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Economics of Money, Banking and Financial Markets, The, Business School Edition, 5th Edition Solution Manual

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    P ART T HREE Answers to End - of - Chapter Questions and Problems

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 57 Chapter 1 ANSWERS TO QUESTIONS 1. What is the typical relationship among interest rates on three - month Treasury bills, long - term Treasury bonds, and Baa corporate bonds? The interest rate on three - month Treasury bills fluctuates more than the other interest rates and is lower on average. The interest rate on Baa corporate bonds is higher on average than the other interest rates. 2. What effect might a fall in stock prices have on business investment? The lower price for a firm’s shares means that it can raise a smaller amount of funds, so investment in facilities and equipment will fall. 3. Explain the main difference between a bond and a common stock. A bond is a debt instrument, which entitles the owner to receive periodic amounts of money (predetermined by the characteristics of the bond) until its maturity date. A common stock, however, represents a share of ownership in the institution that has issued the stock. In addition to its definition, it is not the same to hold bonds or stock of a given corporation, since regulations state that stockholders are residual claimants (i.e. the corporation has to pay all bondholders before paying stockholders). 4. Explain the link between well - performing financial markets and economic growth. Name one channel through which financial markets might affect economic growth and poverty. Well performing financial markets tend to allocate funds to its more efficient use, thereby allowing the best investment opportunities to be undertaken. The improvement in the allocation of funds results in a more efficient economy, which stimulates economic growth (and thereby poverty reduction). 5. What was the main cause of the recession that began in 2007? The United States ’ economy was hit by the worst financial crisis since the Great Depression. Defaults in subprime residential mortgages led to major losses in financial institutions, producing not only numerous bank failures but also the demise of two of the largest investment banks in the United States . These factors led to the “Great Recession” that began late in 2007.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 58 6. Can you think of a reason why people in general do not lend money to one another to buy a house or a car? How would your answer explain the existence of banks? In general , people do not lend large amounts of money to one another because of several information problems. In particular, people do not know about the capacity of other people of repaying their debts, or the effort they will provide to repay their debts. Financial intermediaries, in particular commercial banks, tend to solve these problems by acquiring information about potential borrowers and writing and enforcing contracts that encourage lenders to repay their debt and/or maintain the value of the collateral. 7. What are the other important financial intermediaries in the economy, besides banks? Savings and loan associations, mutual savings banks, credit unions, insurance companies, mutual funds, pension funds, and finance companies. 8. Can you date the latest financial crisis in the United States or in Europe? Are there reasons to think that these crises might have been related? Why? The latest financial crisis in the U nited States and Europe occurred in 2007 – 2009. At the beginning it hit mostly the US financial system, but it then quickly moved to Europe, since financial markets are highly interconnected. One specific way in which these markets were related is that some financial intermediaries in Europe held securities backed by mortgages originated in the U nited States , and when these securities lost their a considerable part of their value, the balance sheet of European financial intermediaries w as adversely affected. 9. Has the inflation rate in the United States increased or decreased in the past few years? What about interest rates? From 2014 to mid - 2017, inflation has been somewhat low, but increased more recently to near 2%; interest rates have moved in a fairly narrow range, with the benchmark 10 - year US treasury rate moving from a high of around 2.5%, to as low as about 1.5% then increasing again. 10. If history repeats itself and we see a decline in the rate of money growth, what might you expect to happen to a. real output? b. the inflation rate? c. interest rates? The data in Figures 3, 5, and 6 suggest that real output, the inflation rate, and interest rates would all fall.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 59 11. When interest rates decrease, how might businesses and consumers change their economic behavior? Businesses would increase investment spending because the cost of financing this spending is now lower, and consumers would be more likely to purchase a house or a car because the cost of financing their purchase is lower. 12. Is everybody worse off when interest rates rise? No. It is true that people who borrow to purchase a house or a car are worse off because it costs them more to finance their purchase; however, savers benefit because they can earn higher interest rates on their savings. 13. Why do managers of financial institutions care so much about the activities of the Federal Reserve System? Because the Federal Reserve affects interest rates, inflation, and business cycles, all of which have an important impact on the profitability of financial institutions. 14. How does the current size of the U.S. budget deficit compare to the historical budget deficit or surplus for the time period since 1950? The deficit as a percentage of GDP expanded dramatically in 2007 but improved starting in 2010; in 2009 , the deficit to GDP ratio was 9.8%, and in 2016 was 3.2%, still above the historical average of around 2% since 1950. 15. How would a fall in the value of the pound sterling affect British consumers? It makes foreign goods more expensive, so British consumers will buy fewer foreign goods and more domestic goods. 16. How would an increase in the value of the pound sterling affect American businesses? It makes British goods more expensive relative to American goods. Thus , American businesses will find it easier to sell their goods in the United States and abroad, and the demand for their products will rise. 17. How can changes in foreign exchange rates affect the profitability of financial institutions? Changes in foreign exchange rates change the value of assets held by financial institutions and thus lead to gains and losses on these assets. Also changes in foreign exchange rates affect the profits made by traders in foreign exchange who work for financial institutions.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 60 18. According to Figure 8, in which years would you have chosen to visit the Grand Canyon in Arizona rather than the Tower of London? In the mid - to late 1970s , the late 1980s to early 1990s , and 2008 to 2015, the value of the dollar was low, making travel abroad relatively more expensive; thus , it was a good time to vacation in the United States and see the Grand Canyon. With the rise in the dollar’s value in the early 1980s, late 1990s, and after 2015, travel abroad became relatively cheaper, making it a good time to visit the Tower of London. This was also true, to a lesser extent, in the early 2000s. The following table lists the foreign exchange rate between U.S. dollars and British pounds (GBP) during May 2017. Which day would have been the best for converting $200 into British pounds? Which day would have been the worst? What would be the difference in pounds? Date $/£ 5 - 01 1.2917 5 - 02 1.2921 5 - 03 1.2916 5 - 04 1.2910 5 - 05 1.2950 05 - 08 1.2942 05 - 09 1.2939 05 - 10 1.2939 05 - 11 1.2885 05 - 12 1.2880 05 - 15 1.2917 05 - 16 1.2912 05 - 17 1.2944 05 - 18 1.3009 05 - 19 1.3018 05 - 22 1.3006 05 - 23 1.2984 05 - 24 1.2935 05 - 25 1.2954 05 - 26 1.2795 05 - 30 1.2858 05 - 31 1.2905

