Financial Management, Spring 2002 Dr. Brett A. King Accounting Fundamentals & Financial Analysis 1. What is the goal of the financial manager? 2. What is meant by an “agency” relationship? Are there costs associated with such a problem? How is this problem mitigated in corporations? 3. How does the presence of stock market analysts help mitigate the agency relationship between shareholders and the management of a publicly traded corporation? 4. What is meant by “liquidity” when describing a firm’s assets? 5. How does an increase in accounts payable affect a firm’s cash flow? How does a decrease in accounts payable affect the cash flow? 6. How does an increase in accounts receivable affect a firm’s cash flow? How does a decrease in accounts receivable affect a firm’s cash flow? 7. How do changes in accruals affect the cash flow of a company? 8. What does the Stockholders’ Equity on the balance sheet represent? 9. Why can depreciation expense actually be considered a good thing? 10. Is the goal of maximizing the wealth of shareholders inconsistent with behaving in a socially responsible manner? 1 Financial Management, Spring 2002 Dr. Brett A. King For problems 11 & 12: Sales Operating Expenses Operating Income Depreciation Interest Expense Taxable Income Taxes Net Income $6,000 $2,000 $500 11. If total debt is $5,000 at an interest rate of 10%, what is taxable income? 12. If the tax rate is 35%, what is net income? For problems 13 & 14: Sales Operating Expenses Operating Income Depreciation Interest Expense Taxable Income Taxes Net Income $7,000 $3,000 $1000 13. If total debt is $7,000 at an interest rate of 11%, what is taxable income? (5 pts.) 14. From the previous problem, if the tax rate is 36%, what is net income? (5 pts.) 2 Financial Management, Spring 2002 Dr. Brett A. King For questions 15 -17: Here are selected balance sheet items for the Everlast company: Assets Current Assets Net Fixed Assets 2005 360 1250 2006 670 1100 Liab/SE Current Liabilities Long-term debt 2005 260 880 2006 290 900 15. What was owner’s equity at year end 2006? 16. If Everlast paid dividends of $145 in 2006, what must have been net income during the year? 17. If Everlast purchased no fixed assets during the year, what must have been the depreciation expense on the income statement? For questions 18 - 19: Here are selected balance sheet items for Bruno Inc.: Assets Current Assets Net Fixed Assets 2005 360 1350 2006 960 1120 Liab/SE Current Liabilities Long-term debt 2005 220 880 18. What was owner’s equity at year end 2006? 19. If Bruno paid dividends of $105 in 2006, what must have been net income during the year? 3 2006 230 900 Financial Management, Spring 2002 Dr. Brett A. King For questions 20 - 21: Here are selected balance sheet items for Polo Inc.: Assets Current Assets Net Fixed Assets 2005 360 1250 2006 470 1470 Liab/SE Current Liabilities Long-term debt 2005 260 880 20. What was owner’s equity at year end 2006? 21. If Polo paid dividends of $125 in 2006, what must have been net income during the year? Consider the following information for problems 22 – 24: Sales Operating Expense Operating Income Depreciation Expense Interest Expense Taxable Income Taxes Net Income $500,000 240,000 260,000 10,000 50,000 200,000 60,000 140,000 Beginning of year balance sheet: PP&E 1,200,000 LT Debt Inventories 195,000 Current Liab. Cash 5,000 SE Total Assets 1,400,000 Total Lib. & SE 500,000 400,000 500,000 1,400,000 22. If the firm pays out 45% of net income as dividends, what would be the new shareholders’ equity balance? 23. Using the DuPont model, what is the ROE? 24. What, if any, liquidity issues does the firm have? 4 2006 290 970 Financial Management, Spring 2002 Dr. Brett A. King 25. Why is depreciation expense added back to net income when analyzing a firms cash flows? 26. JB Corp. has $600,000 of debt outstanding, and it pays an interest rate of 8% annually. Annual sales are $2.15 million, the tax rate is 33% and its net profit margin (NI / Sales) is 7%. What is the TIE (EBIT / INT) for this company? 27. A company has an equity multiplier (TA / TE) of 2.7. Assets are financed with a combination of debt and equity. What is the company’s debt ratio (Debt / Assets)? 28. A company maintains a profit margin of 7% and an asset turnover ratio of 4 (Asset Turnover = Sales / Total Assets, Profit Margin = NI / Sales). What is the ROA (NI / TA)? 29. In problem 28, what is the company’s ROE ( NI / TE ), if the debt-equity ratio (Debt / TE) is 2, its interest payments and taxes are each $6000 and EBIT is $25,000? 30. Investors and analysts closely monitor the financial characteristics of a company by analyzing financial ratios. However, what are some important qualitative aspects of a company that should be considered when conducting sound financial analysis? 31. If a firm has a total market capitalization of $7.5 Billion, and the stock price is $60, how many shares must be outstanding? 5 Financial Management, Spring 2002 Dr. Brett A. King Financial Planning 1. Consider the following financial information for Peart Inc.: Balance Sheet as of December 31, 2000 Cash Receivables Inventories Total CA Net FA $1,080 6,480 9,000 $16,560 12,600 Total Assets $29,160 Accounts Payable Accruals Notes Payable Total CL $4,320 2,880 2,100 $9,300 LT Bonds Common Stock Retained Earnings Total Liab./Equity 3,500 3,500 12,860 $29,160 Income Statement as of December 31, 2000 Sales OE EBIT Interest EBT Taxes (40%) Net Income Dividends Addition to RE $36,000 32,440 $ 3,560 560 $ 3,000 1,200 $ 1,800 $ $ 810 990 Suppose 2001 sales are projected to increase by 15% over the previous year. Determine the AFN. Assume the company was operating at full capacity in 2000, that it cannot sell off any of its fixed assets, and that any required financing will be borrowed as notes payable. Also assume that assets, spontaneous liabilities, and operating costs increase proportional to sales. Use the percent of sales method to develop a pro forma balance sheet and income statement for the company for December 31, 2001. (Ignore financing feedbacks) 6 Financial Management, Spring 2002 Dr. Brett A. King 2. Consider the following financial information for IM Inc.: Balance Sheet as of December 31, 2003 Cash Receivables Inventories Total CA Net FA $2,050 5,750 12,000 $19,800 13,700 Total Assets $33,500 Accounts Payable Accruals Notes Payable Total CL $6,520 1,970 3,100 $11,590 LT Bonds Common Stock Retained Earnings Total Liab./Equity 2,500 5,500 13,910 $33,500 Income Statement as of December 31, 2003 Sales OE EBIT Interest EBT Taxes (40%) Net Income $58,000 41,560 $16,440 1,250 $15,190 6,076 $ 9,114 Dividends Addition to RE $ 5,810 $ 3,304 Suppose 2004 sales are projected to increase by 65% over the previous year. Determine the EFR. Assume the company was operating at 85% of capacity in 2003, that it cannot sell off any of its fixed assets, and that any required financing will be borrowed as longterm bonds. Also assume that assets, spontaneous liabilities, and operating costs increase proportional to sales. Use the percent of sales method to develop a pro forma balance sheet and income statement for the company for December 31, 2004. (Ignore financing feedbacks) 7 Financial Management, Spring 2002 Dr. Brett A. King 3. Total assets were $1.8 million at year end, and accounts payable were $325,000. Sales were $2.6 million are expected to increase by 30% over the next year. Total assets and accounts payable are directly proportional to sales, and will remain that way. Accounts payable represents the only current liability. Common stock amounted to $425,000 at the beginning of the year, and retained earnings were $285,000. The profit margin (NI/Sales) is 9% and 35% of earnings will be retained. What additional funds are necessary for this company over the next year? 8 Financial Management, Spring 2002 Dr. Brett A. King Financial Markets 1. What is the difference between money markets and capital markets? 2. What is the difference between a primary market and a secondary market? 3. What are the factors that affect the “cost of money”? 4. Draw a simple graph which shows what happens to interest rates when the supply or demand for money changes. 5. Explain the following equation in simple terms: K = k* + IP + DRP + LP + MRP 6. Why is the yield curve usually upward sloping? What is the “yield curve”? 7. Suppose you observe the following in the WSJ: T-bills 1-yr. 2-yr. 3-yr. 4-yr. Rate 5.6 6 6.5 7.2 The real risk-free rate is expected to remain at 2%. a) If the pure expectations theory is correct, what does the market believe 1-yr. and 2-yr. T-bills will be yielding 1 year from now? b) If inflation is expected to be 3% this year, 4% next year and 3.5% thereafter, while the maturity premium is expressed as .0005x(t-1), where t = number of years to maturity, what is the nominal interest rate we would expect for a 10yr. T-bill? 9 Financial Management, Spring 2002 Dr. Brett A. King 8. How might the following affect the general level of interest rates? a) b) c) d) e) f) g) Budget surplus Budget deficit Interest rates in Europe Level of business activity Federal reserve policy Political instability An asteroid is discovered headed for Earth and total annihilation is imminent 9. What is the liquidity preference theory for the term structure of interest rates? 