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fundamentals of corporate finance

Questions and Answers of Fundamentals Of Corporate Finance

c. Use the Excel function CORREL to calculate the correlation coefficient between the monthly returns for each pair of stocks. Which pair provides the greatest gain from diversification?
b. Calculate the monthly standard deviation of those returns (see Section 7-2). Use the Excel function STDEV.P to check your answer. Find the annualized standard deviation by multiplying by the
1. Download to a spreadsheet the last three years of monthly adjusted stock prices for Coca-Cola (KO), Citigroup (C), and Pfizer (PFE).a. Calculate the monthly returns.
31. Sharpe ratio (S7.4) Look back at the calculations for Southwest Airlines and Amazon in Section 7.4. What combination of the two stocks offers the highest Sharpe ratio if the interest rate is 2%?
c. Can the minimum risk portfolio ever offer the highest Sharpe ratio?
b. How would your answer to part (a) change if the interest rate were 2%?
30. Efficient portfolios (S7.4) Look again at the set of the three efficient portfolios that we calculated in Section 7-4.a. If the interest rate is 5%, which of the three efficient portfolios has
d. What combination of Ford and Harley Davidson offers the minimum risk.
c. What is the standard deviation if the portfolio is split evenly between Ford and Harley Davidson and is financed at 50% margin, that is, the investor puts up only 50% of the total amount and
b. What is the standard deviation of a portfolio invested one-third in Ford, one-third in Harley Davidson, and one-third in risk-free Treasury bills?
The standard deviation of the return on the market was 12.3%.a. The correlation coefficient of Ford’s return versus Harley Davidson was 0.40. What is the standard deviation of a portfolio invested
26. Portfolio risk and return (S7.4) Here are returns and standard deviations for four investments.Chapter 7 Introduction to Risk, Diversification, and Portfolio Selection 219 7.1 The historic risk
29. Portfolio risk (S7.4) Here are some historical data on the risk characteristics of Ford and Harley Davidson:Ford Harley Davidson Yearly standard deviation of return (%) 23.5 26.4 Return (%)
28. Portfolio risk and return (S7.4) Suppose that Treasury bills offer a return of about 6% and the expected market risk premium is 8.5%. The standard deviation of Treasury-bill returns is zero and
b. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is +0.1.
27. Portfolio risk and return (S7.4) Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9%, and the annual standard
d. Stock Q has a lower return than R but a higher standard deviation. Does that mean that Q’s price is too high or that R’s price is too low?
c. Plot a figure like Figure 7.12 for Q and R, assuming a correlation coefficient of 0.5.
25. Sharpe ratio (S7.4) Calculate the Sharpe ratios for portfolios A, B, and T in Table 7.5. Which portfolio offers the highest ratio?218 Part Two Risk Calculate the standard deviations of the
c. Is Mr. Scrooge’s portfolio better or worse than one invested entirely in share A, or is it not possible to say?
b. How would your answer change if the correlation coefficient were 0 or –0.5?
24. Portfolio risk and return (S7.4) Ebenezer Scrooge has invested 60% of his money in share A and the remainder in share B. He assesses their prospects as follows:A B Expected return (%) 15 20
23. Portfolio risk and return (S7.4) George Dupree proposes to invest in two shares, X and Y.He expects a return of 12% from X and 8% from Y. The standard deviation of returns is 8%for X and 5% for
b. Repeat the problem for ρ12 = +0.5.
22. Portfolio risk and return (S7.4) Look back at the calculation for Southwest Airlines and Amazon in Section 7.4.a. Recalculate the expected portfolio return and standard deviation for different
e. What is your optimal strategy if you can borrow or lend at 12% and are prepared to tolerate a standard deviation of 25%? What is the maximum expected return that you can achieve with this risk?
d. Suppose you are prepared to tolerate a standard deviation of 25%. What is the maximum expected return that you can achieve if you cannot borrow or lend?
c. Suppose you can also borrow and lend at an interest rate of 12%. Which of the portfolios has the highest Sharpe ratio?Chapter 7 Introduction to Risk, Diversification, and Portfolio Selection 217
b. Five of these portfolios are efficient, and three are not. Which are inefficient ones?
