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principles corporate finance
Corporate Finance 6th International Edition Stephen Ross, Randolph Westerfield, Jeffrey Jaffe - Solutions
4.39 You are saving for the college education of your two children. They are two years apart in age; one will begin college in 15 years, the other will begin in 17 years. You estimate your children’s college expenses to be $21,000 per year per child. The annual interest rate is 15 percent. How
4.38 Assume that the cost of a college education will be $20,000 per year when your child enters college 12 years from now. You currently have $10,000 to invest. What rate of interest must your investment earn to pay the cost of a four-year college education for your child? For simplicity, assume
4.37 On September 1, 1998, Susan Chao bought a motorcycle for $10,000. She paid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate of 9.6 percent, compounded monthly. She started the monthly payment exactly one month after the purchase, i.e., October, 1998.
4.36 You have recently won the super jackpot in the Illinois state lottery. On reading the fine print, you discover that you have the following two options:a. You receive $160,000 at the beginning of each year for 31 years. The income would be taxed at a rate of 28 percent. Taxes are withheld when
4.35 Peter Green bought a $15,000 Honda Civic with 20 percent down and financed the rest with a four-year loan at 8 percent stated annual interest rate, compounded monthly. What is his monthly payment if he starts the payment one month after the purchase?
4.34 Jack Ferguson has signed a three-year contract to work for a computer software company.He expects to receive a base salary of $5,000 a month and a bonus of $10,000 at year-end.All payments are made at the end of periods. What is the present value of the contract if the stated annual interest
4.33 Nancy Ferris bought a building for $120,000. She paid 15 percent down and agreed to pay the balance in 20 equal annual installments. What are the equal installments if the annual interest rate is 10 percent?
4.32 You need $25,000 five years from now. You budget to make equal payments at the end of every year into an account that pays an annual interest rate of 7 percent.a. What are your annual payments?b. Your rich uncle died and left you $20,000. How much of it must you put into the same account as a
4.31 You are offered the opportunity to buy a note for $12,800. The note is certain to pay$2,000 at the end of each of the next 10 years. If you buy the note, what rate of interest will you receive?
4.30 What is the value of a 15-year annuity that pays $500 a year? The annuity’s first payment is at the end of year 6 and the annual interest rate is 12 percent for years 1 through 5 and 15 percent thereafter.
4.29 What is the present value of end-of-year cash flows of $2,000 per year, with the first cash flow received three years from today and the last one 22 years from today? Use a discount rate of 8 percent.
4.28 Should you buy an asset that will generate income of $1,200 per year for eight years? The price of the asset is $6,200 and the annual interest rate is 10 percent.
4.27 IDEC Pharmaceuticals is considering a drug project that costs $100,000 today and is expected to generate end-of-year annual cash flow of $50,000 forever. At what discount rate would IDEC be indifferent between accepting or rejecting the project?
4.26 Mark Weinstein has been working on an advanced technology in laser eye surgery. The technology is expected to be available to the medical industry two years from today and will generate annual income of $200,000 growing at 5 percent perpetually. What is the present value of the technology if
4.25 In its most recent corporate report,Williams, Inc., apologized to its stockholders for not paying a dividend. The report states that management will pay a $1 dividend next year.That dividend will grow at 4 percent every year thereafter. If the discount rate is 10 percent, how much are you
4.24 Harris, Inc., paid a $3 dividend yesterday. If the firm raises its dividend at 5 percent every year and the appropriate discount rate is 12 percent, what is the price of Harris stock?
4.23 Given an interest rate of 10 percent per year, what is the value at date t 5 (i.e., the end of year 5) of a perpetual stream of $120 annual payments starting at date t 9?
4.22 Assuming an interest rate of 10 percent, calculate the present value of the following streams of yearly payments:a. $1,000 per year forever, with the first payment one year from today.b. $500 per year forever, with the first payment two years from today.c. $2,420 per year forever, with the
4.21 World Transportation, Inc., is expected to initiate its quarterly dividend of $1 five years from today and the dividend is expected to remain constant permanently. What is the price of World Transportation stock if the stated annual interest rate is 15 percent, compounded quarterly?
4.20 A prestigious investment bank designed a new security that pays a quarterly dividend of$10 permanently. What is the price of the security if the stated annual interest rate is 12 percent, compounded quarterly?
4.19 The market interest rate is 15 percent. What is the price of a consol bond that pays$120 annually?
4.18 Bank America offers a stated annual interest rate of 4.1 percent, compounded quarterly, while Bank USA offers a stated annual interest rate of 4.05 percent, compounded monthly.In which bank should you deposit your money?
