in the security. 3. Most bonds pay a stated coupon rate of interest to the holders of the bonds. These bonds are called coupon bonds. The interest, or coupon, payments per year are generally constant (are fixed) over the life of the bond. Thus, the fixed interest payment is essentially an annuity paid to the bond holder periodically (normally semiannually) over the life of the bond. Bonds that do not pay coupon interest are called zero-coupon bonds. For these bonds interest payments are zero. 4.
a. Premium bond b. Par bond c. Discount bond d. Discount bond e. Premium bond f. Discount bond
5. Most bonds pay a stated coupon rate of interest to the holders of the bonds. The interest, or coupon, payments per year are generally constant (fixed) over the life of the bond. Thus, the fixed interest payment is essentially an annuity paid to the bond holder periodically (normally semiannually) over the life of the bond. In addition to coupon payments, the face or par value of the bond is a lump sum payment received by the bond holder when the bond matures. Face value is generally set at $1,000 in the U.S. bond market. In contrast, the valuation process for an equity instrument (such as common stock or a share) involves finding the present value of an infinite series of unequal cash flows on the equity discounted at an appropriate interest rate. Cash flows from holding equity come from dividends paid out by the firm over the life of the stock, which in expectation can be viewed as infinite since a firm (and thus the dividends it pays) has no defined maturity or life. Even if an equity holder decides not to hold the stock forever, he or she can sell it to someone else who in a fair and efficient market is willing to pay the present value of the remaining (expected) dividends to the seller at the time of sale. 6. The present values of the cash flows on bonds decreases as the required rate of return increases. This is the inverse relationship between present values and interest rates we discussed in Chapter 2. While the examples in the chapter refer to the relation between fair present values and required rates of returns, the inverse relation also exists between current market prices and expected rates of return—as yields on bonds increase, the current market prices of bonds decrease. The relationship between bond prices and the required rate of return is not linear. Rather, the percentage change in the present value of a bond to a given change in the required rate of return is smaller when interest rates are higher. The same nonlinear relation exists for current market prices and yield to maturities. Thus, as interest rates increase, present values of bonds (and bond prices) decrease at a decreasing rate. 7. All else equal, a long-term bond experiences larger price changes when interest rates change than a short-term bond. A bond’s price is the present value of all its cash flows. Changes in the discount rate (the interest rate) impact present values more for cash flows that are further out in time. Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e 8. The price of the bond with the small coupon will be impacted more by a change in interest rates than the price of the large coupon bond. For a small coupon bond, the cash flows are weighted much more toward the maturity date because of the small interest payments. The large coupon bond has high interest payments, many of which occur soon. These higher cash flows made earlier dampen the impact of interest rate changes because those changes in the discount rate impact the earlier cash flows to a lesser degree than the later cash flows. 9. Duration is the elasticity, or sensitivity, of the bond’s price to small interest rate (either required rate of return or yield to maturity) changes, and is represented as follows: -D = [P/P]/[rb/(1+ rb)] The negative sign in front of the D indicates the inverse relationship between interest rate changes and price changes. That is, -D describes the percentage value decrease —capital loss—on the security (P/P) for any given (discounted) small increase in interest rates (rb /(1 + rb)), where rb is the change in interest rates and 1 + rb is 1 plus the current (or beginning) level of interest rates. In other words, if duration is known, then the change in the price of a bond due to a small change in interest rates, rb, can be estimated using the above formula. 