21. Efficient portfolios (S7.4)a. Plot the following risky portfolios on a graph:
20. Efficient portfolios (S7.4) Figure 7.17 purports to show the range of attainable combinations of expected return and standard deviation.a. Which diagram is incorrectly drawn and why?b. Which is
19. Portfolio risk (S7.4) Hyacinth Macaw invests 60% of her funds in stock I and the balance in stock J. The standard deviation of returns on I is 10%, and on J it is 20%. Calculate the variance and
18. Portfolio risk (S7.4) Your eccentric Aunt Claudia has left you $50,000 in BP shares plus$50,000 cash. Unfortunately, her will requires that the BP stock not be sold for one year and the $50,000
17. Portfolio risk (S7.4) Table 7.6 shows standard deviations and correlation coefficients for seven stocks from different countries. Calculate the variance of a portfolio with equal investments in
c. Now repeat the problem, assuming that the correlation between each pair of stocks is zero.
b. Use your estimates to draw a graph like Figure 7.12. How large is the underlying market variance that cannot be diversified away?
16. Portfolio risk (S7.4) Suppose that the standard deviation of returns from a typical share is about 0.4 (or 40%) a year. The correlation between the returns of each pair of shares is about 0.3.a.
c. What is the standard deviation of a fully diversified portfolio of such stocks?
b. Suppose all stocks had a standard deviation of 30% and a correlation with each other of 0.4. What is the standard deviation of the returns on a portfolio that has equal holdings in 50 stocks?
15. Portfolio risk (S7.4)a. How many variance terms and how many different covariance terms do you need to calculate the risk of a 100-share portfolio?
14. Portfolio risk (S7.4) To calculate the variance of a three-stock portfolio, you need to add nine boxes:Use the same symbols that we used in this chapter; for example, x1 = proportion invested in
13. Portfolio risk (S7.3–S7.4) True or false?a. Investors prefer diversified companies because they are less risky.b. If stocks were perfectly positively correlated, diversification would not
12. Risk and diversification (S7.3) In which of the following situations would you get the largest reduction in risk by spreading your investment across two stocks?a. The two shares are perfectly
c. Is the variance more or less than half way between the variance of the two individual stocks?Month Digital Cheese Executive Fruit January +15% +7%February –3 +1 March +5 +4 April +7 +13 May –4
b. Now calculate the variance and standard deviation of the returns on a portfolio that invests an equal amount each month in the two stocks.
11. Diversification (S7.3) Here are the percentage returns on two stocks.a. Calculate the monthly variance and standard deviation of each stock. Which stock is the riskier if held on its own?
10. Risk and diversification (S7.3) Hippique s.a., which owns a stable of racehorses, has just invested in a mysterious black stallion with great form but disputed bloodlines. Some experts in
c. Would you be more likely to congratulate if the interest rate was high or low?
b. Why do you need to know the interest rate to judge whether Ms. Sauros performed better or worse than the market?214 Part Two Risk
9. Average returns and standard deviation (S7.2) During the boom years of 2010–2014, ace mutual fund manager Diana Sauros produced the following percentage rates of return. Rates of return on the
b. Calculate the average real return.
8. Average returns and standard deviation (S7.2) The following table shows the nominal returns on Brazilian stocks and the rate of inflation.a. What was the standard deviation of the market returns?
What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation of this rate of return. (Do not make the adjustment for degrees of freedom described in
7. Expected return and standard deviation (S7.2) A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100.Year
c. The best practical forecast of future rates of return on the stock market is a 5- or 10-year average of historical returns.
b. All investors should prefer stocks to bonds because stocks offer higher long-run rates of return.