10. Differentiate between reinvestment rate risk and interest rate risk. 11. How might an increase in the Producers Price Index (PPI) affect interest rates? 12. Discuss how production opportunities and risk affect interest rates. 10 Financial Management, Spring 2002 Dr. Brett A. King Risk & Return The total rates of return on equity securities is obviously affected by the business cycle. Business economists for the Masseratti Co. predict the following outcomes for the economy, and the associated outcomes on their shares: Probability % Return Growth .30 28% Stagnant .50 -3% Recession .20 24% 1. What is the expected return and standard deviation of returns for the Masseratti shares? You are looking at investing in shares of either Masseratti or OzBank. The expected return for Ozbank under the different economic conditions are as follows: Probability % Return Growth .30 0% Stagnant .50 12% Recession .20 10% 2. If you cannot invest in both companies, but rather must select only one, explain your choice. 3. You have a friend who owns OmniCom, which has an expected return of 10% and a standard deviation equal to 16%. How does this stock compare to the other two? 4. Suppose you invest 25% of your funds in Masseratti, and the remainder in OzBank. What is the expected return and risk for the portfolio? 5. Are there any diversification benefits to the portfolio? 11 Financial Management, Spring 2002 Dr. Brett A. King 6. What is the difference between systematic and unsystematic risk? For 7 & 8: You have observed the following returns over time: Year 1990 1991 1992 1993 1994 BMG 18% 4% -12% 16% 18% Market 13% 8% 3% 10% 11% 7. What is the beta for BMG? 8. If the risk-free rate were 5% and the return on the market was expected to be 12% over the next year, what rate of return would be required by investors holding BMG stock, assuming the CAPM is correct? 9. Why do we use beta as a measure of risk instead of a stock returns’ standard deviation? 10. Investors expect the market to return 15% this year. A stock with a beta of 1.2 is expected to return 18%. If the market return turns out to be 12%, what do you expect the rate of return on the stock to be? For 11 – 12: The total rates of return on equity securities is obviously affected by the business cycle. Business economists for the Badd Co. and Guud Co. predict the following outcomes for the economy, and the associated outcomes on their shares: Probability Badd %Return Guud %Return Growth .3 20% -5% Stagnant .40 12% 13% Recession .3 -4% 24% 11. What is the expected return of returns for a portfolio with 50% invested in the Badd shares and 50% invested in the Guud shares? 12 Financial Management, Spring 2002 Dr. Brett A. King 12. What is the risk of the portfolio as measured by the standard deviation of expected returns? 13. If the CAPM holds true and T-bills are expected to yield 2.5% while the expected return on the market is 11%, what is the expected return on a stock with a beta of 1.95? 14. You have observed the following returns over time: Year 1990 1991 1992 1993 1994 BMG 12% 14% -12% 16% 9% Market 14% 7% -4% 11% 6% What is the beta for BMG, AND does the beta indicate more or less risk than an average stock and why? The total rates of return on equity securities is obviously affected by the business cycle. Business economists for the Boopie Co. predict the following outcomes for the economy, and the associated outcomes on their shares: Probability % Return Growth .30 28% Stagnant .50 -3% Recession .20 24% 15. What is the expected return and standard deviation of returns for the Boopie shares? You are looking at investing in shares of either Boopie or Bruno. The expected return for Bruno under the different economic conditions are as follows: Probability % Return Growth .30 35% Stagnant .50 22% Recession .20 30% 16. If you cannot invest in both companies (in problem 15), but rather must select only one, explain your choice. 13 Financial Management, Spring 2002 Dr. Brett A. King Consider the following information: Suppose the risk-free rate is 4.5%, and the following are returns for the S&P 500 and the stock for ALEX: Year 1995 1996 1997 1998 1999 S&P 500 21% 18% 13% 2% 10% ALEX 19% 21% 12% (8%) 17% 17. What is the beta for ALEX? (10 pts.) 18. If the market is expected to yield a 12% rate of return over the next year, what rate of return should ALEX yield? (10 pts.) Consider the following information regarding the possible returns of assets A and B and the market index: Economic Outlook Excellent Good Average Poor Probability .20 .30 .40 .10 A returns B returns Mkt Index 15% 6% 12% 11% 13% 9% 4% 3% 6% -2% 10% 5% 19. For a portfolio in which 65% of funds are invested in asset A, and the remainder in asset B, calculate the: a) expected return: b) risk (as measured by standard deviation of returns): 20. Which asset in the above questions (A and B)exhibits the most risk in the context of a well-diversified portfolio? Quantify and explain your answer. 14 Financial Management, Spring 2002 Dr. Brett A. King 21. Consider the following two assets: Probability .20 .30 .30 .20 Returns on A Returns on B 6% 10% 14% 4% 21% 8% 11% 12% What is the expected return AND standard deviation of a portfolio in which 78% is invested in asset B, with the remainder in asset A? 22. Consider the following possible economic conditions, the probabilities and possible returns for the following: Probability .05 .10 .30 .40 .15 Economy Recession Sluggish Moderate Recovery Growth Market -12% -9 2 6 13 AAA -17% -14 -5 8 22 Buzzco -4% 0 2 4 6 Samco 9% 5 3 8 -2 a) For AAA, Buzzco and Samco, find the expected returns and standard deviations. b) What are the correlation coefficients for AAA, Buzzco and Samco with the market? c) Calculate the beta for each security under this scenario. (Note that the probabilities aren’t equal) d) Based on the information in part a, what would the rate of return be if you held AAA and Buzzco such that the variance of that portfolio would be minimized? Do the same for Buzzco and Samco. e) Do any of these assets appear to dominate any of the others? Why or why not? 15 Financial Management, Spring 2002 Dr. Brett A. King f) Two years later, short-term Treasury securities are yielding 3.6% and the return on an average stock is expected to be 11%. Do any of these appear over or undervalued? Consider these expectations for the next year: Security AAA Buzzco Samco Dividend Yield 4% 2 3.5 Growth Rate – Earnings 8% 6 9 g) What assumptions underly your reasoning for deciding which securities are over or undervalued? 23. Your aunt holds the shares of a single company that have been passed down through generations, and have always performed quite well. She also believes (and you agree) that the company will continue to perform well over the foreseeable future. You then proceed to explain why holding just this one company – even though it is not risky, and is providing a nice rate of return – is not a very wise decision. What is your explanation? 16 Financial Management, Spring 2002 Dr. Brett A. King Time Value of Money 1. (This is not covered in the text) You have been tracking a non-dividend paying share that you purchased. Its price since you purchased it (t = 0) until today (t = 3) has been P0 = $27.50, P1 = $17.50, P2 = $31.50 and P3 = $26.50. a) Compute the periodic rates of return. b) Compute the arithmetic and geometric rate of return for this stock over the past three years. Which is the most appropriate measure? 2. With an 8% annual interest rate, how long does it take a sum of money to double given a) annual compounding, b) semi-annual compounding and c) daily compounding? 3. You are considering selling for $6,250 a Volvo which you purchased five years ago for $4,670. What would be your annualized rate of return on the Volvo investment? 4. Some day, you will buy an Acura NSX, drive it for 10 years and sell it for more than you paid for it. If you pay $89,000 for it and your expected rate of return is 6%, how much must you sell it for? 5. You deposit $1,200 into an account paying 8% compounded quarterly. How long does it take to accumulate $2,000. 6. Exactly three years ago you deposited $2,000 in an account paying 8.25% compounded monthly. Over the next one year, how much interest-on-interest, and interest-on-principal will be earned? 7. Your uncle marvels at the power of compound interest. He tells you that 10 years ago he deposited $10,000 in a savings account. Today, interest for the past year is being credited to the account; of that, the interest-on-interest will equal the interest-onprincipal. What is the savings rate on the account? 17 Financial Management, Spring 2002 Dr. Brett A. King 8. Joe and Ed, both of whom are 25 years old, are planning to retire at age 65. Joe decides to wait until he is 30 years old, at which time he will save $300 a month until he retires. Ed decides to start now and invest $300 a month until he is 30 years old – at which time he will not invest any more. If both can earn a 12% rate of return, who will have more at retirement? What is the difference in the actual out-of-pocket money invested between the two? 9. You wish to start a Christmas account at the local bank. Deposits will be made every week, with the first one in one week. In 40 weeks, at the time you make the final deposit, you will withdraw all accumulated funds. If your deposits are $75 weekly, and the interest rate is 7.5% compounded weekly, how much will be available for the withdrawal? 