4.17 Calculate the present value of $5,000 in 12 years at a stated annual interest rate of 10 percent, compounded quarterly.
4.16 Compute the future value of $1,000 continuously compounded fora. 5 years at a stated annual interest rate of 12 percent.b. 3 years at a stated annual interest rate of 10 percent.c. 10 years at a stated annual interest rate of 5 percent.d. 8 years at a stated annual interest rate of 7 percent.
4.15 What is the future value three years hence of $1,000 invested in an account with a stated annual interest rate of 8 percent,a. compounded annually?b. compounded semiannually?c. compounded monthly?d. compounded continuously?e. Why does the future value increase as the compounding period
4.14 Your aunt owns an auto dealership. She promised to give you $3,000 in trade-in value for your car when you graduate one year from now, while your roommate offered you$3,500 for the car now. The prevailing interest rate is 12 percent. If the future value of benefit from owning the car for one
4.13 Today a firm signed a contract to sell a capital asset for $90,000. The firm will receive payment five years from today. The asset costs $60,000 to produce.a. If the appropriate discount rate is 10 percent, is the firm making a profit on this item?b. At what appropriate discount rate will the
4.12 You have the opportunity to invest in a machine that will cost $340,000. The machine will generate cash flows of $100,000 at the end of each year and require maintenance costs of$10,000 at the beginning of each year. If the economic life of the machine is five years and the relevant discount
4.11 You have the opportunity to make an investment that costs $900,000. If you make this investment now, you will receive $120,000 one year from today, $250,000 and $800,000 two and three years from today, respectively. The appropriate discount rate for this investment is 12 percent.a. Should you
4.10 Ann Woodhouse is considering the purchase of a house. She expects that she will own the house for 10 years and then sell it for $5 million. What is the most she would be willing to pay for the house if the appropriate discount rate is 12 percent?
4.9 Suppose you deposit $1,000 in an account at the end of each of the next four years. If the account earns 12 percent, how much will be in the account at the end of seven years?
4.8 Suppose you bought a bond that will pay $1,000 in 20 years. No intermediate coupon payments will be made. If the appropriate discount rate for the bond is 8 percent,a. what is the current price of the bond?b. what will the price be 10 years from today?c. what will the price be 15 years from
4.7 You are selling your house. The Smiths have offered you $115,000. They will pay you immediately. The Joneses have offered you $150,000, but they cannot pay you until three years from today. The interest rate is 10 percent. Which offer should you choose?
4.6 You have won the Florida state lottery. Lottery officials offer you the choice of the following alternative payouts:Alternative 1: $10,000 one year from now.Alternative 2: $20,000 five years from now.Which alternative should you choose if the discount rate is:a. 0 percent?b. 10 percent?c. 20
4.5 A firm has an estimated pension liability of $1.5 million due 27 years from today. If the firm can invest in a risk-free security that has a stated annual interest rate of 8 percent, how much must the firm invest today to be able to make the $1.5 million payment?
4.4 The government has issued a bond that will pay $1,000 in 25 years. The bond will pay no interim coupon payments. What is the present value of the bond if the discount rate is 10 percent?
4.3 Would you rather receive $1,000 today or $2,000 in 10 years if the discount rate is 8 percent?
4.2 Calculate the present value of the following cash flows discounted at 10 percent.a. $1,000 received seven years from today.b. $2,000 received one year from today.c. $500 received eight years from today.
4.1 Compute the future value of $1,000 compounded annually fora. 10 years at 5 percent.b. 10 years at 7 percent.c. 20 years at 5 percent.d. Why is the interest earned in part c not twice the amount earned in part a?
1. The Trojan Pizza Company is contemplating investing $1 million in four new outlets in Los Angeles. Andrew Lo, the firm’s Chief Financial Officer (CFO), has estimated that the investments will pay out cash flows of $200,000 per year for nine years and nothing thereafter. (The cash flows will
1. WHAT IS A FIRM WORTH?
• What are four tricks concerning annuities?
• What are three important points concerning the growing-perpetuity formula?
• What are the formulas for perpetuity, growing perpetuity, annuity, and growing annuity?
$#!#$1. Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate of 20 percent, what is the present value of his lifetime salary?2. In a previous
3. Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first payment a year from now. The state advertises this as the Million Dollar Lottery because $1,000,000 = $50,000* 20. If the interest rate is 8 percent, what is the true value of the lottery
2. Rothstein Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the annual dividend will rise by 6 percent a year forever. The applicable interest rate is 11 percent. What is the price of the stock today?
1. Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value of the consol?