10. The higher the coupon or promised interest payment on the bond, the shorter its duration. This is due to the fact that the larger the coupon or promised interest payment, the more quickly investors receive cash flows on a bond and the higher are the present value weights of those cash flows in the duration calculation. On a time value of money basis, the investor recoups his or her initial investment faster when coupon payments are higher. 11. The 8 percent yield to maturity bond has the longer duration. This is because duration decreases as rate of return increases. This makes intuitive sense since the higher the rate of return on the bond, the lower the present value cost of waiting to receive the later cash flows on the bond. Higher rates of return discount later cash flows more heavily, and the relative importance, or weights, of those later cash flows decline when compared to cash flows received earlier. 12. Duration, which measures the weighted-average time to maturity of the asset or liability, also has economic meaning as the sensitivity (or elasticity) of that asset’s or liability’s value to small interest rate changes (either required rate of return or yield to maturity). That is, duration describes the percentage price, or present value, change of a financial security for a given (small) change in interest rates. Problems: 1. 935 = 75{[1 - (1/(1 +
´ 5 ´ r ) )]/ r } + 980/(1 +
´ 5 ´ r ) => r
= 8.83%
Or, on a financial calculator: N = 5, PV = -935, PMT = 75, FV = 980, => I =
´ r
= 8.83%
2. 980 = 75{[1 - (1/(1 + E(rb))3)]/E(rb)} + 990/(1 + E(rb))3 => E(rb) = 7.97% Or, on a financial calculator: N = 3, PV = -980, PMT = 75, FV = 990, => I = E(r) = 7.97% 3. Vb = 1,000(0.08) {[1 - (1/(1 + 0.09)10)]/0.09} + 1,000(1 + 0.09)10 = $935.82 Or, on a financial calculator: N = 10, I = 9, PMT = 80, FV = 1,000, => PV = $935.82 4. EXCEL Problem:
Bond Value (required return = 5%) = $1,268.27 Bond Value (required return = 6%) = $1,169.36 Bond Value (required return = 8%) = $1,000.00 Bond Value (required return = 10%) = $862.01
5. $1,100 = 1,000(0.12) {[1 - (1/(1 + ytm/2)2(10))]/ytm/2} + 1,000/(1 + ytm/2)2(10) => ytm = 10.37% Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e 2 Or, on a financial calculator: N = 20, PV= -1,100, PMT = 60, FV = 1,000, => I = ytm = 5.185% for 6 months or 10.37% per year 6. EXCEL Problem:
Yield to Maturity (current market value = $945.50) = 9.87% Yield to Maturity (current market value = $987.50) = 9.19% Yield to Maturity (current market value = $1,090.00) = 7.69% Yield to Maturity (current market value = $1,225.875) = 5.97%
7. Vb = 1,000(0.07) {[1 - (1/(1 + 0.14/4)4(4))]/0.14/4} + 1,000/(1 + 0.14/4)4(4) = $788.35 4 Or, on a financial calculator: N = 16, I = 3.5, PMT = 17.5, FV = 1,000, => PV = $788.35 8.
$863.73 = 1,000(0.08) {[1 - (1/(1 + 0.10)n)]/0.10} + 1,000/(1 + 0.10)n => n = 12 years Or, on a financial calculator: I = 10, PV = -863.73, PMT = 80, FV = 1,000, => n = 12 years
9. a. Vb = 1,000(0.10) {[1 - (1/(1 + 0.06/2)2(10))]/(0.06/2)} + 1,000/(1 + 0.06/2)2(10) = $1,297.55 2 On a financial calculator: N = 20, I = 3, PMT = 50, FV = 1,000, => PV = $1,297.55 b. Vb = 1,000(0.10) {[1 - (1/(1 + 0.08/2)2(10))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(10) = $1,135.90 2 On a financial calculator: N = 20, I = 4, PMT = 50, FV = 1,000, => PV = $1,135.90 c. From parts a. and b. of this problem, there is a negative relation between required rates of return and fair values of bonds. 