1 Million+ Step-by-step solutions

Define each of the following terms:

a. Sole proprietorship; partnership; corporation

b. Limited partnership; limited liability partnership; Professional Corporation

c. Stockholder wealth maximization

d. Money market; capital market; primary market; secondary market

e. Private markets; public markets; derivatives

f. Investment banker; financial service corporation; financial intermediary

g. Mutual fund; money market fund

h. Physical location exchanges; computer/telephone network

i. Open outcry auction; dealer market; electronic communications network (ECN)

j. Production opportunities; time preferences for consumption

k. Real risk-free rate of interest, r*; nominal risk-free rate of interest, rRF

l. Inflation premium (IP); default risk premium (DRP); liquidity; liquidity premium (LP)

m. Interest rate risk; maturity risk premium (MRP); reinvestment rate risk

n. Term structure of interest rates; yield curve

o. “Normal” yield curve; inverted (“abnormal”) yield curve

p. Expectations theory

q. Foreign trade deficit

What are the three principal forms of business organization? What are the advantages and disadvantages of each?

What are the three primary determinants of a firm’s cash flow?

What are financial intermediaries, and what economic functions do they perform?

Which fluctuate more long-term or short-term interest rates? Why?

Suppose the population of Area Y is relatively young while that of Area O is relatively old, but everything else about the two areas is equal.

a. Would interest rates likely be the same or different in the two areas? Explain.

b. Would a trend toward nationwide branching by banks and savings and loans, and the development of nationwide diversified financial corporations, affect your answer to part a?

Suppose a new and much more liberal Congress and administration were elected, and their first order of business was to take away the independence of the Federal Reserve System, and to force the Fed to greatly expand the money supply. What effect would this have?

a. On the level and slope of the yield curve immediately after the announcement?

b. On the level and slope of the yield curve that would exist two or three years in the future?

Why is corporate finance important to all managers?

Describe the organizational forms a company might have as it evolves from a start-up to a major corporation. List the advantages and disadvantages of each form.

How do corporations “go public” and continue to grow? What are agency problems?

What should be the primary objective of managers?

Do firms have any responsibilities to society at large?

Is stock price maximization good or bad for society?

Should firms behave ethically?

The real risk-free rate of interest is 3 percent. Inflation is expected to be 2 percent this year and 4 percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?

A Treasury bond that matures in 10 years has a yield of 6 percent. A 10-year corporate bond has a yield of 8 percent. Assume that the liquidity premium on the corporate bond is 0.5 percent. What is the default risk premium on the corporate bond?

The real risk-free rate is 3 percent, and inflation is expected to be 3 percent for the next 2 years. A 2-year Treasury security yields 6.2 percent. What is the maturity risk premium for the 2-year security?

The real risk-free rate is 3 percent. Inflation is expected to be 3 percent this year, 4 percent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated to be 0.0005 = (t = 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security?

Assume that the real risk-free rate, r*, is 3 percent and that inflation is expected to be 8 percent in Year 1, 5 percent in Year 2, and 4 percent thereafter. Assume also that all Treasury securities are highly liquid and free of default risk. If 2-year and 5-year Treasury notes both yield 10 percent, what is the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is MRP5 minus MRP2?

Due to a recession, the inflation rate expected for the coming year is only 3 percent. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3 percent. Assume that the real risk-free rate is r* _ 2% for all maturities and that there are no maturity premiums. If 3-year Treasury notes yield 2 percentage points more than 1-year notes, what inflation rate is expected after Year 1?

Suppose you and most other investors expect the inflation rate to be 7 percent next year, to fall to 5 percent during the following year, and then to remain at a rate of 3 percent thereafter. Assume that the real risk-free rate, r*, will remain at 2 percent and that maturity risk premiums on Treasury securities rise from zero on very short-term securities (those that mature in a few days) to a level of 0.2 percentage point for 1-year securities. Furthermore, maturity risk premiums increase 0.2 percentage point for each year to maturity, up to a limit of 1.0 percentage point on 5-year or longer-term T-notes and T-bonds.

a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities, and plot the yield curve.

b. Now suppose Exxon Mobil, an AAA-rated company, had bonds with the same maturities as the Treasury bonds. As an approximation, plot an Exxon Mobil yield curve on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on Exxon Mobil’s long-term versus its short-term bonds.)

c. Now plot the approximate yield curve of Long Island Lighting Company, a risky nuclear utility.