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 61 19. When the dollar is worth more in relation to currencies of other countries, are you more likely to buy American - made or foreign - made jeans? Are U.S. companies that manufacture jeans happier when the dollar is strong or when it is weak? What about an American company that is in the business of importing jeans into the United States? When the dollar increases in value, foreign goods become less expensive relative to American goods; thus , you are more likely to buy French - made jeans than American - made jeans. The resulting drop in demand for American - made jeans because of the strong dollar hurts American jeans manufacturers. On the other hand, the American company that imports jeans into the United States now finds that the demand for its product has risen, so it is better off when the dollar is strong. 20. Much of the U.S. government debt is held by foreign investors as treasury bonds and bills. How do fluctuations in the dollar exchange rate affect the value of that debt held by foreigners? As the dollar becomes stronger (worth more) relative to a foreign currency, one dollar is equivalent to (can be exchanged for) more foreign currency. Thus, for a given face value of bond holdings, a stronger dollar will yield more home currency to foreigners, so the asset will be worth more to foreign investors . Likewise, a weak dollar will lead to foreign bond holdings worth less to foreigners. ANSWERS TO APPLIED PROBLEMS 21. The following table lists the foreign exchange rate between U.S. dollars and British pounds (GBP) during May 2017. Which day would have been the best for converting $200 into British pounds? Which day would have been the worst? What would be the difference in pounds? 5 - 01 1.2917 5 - 02 1.2921 5 - 03 1.2916 5 - 04 1.2910 5 - 05 1.2950 05 - 08 1.2942 05 - 09 1.2939 05 - 10 1.2939 05 - 11 1.2885 05 - 12 1.2880 05 - 15 1.2917 05 - 16 1.2912 05 - 17 1.2944 05 - 18 1.3009 05 - 19 1.3018

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 62 05 - 22 1.3006 05 - 23 1.2984 05 - 24 1.2935 05 - 25 1.2954 05 - 26 1.2795 05 - 30 1.2858 05 - 31 1.2905 The best day is 5/26. At a rate of $1.2795/pound, you would have £156.31. The worst day is 5/19. At $1.3018/pound, you would have £153.63, or a difference of £2.68 ANSWERS TO DATA ANALYSIS PROBLEMS 1. Go to the St. Louis Federal Reserve FRED database and find data on the three - month treasury bill rate (TB3MS), the three - month AA nonfinancial commercial paper rate (CPN3M), the 30 - year treasury bond rate (GS30), the 30 - year fixed rate mortgage average (MORTGAGE30US), and the NBER recession indicators (USREC). For the mortgage rate indicator, set the frequency setting to ‘monthly’. a. In general, how do these interest rates behave during expansionary periods? Generally speaking, the interest rates fall during recessions, and rise during expansionary periods. b. In general, how do the three - month interest rates compare to the 30 - year rates? How do the Treasury rates compare to the respective commercial paper and mortgage rates? In nearly all instances, the 30 - year rates are significantly higher than the three - month rates. Likewise, in most cases, the 30 - year mortgage rate is higher than the 30 - year treasury rate, and the three - month commercial paper rate is higher than the three - month treasury rate. c. For the most recent available month of data, take the average of each of the three - month rates and compare it to the average of the three - month rates from January 2000. How do the averages compare? d. For the most recent available month of data, take the average of each of the 30 - year rates and compare it to the average of the 30 - year rates from January 2000. How do the averages compare? May 2017 January 2000 Three - month rate avg. 0.92 5.53 30 - year rate avg. 3.49 7.42 See table above. For both rate averages, they have decreased significantly since January

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 63 2000. 2. Go to the St. Louis Federal Reserve FRED database and find data on the M1 money supply (M1SL) and the 10 - year treasury bond rate (GS10). Add the two series into a single graph by using the “Add Data Series” feature. Transform the M1 money supply variable into the M1 growth rate by adjusting the units for the M1 money supply to “Percent Change from Year Ago.” a. In general, how have the growth rate of the M1 money supply and the 10 - year treasury bond rate behaved during recessions and during expansionary periods since the year 2000? Generally, the 10 - year treasury rate fell during the recessionary periods of 2001 and 2007 – 2009; during expansionary periods, there was less of a pattern, but there seems to be a long - run downward trend in the interest rate. The money growth rate increased significantly during recessionary periods ; however , during expansions , there is less of a pattern; following the 2001 recession, money growth gradually declined, but after the 2007 – 2009 recession, money growth was relatively high and variable. b. In general, is there an obvious, stable relationship between money growth and the 10 - year interest rate since the year 2000? When money growth rises, the 10 - year treasury rate appears to fall, and vice - versa ; however , this effect is more obvious over some periods than others. c. Compare the money growth rate and the 10 - year interest rate for the most recent month available to the rates for January 2000. How do the rates compare? May 2017 January 2000 M1 Money Growth 8.00 2.19 10 - year t reasury rate 2.30 6.66 The money growth rate is significantly higher in May 2017 than it was in January 2000. The 10 - year treasury rate is significantly lower in May 2017 than it was in January 2000.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 64 Chapter 2 ANSWERS TO QUESTIONS 1. If I can buy a car today for $5,000 and it is worth $10,000 in extra income to me next year because it enables me to get a job as a traveling salesman, should I take out a loan from Larry the Loan Shark at a 90% interest rate if no one else will give me a loan? Will I be better or worse off as a result of taking out this loan? Can you make a case for legalizing loan sharking? Yes, I should take out the loan, because I will be better off as a result of doing so. My interest payment will be $4,500 (90% of $5,000), but as a result, I will earn an additional $10,000, so I will be ahead of the game by $5,500. Since Larry’s loan - sharking business can make some people better off, as in this example, loan sharking may have social benefits. (One argument against legalizing loan sharking, however, is that it is frequently a violent activity.) 2. Some economists suspect that one of the reasons economies in developing countries grow so slowly is that they do not have well - developed financial markets. Does this argument make sense? Yes, because the absence of financial markets means that funds cannot be channeled to people who have the most productive use for them. Entrepreneurs then cannot acquire funds to set up businesses that would help the economy grow rapidly. 3. Give at least three examples of a situation in which financial markets allow consumers to better time their purchases. Examples of how financial markets allow consumers to better time their purchases include • The purchase of a durable good, like a car or furniture. • Paying for tuition. • Paying the cost of repairing a flooded basement. In all three cases, consumers were able to pay for a good or service (education or the reparation of a flooded basement) without having to wait to save enough and only then being able to afford such goods and services. 