Business Finance Module 2
Fiona plans to invest $500 later today. She wants to know to what amount her investment will grow in 20 years if she earns 12 percent interest compounded (a) annually, (b) quarterly, and (c) monthly.
A) FV20 = $500(1.12)20 = $500(9.64629) = $4,823.15 B) FV20 = $500(1.03)80 = $500(10.64089) = $5,320.45 C) FV20 = $500(1.01)240 = $500(10.89255) = $5,446.28
Suppose you invest $385 at the end of each of the next eight years. (a) If your opportunity cost rate is 7 percent compounded annually, how much will your investment be worth after the last $385 payment is made? (b) What will be the ending amount if the payments are made at the beginning of each year?
A) FVA = 385[((1.07)^8-1)/.07] = 385(10.259803) = 3950.02 B) FVA(DUE) = 385{[((1.07)^8-1)/.07]*1.07} = 385(10.977989) = 4226.53
At the end of each of the past 14 years, Vanessa deposited $450 in an account that earned 8 percent compounded annually. (a) How much is in the account today? (b) How much would be in the account if the deposits were made at the beginning each year rather than at the end of each year?
A) FVA = 450[((1.08)^14-1)/.07] = 450(24.214920) = 10896.71 B) FVA(DUE) = 450{[((1.08)^14-1)/.08]*1.08} = 450(24.214920) = 11768.45
What is the present value of $1,500 due in 14 years at a (a) 5 percent interest rate and (b) 10 percent rate. Explain why the present value is lower when the interest rate is higher.
A) PV = $1,500/(1.05)14 = $1,500(0.505068) = $757.60) B) PV = $1,500/(1.10)14 = $1,500(0.263331) = $395.00 In this problem, we showed that if a person wants an investment to be worth $1,500 in 14 years and the opportunity cost rate was 5 percent, he or she would have to invest $757.60 today. On the other hand, if the opportunity cost rate was 10 percent, more interest would be earned over the 14-year investment period, which means that the investor would only need to invest $395 today to end up with $1,500 in 14 years. Simply stated, the more interest you can earn during an investment period, the less you need to invest today to receive a particular amount in the future.
What is the present value (PV) of an investment that will pay $2,500 in five years if the opportunity cost rate is 9 percent compounded (a) annually, (b) quarterly, and (c) monthly? Explain why the PV is lowest when interest is compounded monthly.
A) PV = $2,500/(1.09)5 = $2,500(0.649931) = $1,624.83 B) PV = $2,500/(1.0225)20 = $2,500(0.640816) = $1,602.04 C) PV = $2,500/(1.0075)60 = $2,500(0.638700) = $1,596.75 The more interest you can earn during an investment period, the less you need to invest today to receive a particular amount in the future. Everything else equal, more interest is earned when more compounding occurs. Stated differently, when more compounding occurs, the effective annual rate of return on an investment is greater, which means more interest is earned.
Suppose your opportunity cost rate is 11 percent compounded annually. (a) How much must you deposit in an account today if you want to pay yourself $230 at the end of each of the next 15 years? (b) How much must you deposit if you want to pay yourself $230 at the beginning of each of the next 15 years?
A) PVA = 230[(1-(1.11)^-15)/.11] = 230(7.190870) = 1653.90 B) PVA = 230{[(1-(1.11)^-15)/.11]*1.11} = 230(7.981865) = 1835.83
Do you think investors can earn abnormal returns in financial markets that are at least semistrong-form efficient?
Even when financial markets are informationally efficient, investors can earn abnormal returns. But, such opportunities should be random, which means trading rules that permit investors to earn abnormal returns on a consistent basis do not exist.
How do financial institutions in the United States differ from financial institutions in other parts of the world? Why?