Define each of the following terms:

a. PV; i; INT; FVn; PVAn; FVAn; PMT; m; iNom

b. FVIFi,n; PVIFi,n; FVIFAi,n; PVIFAi,n

c. Opportunity cost rate

d. Annuity; lump sum payment; cash flow; uneven cash flow stream

e. Ordinary (deferred) annuity; annuity due

f. Perpetuity; consol

g. Outflow; inflow; time line; terminal value

h. Compounding; discounting

i. Annual, semiannual, quarterly, monthly, and daily compounding

j. Effective annual rate (EAR); nominal (quoted) interest rate; APR; periodic rate

k. Amortization schedule; principal versus interest component of a payment; amortized loan

What is an opportunity cost rate? How is this rate used in discounted cash flow analysis, and where is it shown on a time line? Is the opportunity rate a single number that is used in all situations?

An annuity is defined as a series of payments of a fixed amount for a specific number of periods. Thus, $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity. However, the second series contains an annuity. Is this statement true or false?

If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100 percent, but the annual growth rate would be less than 10 percent true or false? Explain.

Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can “override” the variable which changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

a. An initial $500 compounded for 1 year at 6 percent.

b. An initial $500 compounded for 2 years at 6 percent.

c. The present value of $500 due in 1 year at a discount rate of 6 percent.

d. The present value of $500 due in 2 years at a discount rate of 6 percent.

Use equations and a financial calculator to find the following values. See the hint for Problem 2-1.

a. An initial $500 compounded for 10 years at 6 percent.

b. An initial $500 compounded for 10 years at 12 percent.

c. The present value of $500 due in 10 years at a 6 percent discount rate.

d. The present value of $1,552.90 due in 10 years at a 12 percent discount rate and at a 6 percent rate. Give a verbal definition of the term present value, and illustrate it using a time line with data from this problem. As a part of your answer, explain why present values are dependent upon interest rates.

To the closest year, how long will it take $200 to double if it is deposited and earns the following rates? [Notes: (1) See the hint for Problem 2-1. (2) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV _ _200, PMT _ 0, FV _ 400, and I _ 7 in an HP-12C, and then press the N key, you will get 11 years for part a. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP-10B gives the correct answer.]

a. 7 percent.

b. 10 percent.

c. 18 percent.

d. 100 percent.

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. (Note: See the hint to Problem 2-1. Also, note that you can leave values in the TVM register, switch to “BEG,” press FV, and find the FV of the annuity due.)

a. $400 per year for 10 years at 10 percent.

b. $200 per year for 5 years at 5 percent.

c. $400 per year for 5 years at 0 percent.

d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Find the present value of the following ordinary annuities (see note to Problem 2-4):

a. $400 per year for 10 years at 10 percent.

b. $200 per year for 5 years at 5 percent.

c. $400 per year for 5 years at 0 percent.

d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

a. Find the present values of the following cash flow streams. The appropriate interest rate is 8 percent. It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note, if you do work with the cash flow register, then you must enter CF0 = 0.

b. What is the value of each cash flow stream at a 0 percent interest rate?

Find the interest rates, or rates of return, on each of the following:

a. You borrow $700 and promise to pay back $749 at the end of 1 year.

b. You lend $700 and receive a promise to be paid $749 at the end of 1 year.

c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years.

d. You borrow $9,000 and promise to make payments of $2,684.80 per year for 5 years.

Find the amount to which $500 will grow under each of the following conditions:

a. 12 percent compounded annually for 5 years.

b. 12 percent compounded semiannually for 5 years.

c. 12 percent compounded quarterly for 5 years.

d. 12 percent compounded monthly for 5 years.

Find the present value of $500 due in the future under each of the following conditions:

a. 12 percent nominal rate, semiannual compounding, discounted back 5 years.

b. 12 percent nominal rate, quarterly compounding, discounted back 5 years.

c. 12 percent nominal rate, monthly compounding, discounted back 1 year.

Find the future values of the following ordinary annuities:

a. FV of $400 each 6 months for 5 years at a nominal rate of 12 percent, compounded semiannually.

b. FV of $200 each 3 months for 5 years at a nominal rate of 12 percent, compounded quarterly.

c. The annuities described in parts a and b have the same amount of money paid into them during the 5-year period and both earn interest at the same nominal rate, yet the annuity in part b earns $101.60 more than the one in part a over the 5 years. Why does this occur?