4. If you suspect that a company will go bankrupt next year, which would you rather hold, bonds issued by the company or equities issued by the company? Why? You would rather hold bonds, because bondholders are paid off before equity holders, who are the residual claimants. 5. Suppose that Toyota sells yen - denominated bonds in Tokyo. Is this debt instrument considered a Eurobond? How would your answer change if the bond were sold in New York? If the Yen denominated bond is sold in Tokyo, then it is not considered a Eurobond. If the bond is sold in New York, then it is considered a Eurobond.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 65 6. Describe who issues each of the following money market instruments: a. Treasury bills b. Certificates of deposit c. Commercial paper d. Repurchase agreement e. Fed funds Treasury bills are short - term debt instruments issued by the US government to cover immediate spending obligations, i.e. finance deficit spending. Certificates of deposit (CD) are issued by banks and sold to depositors. Corporations and large banks issue commercial paper as a method of short - term funding in debt markets. Repos are issued primarily by banks and funded by corporations and other banks through loans in which treasury bills serve as collateral, with an explicit agreement to pay off the debt (repurchase the treasuries) in the near future. Fed funds are overnight loans from one bank to another. 7. What is the difference between a mortgage and a mortgage - backed security? Mortgages are loans to households or firms to purchase housing, land, or other real structures, where the structure or land itself serves as collateral for the loans. Mortgage - backed securities are bond - like debt instruments that are backed by a bundle of individual mortgages, whose interest and principal payments are collectively paid to the holders of the security. In other words, when an individual takes out a mortgage, that loan is bundled with other individual mortgages to create a composite debt instrument, which is then sold to investors. 8. The U.S. economy borrowed heavily from the British in the nineteenth century to build a railroad system. Why did this make both countries better off? The British gained because they were able to earn higher interest rates as a result of lending to Americans, while the Americans gained because they now had access to capital to start up profitable businesses such as railroads. 9. A significant number of European banks held large amounts of assets as mortgage - backed securities derived from the U.S. housing market, which crashed after 2006. How does this demonstrate both a benefit and a cost to the internationalization of financial markets? The international trade of mortgage - backed securities is generally beneficial in that the European banks that held the mortgages could earn a return on those holdings, while providing needed capital to U.S. financial markets to support borrowing for new home construction and other productive uses. In this sense, both European banks and U.S. borrowers should have benefitted. However, with the sharp decline in the U.S. housing market, default rates on mortgages rose sharply, and the value of the mortgage - backed securities held by European banks fell sharply. Even though the financial crisis began primarily in the United States as a housing downturn, it significantly affected European markets; Europe would have been much less affected without such internationalization of financial markets.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 66 10. How does risk sharing benefit both financial intermediaries and private investors? Financial intermediaries benefit by carrying risk at relatively low transaction costs. Since higher risk assets on average earn a higher return, financial intermediaries can earn a profit on a diversified portfolio of risky assets. Individual investors benefit by earning returns on a pooled collection of assets issued by financial intermediaries at lower risk. The financial intermediary lowers risk to individual investors through the pooling of assets. 11. How can the adverse selection problem explain why you are more likely to make a loan to a family member than to a stranger? Because you know your family member better than a stranger, you know more about the borrower’s honesty, propensity for risk - taking, and other traits. There is less asymmetric information than with a stranger and less likelihood of an adverse selection problem, with the result that you are more likely to lend to the family member. 12. One of the factors contributing to the financial crisis of 2007 – 2009 was the widespread issuance of subprime mortgages. How does this demonstrate adverse selection? The issuance of subprime mortgages represents lenders loaning money to the pool of potential homeowners who are the highest credit risk and have the lowest net wealth and other financial resources. In other words, this group of borrowers most in need of mortgage credit was also the highest risk to lenders, a perfect example of adverse selection. 13. Why do loan sharks worry less about moral hazard in connection with their borrowers than some other lenders do? Loan sharks can threaten their borrowers with bodily harm if borrowers take actions that might jeopardize their paying off the loan. Hence , borrowers from a loan shark are less likely to increase moral hazard. 14. If you are an employer, what kinds of moral hazard problems might you worry about with regard to your employees? They might not work hard enough while you are not looking or may steal or commit fraud. 15. If there were no asymmetry in the information that a borrower and a lender had, could a moral hazard problem still exist? Yes, because even if you know that a borrower is taking actions that might jeopardize paying off the loan, you must still stop the borrower from doing so. Because that may be costly, you may not spend the time and effort to reduce moral hazard, and so the problem of moral hazard still exists.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 67 16. “In a world without information costs and transaction costs, financial intermediaries would not exist.” Is this statement true, false, or uncertain? Explain your answer. True. If there are no informational or transactions costs, people could make loans to each other at no cost and would thus have no need for financial intermediaries. 17. Why might you be willing to make a loan to your neighbor by putting funds in a savings account earning a 5% interest rate at the bank and having the bank lend her the funds at a 10% interest rate, rather than lend her the funds yourself? Because the costs of making the loan to your neighbor are high (legal fees, fees for a credit check, and so on), you will probably not be able earn 5% on the loan after your expenses even though it has a 10% interest rate. You are better off depositing your savings with a financial intermediary and earning 5% interest. In addition, you are likely to bear less risk by depositing your savings at the bank rather than lending them to your neighbor. 18. How do conflicts of interest make the asymmetric information problem worse? Potentially competing interests may lead an individual or firm to conceal information or disseminate misleading information. A substantial reduction in the quality of information in financial markets increases asymmetric information problems and prevents financial markets from channeling funds into the most productive investment opportunities. Consequently, the financial markets and the economy become less efficient. That is, false information as a result of a conflict of interest can lead to a more inefficient allocation of capital than just asymmetric information alone. 