Even with recent deregulation, the banking industry in the United States is very heavily regulated. U.S. banks are prohibited from many activities that banks in other countries are not, such as owning the stocks of corporations. In addition, U.S. banks are not as free as foreign banks to conduct business nationally—banking in the United States is still mostly fragmented from state to state because, even though regulations have been relaxed in the past few decades, limitations on interstate banking still exist. For these reasons, there are many more (and much smaller) banks in the United States than in other countries.
Fifteen (15) years ago, your parents purchased an investment for $2,500. If the investment earned 6 percent interest each year, how much is it worth today?
FV15 = $2,500(1.06)15 = $2,500(2.39656) = $5,991.40
If Samantha invests $700 today in an account that pays 4 percent interest compounded annually, how much will she have in her account four years from today?
FV4 = $700(1.04)4 = $700(1.16986) = $818.90
What economic functions do financial intermediaries perform?
Financial intermediaries are business organizations that receive funds in one form and repackage them for use by those who need funds. For example, a financial intermediary might bundle the savings of many depositors to create mortgages for borrowers. Through financial intermediation, resources are allocated more effectively, and the real output of the economy is thereby increased.
How do financial markets that run freely and efficiently affect the standard of living in a country?
Free and efficient financial markets allocate funds more efficiently than would occur without free financial markets. as a result the real output of the economy is increased with such financial markets; that is, the net cost of funds is lower and the net returns investors earn are higher then they would be otherwise. Stated differently, the more efficient the financial system, the lower the costs of intermediation, the lower the costs to the borrower, and, hence, the lower the prices of goods and services to consumers.
What does it mean for a financial market to be considered (a) informationally efficient and (b) economically efficient?
In economically efficient markets, funds are allocated to their optimal use at the lowest costs, which means that funds are invested in the assets that yield the highest returns and the costs associated with investing funds are lower than they would be in markets that are less economically efficient. In markets that are informationally efficient, the prices of investments reflect existing information and they adjust quickly when new information enters the markets.
Mom's Motel Corporation (MM) plans to issue bonds to raise $175 million that it needs to support future operations. MM's investment banker will charge 2.5 percent of the total amount issued to help MM raise the funds. In addition, MM will incur other costs associated with the issue that equal $500,000. The market value of each bond at issue time will be $1,000. How many bonds must MM sell to net $175 million after flotation costs? Assume that fractions of bonds cannot be issued. Show how much of the issue will consist of flotation costs and how much MM will receive after flotation costs are paid.
Net proceeds = Amount of issue - Flotation costs $175,000,000 = Amount of issue x (1 - 0.025) - $500,000 Amount of issue = ($175,000,000 + $500,000)/0.975 = $180,000,000 Number of bonds = $180,000,000/$1,000 = 180,000 bonds
United Uninsured Underwriters (U3) needs to raise $192 million. If it issues new common stock to raise the funds, the flotation costs will be 8 percent. The new issue will also require U3 to pay $280,000 in fees to its lawyers, printing costs, and other costs associated with the issue. U3 can issue stock at $25 per share. How many shares of common stock must be issued so that it has $192 million after flotation costs? Show how much of the total dollar amount will be flotation costs and how much U3 will receive after the flotation costs are paid.
Net proceeds = Amount of issue - Flotation costs $192,000,000 = Amount of issue x (1 - 0.08) - $280,000 Amount of issue = ($192,000,000 + $280,000)/0.92 = $209,000,000 Number of shares = $209,000,000/$25 = 8,360,000
Jasmine Flowers must raise $345 million for its future expansion. To do so, Jasmine expects to issue new common stock. Investment bankers have informed the company that the flotation costs will be 6.5 percent of the total amount issued and that the company will incur another $576,000 in costs associated with the issue. Jasmine can issue its stock for $55 per share. Determine how many shares Jasmine must sell to net $345 million after flotation costs.