(2-11) Universal Bank pays 7 percent interest, compounded annually, on time deposits.

Regional Bank pays 6 percent interest, compounded quarterly.

a. Based on effective interest rates, in which bank would you prefer to deposit your money?

b. Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during the entire compounding period in order for you to receive any interest.

a. Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10 percent.

b. How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10 percent and that the loan is paid off over 5 years.

c. How large must each payment be if the loan is for $50,000, the interest rate is 10 percent, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b?

Hanebury Corporation’s current sales were $12 million. Sales were $6 million 5 years earlier.

a. To the nearest percentage point, at what rate have sales been growing?

b. Suppose someone calculated the sales growth for Hanebury Corporation in part a as follows: “Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so, dividing 100 percent by 5, we find the growth rate to be 20 percent per year.” Explain what is wrong with this calculation.

Washington-Pacific invests $4 million to clear a tract of land and to set out some young pine trees. The trees will mature in 10 years, at which time Washington-Pacific plans to sell the forest at an expected price of $8 million. What is Washington- Pacific’s expected rate of return?

A mortgage company offers to lend you $85,000; the loan calls for payments of $8,273.59 per year for 30 years. What interest rate is the mortgage company charging you?

To complete your last year in business school and then go through law school, you will need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your rich uncle offers to put you through school, and he will deposit in a bank paying 7 percent interest a sum of money that is sufficient to provide the four payments of $10,000 each.

His deposit will be made today.

a. How large must the deposit be?

b. How much will be in the account immediately after you make the first withdrawal after the last withdrawal?

While Mary Corns was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 9 percent. If Mary repays $1,500 per year, how long, to the nearest year, will it take her to repay the loan?

You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 percent annual interest. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be?

What is the present value of perpetuity of $100 per year if the appropriate discount rate is 7 percent? If interest rates in general were to double and the appropriate discount rate rose to 14 percent, what would happen to the present value of the perpetuity?

Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities that call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays an 8 percent nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?

Assume that your aunt sold her house on December 31 and that she took a mortgage in the amount of $10,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10 percent, but it calls for payments every 6 months, beginning on June 30, and the mortgage is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house of the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?

Your company is planning to borrow $1,000,000 on a 5-year, 15%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal?

a. It is now January 1. You plan to make 5 deposits of $100 each, one every 6 months, with the first payment being made today. If the bank pays a nominal interest rate of 12 percent but uses semiannual compounding, how much will be in your account after 10 years?

b. You must make a payment of $1,432.02 ten years from today. To prepare for this payment, you will make 5 equal deposits, beginning today and for the next 4 quarters, in a bank that pays a nominal interest rate of 12 percent, quarterly compounding. How large must each of the 5 payments be?

Anne Lockwood, manager of Oaks Mall Jewelry, wants to sell on credit, giving customers 3 months in which to pay. However, Anne will have to borrow from her bank to carry the accounts payable. The bank will charge a nominal 15 percent, but with monthly compounding. Anne wants to quote a nominal rate to her customers (all of whom are expected to pay on time) that will exactly cover her financing costs. What nominal annual rate should she quote to her credit customers?

Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal?

Define each of the following terms:

a. Annual report; balance sheet; income statement

b. Common stockholders’ equity, or net worth; retained earnings

c. Statement of retained earnings; statement of cash flows

d. Depreciation; amortization; EBITDA

e. Operating current assets; operating current liabilities; net operating working capital; total net operating capital

f. Accounting profit; net cash flow; NOPAT; free cash flow

g. Market Value Added; Economic Value Added

h. Progressive tax; taxable income; marginal and average tax rates

i. Capital gain or loss; tax loss carry-back and carry-forward

j. Improper accumulation; S corporation

What four statements are contained in most annual reports?

If a “typical” firm reports $20 million of retained earnings on its balance sheet, could its directors declare a $20 million cash dividend without any qualms whatsoever?

What is operating capital, and why is it important?

Explain the difference between NOPAT and net income. Which is a better measure of the performance of a company’s operations?

What is free cash flow? Why is it the most important measure of cash flow?