10. Four years from today, you expect to place a downpayment on a house. If the required downpayment is $14,000 and the interest rate is 7.25% compounded monthly, how much must you save each month (the first savings deposit occurs today, the last 4 years from today)? 11. If your savings target is $6,000 and you can afford to save $85 monthly, how many months must you save given the savings rate is 6.5% compounded monthly? 12. You are going to give your kid sister a nice $5,000 wedding gift and want to save up for it. You are going to begin saving four years from today. You expect she’ll get married 7 years from today. Suppose you make annual deposits with the last one in 7 years. Given an 8% interest rate, how much is the total principal you must save? 13. You wish to save $3,200 for a special present for aunt’s eightieth birthday party in California. You will begin saving exactly 2 months from now and will continue saving every month until you purchase and mail her gift in 18 months. With a savings rate of 6.75% compounded monthly, how much total interest will you earn on your savings? 18 Financial Management, Spring 2002 Dr. Brett A. King 14. You wish to establish an endowment fund that will generate a $2,000 scholarship each year perpetually. If the first scholarship is to be given one year from now, and the relevant interest rate is 8% compounded annually, how much must you deposit today? 15. You wish to establish an endowment fund that will generate a $2,000 scholarship each year perpetually. You make annual deposits, with the first one today and the final one in four years. If the first scholarship is to be given 5 years from today and the savings rate is 7.75% compounded annually, how much is each deposit? 16. You are setting up a scholarship fund for your favorite university by making monthly deposits into a savings account earning 9.75% compounded monthly. Your first deposit is today, and the last is in 4 years. You expect the perpetual endowment will finance student scholarships of $2,250 per year, with the first scholarship awarded exactly one year after the final deposit is made. The principal in the account will never be drawn-down (it too earns 9.75% compounded monthly ). According to this scenario, approximately how much must you deposit each month? 17. Your business partner offers you a position that should pay-off $900 per year for 8 years, followed by $600 per year for 6 years. In order to earn a rate of return equal to 12.5%, how much should you pay to get into the position? 18. You purchase a small business that costs $1,250. At the end of the first year, it returns profit to you of $750. At the end of the second and third years, respectively, it returns profit to you of $450 and $280. Then the business falls apart and is worthless. What was your rate of return? 19 Financial Management, Spring 2002 Dr. Brett A. King The following information pertains to problems 19 & 20: Eighteen months ago you borrowed $11,500 to purchase a used Rolls. The annual interest rate is 12% and the loan is to be repaid with monthly payments over two years. You have just remitted your eighteenth payment. 19. How much is each payment? 20. What is the total interest-to date you have paid? Problems 21 -23 go together 21. How much is the payment on a $10,000 loan given an interest rate of 12%, and 48 monthly payments? 22. How much of the eighth payment is interest expense? 23. How much of the eighth payment is principal repayment? The following information pertains to problems 24 & 25: The company borrowed $140,000 at 8.5% from The Bank. The loan was to be repaid over 20 years with 4 payments each year. They just remitted payment number 19. 24. How much interest will be paid over the life of the loan? 25. Due to a cash flow problem, The Bank needs to recover their money from the loan sooner than they had planned. They have made arrangements to sell the loan to another financial institution. The other institution intends to pick up 175 basis points beyond the 8.5% that The Bank was earning. How much does the other institution pay to purchase the loan? 26. With a 12% annual interest rate, how many years does it take a sum of money to double given quarterly compounding? 20 Financial Management, Spring 2002 Dr. Brett A. King 27. What is the monthly payment on a $3,000,000 loan financed at 7% over 15 years? 28. Five years from today, you expect to place a down payment on a house. If the required down payment is $40,000 and the interest rate is 4.85% compounded monthly, how much must you save each month (the first savings deposit occurs today, the last 5 years from today)? 29. You are setting up a scholarship fund for your favorite university by making monthly deposits into a savings account earning 4.35% compounded monthly. Your first deposit is today, and the last is in 4 years. You expect the perpetual endowment will finance student scholarships of $5,000 per year, with the first scholarship awarded exactly one year after the final deposit is made. The principal in the account will never be drawn-down (it too earns 4.35% compounded monthly ). According to this scenario, approximately how much must you deposit each month? 30. How much of the 16th payment on a $500,000 loan financed at 6% with monthly payments over 30 years will be applied towards the reduction of principal? 31. Your uncle marvels at the power of compound interest. He tells you that 8 years ago he deposited $20,000 in a savings account. Today, interest for the past year is being credited to the account; of that, the interest-on-interest will equal the interest-onprincipal. What is the savings rate on the account? 32. You currently have a 30-year fixed-rate mortgage financed at 7.25% on a $200,000 home. There are 25 years remaining on the mortgage. Your banker friend tells you that for a small fee (2% of the principal borrowed), you can refinance the remaining balance of your mortgage at a fixed rate of 5.75% for 25 years. What is the present value of the benefit (savings) to refinancing? 21 Financial Management, Spring 2002 Dr. Brett A. King 33. Your business partner offers you a position that should pay-off $5,000 per year for 8 years, followed by $1000 per year forever. In order to earn a rate of return equal to 16.5%, how much should you pay to get into the position? 34. You purchase a small business that costs $25,000. At the end of the first year, it returns profit to you of $5000. At the end of the second and third years, respectively, it returns profit to you of $7000 and $12000. Then, after 4 years, you sell the business for $30,000. What is your rate of return on this investment? 35. You currently have a 30-year fixed-rate mortgage financed at 10.25% on a $250,000 home. There are 20 years remaining on the mortgage. Your banker friend tells you that for a small fee (3% of the principal borrowed), you can refinance the remaining balance of your mortgage at a fixed rate of 9% for 20 years. Should you refinance, why or why not? 36. Your business partner offers you a position that should pay-off $1,000 per year for 8 years, followed by $800 per year forever. In order to earn a rate of return equal to 13.5%, how much should you pay to get into the position? 37. You wish to establish an endowment fund that will generate a $2,000 scholarship each year perpetually. You make annual deposits, with the first one today and the final one in four years. If the first scholarship is to be given 5 years from today and the savings rate is 7.75% compounded annually, how much is each deposit? The following information pertains to problems 38- 40: Eighteen months ago you borrowed $11,500 to purchase a used Rolls Royce. The annual interest rate is 12% and the loan is to be repaid with monthly payments over two years. You have just remitted your eighteenth payment. 38. How much is each payment? 39. What is the total interest-to date you have paid? 40. How much of this payment will be applied towards principal reduction? 22 Financial Management, Spring 2002 Dr. Brett A. King Bonds For problems 1 - 3: A bond with a 20-year maturity was issued last year. Interest rates for similar bonds were 12.5%. The bond was issued at par and promises semiannual coupons. 1. What are the expected cash flows for the bond? What was its price when issued? If interest rates were unchanged as of today, what would be the market price of the bond today? For this scenario, what would have been an investors annual ROR? 2. Suppose that today, one year later, interest rates are 11.8%. What is the bond price today? 3. Consider the individual that purchased the bond one year ago and is selling it today. What was their rate of return if interest rates today are 11.8%? For problems 4 - 8: It is January 1995, and you observe the following price quote: IBM 6 1/2s06 Close 88 3/4 4. What is today’s annual yield to maturity for this bond? 5. Suppose interest rates were to remain constant. What would be the bond price on Jan. 1, 1996? 