Net proceeds = Amount of issue - Flotation costs $345,000,000 = Amount of issue x (1 - 0.065) - $576,000 Amount of issue = ($345,000,000 + $576,000)/0.935 = $369,600,000 Number of shares = $369,600,000/$55 = 6,720,000
Wilderness World (WW) needs to raise $84 million in debt. To issue the debt, WW must pay its underwriter a fee equal to 3 percent of the total issue. The company estimates that other expenses associated with the issue will total $487,000. If the face value of each bond is $1,000, how many bonds must be issued to net the needed $84 million? Assume that the firm cannot issue a fraction of a bond.
Net proceeds = Amount of issue - Flotation costs $84,000,000 = Amount of issue x (1 - 0.03) - $487,000 Amount of issue = ($84,000,000 + $487,000)/0.97 = $87,100,000 Number of bonds = $87,100,000/$1,000 = 87,100 bonds
Bushwhacker Mowing needs $360 million to support growth. If it issues new common stock to raise the funds, the flotation costs charged by the investment banker will be 4 percent. Additional costs associated with the issue will total $288,000. If Bushwhacker can issue stock at $60 per share, how many shares of common stock must be issued so that it has $360 million after flotation costs? Show how much of the issue will consist of flotation costs and how much Bushwhacker will receive after flotation costs are paid.
Net proceeds = Amount of issue - Flotation costs) $360,000,000 = Amount of issue x (1 - 0.04) - $288,000 Amount of issue = ($360,000,000 + $288,000)/0.96 = $375,300,000 Number of shares = $375,300,000/$60 = 6,255,000 shares
Bearskin Rugs needs $115 million to build a new distribution center. If it issues common stock to raise the funds, the issuance costs will be 8 percent of the total amount issued. If Bearskin can issue stock at $40 per share, how many shares of common stock must be issued so that it has $115 million after flotation costs to use to fund the construction of its distribution center?
Net proceeds = Amount of issue x (1 - Flotation costs) $115,000,000 = Amount of issue x (1 - 0.08) Amount of issue = $115,000,000/0.92 = $125,000,000 Number of shares = $125,000,000/$40 = 3,125,000 shares
Express Courier (EC) needs $141 million to support future growth. If it issues common stock to raise the needed funds, EC will have to pay its investment banker 6 percent of the issue's total value. If EC can issue common stock at a market price of $80 per share, how many shares must be issued so that the company has $141 million after flotation costs to fund the planned growth?
Net proceeds = Amount of issue x (1 - Flotation costs) $141,000,000 = Amount of issue x (1 - 0.06) Amount of issue = $141,000,000/0.94 = $150,000,000 Number of shares = $150,000,000/$80 = 1,875,000 shares
Boat Emporium (BE) must raise $225 million. To do so, BE expects to issue new common stock. BE's Investment banker will charge issuing costs equal to 10 percent of the total amount issued. If the stock can be issued for $160 per share, how many shares must BE sell to net $225 million after flotation costs. Show how much of the issue will consist of flotation costs and how much BE will receive after the flotation costs are paid.
Net proceeds = Amount of issue x (1 - Flotation costs) $225,000,000 = Amount of issue x (1 - 0.10) Amount of issue = $225,000,000/0.90 = $250,000,000 Number of shares = $250,000,000/$160 = 1,562,500 shares
Jewel Regal Cars (JRC) must raise $240 million to support operations. To do so, JRC plans to issue new bonds. Investment bankers have informed JRC that the flotation costs will be 4 percent of the total amount issued. If the market value of each bond is $1,000, how many bonds must JRC sell to net $240 million after flotation costs? Assume that fractions of bonds cannot be issued.
Net proceeds = Amount of issue x (1 - Flotation costs) $240,000,000 = Amount of issue x (1 - 0.04) Amount of issue = $240,000,000/0.96 = $250,000,000 Number of bonds = $150,000,000/$1,000 = 250,000 bonds
Grand Energy Corporation (GE) plans to issue bonds to raise $345 million. GE's investment banker will charge flotation costs equal to 8 percent of the total amount issued. The market value of each bond at issue time will be $1,000. How many bonds must GE sell to net $345 million after flotation costs? Assume that fractions of bonds cannot be issued. Show how much of the total amount issued will consist of flotation costs and how much GE will receive after flotation costs are paid.