If you were starting a business, what tax considerations might cause you to prefer to set it up as a proprietorship or a partnership rather than as a corporation?

An investor recently purchased a corporate bond which yields 9 percent. The investor is in the 36 percent combined federal and state tax bracket. What is the bond’s after-tax yield?

Corporate bonds issued by Johnson Corporation currently yield 8 percent. Municipal bonds of equal risk currently yield 6 percent. At what tax rate would an investor be indifferent between these two bonds?

The Talley Corporation had a taxable income of $365,000 from operations after all operating costs but before (1) interest charges of $50,000, (2) dividends received of $15,000, (3) dividends paid of $25,000, and (4) income taxes. What is the firm’s income tax liability and its after-tax income? What are the company’s marginal and average tax rates on taxable income?

The Wendt Corporation had $10.5 million of taxable income.

a. What is the company’s federal income tax bill for the year?

b. Assume the firm receives an additional $1 million of interest income from some bonds it owns. What is the tax on this interest income?

c. Now assume that Wendt does not receive the interest income but does receive an additional $1 million as dividends on some stock it owns. What is the tax on this dividend income?

The Shrives Corporation has $10,000 that it plans to invest in marketable securities. It is choosing among AT&T bonds, which yield 7.5 percent, state of Florida mu ni bonds, which yield 5 percent, and AT&T preferred stock, with a dividend yield of 6 percent. Shrieves’s corporate tax rate is 35 percent, and 70 percent of the dividends received are tax exempt. Assuming that the investments are equally risky and that Shrieves chooses strictly on the basis of after-tax returns, which security should be selected? What is the after-tax rate of return on the highest-yielding security?

The Klaven Corporation has operating income (EBIT) of $750,000. The company’s depreciation expense is $200,000. Klaven is 100 percent equity financed, and it faces a 40 percent tax rate. What is the company’s net income? What is its net cash flow?

The Menendez Corporation expects to have sales of $12 million. Costs other than depreciation are expected to be 75 percent of sales, and depreciation is expected to be $1.5 million. All sales revenues will be collected in cash, and costs other than depreciation must be paid for during the year. Menendez’s federal-plus-state tax rate is 40 percent.

a. Set up an income statement. What is Menendez’s expected net cash flow?

b. Suppose Congress changed the tax laws so that Menendez’s depreciation expenses doubled. No changes in operations occurred. What would happen to reported profit and to net cash flow?

c. Now suppose that Congress, instead of doubling Menendez’s depreciation, reduced it by 50 percent. How would profit and net cash flow be affected?

d. If this were your company, would you prefer Congress to cause your depreciation expense to be doubled or halved? Why?

You have just obtained financial information for the past 2 years for Powell Panther Corporation. Answer the following questions.

a. What is the net operating profit after taxes (NOPAT) for 2004?

b. What are the amounts of net operating working capital for both years?

c. What are the amounts of total net operating capital for both years?

d. What is the free cash flow for 2004?

e. How can you explain the large increase in dividends in 2004?

The Herrmann Company has made $150,000 before taxes during each of the last 15 years, and it expects to make $150,000 a year before taxes in the future. However, in 2004 the firm incurred a loss of $650,000. The firm will claim a tax credit at the time it files its 2004 income tax return, and it will receive a check from the U.S. Treasury. Show how it calculates this credit, and then indicate the firm’s tax liability for each of the next 5 years. Assume a 40 percent tax rate on all income to ease the calculations.

Define the following terms, using graphs or equations to illustrate your answers wherever feasible:

a. Stand-alone risk; risk; probability distribution

b. Expected rate of return, r

c. Continuous probability distribution

d. Standard deviation, variance, 2; coefficient of variation, CV

e. Risk aversion; realized rate of return, r

f. Risk premium for Stock i, RPi; market risk premium, RPM

g. Capital Asset Pricing Model (CAPM)

h. Expected return on a portfolio, ˆ rp; market portfolio

i. Correlation coefficient, ; correlation

j. Market risk; diversifiable risk; relevant risk

k. Beta coefficient, b; average stock’s beta, bA

l. Security Market Line (SML); SML equation

m. Slope of SML as a measure of risk aversion

The probability distribution of a less risky return is more peaked than that of a riskier return. What shape would the probability distribution have for?

(a) Completely certain returns and

(b) Completely uncertain returns?