6. Suppose interest rates were to remain constant. What would be the rate of return from buying the bond, holding it for one year, and selling it at its new market price? 7. You would like to make a bid on Jan. 1, 1995, such that the yield to maturity is 8.5%. What price should you offer? 23 Financial Management, Spring 2002 Dr. Brett A. King 8. Suppose you buy the bond on Jan. 1, 1995 at the quoted price. If you sell the bond after exactly one year and expect that interest rates will have increased by 200BP, what will be the selling price and your rate of return? 9. The yield to maturity for a 2-year zero-coupon bond is 8.25%. Sketch the cash flows and rate of return for a 2-year investment in this asset. 10. For a 4-year zero-coupon bond, the yield to maturity is 8.45%. You expect that for a given term, interest rates will remain unchanged. As is normal, the yield curve is sloped upward and yield increases with term. You are going to enhance your returns by following a strategy called “riding the yield curve”: you buy the long-term bond and sell it after its yield has fallen to the short-term rate (as given in problem 9). What is your rate of return from following this strategy? 11. It is January 2005, and you observe the following price quote: BK Corp. 5 1/2s17Dec Close 87 3/4 Suppose interest rates were to fall by 2.0% over the next year. What would be the rate of return from buying the bond today, holding it for one year, and selling it at its new market price? For problems 12 -14: It is January 2005, and you observe the following price quote: COR 8 1/2s22 Close 97 3/4 12. (10 pts.) What is today’s annual yield to maturity for this bond? 13. (10 pts.) You would like to make a bid on Jan. 1, 2005, such that the yield to maturity is 8.5%. What price should you offer? 14. (15 pts.) Suppose you buy the bond on Jan. 1, 2005 at the quoted price. If you sell the bond after exactly two years and expect that interest rates will have decreased by 140 BP, what rate of return would you realize? 24 Financial Management, Spring 2002 Dr. Brett A. King For problems 16 -17: It is January 2002, and you observe the following price quote: IBM 8 1/2s12Dec Close 86 ¾ 15. What is today’s annual yield to maturity for this bond? 16. Suppose you buy the bond on Jan. 1, 2002 at the quoted price. If you sell the bond after exactly one year and expect that interest rates will have decreased by 150BP, what will be the selling price and your rate of return? For problems 17 - 18: It is January 2005, and you observe the following price quote: IBM 7 1/2s17 Close 91 3/4 17. What is today’s annual yield to maturity for this bond? 18. Suppose interest rates were to fall by 1.5%. What would be the rate of return from buying the bond, holding it for one year, and selling it at its new market price? 19. The yield to maturity for a 2-year zero-coupon bond is 6.45%. For a 4-year zerocoupon bond, the yield to maturity is 5.85%. You expect that for a given term, interest rates will remain unchanged. As is normal, the yield curve is sloped upward and yield increases with term. You are going to enhance your returns by following a strategy called “riding the yield curve”: you buy the long-term bond and sell it after its yield has fallen to the short-term rate. However, when you sell the bond, the yield curve has shifted such that 2-year bonds are now yielding 85 basis points higher than they were 2 years ago. What is your rate of return from following this strategy? 25 Financial Management, Spring 2002 Dr. Brett A. King 20. The yield-to-maturity of a bond (YTM) makes an assumption regarding reinvestment. Which poses more reinvestment risk: an environment in which interest rate are increasing, or where rates are decreasing – and why? For problems 21 - 22: It is January 2004, and you observe the following price quote: IBM 9 1/2s26 Close 94 1/4 21. What is today’s annual yield to maturity for this bond? (5 pts.) 22. Suppose interest rates were to remain constant. What would be the bond price on Jan. 1, 2006? (5 pts.) 23. Suppose interest rates were to fall by 2.5% three years later. What would be the rate of return from buying the bond, holding it for three years, and selling it at its new market price? (10 pts.) 24. What are “call provisions”, and how do they affect a bond’s value? 26 Financial Management, Spring 2002 Dr. Brett A. King Stocks The following information pertains to questions 1 & 2: Your best assessment is that a particular share will be paying dividends of $1.40 one year from now, $1.75 in 2 years and $2.00 in 3 years. You believe this share could be sold in 3 years for $30. 1. If the stock’s current price is $24, and your assessment seems in line with popular opinion, what is the implied total rate of return on the investment? 2. On the other hand, you won’t undertake the investment for an expected return less than 16%. What price should you bid for the share? 3. A share of stock paid its annual dividend of $1.16 exactly 4 years ago and you expect that next year’s dividend will equal $1.60. Your analyst tells you the stock’s expected total return is 11.89%, and that the stock’s current price is $35.04. According to the constant dividend growth model, what is the stock’s intrinsic value and, more importantly, should you buy the stock? The following information pertains to questions 4 - 6: Assume the constant growth model is true. A share of stock paid its annual dividend of $.90 exactly 4 years ago and just yesterday it paid a $1.45 dividend. Your analyst tells you the stock’s expected dividend yield is 8.15%. 4. What is the dividend growth rate for the stock? 5. What is the expected total rate of return for the stock? 6. What is the stock’s intrinsic value? 27 Financial Management, Spring 2002 Dr. Brett A. King 7. You pick up the Wall Street Journal and see that short-term government securities are offering 6.35%. You read that the company just increased their annual dividend by $.12 so that today it is paying a $1.94 dividend per share. You also read that the share price is $36.20. What is the implied risk premium that is earned from owning the stock; that is, by how much does the expected return on the stock exceed the riskless rate? 8. A share of stock just paid a $2.30 dividend. If the total return on the security is 14% and the dividend yield is 4%, what should the stock be selling for today? 9. You are interested in purchasing some shares in a company that you believe will experience tremendous growth over the next few years. Specifically you expect that no dividends will be paid for the next two years. However, in year three, you expect that a dividend of $.65 will be paid. Further more, in years four through six, you expect the dividend to increase by 25% each year. After which, the company growth rate will slow to 7% annually. If the required return on this investment is 15%, what would the intrinsic value of this stock be? (20 pts.) 10. A share of stock paid its annual dividend of $1.20 exactly 4 years ago and you expect that next year’s dividend will equal $1.35. Your analyst tells you the stock’s expected total return is 17%, and that the stock’s current price is $36.00. According to the constant dividend growth model, what is the stock’s intrinsic value and, more importantly, should you buy the stock? 11. Your best assessment is that a particular share will be paying dividends of $1.40 one year from now, $1.95 in 2 years and $2.15 in 3 years. You believe this share could be sold in 3 years for $42. At what price would this stock provide a 10% return? 12. If the stock’s current price is $28, and your assessment seems in line with popular opinion, what is the implied total rate of return on the investment? 13. On the other hand, you won’t undertake the investment for an expected return less than 25%. What price should you bid for the share? 28 Financial Management, Spring 2002 Dr. Brett A. King 14. You pick up the Wall Street Journal and see that short-term government securities are offering 6.35%. You read that the company just increased their annual dividend by $.20 so that today it is paying a $1.75 dividend per share. You also read that the share price is $34.70. What is the implied risk premium that is earned from owning the stock; that is, by how much does the expected return on the stock exceed the riskless rate? 15. A share of stock paid its annual dividend of $1.12 exactly 3 years ago and you expect that next year’s dividend will equal $1.40. Your analyst tells you the stock’s expected total return is 14.25%, and that the stock’s current price is $31.50. According to the constant dividend growth model, what is the stock’s intrinsic value and, more importantly, does the stock appear to be over-priced or under-priced? 16. A share of stock paid its annual dividend of $1.25 exactly 2 years ago and you expect that next year’s dividend will equal $1.80. Your analyst tells you the stock’s expected total return is 24%, and that the stock’s current price is $28.12. According to the constant dividend growth model, what is the stock’s intrinsic value and, more importantly, should you buy the stock? The following information pertains to questions 17 - 19: Assume the constant growth model is true. A share of stock paid its annual dividend of $.95 exactly 5 years ago and just yesterday it paid a $1.65 dividend. Your analyst tells you the stock’s expected dividend yield is 8.15%. 