19. How can the provision of several types of financial services by one firm be both beneficial and problematic? Financial firms that provide multiple types of financial services can be more efficient through economies of scope, that is, by lowering the cost of information production. However, this can be problematic since it can also lead to conflicts of interest, in which the financial firm provides false or misleading information to protect its own interests. This can lead to a worsening of the asymmetric information problem, making financial markets less efficient. 20. If you were going to get a loan to purchase a new car, which financial intermediary would you use: a credit union, a pension fund, or an investment bank? You would likely use a credit union if you were a member, since their primary business is consumer loans. In some cases , it is possible to borrow directly from pension funds, but it can come with high borrowing costs and tax implications. Investment banks do not provide loans to the general public.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 68 21. Why would a life insurance company be concerned about the financial stability of major corporations or the health of the housing market? Most life insurance companies hold large amounts of corporate bonds and mortgage assets, thus poor corporate profits or a downturn in the housing market can significantly adversely impact the value of asset holdings of insurance companies. 22. In 2008, as a financial crisis began to unfold in the United States, the FDIC raised the limit on insured losses to bank depositors from $100,000 per account to $250,000 per account. How would this help stabilize the financial system? During the financial panic, regulators were concerned that depositors worried their banks would fail, and that depositors (especially with accounts over $100,000) would pull money from banks, leaving cash - starved banks with even less cash to satisfy customer demands and day - to - day operations. This could create a contagious bank panic in which otherwise healthy banks would fail. Raising the insurance limit would reassure depositors that their money was safe in banks and prevent a bank panic, helping to stabilize the financial system. 23. Financial regulation is similar, but not exactly the same, in industrialized countries. Discuss why it might be desirable — or undesirable — to have the same financial regulation across industrialized countries. This is a topic for which there is no clear answer. On one side, it would be beneficial to have financial regulations that are identical in all countries to avoid financial markets participants to migrate their business to countries with fewer regulations. On the other side, all countries are different and designing a common set of financial regulations seems to be a rather difficult task. Most countries would want to maintain at least part of their regulations, so consensus is difficult to reach. ANSWERS TO APPLIED PROBLEMS 24. Suppose you have just inherited $10,000 and are considering the following options for investing the money to maximize your return: Option 1 : Put the money in an interest - bearing checking account that earns 2%. The FDIC insures the account against bank failure. Option 2 : Invest the money in a corporate bond with a stated return of 5%, although there is a 10% chance the company could go bankrupt. Option 3 : Loan the money to one of your friend’s roommates, Mike, at an agreed - upon interest rate of 8%, even though you believe there is a 7% chance that Mike will leave town without repaying you. Option 4: Hold the money in cash and earn zero return.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 69 a. If you are risk - neutral ( i.e. , neither seek out nor shy away from risk), which of the four options should you choose to maximize your expected return? ( Hint: To calculate the expected return of an outcome, multiply the probability that an event will occur by the outcome of that event.) b. Suppose Option 3 and Option 4 are your only choices. If you could pay your friend $100 to find out extra information about Mike that would indicate with certainty whether he will leave town without paying, would you pay the $100? What does this say about the value of better information regarding risk? a. With Option 1, since deposits are insured it can be assumed a riskless investment. Thus, the expected total payoff would be $10,000 × 1.02 = $10,200. With Option 2, a bond return of 5% implies a potential payoff of $10,000 × 1.05 = $10,500, and there is a 90% chance that this outcome will occur, thus the expected payoff is $10,500 × 0.9 = $9450. Under Option 3, the expected payoff is $10,000 × 1.08 × 0.93 = $10,044. Option 4 is riskless, so the expected total payoff is $10,000. Given these choices and the assumption that you don’t care about risk, Option 1 is the best investment. b. Option 3 implies the very real possibility of either receiving nothing (if he actually leaves town), or $10,800 (if he indeed pays as promised). If you don’t pay Mike, you have an expected return of $10,044 as shown above. If you paid your friend the $100 and learned that Mike would leave without paying, then obviously you wouldn’t loan Mike the money, and you would be left with $9900. However, if you paid the friend $100 and learned that Mike would pay, you would have $10,700 (= $10,000 × 1.08 - $100). After paying your friend Mike, but before knowing the true outcome, your expected return would be $10,644 ($9900 × 0.07 + $10,700 × 0.93). Under Option 3, paying your friend the $100 is definitely worth it because it increases your expected return and in addition dramatically reduces the downside risk that you make a bad loan, and increases the certainty of the payoff amount. That is, with asymmetric information (not paying your roommate), you have a range of payoffs of $0 to $10,800 versus $9900 to $10,700 without asymmetric information. Thus, paying a small amount to improve risk assessment under Option 3 can be very beneficial, a task for which financial intermediaries are well suited. Option 4 is riskless, so the expected total payoff is $10,000. If you are more risk averse, Option 4 is likely the better option. However, if you are more risk neutral then paying your roommate the $100 to have a minimum $9900 payment and possibly as much as $10,700 is the better scenario.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 70 ANSWERS TO DATA ANALYSIS PROBLEMS 1. Go to the St. Louis Federal Reserve FRED database, and find data on federal debt held by the Federal Reserve (FDHBFRBN), by private investors (FDHBPIN), and by international and foreign investors (FDHBFIN). Using these series, calculate the total amount held and the percentage held in each of the three categories for the most recent quarter available. Repeat for the first quarter of 2000 and compare the results. See table. Since the year 2000, the Fed has increased its share of federal debt held, and foreign investors have significantly increased its share of debt held. This reflects a significant decline in the share of federal debt held by private investors. 2017:Q1 2000:Q1 Held ($bil.) % Share Held ($bil.) % Share Fed 2859.1 13.7 501.7 10.5 Private Investors 11904.8 57.1 3182.8 66.7 Foreign Investors 6079.3 29.2 1085.0 22.7 Total 20843.2 4769.5 2. Go to the St. Louis Federal Reserve FRED database, and find data on the total assets of all commercial banks (TLAACBM027SBOG) and the total assets of money market mutual funds (MMMFFAQ027S). Transform the commercial bank assets series to quarterly by adjusting the Frequency setting to “Quarterly.” Calculate the percent increase in growth of assets for each series, from January 2000 to the most recent quarter available. Which of the two financial intermediaries has experienced the most growth? See table below. Commercial bank assets have increased by 187% from 2000:Q1 to 2017:Q1, while money market mutual fund assets have increased also, but by less than commercial banks during that time, at 57.1%. 