• Define continuous compounding.
• What is the relationship between the stated annual interest rate and the effective annual interest rate?
• What is an effective annual interest rate?
• What is a stated annual interest rate?
1. What is the end-of-year wealth if Jane Christine receives a stated annual interest rate of 24 percent compounded monthly on a $1 investment?
• What is the formula for the net present value of a project?
6. Finance.com has an opportunity to invest in a new high-speed computer that costs$50,000. The computer will generate cash flows (from cost savings) of $25,000 one year from now, $20,000 two years from now, and $15,000 three years from now. The computer will be worthless after three years, and no
5. A customer of the Chaffkin Corp. wants to buy a tugboat today. Rather than paying immediately, he will pay $50,000 in three years. It will cost the Chaffkin Corp.$38,610 to build the tugboat immediately. The relevant cash flows to Chaffkin Corp. are displayed in Figure 4.10. By charging what
4. Bernard Dumas will receive $10,000 three years from now. Bernard can earn 8 percent on his investments, and so the appropriate discount rate is 8 percent.What is the present value of his future cash flow?
3. Carl Voigt, who recently won $10,000 in the lottery, wants to buy a car in five years. Carl estimates that the car will cost $16,105 at that time. His cash flows are displayed in Figure 4.7.What interest rate must he earn to be able to afford the car?
• How does one use net present value when making an investment decision?
• Define future value and present value.
11.8 Assume that the returns of individual securities are generated by the following two-factor model:Rit is the return for security i at time t. F1t and F2t are market factors with zero expectation and zero covariance. In addition, assume that there is a capital market for four securities, where
11.7 Assume that the following market model adequately describes the return-generating behavior of risky assets.RMt and it are statistically independent.Suppose the following data are true.a. Calculate the standard deviation of returns for each asset.b. Assume short selling is allowed.i. Calculate
11.6 There are two stock markets, each driven by the same common force F with an expected value of zero and standard deviation of 10 percent. There are a large number of securities in each market; thus, you can invest in as many stocks as you wish. Due to restrictions, however, you can invest in
11.5 You are forming an equally weighted portfolio of stocks. There are many stocks that all have the same beta of 0.84 for factor 1 and the same beta of 1.69 for factor 2. All stocks also have the same expected return of 11 percent. Assume a two-factor model describes the returns on each of these
11.4 The following three stocks are available in the market.Assume the market model is valid.a. Write the market-model equation for each stock.b. What is the return on a portfolio that is 30-percent stock A, 45-percent stock B, and 25-percent stock C?c. Suppose the return on the market is 15
11.3 Suppose a factor model is appropriate to describe the returns on a stock. Information about those factors is presented in the following chart.a. What is the systematic risk of the stock return?b. The firm announced that its market share had unexpectedly increased from 23 percent to 27 percent.
11.2 Suppose a three-factor model is appropriate to describe the returns of a stock. Information about those three factors is presented in the following chart. Suppose this is the only information you have concerning the factors.a. What is the systematic risk of the stock return?b. Suppose
• What is wrong with measuring the performance of a U.S. growth stock manager against a benchmark composed of English stocks?
• What is data mining and why might it overstate the relation between some stock attribute and returns?
• Empirical models are sometimes called factor models. What is the difference between a factor as we have used it previously in this chapter and an attribute as we use it in this section?
• What risk is diversified away in a large portfolio?
• Define the beta coefficient.
• What is the difference between a k-factor model and the market model?
• What is an inflation beta? A GNP beta? An interest-rate beta?
• Why is unsystematic risk sometimes referred to as idiosyncratic risk?
• Under what conditions will some news have no effect on common stock prices?
10.41 There are two stocks in the market, stock A and stock B. The price of stock A today is$50. The price of stock A next year will be $40 if the economy is in a recession, $55 if the economy is normal, and $60 if the economy is expanding. The attendant probabilities of recession, normal times,
10.40 You have been provided the following data on the securities of three firms and the market:Assume the CAPM holds true.a. Fill in the missing values in the table.b. Provide an evaluation of the investment performance of the three firms.c. What is your investment recommendation? Why? Security R
10.39 Suppose you have invested $30,000 in the following four stocks.The risk-free rate is 4 percent and the expected return on the market portfolio is 15 percent.Based on the CAPM, what is the expected return on the above portfolio? Security Amount Invested Beta Stock A $ 5,000 0.75 Stock B 10,000
10.38 Is the following statement true or false? Explain.A risky security cannot have an expected return that is less than the risk-free rate because no risk-averse investor would be willing to hold this asset in equilibrium.