Security A has an expected return of 7 percent, a standard deviation of returns of 35 percent, a correlation coefficient with the market of _0.3, and a beta coefficient of _1.5. Security B has an expected return of 12 percent, a standard deviation of returns of 10 percent, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?

Suppose you owned a portfolio consisting of $250,000 worth of long-term U.S. government bonds.

a. Would your portfolio be risk less?

b. Now suppose you hold a portfolio consisting of $250,000 worth of 30-day Treasury bills. Every 30 days your bills mature, and you reinvest the principal ($250,000) in a new batch of bills. Assume that you live on the investment income from your portfolio and that you want to maintain a constant standard of living. Is your portfolio truly risk less?

c. Can you think of any asset that would be completely risk less? Could someone develop such an asset? Explain.

If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase more or less than that on a low-beta stock? Explain.

If a company’s beta were to double, would its expected return double?

Is it possible to construct a portfolio of stocks which has an expected return equal to the risk-free rate?

A stockâ€™s return has the following distribution:

Calculate the stockâ€™s expected return, standard deviation, and coefficient of variation.

An individual has $35,000 invested in a stock which has a beta of 0.8 and $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio’s beta?

Assume that the risk-free rate is 5 percent and the market risk premium is 6 percent. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2?

Assume that the risk-free rate is 6 percent and the expected return on the market is 13 percent. What is the required rate of return on a stock that has a beta of 0.7?

The market and Stock J have the following probability distributions:

a. Calculate the expected rates of return for the market and Stock J.

b. Calculate the standard deviations for the market and Stock J.

c. Calculate the coefficients of variation for the market and Stock J.

Suppose rRF = 5%, rM = 10%, and rA = 12%.

a. Calculate Stock A’s beta.

b. If Stock A’s beta were 2.0, what would be A’s new required rate of return?

Suppose rRF = 9%, rM = 14%, and bi = 1.3.

a. What is ri, the required rate of return on Stock i?

b. Now suppose rRF (1) increases to 10 percent or (2) decreases to 8 percent.

The slope of the SML remains constant. How would this affect rM and ri?

c. Now assume rRF remains at 9 percent but rM (1) increases to 16 percent or (2) falls to 13 percent. The slope of the SML does not remain constant. How would these changes affect ri?

Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7,500 and to use these proceeds to buy another stock for your portfolio. Assume the new stock’s beta is equal to 1.75. Calculate your portfolio’s new beta.

Suppose you are the money manager of a $4 million investment fund. The fund consists of 4 stocks with the following investments and betas:

If the market required rate of return is 14 percent and the risk-free rate is 6 percent, what is the fundâ€™s required rate of return?

You have a $2 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta equal to 1.1. You are considering selling $100,000 worth of one stock which has a beta equal to 0.9 and using the proceeds to purchase another stock which has a beta equal to 1.4. What will be the new beta of your portfolio following this transaction?

Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return on an average stock is 13 percent, and the risk-free rate of return is 7 percent. By how much does the required return on the riskier stock exceed the required return on the less risky stock?

Stocks A and B have the following historical returns:

a. Calculate the average rate of return for each stock during the 5-year period.

b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio.

d. Calculate the coefficient of variation for each stock and for the portfolio.

e. If you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

You have observed the following returns over time:

Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent.

a. What are the betas of Stocks X and Y?

b. What are the required rates of return for Stocks X and Y?

c. What is the required rate of return for a portfolio consisting of 80 percent of Stock X and 20 percent of Stock Y?

d. If Stock Xâ€™s expected return is 22 percent, is Stock X under- or overvalued?

Define the following terms, using graphs or equations to illustrate your answers wherever feasible:

a. Portfolio; feasible set; efficient portfolio; efficient frontier

b. Indifference curve; optimal portfolio

c. Capital Asset Pricing Model (CAPM); Capital Market Line (CML)

d. Characteristic line; beta coefficient, b

e. Arbitrage Pricing Theory (APT); Fama-French three-factor model; behavioral finance

Security A has an expected rate of return of 6 percent, a standard deviation of expected returns of 30 percent, a correlation coefficient with the market of - 0.25, and a beta coefficient of 0.5. Security B has an expected return of 11 percent, a standard deviation of returns of 10 percent, a correlation with the market of 0.75, and a beta coefficient of 0.5. Which security is more risky? Why?