10. a. 985 = 1,000(0.09) {[1 - (1/(1 + ytm/2)2(15))]/ytm/2} + 1,000/(1 + ytm/2)2(15) => ytm = 9.186% 2 On a financial calculator: N = 30, PV= -985, PMT = 45, FV = 1,000, => I = ytm = 4.593% for 6 months or 9.186% per year b. 915 = 1,000(0.08) {[1 - (1/(1 + ytm/4)4(10))]/ytm/4} + 1,000/(1 + ytm/4)4(10) => ytm = 9.316% 4 On a financial calculator: N = 40, PV= -915, PMT = 20, FV = 1,000, => I = ytm = 2.329% for 3 months or 9.316% per year c. 1,065 = 1,000(0.11) {[1-(1/(1 + ytm)6)]/ytm} + 1,000/(1 + ytm)6 => ytm = 9.528% On a financial calculator: N = 6, PV= -1,065, PMT = 110, FV = 1,000, => I = ytm = 9.528% 11. a. Vb = 1,000(0.06) {[1 - (1/(1 + 0.10/2)2(12))]/(0.10/2)} + 1,000/(1 + 0.10/2)2(12) = $724.03 2 On a financial calculator: N = 24, I = 5, PMT = 30, FV = 1,000, => PV = $724.03 b. Vb = 1,000(0.08) {[1 - (1/(1 + 0.10/2)2(12))]/(0.10/2)} + 1,000/(1 + 0.10/2)2(12) = $862.01 2 On a financial calculator: N = 24, I = 5, PMT = 40, FV = 1,000, => PV = $862.01 c. Vb = 1,000(0.10) {[1 - (1/(1 + 0.10/2)2(12))]/(0.10/2)} + 1,000/(1 + 0.10/2)2(12) = $1,000.00 2 On a financial calculator: N = 24, I = 5, PMT = 50, FV = 1,000, => PV = $1,000.00 d. From parts a. through c. in this problem, there is a positive relation between coupon rates and present values of bonds.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e 12. a. Vb = 1,000(0.06) {[1 - (1/(1 + 0.08/2)2(12))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(12)= $847.53 2 On a financial calculator: N = 24, I = 4, PMT = 30, FV = 1,000, => PV = $847.53 b. Vb = 1,000(0.08) {[1 - (1/(1 + 0.08/2)2(12))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(12) = $1,000.00 2 On a financial calculator: N = 24, I = 4, PMT = 40, FV = 1,000, => PV = $1,000.00 % change in bond value versus part (a) = ($1,000 - $847.53)/$847.53 = 17.99% c. Vb = 1,000(0.10) {[1 - (1/(1 + 0.08/2)2(12))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(12) = $1,152.47 2 On a financial calculator: N = 24, I = 4, PMT = 50, FV = 1,000, => PV = $1,152.47 % change in bond value versus part (b) = ($1,152.47 - $1,000)/$1,000 = 15.25% From these results we see that as coupon rates increase, price volatility decreases. 13. a. Vb = 1,000(0.10) {[1 - (1/(1 + 0.08/2)2(10))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(10) = $1,135.90 2 On a financial calculator: N = 20, I = 4, PMT = 50, FV = 1,000, => PV = $1,135.90 b. Vb = 1,000(0.10) {[1-(1/(1 + 0.08/2)2(15))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(15) = $1,172.92 2 On a financial calculator: N = 30, I = 4, PMT = 50, FV = 1,000, => PV = $1,172.92 c. Vb = 1,000(0.10) {[1 - (1/(1 + 0.08/2)2(20))]/(0.08/2)} + 1,000/(1 + 0.08/2)2(20) = $1,197.93 2 On a financial calculator: N = 40, I = 4, PMT = 50, FV = 1,000, => PV = $1,197.93 d. From these results we see that there is a positive relation between time to maturity and the difference between present values and face values on bonds. 14. a. Vb = 1,000(0.10) {[1 - (1/(1 + 0.11/2)2(10))]/(0.11/2)} + 1,000/(1 + 0.11/2)2(10) = $940.25 2 On a financial calculator: N = 20, I = 5.5, PMT = 50, FV = 1,000, => PV = $940.25 % change in bond value = ($940.25 - $1,135.90)/$1,135.90 = -17.22% b. Vb = 1,000(0.10) {[1 - (1/(1 + 0.11/2)2(15))]/(0.11/2)} + 1,000/(1 + 0.11/2)2(15) = $927.33 2 On a financial calculator: N = 30, I = 5.5, PMT = 50, FV = 1,000, => PV = $927.33
% change 3.72%
% change in bond value = ($927.33 - $1,172.92)/$1,172.92 = -20.94% c. Vb = 1,000(0.10) {[1 - (1/(1 + 0.11/2)2(20))]/(0.11/2)} + 1,000/(1 + 0.11/2)2(20) = $919.77 2 On a financial calculator: N = 40, I = 5.5, PMT = 50, FV = 1,000, => PV = $919.77
% change 2.28%
% change in bond value = ($919.77 - $1,197.93)/$1,197.93 = -23.22% As interest rates increase the variability in bond prices increases as time to maturity increases but at a decreasing rate. 15. Price before the change in interest rates: Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Vb = 1,000(0.06) {[1 - (1/(1 + 0.05/2)2(5))]/(0.05/2)} + 1,000/(1 + 0.05/2)2(5) = $1,043.76 2 On a financial calculator: N = 10, I = 2.5, PMT = 30, FV = 1,000 => PV = $1,043.76 Price after the change in interest rates: Vb = 1,000(0.06) {[1 - (1/(1 + 0.055/2)2(5))]/(0.055/2)} + 1,000/(1 + 0.055/2)2(5) = $1,021.60 2 On a financial calculator: N = 10, I = 2.75, PMT = 30, FV = 1,000 => PV = $1,021.60. Or, the bond decreases in price by $22.16. 16. Vb = 945.80 = 1,000(0.09) {[1 - (1/(1 + ytm/2)2(7))]/ytm/2} + 1,000/(1 + ytm/2)2(7) => ytm = 10.099% 2 On a financial calculator: N = 14, PV= -945.80, PMT = 45, FV = 1,000, => I = ytm = 5.049% for 6 months or 10.10% per year 17.