17. What is the dividend growth rate for the stock? 18. What is the expected total rate of return for the stock? 19. What is the stock’s intrinsic value? 20. A share of stock paid its annual dividend of $1.07 exactly 5 years ago and you expect that next year’s dividend will equal $1.60. Your analyst tells you the stock’s expected total return is 16%, and that the stock’s current price is $25.50. 29 Financial Management, Spring 2002 Dr. Brett A. King According to the constant dividend growth model, what is the stock’s intrinsic value and, more importantly, should you buy the stock? Weighted Average Cost of Capital 1. Your boss is considering borrowing $10,000 from a bank at 8% for a project. She has determined that the rate of return on the project is expected to be 12%. She comments that since the project is earning more than the cost of the debt, it should definitely be undertaken. You assert that the company’s average cost of capital is 13% and the project should not be undertaken. Surprised with your assertiveness she replies, “I don’t care about the average cost of capital. I am only using this debt to finance the project. Since this debt only costs 8%, and the project should earn 12%, it will be profitable!!” Defend your assertion that the project should not be undertaken. Consider the following components of the firm’s balance sheet: Debt………………$25,000 Common Equity….$95,000 Preferred Equity….$35,000 Total assets equal $155,000. The preferred stock is currently selling at $35 and receives an annual dividend of $4.00. Currently, the common stock is trading at $67.75. The last dividend paid was $3.25, which was up $.25 from the prior year. The bonds for the firm are trading at 95% of par and pay a semi-annual coupon of 7.5%. The tax rate is 38%. 2. What is the WACC for the firm? 3. If the firm issued new stock, the float cost would be $1 per share. How would this affect the cost of capital if new shares had to be issued? 30 Financial Management, Spring 2002 Dr. Brett A. King 4. Consider the following components of the firm’s balance sheet: Debt………………$45,000 Common Equity….$85,000 Preferred Equity….$15,000 Total assets equal $145,000. The preferred stock is currently selling at $37 and receives an annual dividend of $3.95. Currently, the common stock is trading at $55. The last dividend paid was $3.15, which was up $.25 from the prior year. The bonds for the firm are trading at 97% of par mature in 10 years and pay a semi-annual coupon of 9.5%. The tax rate is 40%. What is the WACC for the firm? For problems 5 – 8: TK estimates that it can issue debt at a before-tax cost of 12%, and its tax rate is 36%. The company can also issue preferred stock at $45 per share, which pays a constant dividend of $3.50 annually. Floatation costs on the preferred are $1.50 per share. Net income is estimated to be $3,200, and the firm plans to maintain its policy of paying out 30% as dividends. The company’s stock currently sells for $37 per share. The next dividend is expected to be $2.55, which is $.17 higher than the most recent dividend. Furthermore, these dividends are expected to continue to grow at the same rate. Float costs on newly issued common stock are $2.50 per share. The company’s balance sheet is as follows: PP&E $4,500 Cash $1,500 Inventories $3,000 Total Assets $9,000 Debt $2,200 Preferred Stock $ ? Common Equity $4,500 Total Liab. $ ? 5. What is the cost of retained earnings? 6. What is the relevant cost of debt? 7. What is the cost of preferred financing if new preferred stock is issued? 8. What is the current WACC for the company? 31 Financial Management, Spring 2002 Dr. Brett A. King Consider the following information: VK estimates that it can issue debt at a before-tax cost of 10%, and its tax rate is 35%. The company can also issue preferred stock at $40 per share, which pays a constant dividend of $5 annually. Floatation costs on the preferred are $1 per share. Net income is estimated to be $253,900, and the firm plans to maintain its policy of paying out 30% as dividends. The company’s stock currently sells for $41 per share. The next dividend is expected to be $2.75, which is $.20 higher than the most recent dividend. Furthermore, these dividends are expected to continue to grow at the same rate. Float costs on newly issued common stock are $3 per share. The company’s balance sheet is financed with optimal proportions of debt and equity and is as follows: PP&E $250,000 Cash $100,000 Inventories $300,000 Total Assets $650,000 9. What is the cost of retained earnings? 10. What is the relevant cost of debt? 11. What is VK’s WACC? 32 Debt $250,000 Preferred Stock $ ? Common Equity $300,000 Total Liab. $ ? Financial Management, Spring 2002 Dr. Brett A. King For problems 12 - 15: Consider the following: VK estimates that it can issue debt at a before-tax cost of 8%, and its tax rate is 40%. The company can also issue preferred stock at $30 per share, which pays a constant dividend of $4.00 annually. Floatation costs on the preferred are $3 per share. Net income is estimated to be $45,000, and the firm plans to maintain its policy of paying out 60% as dividends. The company’s stock currently sells for $26 per share. The next dividend is expected to be $1.15, which is $.20 higher than the most recent dividend. Furthermore, these dividends are expected to continue to grow at the same rate. If the company maintains its capital structure, the cost of debt will remain constant. Furthermore, while there are float costs associated with the issuance of new preferred stock, the company has shelf-registered common stock that it can issue without incurring float costs. The company’s balance sheet is as follows (in 000s): PP&E $5,800 Cash $1,200 Inventories $3,000 Total Assets $10,000 12. What is the retained earnings breakpoint? 13. What is the cost of retained earnings? 14. What is the relevant cost of debt? 15. What is the current WACC for VK company? 33 Debt $3,000 Preferred Stock $2,000 Common Equity $5,000 Total Liab. $10,000 Financial Management, Spring 2002 Dr. Brett A. King For problems 16 – 19: Consider the following: BK estimates that it can issue debt at a before-tax cost of 9%, and its tax rate is 40%. The company can also issue preferred stock at $40 per share, which pays a constant dividend of $4.00 annually. Floatation costs on the preferred are $3 per share. Net income is estimated to be $75,000, and the firm plans to maintain its policy of paying out 50% as dividends. The company’s stock currently sells for $26 per share. The next dividend is expected to be $1.35, which is $.20 higher than the most recent dividend. Furthermore, these dividends are expected to continue to grow at the same rate. If the company maintains its capital structure, the cost of debt will remain constant. Furthermore, while there are float costs associated with the issuance of new preferred stock, the company has shelf-registered common stock that it can issue without incurring float costs. The company’s balance sheet is as follows (in 000s): PP&E $5,800 Cash $1,200 Inventories $3,000 Total Assets $10,000 Debt $2,200 Preferred Stock $3,800 Common Equity $4,500 Total Liab. $10,000 16. What is the retained earnings breakpoint? 17. What is the cost of retained earnings? 18. What is the relevant cost of debt? 19. What is the WACC for BK company assuming they have to raise new capital? 20. Your boss is considering borrowing $10,000 from a bank at 8% for a project. She has determined that the rate of return on the project is expected to be 12%. She comments that since the project is earning more than the cost of the debt, it should definitely be undertaken. You assert that the company’s average cost of capital is 13% and the project should not be undertaken. Surprised with your assertiveness she replies, “I don’t care about the average cost of capital. I am only using this debt to finance the project. Since this debt only costs 8%, and the project should earn 12%, 34 Financial Management, Spring 2002 Dr. Brett A. King it will be profitable!!” Defend your assertion that the project should not be undertaken. NPV / IRR For problems 1 & 2: Consider the following cash flows for two mutually exclusive investments: A B t=0 ($97) ($198) t=1 $51 $56 t=2 $51 $54 t=3 $22 $128 1. What are the internal rates of return for the projects? Which project is best? 2. Accurately sketch the NPV profiles for the projects. What are the NPV decision rules throughout the domain of financing rates? 