Net proceeds = Amount of issue x (1 - Flotation costs) $345,000,000 = Amount of issue x (1 - 0.08) Amount of issue = $345,000,000/0.92 = $375,000,000 Number of bonds = $375,000,000/$1,000 = 375,000 bonds
Persian Rugs needs $600 million to support growth next year. If it issues new common stock to raise the funds, the flotation (issuance) costs will be 4 percent. If Persian can issue stock at $125 per share, how many shares of common stock must be issued so that it has $600 million after flotation costs to use for its planned growth?
Net proceeds = Amount of issue x (1 - Flotation costs) $600,000,000 = Amount of issue x (1 - 0.04) Amount of issue = $600,000,000/0.96 = $625,000,000 Number of shares = $625,000,000/$125 = 5,000,000 shares
Gerald Morris Corporation (GM) plans to issue bonds to raise $95 million. GM's investment banker will charge flotation costs equal to 5 percent of the total amount issued. The market value of each bond at issue time will be $1,000. How many bonds must GM sell to net $95 million after flotation costs? Assume that fractions of bonds cannot be issued. Show how much of the total amount issued will consist of flotation costs and how much GM will receive after flotation costs are paid.
Net proceeds = Amount of issue x (1 - Flotation costs) $95,000,000 = Amount of issue x (1 - 0.05) Amount of issue = $95,000,000/0.95 = $100,000,000 Number of bonds = $100,000,000/$1,000 = 100,000 bonds
When the SEC approves a stock issue, it does not provide an opinion about the value of the stock. Do you think the SEC should give an opinion to investors on the appropriate value of the stock being issued? Explain.
No, the real value of a security is determined by the equilibrium forces of an efficient market. Assuming that the information provided on newly issued securities is accurate, the market will establish the value of a security regardless of the opinions rendered by the SEC, or, for that matter, opinions offered by any advisory service or analyst.
Matt is considering the purchase of an investment that will pay him $12,500 in 12 years. If Matt wants to earn a return equal to 7 percent per year (annual compounding), what is the maximum amount he should be willing to pay for the investment today?
PV = $12,500/(1.07)12 = $12,500(0.444012) = $5,550.15
If Quincy can invest at an opportunity cost rate equal to 12 percent compounded monthly, what lumpsum amount should he invest today so that he has $22,000 to buy a new car in three years?
PV = $22,000/(1.01)36 = $22,000(0.698925) = $15,376.35
Staci invested $950 five years ago. Her investment paid 7.2 percent interest compounded monthly. Staci's twin sister Shelli invested $900 at the same time. But Shelli's investment earned 8 percent interest compounded quarterly. How much is each investment worth today?
Staci) FV5 = $950(1.006)60 = $950(1.43179) = $1,360.20 Shelli) FV5 = $900(1.02)20 = $900(1.48595) = $1,337.35
How do you think intermediaries' characteristics will change in the future?
The primary change that is evident from the deregulation of the financial services industry is that the differences that previously existed among the various financial institutions are disappearing. Now commercial banks offer mortgage loans and thrift institutions offer commercial loans. In addition, intermediaries now are allowed to venture into areas of business that were previously "off limits" to them, and they can conduct business nationally rather than just in their native state. If this trend continues, there will be fewer, but larger financial intermediaries in the United States in the future.
Do you think that the financial services industry will be more reregulated or deregulated in the future? Explain.
When financial catastrophes occur, such as the near collapse of the financial markets during the 2007 through 2009 period, Congress is quick to call for greater regulation of financial institutions and markets. As a result, generally we see more regulation of the markets immediately following financial crises. On the other hand, when the financial markets are performing well, as they did in the 1990s, Congress favors deregulation.