6. Stocks vs. bonds (S7.1) Each of the following statements is dangerous or misleading.Explain why.a. A long-term U.S. government bond is always absolutely safe.
b. If you now use past returns to estimate the expected risk premium, will the inclusion of data for 2030 cause you to underestimate or overestimate the return that investors required in the
5. Risk Premium (S7.1) Suppose that in year 2030, investors become much more willing than before to bear risk. As a result, they require a return of 8% to invest in common stocks rather than the 10%
d. What was the average risk premium?
c. What was the risk premium in each year?
b. What was the average real return?
4. Risk premium (S7.1) Here are inflation rates and U.S. stock market and Treasury bill returns between 1929 and 1933:Year Inflation, % Stock Market Return, % T-Bill Return, %1929 –0.2 –14.5 4.8
e. If you were to discount IPC’s expected price at year-end from part (a) by this number, would you underestimate, overestimate, or correctly estimate the stock’s present value?
d. If you could observe the returns of IPC over a large number of years, what would be the compound (geometric average) rate of return?
c. If you were to discount IPC’s expected price at year-end from part (a) by this number, would you underestimate, overestimate, or correctly estimate the stock’s present value?
b. If the probabilities of future returns remain unchanged and you could observe the returns of IPC over a large number of years, what would be the (arithmetic) average return?
3. Arithmetic average and compound returns (S7.1) Integrated Potato Chips (IPC) does not pay a dividend. Its current stock price is $150 and there is an equal probability that the return over the
2. Real versus nominal returns (S7.1) The Costaguana stock market provided a return of 95%.The inflation rate in Costaguana during the year was 80%. In Ruritania the stock market return was 12%, but
1. Rate of return (S7.1) The level of the Syldavia market index is 21,000 at the start of the year and 25,500 at the end. The dividend yield on the index is 4.2%.a. What is the return on the index
=4/Is an arbitrage of this sort really without risk?
=3/A market trader is offering a $500m loan agreement in three months, for a period of three months, on the following terms: 3 3/4% – 3 7/8%. Using the information provided in Questions 1 and 2,
=2/Calculate the six-month interest rate of the dollar on the basis of the following information:◦ the six-month euro rate is equal to 4 4/8 – 4 5/8%;◦ the euro is currently trading at
=1/Calculate the future buy and sell price at three months (dollar against euro) using the following information:◦ the three-month euro rate is equal to 4 6/8 – 4 7/8%;◦ the three-month dollar
=16/A company is hedging more than its actual position. In doing so what is it actually doing?
=14/Should traders take advantage of any arbitrages that they detect on the markets?
=13/Should corporate treasurers take advantage of any arbitrages that they detect on the markets?
=12/What category of derivative products would personal injury insurance fit into?
=11/Can you provide examples of hedging products used by individuals?
=10/Does a derivative product have to be sufficiently liquid to be attractive?
=9/Can credit derivatives be based on options?
=8/What role does a clearing house play?
=6/What is a future?
=5/A Portuguese company imports maize from Mexico, which it in turn exports to Canada.The company pays and is paid at three months (the maize is, in fact, shipped direct from Mexico to Canada).
=4/What is an FRA?
=3/Use arbitrage to calculate forward selling of yen against euros at three months. What information do you need to do the calculation?
=2/Describe four ways for a company to deal with risk.
=15/In an environment with very low interest rates, what might the treasurer be tempted to do?
=13/Why do treasurers avoid investing their cash in shares?
=12/Can an investment yield more than a debt? What is then the consequence?
=11/Is an investment that can be quickly sold on a vast market without risk?
=10/What common practice is the principal of value dates based on?
=4/What is a concentration account?
=3/What is a value date?
=2/What are the three cash positions for a company?
=1/What are the three key objectives of a corporate treasurer?
=5/A company posts monthly sales of €100 000 with a customer for which its gross margin is 25%. How long after the start of the relationship with this customer can the customer go bankrupt without
= What is the impact on the income statement if the company is currently borrowing at 4%?
= The payment period has to be reduced to 60 days for legal reasons. How much extra cash will this mean for the company?
=4/A company makes annual sales of €10m (excl. VAT) and is subject to VAT at a rate of 20%.Its actual collection time is 75 days. What is the average outstanding amount receivable?

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