P0 = 5/0.10 = $50
18.
P0 = 2.10/0.054 = $38.89
19.
P0 = 3.50/0.068 = $51.47
20.
Po = 1.20(1 + 0.10) = $66.00 0.12 - 0.10
21.
Po = 0.60(1 + 0.125) = $33.75 0.145 - 0.125
22. a.
Po = 2.50(1 + 0.015) = $24.167 0.12 - 0.015
b.
P4 = 2.50(1 + 0.015)5 = $19.95 0.15 - 0.015
23. a.
E(rs) = 4.50 + 0.03 = 10.03% 64
b. E(rs) = 4.50 + 0.05 = 12.03% 64 c. From parts a. and b. of this problem, there is a positive relation between the dividend growth rate and the expected rate of return on stocks. 24. Step 1: Find the present value of dividends during the period of supernormal growth. Year 1 2 3 4 5 6
Dividends (D0(1 + gs)t) 5.5(1 + 0.08)1 = 5.940 5.5(1 + 0.08)2 = 6.415 5.5(1 + 0.08)3 = 6.928 5.5(1 + 0.08)4 = 7.483 5.5(1 + 0.08)5 = 8.081 5.5(1 + 0.08)6 = 8.728
1/(1 + 0.10)t 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645
Present Value 5.400 5.302 5.205 5.111 5.018 4.927
Present value of dividends during supernormal growth period $30.963 Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e Step 2: Find present value of dividends after period of supernormal growth a. Find stock value at beginning of constant growth period P6 = D7 = D0(1 + gs)6(1 + g)1 = 5.5 (1 + 0.08 )6(1 + 0.03)1 = $128.423 rs - g rs - g 0.10 - 0.03 b. Find present value of constant growth dividends P0 = P6/(1 + 0.10)6 = 128.423(0.5645) = $72.492 Step 3: Find present value of stock = value during supernormal growth period + value during normal growth period $30.963 + $72.492 = $103.455 25.
E(rs) = 0.46(1 + 0.145) + 0.145 = 15.69% 44.12
26.
E(rs) = 0.84(1 + 0.15) + 0.15 = 17.41% 40.11
27.
P0 = $41.30 = ($1.32 × (1 + 0.095))/(0.13 − 0.095)
28.
E(rs) = 12.09% = [$0.35 × (1 + 0.105)/ $24.25] + 0.105
29. a.