2017:Q1 2000:Q1 Commercial Banks $16,158.7 Bil. $5,639.9 Bil. Money Market Mutual Funds $2,664.3 Bil. $1,696.1 Bil.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 71 Chapter 3 ANSWERS TO QUESTIONS 1. Why is simply counting currency an inadequate measure of money? Since a lot of other assets have liquidity properties that are similar to currency but can be used as money to purchase goods and services, not counting them would understate an economy’s access to liquidity for transactions purposes. For this reason, counting assets such as checking deposits or savings accounts more accurately reflects the stock of assets that can be considered money. 2. In prison, cigarettes are sometimes used among inmates as a form of payment. How is it possible for cigarettes to solve the “double coincidence of wants” problem, even if a prisoner does not smoke? Even if he or she were a nonsmoker, since the prisoner knows that others in the prison will accept cigarettes as a form of payment, they themselves would be willing to accept cigarettes as a form of payment. So, rather than prisoners having to barter and trade favors, cigarettes satisfy the double coincidence of wants in that both parties to a trade stand ready to use them to “purchase” goods or services. 3. Three goods are produced in an economy by three individuals: Good Producer Apples Orchard Owner Bananas Banana Grower Chocolate Chocolatier If the orchard owner likes only bananas, the banana grower likes only chocolate, and the chocolatier likes only apples, will any trade between these three persons take place in a barter economy? How will introducing money into the economy benefit these three producers? Because the orchard owner likes only bananas but the banana grower doesn’t like apples, the banana grower will not want apples in exchange for his bananas, and they will not trade. Similarly, the chocolatier will not be willing to trade with the banana grower because she does not like bananas. The orchard owner will not trade with the chocolatier because he doesn’t like chocolate. Hence, in a barter economy, trade among these three people may well not take place, because in no case is there a double coincidence of wants. However, if money is introduced into the economy, the orchard owner can sell his apples to the chocolatier and then use the money to buy bananas from the banana grower. Similarly, the banana grower can use the money he receives from the orchard owner to buy chocolate from the chocolatier, and the chocolatier can use the money to buy apples from the orchard owner. The result is that the need for a double coincidence of wants is eliminated, and everyone is better off because all three producers are now able to eat what they like best.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 72 4. Why did cavemen not need money? Cavemen did not need money. In their primitive economy, they did not specialize in producing one type of good and they had little need to trade with other cavemen. 5. Most of the time it is quite difficult to separate the three functions of money. Money performs its three functions at all times, but sometimes we can stress one in particular. For each of the following situations, identify which function of money is emphasized. a. Brooke accepts money in exchange for performing her daily tasks at her office, since she knows she can use that money to buy goods and services. This situation illustrates the medium - of - exchange function of money. We often do not think why we accept money in exchange for hours spent working, as we are so accustomed to using money. The medium - of - exchange function of money refers to its ability to facilitate trades (hours worked for money and then money for groceries) in a society. b. Tim wants to calculate the relative value of oranges and apples, and therefore checks the price per pound of each of these goods as quoted in currency units. In this case , we observe money performing its unit - of - account function. If modern societies did not use money as a unit of account, then the price of apples would have to be quoted in terms of all the other items in the market. This quickly becomes an impossible task. Suppose that a pound of apples sells for 0.80 pounds of oranges, half a gallon of milk, one - third of a pound of meat, 2 razor blades, 1.5 pound of potatoes, etc. c. Maria is currently pregnant. She expects her expenditures to increase in the future and decides to increase the balance in her savings account. Maria is contemplating the store - of - value function of money. As a medium of exchange and unit of account, measures of money known as M1 or M2 have no important rivals. With respect to the store - of - value function, however, there are many assets that can preserve value better than a checking account. Maria’s choice to preserve the purchasing power of her income by increasing her savings account balance is fine for a small period of time. For a period of 20 years, however, you might choose to buy a U.S. Treasury bond that matures in 20 years (as many grandparents have done as a way to pay for their grandchildren’s educations). 6. In Brazil, a country that underwent a rapid inflation before 1994, many transactions were conducted in dollars rather than in reals, the domestic currency. Why? Because of the rapid inflation in Brazil, the domestic currency, the real, was a poor store of value. Thus , many people preferred to hold dollars, which were a better store of value, and used them in their daily shopping.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 73 7. Was money a better store of value in the United States in the 1950s than in the 1970s? Why or why not? In which period would you have been more willing to hold money? Because money was losing value at a slower rate (the inflation rate was lower) in the 1950s than in the 1970s, it was a better store of value then, and you would have been willing to hold more of it. 8. Why have some economists described money during a hyperinflation as a “hot potato” that is quickly passed from one person to another? Money loses its value at an extremely rapid rate in hyperinflation, so you want to hold it for as short a time as possible. Thus money is like a hot potato that is quickly passed from one person to another. 9. Why were people in the United States in the nineteenth century sometimes willing to be paid by check rather than with gold, even though they knew there was a possibility that the check might bounce? Because a check was so much easier to transport than gold, people would frequently rather be paid by check even if there was a possibility that the check might bounce. In other words, the lower transactions costs involved in handling checks made people more willing to accept them. 10. In ancient Greece, why was gold a more likely candidate for use as money than wine? Wine is more difficult to transport than gold and is also more perishable. Gold is thus a better store of value than wine and also leads to lower transactions cost. It is therefore a better candidate for use as money. 11. If you use an online payment system such as PayPal to purchase goods or services on the Internet, does this affect the M1 money supply, the M2 money supply, both, or neither? Explain. Neither. Although PayPal and many other e - money systems work as other forms of money do to facilitate purchases of goods and services, it does not count in the M1 or M2 money supplies. Because PayPal and similar payment systems are generally credit - based, this requires payment at a future date for funds used today; those future payments must be made using existing money that is already in the system, such as currency or funds in a bank deposit account. In other words, the M1 and M2 money supplies would theoretically remain the same, but money would move from your checking account to a third party, once the credit transaction is settled.