3. If you spend $100,000 on an advertising campaign and it helps generate the following increases in profits, should you borrow at 8% to undertake this? (10 pts.) Year 1 2 3 4 Profits $25,000 $45,000 $30,000 $10,000 35 Financial Management, Spring 2002 Dr. Brett A. King 4. The company is considering a proposed project for its capital budget. The company estimates that the project’s NPV is $12 million. This estimate assumes that the economy and market conditions will be average over the next few years. The company’s CFO, however, forecasts that there is only a 50% chance that the economy will be average. Recognizing this uncertainty, she has also performed the following scenario analysis: Economic Scenario Recession Below Average Average Above Average Boom Probability .05 .20 .50 .20 .05 NPV ($50 million) (15 million) 12 million 20 million 30 million What is the project’s expected NPV and standard deviation? For problems 5 – 8, consider the expected net cash flows for the following two mutually exclusive investment opportunities: Year 0 1 2 3 4 5 6 7 Project A ($300) (387) (193) (100) 600 600 850 (180) Project B ($405) 134 134 134 134 134 134 0 5. Construct NPV profiles for Projects A and B. Clearly label the graph. 6. If the WACC is 10%, which project should be selected? 7. If the WACC was 17%, which project should be selected? 8. What is the crossover rate for these two projects? 36 Financial Management, Spring 2002 Dr. Brett A. King Cash Flow Estimation and Investment Decisions For problems 1 - 3: A proposed two-year project has expected sales that will begin at $28,000 during the first year and rise 8% during the second year. Its start-up costs are $18,000 and variable costs equal 60% of sales. The start-up costs are depreciated to zero by straight-line over a twoyear tax life. No salvageable assets will remain beyond the project life. The tax rate is 39%. 1. Sketch the project cash flow stream. 2. State the IRR decision rule for this project. 3. Given a 14% financing rate, what is the maximum feasible cost for the project? 37 Financial Management, Spring 2002 Dr. Brett A. King For problems 4 -7: The company is considering a short-term expansion into a new product line making commemorative plates for the Olympics which are scheduled to occur 4 years henceforward. The following factors must be weighted in their decision: a. the plate presser costs $32,000 and may be depreciated for tax purposes along a 7-year MACRS class (wts. 14.29%, 24.49%, 17.49%, 12.49%, 8.93%, 8.93%, 8.93% and 4.45%) b. commemorative plates sell for $30 each and variable costs are $16 per plate c. projected sales over the next four years are 500, 800, 1,000 and 2,000 plates. d. the plate presser loses half of its market value for each year of use; it will be sold after 4 years e. the financing rate is about 14% and the tax rate is 39% f. product research fees of $6,000 were spent on developing the expansion plan 4. What are the depreciation tax savings for this project? 5. What are the net proceeds from selling the asset after its fourth year of use? 6. What are the incremental cash flows for this project? 7. What is the IRR and NPV for the project? 38 Financial Management, Spring 2002 Dr. Brett A. King For problems 8 – 11: You have been asked by the president of your company to evaluate the proposed acquisition of a new hydropropolaser for the R&D department. The price for this equipment is $80,000, and it would cost another $12,000 to modify it for special use by your firm. The hydropropolaser, which has a MACRS 3-year recovery period (wts. 33%, 45%, 15%, 7%) would be sold after 3 years for $40,000. Use of this equipment would require an increase in net working capital of $8,000. The hydropropolaser would have no effect on revenues, but it is expected to save the firm $27,000 per year in before-tax operating costs, mainly labor. The firm’s marginal tax rate is 36%. 8. What is the initial net investment for the machine (CF0)? 9. What are the net operating cash flows from this project for years 1 –3? 10. What are the additional cash flows from this project in year 3? 11. If the firm’s WACC is 12%, should they purchase the hydrpropolaser? 39 Financial Management, Spring 2002 Dr. Brett A. King 12. Your firm is considering expanding operations into Thailand. The government there has donated land if you build a plant there. The plant would cost roughly 25,000,000 $US. The plant could be depreciated on a 7-yr. MACRS schedule (same as in US). The firm’s marginal tax rate is 36%. The operation is expected to generate the following number of units over the coming years: Year 1 2 3 4 Number of Units 160,000 240,000 310,000 350,000 After the fourth year, unit production will be maintained at 350,000 per year. Variable costs are expected to be $28 per unit and the selling price is expected to be $39. Furthermore, production at this plant is expected to save the firm $50,000 per year in pretax expenses by producing the product there instead of in their current facilities. Furthermore, the current stock price for the common shares outstanding is $28. The last dividend paid was $1.55, and has been growing at a constant 12% annually. Preferred shares are trading at $35 and pay a $5 dividend annually. The bonds of the firm are trading at 97.7% of par, have 14 years until maturity and a coupon rate of 12%. The capital structure, with assets financed with 35% debt, 55% common and 10% preferred is deemed optimal, and should remain constant in the future. The firm currently has no retained earnings available. All funds would need to be raised by issuing new common, preferred and debt. After incurring investment banking fees, the firm would receive $985 for each bond (and would mature in 25 years at a coupon set at current market rates for the old bonds), $34.5 on new preferred and $26.50 on new common stock issuance. a) What is the relevant cost of debt to the firm if they undertake this project? b) What is the cost of common equity if the project is undertaken? c) What is the cost of preferred stock if the project is undertaken? d) What would the appropriate discount rate be for this project – assuming it’s risk characteristics were identical to the rest of the firm’s assets – and assuming the firm maintains it’s capital structure? 40 Financial Management, Spring 2002 Dr. Brett A. King e) What are the relevant cash flows for this project? f) Should the firm invest in the Thailand project? WHY or WHY NOT? Consider the following information for problems 13 - 16.: . Your firm is considering expanding operations into Malaysia. The government will donated the land if you build a plant there. The plant would cost roughly 12,000,000 $US. The plant could be depreciated on a 7-yr. MACRS schedule (same as in US). The firm’s marginal tax rate is 38%. The operation is expected to generate the following number of units over the coming years: Year 5 6 7 8 Number of Units 125,000 150,000 200,000 250,000 After the fourth year, unit production will be maintained at 300,000 per year. Variable costs are expected to be $23 per unit and the selling price is expected to be $32. Furthermore, production at this plant is expected to save the firm $20,000 per year in pretax expenses by producing the product there instead of in their current facilities. Research and development costs for this project have totaled $50,000 Furthermore, the current stock price for the common shares outstanding is $32. The last dividend paid was $1.75, and has been growing at a constant 12% annually. Preferred shares are trading at $40 and pay a $5 dividend annually. The bonds of the firm are trading at 96.7% of par, have 12 years until maturity and a coupon rate of 8%. Net income for the coming year is expected to be $15,000,000 and the retention ratio is set at 30%. The capital structure, with assets financed with 35% debt, 55% common and 10% preferred is deemed optimal, and should remain constant in the future. The firm currently has no common, preferred or bonds left to issue. Any new external funds would need to be raised by issuing new common, preferred and debt. After incurring investment banking fees, the firm would receive $990 for each bond (and would mature in 20 years at a coupon set at current market rates for the old bonds), $38 on new preferred and $28 on new common stock issuance. 41 Financial Management, Spring 2002 Dr. Brett A. King 13. What is the payback period on this project? 14. If the payback period is not an issue, should the firm undertake this project? 15. Would the firm want invest in the project if the unit production levels after year 4 dropped to 100,000 per year? 16. What if another project, Project D, had an expected return of 54% and was mutually exclusive of this project (with the original production estimates). Should the company automatically choose project D? Why or why not? 17. A proposed 2-year project has expected sales that will begin at $20,000 during the first year and rise by 15% in each of the next following years. Start-up costs are $29,000 and variable costs are expected to be 55% of sales. The start-up costs can be depreciated under the straight-line method over 6 years. The equipment is expected to be sold in 6 years for $5,000. The tax rate is 39%. If the WACC is 14%, should the project be undertaken? (Show all relevant cash flows) 42 Financial Management, Spring 2002 Dr. Brett A. King Cash and Current Asset Management 1. On a typical day, TK Corp. writes $10,000 in checks. It generally takes 4 days for those checks to clear. Each day, the firm typically receives $10,000 in checks that take 3 days to clear. What is the firm’s average net float? 