Year 1 2
Cash Flows (CF) 100 1,100
1/(1 + 0.12)t 0.8929 0.7972
PV of CF 89.29 876.91 966.20
PV of CF t 89.29 1,753.83 1,843.12
Duration = $1,843.12/$966.20 = 1.9076 years b. The duration of a two-year zero coupon bond is 2 years. c. Duration always will be lower than the maturity for a coupon bond. That is because duration takes into account the timing of cash flows. The only time duration equals maturity is when there is only one single payment, as is the case with zero-coupon bonds. 30. a. The value of the Bank 1’s loan is $945,737.57 = 120,000 {[1 - (1/(1 + 0.12)10)]/0 .12} + 1,000,000/(1 + 0.12)10 On a financial calculator: N = 10, I = 12, PMT = 120,000, FV = 1,000,000 => PV = 1,000,000 If interest rates rise by 1%, the value of the Bank 1’s loan will be $945,737.57 = 120,000 {[1 - (1/(1 + 0.13)10)]/0.13} + 1,000,000/(1 + 0.13)10 On a financial calculator: N = 10, I = 13, PMT = 120,000, FV = 1,000,000 => PV = $945,737.57. The value of the CD is $1,000,000 = 100,000{[1 - (1/(1 + 0.10)10)]/0.10} + 1,000,000/(1 + 0.10)10 On a financial calculator: N = 10, I = 11, PMT = 100,000, FV = 1,000,000 => PV = $941,107.68 If interest rates rise by 1%, the value of the CD will be $941,107.68 = 100,000{[1 - (1/(1 + 0.11)10)]/0.11} + 1,000,000/(1 + 0.11)10 On a financial calculator: N = 10, I = 11, PMT = 100,000, FV = 1,000,000 => PV = $941,107.68 The difference in the changes in the assets ($54,262.43) and liabilities ($58,892.32) is $4,629.89. The asset decreased in value by less than the liability. Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Saunders/Cornett/Erhemjamts Financial Markets and Institutions, 8e The value of Bank 2’s the zero-coupon bond is $894,006.20 = 1,976,362.88/(1 + 0.12)7 On a financial calculator: N = 7, I = 12, PMT = 0, FV = 1,000,000 => PV = $894,006.20 The value of Bank 2’s the zero-coupon bond when rates rise by 1% is $840,074.08 = 1,976,362.88/(1 + 0.13)7 On a financial calculator: N = 7, I = 13, PMT = 0, FV = 1,000,000 => PV = $840,074.08 The value of the CD before the interest change is $894,006.22 = 82,750{[1 - (1/(1 + 0.10)10)]/0.11} + 1,000,000/(1 + 0.10)10 On a financial calculator: N = 10, I = 10, PMT = 82,750, FV = 1,000,000 => PV = $894,006.22 The value of the CD after the interest change is $839,518.43 = 82,750{[1 - (1/(1 + 0.11)10)]/0.11} + 1,000,000/(1 + 0.11)10 On a financial calculator: N = 10, I = 11, PMT = 82,750, FV = 1,000,000 => PV = $839,518.43 The value of the Bank 2’s zero-coupon bond was $1,976,362.88 and is now $840,074.08. The value of the Bank 2’s CD was $894,006.22 and is now $839,518.43. The difference in the changes in the assets ($53,932.12) and liabilities ($54,487.79) is $555.67. b. Although the numbers are a bit contrived, the point of the problem is to show that in part a, even though Bank 1’s assets and liabilities had the same face values and maturities, they have different durations and so the changes in prices because of a change in interest rates was different for the assets compared to the liability. Bank 2’s assets and liabilities have the same current values, but different maturities. But students can verify that the duration of the asset is about the same as the duration of the liability. Consequently, a one percent change in interest rates produces approximately the same change in the prices of the asset and liability. 31. Coupon Bond: Par value = $1,000,
Coupon rate = 10%, annual payments, rb = 8%, Maturity = 2 years
t
CF
CF/(1 + 0.08)t
PV of CF × t
1 2
$100 1,100
$92.59 943.07 $1,035.67
$92.59 1,886.15 $1,978.74
Duration = $1,978.74/$1,035.67 = 1.9106
If rb = 10% t
CF
CF/(1 + 0.10)t
PV of CF × t
1 2
$100 1,100
$90.91 909.09 $1,000.00
$90.91 1,818.18 $1,909.09
Duration = $1,909.09/$1,000.00 = 1.9091
If rb = 12% t
CF
CF/(1 + 0.12)t
PV of CF × t
1 2
$100 1,100
$89.29 876.91 $966.20
$89.23 1,753.83 $1,843.11
Duration = $1,843.11/$966.20 = 1.9076
b. Increasing the yield to maturity decreases the duration of the bond. c. Zero Coupon Bond: Par value = $1,000, Coupon rate = 0%, rb = 8%, Maturity = 2 years t
CF
CF/(1 + 0.08)t
PV of CF × t
2
$1,000
$857.34
$1,714.68
$857.34
$1,714.68
Duration = $1,714.68/$857.34 = 2.0000
If rb = 10% Copyright © 2022 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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