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 74 12. Rank the following assets from most liquid to least liquid: a. Checking account deposits b. Houses c. Currency d. Automobiles e. Savings deposits f. Common stock The ranking from most liquid to least liquid is (c), (a), (e), (f), (d), and (b). 13. Which of the Federal Reserve’s measures of the monetary aggregates — M1 or M2 — is composed of the most liquid assets? Which is the larger measure? M1 contains the most liquid assets. M2 is the largest measure. 14. It is not unusual to find a business that displays a sign saying “no personal checks, please.” On the basis of this observation, comment on the relative degree of liquidity of a checking account versus currency. The degree of liquidity of an asset is measured by considering how much time and effort (i.e., transaction costs) are needed to convert that asset into currency. Currency is by definition the most liquid type of money. Different types of money have different degrees of liquidity. A check, which represents a balance on a checking account, is a quite liquid type of money. After all, all that is needed to pay for a good or service using a check is the two minutes it takes to include the date and amount and sign the check. However, the above example shows that some merchants refuse to accept checks as a means of payment. (They cannot refuse to accept dollars, as dollars are legal tender in the United States.) This can result in significant transaction costs in trying to find a bank or an ATM. It is even possible that the transaction never takes place. This example illustrates the point that even inside the same monetary aggregate, different types of money do not have the same degree of liquidity. 15. For each of the following assets, indicate which of the monetary aggregates (M1 and M2) includes them: a. Currency b. Money market mutual funds c. Small - denomination time deposits d. Checkable deposits a. M1 and M2 b. M2 c. M2 d. M1 and M2

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 75 16. Assume that you are interested in earning some return on the idle balances you usually keep in your checking account and decide to buy some money market mutual funds shares by writing a check. Comment on the effect of your action (with everything else the same) on M1 and M2. Your actions will reduce your checking account balance and increase your holdings of money market mutual fund shares. Considering this transaction only, M1 will decrease as one of its components decreased. M2 will remain constant, as M2 is composed of all items that add up to M1 plus some other types of money that are not so liquid to be considered part of M1. One of these categories is money market mutual fund shares. The decrease in your checking account balance is offset by the increase in money market mutual fund shares, and therefore M2 remains constant. 17. In April 2009, the growth rate of M1 fell to 6.1%, while the growth rate of M2 rose to 10.3%. In September 2013, the year - over - year growth rate of the M1 money supply was 6.5%, while the growth rate of the M2 money supply was about 8.3%. How should Federal Reserve policymakers interpret these changes in the growth rates of M1 and M2? During the period in question, the M1 growth rate fell by 0.4%, while the M2 growth rate increased by 2.0%. Because these growth rates moved in opposite directions, it is difficult to judge the appropriateness of monetary policy by just looking at the money supply measures alone. One measure indicates that monetary policy is more expansionary, while the other indicates the opposite. 18. Suppose a researcher discovers that a measure of the total amount of debt in the U.S. economy over the past twenty years was a better predictor of inflation and the business cycle than M1 or M2. Does this discovery mean that we should define money as equal to the total amount of debt in the economy? Not necessarily. Although the total amount of debt has predicted inflation and the business cycle better than M1 or M2, it may not be a better predictor in the future. Without some theoretical reason for believing that the total amount of debt will continue to predict well in the future, we may not want to define money as the total amount of debt.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 76 ANSWERS TO APPLIED PROBLEMS Q.19 The table below shows hypothetical values, in billions of dollars, of different forms of money. a. Use the table to calculate the M1 and M2 money supplies for each year, as well as the growth rates of the M1 and M2 money supplies from the previous year. b. Why are the growth rates of M1 and M2 so different? Explain. 2018 2019 2020 2021 A. Currency 900 920 925 931 B. Money market mutual fund shares 680 681 679 688 C. Saving account deposits 5,500 5,780 5,968 6,105 D. Money market deposit accounts 1,214 1,245 1,274 1,329 E. Demand and checkable deposits 1,000 972 980 993 F. Small denomination time deposits 830 861 1,123 1,566 G. Traveler’s checks 4 4 3 2 H. 3 - month treasury bills 1,986 2,374 2,436 2,502 19. The M1 money supply is the sum of rows A, E, and G for each year. The M2 money supply is the sum of all components A – G for each year. Note that 3 - month treasury bills are not considered part of the M1 or M2 money supply, even though they are fairly liquid assets. The table below shows the M1 and M2 money supplies, along with the growth rates from the previous year. Note that while the M1 money supply is relatively flat (and slightly negative for 2019), the M2 money supply grows at a much higher, positive rate. This is because the components of M2 are rising much more rapidly compared to the components of M1 (which are also included in M2). In particular, small denomination time deposits increase 30% from 2019 to 2020, and 39% from 2020 to 2021, driving much of the growth in M2. Moreover, the narrower components that make up just the M1 money supply represent less than 20% (1904/10128) of the broader M2 indicators. Thus , movements in the money market, savings account, and time deposit measures will have a much bigger impact on M2 growth than the narrower M1 components will. 2018 2019 2020 2021 A. Currency 900 920 925 931 B. Money market mutual fund shares 680 681 679 688 C. Saving account deposits 5,500 5,780 5,968 6,105

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 77 D. Money market deposit accounts 1,214 1,245 1,274 1,329 E. Demand and checkable deposits 1, 000 972 980 993 F. Small denomination time deposits 830 861 1,123 1,566 G. Traveler’s checks 4 4 3 2 H. 3 - month treasury bills 1,986 2,374 2,436 2,502 Total M1 money stock 1904 1896 1908 1926 Total M2 money s tock 10128 10463 10952 11614 M1 growth rate − 0.4 0.6 0.9 M2 growth rate 3.3 4.7 6 ANSWERS TO DATA ANALYSIS PROBLEMS 1. Go to the St. Louis Federal Reserve FRED database, and find data on currency (CURRSL), traveler’s checks (TVCKSSL), demand deposits (DEMDEPSL), and other checkable deposits (OCDSL). Calculate the M1 money supply and calculate the percentage change in M1 and in each of the four components of M1 from the most recent month of data available to the same time one year prior. Which component has the highest growth rate? The lowest growth rate? Repeat the calculations using the data from January 2000 to the most recent month of data available and compare your results. See tables below, showing calculations from the May 2017 benchmark period. Over the one year period from May 2016 to May 2017, demand deposits grew the fastest at 9.1%, while traveler’s checks grew the least, shrinking by 12.5% over the period. A similar result holds over the longer period from May 2017 to January 2000; use of traveler’s checks experienced a substantial decline of 75.3%, while demand deposits increased by 323.1%. May 2017 May 2016 January 2000 Currency $1468.5 Bil. $1375.4 Bil. $524.9 Bil. Traveler ’ s Checks $2.1 Bil. $2.4 Bil. $8.5 Bil. Dema nd Deposits $1465.2 Bil. %1342.8 Bil. $346.3 Bil. Other Checkable Deposits $569.8 Bil. $525.3 Bil. $242.4 Bil. M1 $3505.6 Bil. $3245.9 Bil. $1122.1 Bil.