2. The firm reported sales last year of $10 million and an inventory turnover ratio of 2. The firm is now adopting a just-in-time inventory system which will reduce the firm’s inventory level and increase th turnover ratio to 5, while maintaining the same level of sales. How much cash will be freed up? 3. What is the nominal and effective cost of trade credit (360-day basis) under the terms 3/15 net 30? 4. A large retailer obtains merchandise under the credit terms of 1/15 net 45, but routinely takes 60 days to pay its bills. Given that the retailer is an important customer, suppliers allow the firm to take the discount. What is the retailer’s effective cost of trade credit? (assume 360 day basis) 5. You are negotiating with FirstBank for a $50,000 1-year loan. They have offered you the following alternatives. Which is best from your point of view? a- 12%, simple interest, no compensating balance and interest due at the end of the year. b- 9%, simple interest, 20% compensating balance and interest due at year end. c- 8.75%, discounted loan with 15% compensating balance. d- Interest figured as 8% of loan amount, payable at year end, but principal is repaid monthly. 43 Financial Management, Spring 2002 Dr. Brett A. King 44 Financial Management, Spring 2002 Dr. Brett A. King Options/Futures Strike 155 160 165 170 Calls Jul Aug 10.5 11.75 6 8.125 2.6875 5.25 .8125 3.25 Oct 14 11.125 8.125 6 Puts Jul Aug .1875 1.25 .75 2.75 2.375 4.75 5.75 7.5 Oct 2.75 4.5 6.75 9 It is currently July 6. The stock pays no dividends and is priced at 165 1/8. The expirations are July 17, August 21 and October 16. 1. What is the intrinsic value of the Aug 160 calls? 2. Why is the price of the call higher than it’s intrinsic value? 3. Suppose you purchased the Oct. 170 calls. What would your return be if the stock price ended at $185 on Oct. 16? What if the price ended at $160? How do these rates of return compare to just buying and selling the stock? 4. What would the stock price have to be on Oct 16 for your rate of return on an Oct put option to be 100%? 5. Suppose you entered into a straddle with the Oct. 170 calls and puts. What would your rate of return be if the price ended up being $200? $100? $175? 45 Financial Management, Spring 2002 Dr. Brett A. King 6. Assume the following: Current Stock Price = $20 3 month call option Variance of stock returns = 17% Risk-free rate = 4.5% Exercise price = $15 Using The BS OPM, what would be the value of this option? 7. Assume the following: Current Stock Price = $10 3 month call option Variance of stock returns = 22% Risk-free rate = 4.5% Exercise price = $12 Using The BS OPM, what would be the value of this option? 8. Consider a stock that is currently trading at $85. In 1 year, the stock will be trading at either $120 per share or $60 per share. A call option with a strike price of $90 can be bought or sold on this share of stock. If short-term Treasury securities are yielding 4%, what would the equilibrium value of this option be using the binomial approach? 46 Financial Management, Spring 2002 Dr. Brett A. King Consider the following information for problems 9 & 10.: Strike 155 160 165 170 Calls Jul Aug 10.5 11.75 6 8.125 2.6875 6.45 .8125 3.25 Oct 14 11.125 8.125 5.50 Puts Jul Aug .1875 1.25 .75 2.75 2.375 4.75 5.75 7.5 Oct 2.75 4.5 6.75 9 It is currently July 6. The stock pays no dividends and is priced at $167.00. The expirations are July 17, August 21 and October 16. 9. Suppose you purchased the Oct. 170 calls. What would your return be if the stock price ended at $183 on Oct. 16 AND how does this rate of return compare to just buying and selling the stock? 10. Suppose you entered into a straddle with the Aug. 165 calls and puts. What would your rate of return be if the price ended up being $205? 47 Financial Management, Spring 2002 Dr. Brett A. King 11. UT Socks, Inc. is considering the purchase of a piece of property that sells for $1.8 million. If the property is purchased, the company plans to spend another $4 million immediately to build a dirt manufacturing plant. The after-tax cash flows however, would depend critically on whether the state imposes a dirt tax in this year’s legislative session. If the tax is imposed, the dirt project is expected to produce aftertax inflows of $500,000 at the end of the next 20 years. If the tax is not imposed, the cash flows are expected to be $1 million. The WACC for the company is 11.5%, and Treasury bills are yielding 3.2%. Using decision tree analysis, answer the following: a) What is the project’s expected NPV if the tax is imposed? b) What is the project’s expected NPV if the tax is not imposed? c) If there is a 50% chance that the tax will be imposed, what is the project’s expected NPV if they proceed today? d) While the company does not have an option to delay construction, it does have the option to abandon the project 1 year from now if the tax is imposed. If it does, the plant could be sold in 1 year for $5 million, at which point there would be no further cash flows. Would this option affect the company’s decision to proceed with the project today? e) Now assume that there is no option to abandon or delay the project, but that the company has an option to purchase an adjacent property in one year at a price of $2 million. If the tax is imposed, the NPV of developing the property (at t = 1) is only $275,000 (so it wouldn’t make sense to purchase the property for $2 million. However, if the tax is not imposed, the NPV of future opportunities from developing the property would be $3.75 million (at t = 1). Thus, under this scenario it would make sense to purchase the property. How much would the company be willing to pay today for this option? 48 Financial Management, Spring 2002 Dr. Brett A. King Multinational Finance 1. A currency trader observes that in the spot exchange market, 1 U.S. Dollar can be exchanged for 1,498.2 Rubels or for 111.23 Japanese Yen. What is the crossexchange rate between the Yen and the Rubel. 2. 6-month T-bills have a nominal rate of 7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5%. In the spot exchange market, 1 Yen equals $.009. If interest rate parity holds, what is the 6 month forward exchange rate? 3. A television set costs $500 in the U.S. The same set costs 2,535 Euros. If purchasing power parity holds, what is the spot exchange rate between the Euro and the Dollar? 4. If British Pounds sell for $1.50 (U.S.) per Pound, what should Dollars sell for in Pounds per Dollar? 5. Suppose that 1 Euro could be purchased in the foreign exchange market for 20 U.S. cents today. If the Euro appreciated 10 percent tomorrow against the Dollar, how many Euros would a Dollar buy tomorrow? 6. Suppose current exchange rates are 1.65 Euro/$US and 116.31 Yen/$US. A local trader is offering to exchange 72.225 Yen/Euro. What, if any arbitrage opportunities exist? (Show an example using $1,000,000). 7. Inflation obviously affects exchange rates. Suppose the current exchange rate for Pesos is 7.78/$ and that inflation is 4% in the U.S. and 15% in Mexico. Furthermore, a VW sells for $12,000. All else constant, what would be the new exchange rate for Pesos/$ after 1 year? 8. What is meant by “interest rate parity”? 9. What is the underlying assumption which motivates the expectations theory of exchange rates? 49 Financial Management, Spring 2002 Dr. Brett A. King 10. As CEO of your company, you have agreed to purchase High Definition TVs which you intend to sell in the U.S. The TVs are manufactured in Japan. You agree now on the price you will pay when you take delivery of the TVs in 6 months. What is the risk your shareholders face with respect to the Yen/$ exchange rate? 11. 6 -month T-bills have a nominal rate of 5%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 7.2%. In the spot exchange market, 1 Yen equals $.0085. If interest rate parity holds, what is the 6 month forward exchange rate? 12. Suppose that 1 Euro could be purchased in the foreign exchange market for 17 U.S. cents today. If the Euro appreciated 15 percent tomorrow against the Dollar, how many Euros would a Dollar buy tomorrow? 13. A currency trader observes that in the spot exchange market, 1 U.S. Dollar can be exchanged for 1,562.78 Euros or for 106.27 Japanese Yen. If a bank offers to exchange 14.95 Euro/Yen, what (if any) arbitrage profits could be earned? (Use $1,000,000) 14. 6-month T-bills have a nominal rate of 4%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 6.2%. In the spot exchange market, 1 Yen equals $.0074. If interest rate parity holds, what is the 6 month forward exchange rate? 15. A television set costs $5,500 in the U.S. The same set costs 17,535 Thai Bahts. If purchasing power parity holds, what is the spot exchange rate between the Baht and the Dollar? 16. If forward rates are an unbiased estimate of future exchange rates, what would a discounted forward rate (relative to $US) mean - in terms of profitability - for a European firm with the majority of its sales coming from exports to the U.S.? 50 Financial Management, Spring 2002 Dr. Brett A. King Risk Management Example Problem and Solution Interest rate fluctuations can be hedged with T-bill or T-bond futures contracts. T-bond futures contracts are for a 20-yr., 8% coupon, $100,000 semi-annual bond. For example, a June T-bond contract selling at 112 implies the following: Someone agrees today to purchase a T-bond in June. Thus they can guaranty a rate of return they will receive from purchasing the bond in June, today. What rate of return? PV=1120 FV=1000 PMT=40 P/Y=2 N=40 I/Y=?