10.37 Johnson Paint stock has an expected return of 19 percent with a beta of 1.7, while Williamson Tire stock has an expected return of 14 percent with a beta of 1.2. Assume the CAPM is true. What is the expected return on the market? What is the risk-free rate?
10.36 The following data have been developed for the Durham Company.Variance of market returns 0.04326 Covariance of the returns on Durham and the market 0.0635 Suppose the market risk premium is 9.4 percent and the expected return on Treasury bills is 4.9 percent.a. Write the equation of the
10.35 Suppose the risk-free rate is 6.3 percent and the market portfolio has an expected rate of return of 14.8 percent. The market portfolio has a variance of 0.0121. Portfolio Z has a correlation coefficient with the market of 0.45 and a variance of 0.0169. According to the CAPM, what is the
10.34 Suppose the current risk-free rate is 7.6 percent. Potpourri Inc. stock has a beta of 1.7 and an expected return of 16.7 percent. (Assume the CAPM is true.)a. What is the risk premium on the market?b. Magnolia Industries stock has a beta of 0.8. What is the expected return on the Magnolia
10.33 The expected return on a portfolio that combines the risk-free asset and the asset at the point of tangency to the efficient set is 25 percent. The expected return was calculated under the following assumptions:The risk-free rate is 5 percent.The expected return on the market portfolio of
10.30a. Draw the security market line for the case where the market-risk premium is 5 percent and the risk-free rate is 7 percent.b. Suppose that an asset has a beta of 1 and an expected return of 4 percent. Plot it on the graph you drew in part (a). Is the security properly priced? If not,
10.29 Suppose you observe the following situation:a. Calculate the expected return of each stock.b. Assuming the CAPM is true and stock A’s beta is greater than stock B’s beta by .25, what is the risk premium? Return if a State Occurs State of Economy Probability of State Stock A Stock B Bust
10.28 Consider the following two stocks:Assume the CAPM holds. Based upon the CAPM, what is the return on the market? What is the risk-free rate? Beta Expected Return 25% 0.7 14% Murck Pharmaceutical 1.4 Pizer Drug Corp.
10.27 Suppose the market risk premium is 7.5 percent and the risk-free rate is 3.7 percent. The expected return of TriStar Textiles is 14.2 percent. What is the beta for TriStar Textiles?
10.26 The risk-free rate is 8 percent. The beta for the Jordan Company is 1.5, and the expected return of the market is 15 percent. What is the expected return for the Jordan Company?
10.25 Suppose the beta for the Ross Corporation is 0.80. The risk-free rate is 6 percent, and the market risk premium is 8.5 percent. What is the expected return for the Ross Corporation?
10.24 The Alpha firm makes pneumatic equipment. Its beta is 1.2. The market risk premium is 8.5 percent, and the current risk-free rate is 6 percent. What is the expected return for the Alpha firm?
10.23 Securities A, B, and C have the following characteristics.a. What is the expected return on a portfolio with equal weights?b. What is the beta of a portfolio with equal weights?c. Are the three securities priced in equilibrium? Security E(R)% Beta A 10% 0.7 B 14 1.2 C 20 1.8
10.22 William Shakespeare’s character Polonius in Hamlet says, “Neither a borrower nor a lender be.” Under the assumptions of the CAPM, what would be the composition of Polonius’s portfolio?
10.21 Consider the following information on the returns on the market and Fuji stock.a. Calculate the beta of Fuji. What is the responsiveness of Fuji’s return to movements of the market?b. Suppose the estimate of expected return on the market is 4.0 percent when the type of economy is Bear.
10.20 Assume a world with homogeneous expectations (i.e., everybody agrees on expected returns and standard deviations). In this world the market portfolio has an expected return of 12 percent and a standard deviation of 10 percent. The risk-free asset has an expected return of 5 percent.a. What
10.19 Assume that there are two stocks with the following characteristics. The covariance between the returns on the stocks is 0.001.a. What is the expected return on the minimum variance portfolio? (Hint: Find the portfolio weights XA and XB such that the portfolio variance is minimized. Remember
10.17 Briefly explain why the covariance of a security with the rest of a portfolio is a more appropriate measure of risk than the security’s variance.
10.16 Is the following statement true or false? Explain.The most important characteristic in determining the variance of a well-diversified portfolio is the variance of the individual stocks.
10.14 Suppose that there are two stocks, A and B. Suppose that their returns are independent.Stock A has a 40-percent chance of having a return of 15 percent and 60-percent chance of a return of 10 percent. Stock B has a one-half chance of a 35-percent return and a onehalf chance of a 5-percent
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