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 78 May 2016 to May 2017 January 2000 to May 2017 Currency 6.8% 179.8% Traveler ’ s Checks − 12.5% − 75 .3% Demand Deposits 9.1% 323.1% Other Checkable Deposits 8.5% 135.1% M1 8.0% 212.4% 2. Go to the St. Louis Federal Reserve FRED database, and find data on small - denomination time deposits (STDSL), savings deposits and money market deposit accounts (SAVINGSL), and retail money market funds (RMFSL). Calculate the percentage change of each of these three components of M2 (not included in M1) from the most recent month of data available to the same time one year prior. Which component has the highest growth rate? The lowest growth rate? Repeat the calculations using the data from January 2000 to the most recent month of data available and compare your results. Use your answers from question 1 to determine which grew faster: the non - M1 components of M2 or the M1 money supply. See tables below, showing calculations from the May 2017 benchmark period. Over the one year period from May 2016 to May 2017, savings deposits grew the fastest at 6.6%, while small time deposits grew the least, decreasing by 9.5% over the period. A similar result holds for the period January 2000 to May 2017; savings deposits grew a substantial amount, at 414.6% over the period, while small time deposits decreased significantly, by 63.8%. Overall, the M1 money supply grew more over the one - year period (8.0% versus 5.2%) and the longer period 212.4% versus 183.9%) than the non - M1 components that make up M2 ; however , the non - M1 components of M2 are much larger in size than the M1 components, so will have a larger influence overall on the M2 money supply. May 2017 May 2016 January 2000 Small Time Deposits $349.0 Bil. $385.7 Bil. $963.4 Bil. Savings/MMDA $8962.0 Bil. $8405.9 Bil. $1741.6 Bil. Retail MMMF $679.4 Bil. $704.8 Bil. $814.4 Bil. Non - M1 M2 $9990.4 Bil. $9496.4 Bil. $3519.4 Bil. M1 $3505.6 Bil. $3245.8 Bil. $1122.2 Bil.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 79 May 2016 to May 2017 January 2000 to May 2017 Small Time Deposits − 9.5% − 63.8% Savings/MMDA 6.6% 414.6% Retail MMMF − 3.6% − 16.6% Non - M1 M2 5.2% 183.9% M1 8.0% 212.4%

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 80 Chapter 4 ANSWERS TO QUESTIONS 1. Would a dollar tomorrow be worth more to you today when the interest rate is 20% or when it is 10%? It would be worth 1/(1 + 0.20) = $0.83 when the interest rate is 20%, rather than 1/(1 + 0.10) = $0.91 when the interest rate is 10%. Thus, a dollar tomorrow is worth less with a higher interest rate today. 2. Explain which information you would need to take into consideration when deciding to receive $5,000 today or $5,500 one year from today. When comparing amounts of money that are disbursed at different dates, one has to take into consideration the concept of present value of money. To calculate the present value of the $5,500 promised one year from today one needs to know the annual interest rate. In this case, for an interest rate larger than 10%, one would prefer to accept the $5,000 today (since one can deposit that amount and receive more than $5,500 one year from today). 3. To help pay for college, you have just taken out a $1,000 government loan that makes you pay $126 per year for 25 years. However, you don’t have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than 12%? (This is the yield to maturity on a normal $1,000 fixed - payment loan on which you pay $126 per year for 25 years.) If the interest rate were 12%, the present discounted value of the payments on the government loan are necessarily less than the $1,000 loan amount because they do not start for two years. Thus , the yield to maturity must be lower than 12% in order for the present discounted value of these payments to add up to $1,000. 4. Do bondholders fare better when the yield to maturity increases or when it decreases? Why? When the yield to maturity increases, this represents a decrease in the price of the bond. If the bondholder were to sell the bond at a lower price, the capital gains would be smaller (capital losses larger) , and therefore , the bondholder would be worse off.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 81 5. Suppose today you buy a coupon bond that you plan to sell one year later. Which part of the rate of return formulation incorporates future changes into the bond? Note: Check Equations 7 and 8 in this chapter. The rate of capital gain is the part of the rate of return formula that incorporates future changes in the price of the bond. The other part of the formula, the current yield, is composed of the coupon payment (completely determined by the bond´s face value and coupon rate) and the price you paid for the bond today. The rate of capital gain incorporates the future price of the bond and is therefore the part of the formula that reflects the consequences of future price changes. 6. If mortgage rates rise from 5% to 10% , but the expected rate of increase in housing prices rises from 2% to 9%, are people more or less likely to buy houses? People are more likely to buy houses because the real interest rate when purchasing a house has fallen from 3% ( = 5 – 2%) to 1% ( = 10 – 9%). The real cost of financing the house is thus lower, even though nominal mortgage rates have risen. (If the tax deductibility of interest payments is allowed for, then it becomes even more likely that people will buy houses.) 7. When is the current yield a good approximation of the yield to maturity? The current yield will be a good approximation to the yield to maturity whenever the bond price is very close to par or when the maturity of the bond is over about ten years. This is because cash flows farther in the future have such small present discounted values that the value of a long - term coupon bond is close to a perpetuity with the same coupon rate. 8. Why would a government choose to issue a perpetuity, which requires payments forever, instead of a terminal loan, such as a fixed - payment loan, discount bond, or coupon bond? The near - term costs to maintaining a given size loan are much smaller for a perpetuity than for a similar fixed payment loan, discount, or coupon bond. For instance, assuming a 5% interest rate over 10 years, on a $1000 loan, a perpetuity costs $50 a year (or $500 in payments over 10 years). For a fixed payment loan, this would be $129.50 per year (or $1295 in payments over the same 10 - year period). For a discount loan, this loan would require a lump sum payment of $1628.89 in 10 years. For a coupon bond, assuming the same $50 coupon payment as the perpetuity implies a $1000 face value. Thus, for the coupon bond, the total payments at the end of 10 years will be $1500. 9. Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate? Whenever the current price P is greater than face value F of a discount bond, the yield to maturity will be negative. It is possible for a coupon bond to have a negative nominal interest rate, as long as the coupon payment and face value are low relative to the current price. As an example, with a one - year coupon bond, the yield to maturity is given as i = ( C + F – P )/ P ; in