a. Use a spreadsheet (or a calculator with a linear regression function) to determine Stock Xâ€™s beta coefficient.

b. Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE.

c. Assuming (1) that the situation during Years 1 to 7 is expected to hold true in the future (that is, rX = rX rM = rM; and both oX and bX in the future will equal their past values), and (2) that Stock X is in equilibrium (that is, it plots on the Security Market Line), what is the risk-free rate?

d. Plot the Security Market Line.

e. Suppose you hold a large, well-diversified portfolio and are considering adding to the portfolio either Stock X or another stock, Stock Y, that has the same beta as Stock X but a higher standard deviation of returns. Stocks X and Y have the same expected returns; that is rX = rY = 10.6%. Which stock should you choose?

You are given the following set of data:

Construct a scatter diagram showing the relationship between returns on Stock Y and the market. Use a spreadsheet or a calculator with a linear regression function to estimate beta.

b. Give a verbal interpretation of what the regression line and the beta coefficient show about Stock Y's volatility and relative riskiness as compared with those of other stocks.

c. Suppose the scatter of points had been more spread out, but the regression line was exactly where your present graph shows it. How would this affect (1) the firm's risk if the stock is held in a one-asset portfolio and (2) the actual risk premium on the stock if the CAPM holds exactly?

d. Suppose the regression line had been downward sloping and the beta coefficient had been negative. What would this imply about (1) Stock Y's relative riskiness, (2) its correlation with the market, and (3) its probable risk premium?

The beta coefficient of an asset can be expressed as a function of the assetâ€™s correlation with the market as follows:

a. Substitute this expression for beta into the Security Market Line (SML), Equation 5-9. This results in an alternative form of the SML.

b. Compare your answer to part a with the Capital Market Line (CML), Equation 5-6 what similarities are observed? What conclusions can be drawn?

Suppose you are given the following information. The beta of company i, bi, is 1.1, the risk-free rate, rRF, is 7 percent, and the expected market premium, rM - rRF, is 6.5 percent. (Assume that ai = 0.0.)

a. Use the Security Market Line (SML) of CAPM to find the required return for this company.

b. Because your company is smaller than average and more successful than average (that is, it has a low book-to-market ratio), you think the Fama-French three factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-French three-factor model: The coefficient for the size effect, ci, is 0.7, and the coefficient for the book-to-market effect, di, is -0.3. If the expected value of the size factor is 5 percent and the expected value of the book-to-market factor is 4 percent, what is the required return using the Fama-French three-factor model?

Define each of the following terms:

a. Bond; Treasury bond; corporate bond; municipal bond; foreign bond

b. Par value; maturity date; coupon payment; coupon interest rate

c. Floating-rate bond; zero coupon bond; original issue discount bond (OID)

d. Call provision; redeemable bond; sinking fund

e. Convertible bond; warrant; income bond; indexed, or purchasing power, bond

f. Premium bond; discount bond

g. Current yield (on a bond); yield to maturity (YTM); yield to call (YTC)

h. Reinvestment risk; interest rate risk; default risk

i. Indentures; mortgage bond; debenture; subordinated debenture

j. Development bond; municipal bond insurance; junk bond; investment-grade bond

“The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices.” Is this statement true or false? Explain.

The rate of return you would get if you bought a bond and held it to its maturity date is called the bond’s yield to maturity. If interest rates in the economy rise after a bond have been issued, what will happen to the bond’s price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond’s price?

If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain.

A sinking fund can be set up in one of two ways:

(1) The corporation makes annual payments to the trustee, who invests the proceeds in securities (frequently government bonds) and uses the accumulated total to retire the bond issue at maturity.

(2) The trustee uses the annual payments to retire a portion of the issue each year, either calling a given percentage of the issue by a lottery and paying a specified price per bond or buying bonds on the open market, whichever is cheaper.

Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders.

Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity of 9 percent. What is the current market price of these bonds?

Wilson Wonders’ bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10 percent. The bonds sell at a price of $850. What is their yield to maturity?

Thatcher Corporation’s bonds will mature in 10 years. The bonds have a face value of $1,000 and an 8 percent coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds are callable in 5 years at a call price of $1,050. What is the yield to maturity? What is the yield to call?

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