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 82 this case whenever C + F < P , i will be negative. It is impossible for a perpetuity to have a negative nominal interest rate, since this would require either the coupon payment or the price to be negative. 10. True or False: With a discount bond, the return on the bond is equal to the rate of capital gain. True. The return on a bond is the current yield i C plus the rate of capital gain, g. A discount bond, by definition, has no coupon payments, thus the current yield is always zero (the coupon payment of zero divided by current price) for a discount bond. 11. If interest rates decline, which would you rather be holding, long - term bonds or short - term bonds? Why? Which type of bond has the greater interest - rate risk? You would rather be holding long - term bonds because their price would increase more than the price of the short - term bonds, giving them a higher return. Longer - term bonds are more susceptible to higher price fluctuations than shorter - term bonds, and hence have greater interest - rate risk. 12. Interest rates were lower in the mid - 1980s than in the late 1970s, yet many economists have commented that real interest rates were actually much higher in the mid - 1980s than in the late 1970s. Does this make sense? Do you think that these economists are right? The economists are right. They reason that nominal interest rates were below expected rates of inflation in the late 1970s, making real interest rates negative. The expected inflation rate, however, fell much faster than nominal interest rates in the mid - 1980s, so nominal interest rates were above the expected inflation rate and real rates became positive. 13. Retired persons often have much of their wealth placed in savings accounts and other interest - bearing investments and complain whenever interest rates are low. Do they have a valid complaint? While it would appear to them that their wealth is declining as nominal interest rates fall, as long as expected inflation falls at the same rate as nominal interest rates, their real return on savings accounts will be unaffected. However, in practice, expected inflation as reflected by the cost of living for seniors and retired persons often is much higher than standard measures of inflation, thus low nominal rates can adversely affect the wealth of senior citizens and retired persons.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 83 ANSWERS TO APPLIED PROBLEMS 14. If the interest rate is 10%, what is the present value of a security that pays you $1,100 next year, $1,210 the year after, and $1,331 the year after that? $1,100/(1 + 0.10) + $1,210/(1 + 0.10) 2 + $1,331/(1 + 0.10) 3 = $3,000. 15. Calculate the present value of a $1,000 discount bond with five years to maturity if the yield to maturity is 6% PV = FV /(1 + i ) n , where FV = 1000, i = 0.06, n = 5. Thus, PV = 747.26. 16. A lottery claims its grand prize is $10 million, payable over 5 years at $2,000,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use an interest rate of 6%. In present value terms, the lottery prize is worth $2,000,000 + $2,000,000/(1.06) + $2,000,000/(1.06) 2 + $2,000,000/(1.06) 3 + $2,000,000/(1.06) 4 , or $8,930,211. 17. Suppose that a commercial bank wants to buy Treasury bills. These instruments pay $5,000 in one year and are currently selling for $5,012. What is the yield to maturity of these bonds? Is this a typical situation? Why? The yield to maturity of these bonds solves the following equation: 5,000/(1+i) = 5,012. After some algebra, the yield to maturity happens to be around – 0.24%. This is not a typical situation. In normal times , banks will not choose to pay more than the face value of a discount bond, since that implies negative yields to maturity. This example illustrates situations as the ones described in the Global Box in this chapter. 18. What is the yield to maturity on a simple loan for $1 million that requires a repayment of $2 million in five years’ time? 14.9%, derived as follows: The present value of the $2 million payment five years from now is $2/(1 + i ) 5 million, which equals the $1 million loan. Thus 1 = 2/(1 + i ) 5 . Solving for i , (1 + i ) 5 = 2, so that 5 2 1 0.149 14.9%. i = − = = 19. Which $1,000 bond has the higher yield to maturity, a twenty - year bond selling for $800 with a current yield of 15% or a one - year bond selling for $800 with a current yield of 5%? If the one - year bond did not have a coupon payment, its yield to maturity would be ($1,000 – $800)/ $800 = $200/$800 = 0.25, or 25%. Because it does have a coupon payment, its yield to maturity must be greater than 25%. However, because the current yield is a good approximation of the yield to maturity for a twenty - year bond, we know that the yield to maturity on this bond is approximately 15%. Therefore, the one - year bond has a higher yield to maturity.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 84 20. Consider a bond with a 4% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price? Years to Maturity Yield to Maturity Current Price 2 2% 2 4% 3 4% 5 2% 5 6% Years to Maturity Yield to Maturity Current Price 2 2% 1038.83 2 4% 1000.00 3 4% 1000.00 5 2% 1094.27 5 6% 915.75 21. Consider a coupon bond that has a $1,000 par value and a coupon rate of 10%. The bond is currently selling for $1,044.89 and has two years to maturity. What is the bond’s yield to maturity? When yield to maturity is above the coupon rate, the bond’s current price is below its face value. The opposite holds true when yield to maturity is below the coupon rate. For a given maturity, the bond’s current price falls as yield to maturity rises. For a given yield to maturity, a bond’s value rises as its maturity increases. When yield to maturity equals the coupon rate, a bond’s current price equals its face value regardless of years to maturity. 22. What is the price of a perpetuity that has a coupon of $50 per year and a yield to maturity of 2.5%? If the yield to maturity doubles, what will happen to the perpetuity’s price? $1044.89 = $100/(1 + i ) + $100/(1 + i ) 2 + $1,000/(1 + i ) 2 . Solving for i gives a yield to maturity of 0.075, or 7.5%.

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    Mishkin • Instructor’s Manual for The Economics of Money, Banking, and Financial Markets , Business School Edition, Fifth Edition 85 23. Property taxes in a particular district are 4% of the purchase price of a home every year. If you just purchased a $250,000 home, what is the present value of all the future property tax payments? Assume that the house remains worth $250,000 forever, property tax rates never change, and a 6% interest rate is used for discounting. The price would be $50/0.025 = $2000. If the yield to maturity doubles to 5%, the price would fall to half its previous value, to $1000 = $50/0.05. 24. A $1000 - face - value bond has a 10% coupon rate, its current price is $960, and its price is expected to increase to $980 next year. Calculate the current yield, the expected rate of capital gain, and the expected rate of return. The taxes on the $250,000 home are $250,000  0.04 = $10,000 per year. The PV of all future payments = $10,000/0.06 = $166,666.67 (a perpetuity). 25. Suppose that you want to take out a loan and that your local bank wants to charge you an annual real interest rate equal to 3%. Assuming that the annualized expected rate of inflation over the life of the bond is 1%, determine the nominal interest rate that the bank will charge you. What happens if, over the life of the loan, actual inflation is 0.5%? The bank will charge you a nominal interest rate equal to 1% + 3% = 4%. However, if actual inflation turns out to be lower than expected, then you will be worse off than originally planned, since the real cost of borrowing (measured by the real interest rate) turned out to be 4 – 0.5% = 3.5%.

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