=6.23%. Thus, if interest rates change between now and June, the rate of return is going to be 6.23% regardless. This is an example of “going long”. You do this to protect your return if interest rates were to fall. You can also “short” a contract to protect yourself from adverse returns should interest rate rise between now and the time you plan to borrow or issue debt. Example: You wish to purchase a house sometime between now and June. You are afraid that interest rates will rise before you decide on a house and take out a mortgage. Suppose you are looking to buy a $200,000 house. Currently, interest rates are at a low of 5% for 30-yr. fixed rate mortgages. To hedge against possible interest rate increases, you can short T-bond futures. June contracts are currently listed at 137.654. T-bond futures contracts call for a margin to be placed at the time of the purchase agreement. It is $3,000 per contract. You would want to short 2 contracts, so you would need to deposit $6,000 with your broker. Now suppose interest rates rise to 7.5%. 51 Financial Management, Spring 2002 Dr. Brett A. King First, it’s bad news for your mortgage payment: At 5%: At 7.5%: Difference in monthly payments: PV=200,000 FV=0 N=360 P/Y=12 I/Y=5 PMT=?=1,073.64 PMT=1,398.43 1,398.43 – 1,073.64 = 324.89 The present value of 324.89 a month for 360 months = 46,450. However, on the short futures position: You agreed to deliver 2, $100,000 bonds in June. You agreed on a price of 137.654, which implies: 2 X 100,000 X 1.37654 = $275,308 received now. In June, to cover your position, you will now pay: PV=?=105,137 X 2 = $210,274 FV=100,000 N=40 P/Y=2 PMT=4,000 I/Y=7.5 Your profit on the futures is 275,308 – 210,274 = $65,034 Your net gain/loss = 65,034 – 46,450 = $18,584. 52 Financial Management, Spring 2002 Dr. Brett A. King 1. In problem 10 of the exchange rate problems, how might the CFO hedge the position taken by the CEO to mitigate the possible negative effects against shareholders? 2. In problem 1, do you believe shareholders would want the risk eliminated? 3. A company would like to issue $750,000,000 in new debt (30-year bonds) while rates are low. Currently the investment bank estimates the rates on new bonds for the firm would be set at 8.7%. However, it will be 6 months before the firm can issue the bonds. They decide to hedge using Treasury Bond futures. If interest rates did increase by 125 BP in 6 months before they can issue the bonds, show the net effect of the hedge. Standard T-Bond futures contracts are currently priced at 107.5. 53 Financial Management Problem Solutions – Dr. Brett A. King Accounting Fundamentals & Financial Analysis 11. $3,000 12. $1,950 13. $2,230 14. $1,427 15. $580 16. $255 17. $150 18. $950 19. $445 20. $680 21. $335 22. $577,000 23. .28 x .3571 x 2.8 = 28% 24. Look at CA vs. CL… 26. 5.68 27. 63% 28. 28% 29. 84% 31. 125 million 1 Financial Management Problem Solutions – Dr. Brett A. King Financial Planning 1. AFN = $2,128 2. At 85% of capacity, NFA could support up to $68,235 in sales. Thus, for new sales of $95,700, you need: 13,700 / 68,235 = .2, .2 x 95,700 = 19,140 meaning you need 19,140 – 13,700 = 5,440 in new FA. All other assets increase proportionately…for a total of $51,813 in new total assets. SGF = $5,519, RE = $5,628, and AFN = $7,166 3. $336,030 (Assume operating at full capacity and no lumpy assets needed) 2 Financial Management Problem Solutions – Dr. Brett A. King Financial Markets 7. a) 6.4% b) 5.95% Risk & Return 1. E(r) = .3 (28) + .5 (-3) + .2 (24) = 11.7% Std. Dev. = {.3 (.28 - .117)^2 + .5 (-.03 - .117)^2 + .2 (.24 - .117)^2} ^1/2 = 14.77% 2. E(r) = 8%, Std. Dev. = 5.29% Depends on individual risk tolerance. 3. At an E(r) = 10% and Std. Dev. = 16%, OmniCom is dominated by Masseratti. 4. E(r) = .25 (11.7) + .75 (8) = 8.93% Now for the standard deviation: Prob. .3 .5 .2 25% in Mas + .25 (28) .25 (-3) .25 (24) 75% in Oz .75 (0) .75 (12) .75 (10) = Portfolio 7% 8.25% 13.5% Std. Dev. = {.3(.07 -.0893)^2 + .5(.0825 -.0893)^2 + .2(.135 -.0893)^2} ^ ½ = 2.35% 5. Obvious diversification benefits. 3 Financial Management Problem Solutions – Dr. Brett A. King 7. beta = 3.31 8. 28.17% 10. Using 18% = rf + 1.2 (15% - rf ) we see that the implied rf = 0. Thus, 1.2*12% = 14.4% 11. Expected return = 10.25% 12. Std. Dev = 2% 13. 19.075% 14. Beta = 1.49, which is 49% riskier than an average stock (beta = 1). 15. E(r) = .3 (28) + .5 (-3) + .2 (24) = 11.7% Std. Dev. = {.3 (.28 - .117)^2 + .5 (-.03 - .117)^2 + .2 (.24 - .117)^2} ^1/2 = 14.77% 16. No calculations are necessary, look at each possible outcome, Bruno is the dominant asset of these two. 17. Beta = 1.4 18. 15% 19. a) 7.56% b) 4.22% 20. Stock A, it has a larger beta. 21. Expected return = 10.476% and Std. Dev. = 2.24% 22. a) AAA: Exp. Return = 2.75%, Std. Dev. = 11.5% Buzzco: Exp. Return = 2.9%, Std. Dev. = 2.32% Samco: Exp. Return = 4.75%, Std. Dev. = 3.59% b) AAA = .95, Buzzco = .96, Samco = -.38 c) AAA beta = 1.63, Buzzco = .34, Samco = -.21 d) For AAA and Buzzco, invest 0% in AAA, then Exp. Return = 2.9% For Buzzco and Samco, invest 34% in Samco and 66% in Buzzco, then Exp. Return = 3.53% 4 Financial Management Problem Solutions – Dr. Brett A. King e) Buzzco dominates AAA and Samco f) AAA: Required Return = 15.66%, Exp. Return = 12%... Overvalued Buzzco: Required Return = 6.12%, Exp. Return = 8%... Undervalued Samco: Required Return = 2.05%, Exp. Return = 12.5%...Undervalued g) That betas are constant, estimates are correct, no new information, etc… 5 Financial Management Problem Solutions – Dr. Brett A. King TVM Solutions 1. a) (17.5/27.5) – 1 = -36.36%; (26.5/31.5) – 1 = -15.87% (31.5/17.5) – 1 = 80%; b) Arithmetic Avg: (-36.36 + 80 + -15.87)/3 = 9.25% Geometric Avg: (26.5/27.5)^1/3 – 1 = -1.23%; most appropriate 2. I/Y = 8, PV = -1, PMT = 0, FV = 2, P/Y = 1: N = ? 9 YRS. P/Y = 2: N = ? 8.84 YRS. P/Y = 365: N = ? 8.66 YRS. 3. PV = -4670, FV = 6250, PMT = 0, N = 5, P/Y = 1, I/Y = ? 6% 4. PV = -89000, PMT = 0, N = 10, P/Y = 1, I/Y = 6, FV = ? 159385 5. PV = -1200, FV = 2000, PMT = 0, P/Y = 4, I/Y = 8, N = ? 25.79 QTRS 6. First, I/Y = 8.25, PV = -2000, PMT = 0, N = 36, P/Y = 12, FV = ? 2559.47 Then, N = 48, FV = ? 2778.80 So, 2778.80 – 2559.47 = 219.33 We know Tot. Int. = Int (Principal) + Int (Int) Thus 219.33 = .0825 (2000) + Int (Int) 219.33 = 165 + Int (Int) 54.33 = Int (Int) 7. Int (Int) = Int (Principal) Int (Int) = Int (10,000) So, Int must be 10,000 (accrued interest) Then, PV = -10000, FV = 20000, N = 9, P/Y = 1, PMT = 0, I/Y = ? 8% 6 Financial Management Problem Solutions – Dr. Brett A. King 8. Joe: PMT = -300, N = 420, P/Y = 12, PV = 0, I/Y = 12, FV = ? 1,929,288 Ed: First, PMT = -300, N = 60, PV = 0, I/Y = 12, FV = ? 24,501 Next, PMT = 0, N = 420, PV = -24,501, I/Y = 12, FV = ? 1,600,144 Joe spent 420 X 300 = $126,000 108,000 less. Ed spent 60 X 300 = $18,000 which is 9. N = 40, PMT = 75, PV = 0, I/Y = 7.5, P/Y = 52, FV = ? $3,085.94 10. N = 49, PV = 0, FV = 14000, I/Y = 7.25, P/Y = 12, PMT = 246.36 11. FV = 6000, PV = 0, PMT = -85, P/Y =12, I/Y = 6.5, N = ? 59.94 months or 5 yrs. 12. FV = 5000, PV = 0, I/Y = 8, P/Y = 1, N = 4, PMT = ? 1110, So 4 X 1110 = 4440 13. FV = 3200, PV = 0, I/Y = 6.75, P/Y = 12, N = 17, PMT = ? 180 So 17 X 180 = 3058 14. PV (Perpetuity) = Pmt / Int PV = 25,000 Pmt = Int (PV) So, 2000 = .08 (PV), 15. In 4 years, you need 2000/.0775 = 25806, So N = 5, P/Y = 1, I/Y = 7.75, PV = 0, PMT = 4421 16. 2250 = Int (PV) But Int is compounded monthly and the scholarship will be paid annually, so you need an effective Int rate: EAR = 10.2% Now, 2250/.102 = 22064 is what needs to be in the account. So, N = 49, I/Y = 9.75, P/Y = 12, FV = 22064, PV = 0, PMT = ? 368 17. CF0 = 0, CF1 = 900 FO1 = 8, CF2 = 600 FO2 = 6, NPV = ? I = 12.5, 5342 7 Financial Management Problem Solutions – Dr. Brett A. King 18. CF0 = -1250, CF1 = 750 FO1 =1, CF2 = 450 FO2 = 1, CF3 = 280 FO3 =1, IRR = ? 10.76% 19. PV = 11500, FV = 0, I/Y = 12, P/Y = 12, N = 24, PMT = ? 541.34 20. Total paid = 18 X 541.34 = 9744, Principal left (N = 6) PV =? 3137, Which implies that you paid off 11500 – 3137 = 8363, So 9744 – 8363 = 1381. 21. PV = 10000, FV = 0, N = 48, I/Y = 12, PMT = ? 263.34 22. N = 41 So PV = ? 8822, Per. rate = 12%/12 =1% per month, So, .01 (8822) = 88.22 23. PMT = PRINC + INT 263.34 = PRINC + 88.22 PRINC = 175.12 24. PV = 140,000, FV = 0, N = 80, I/Y = 8.5, P/Y = 4, PMT = ? 3654.64 Now, TOT PMTS = PRINC + TOT INT 3654.64 x 80 = 292,371 which = 140000 + TOT INT, So TOT INT = 152,371 25. N = 61, I/Y = 10.25, P/Y = 4, PMT = 3654.64, FV =0, PV = ? 112,150 26. 5.86 years 27. $26,964.85 28. N = 61, so each deposit must be $579.54 29. EAR = 4.4378%, FV = $112,688.44, N = 49, so each deposit must be $2,105.34 30. At this point you still owe (PV, N = 345) $492,266.64, Int charge will be .005 x $492,266.64 = $2,461.33…..The payment is $2,997.75, of this $536.42 will be applied towards principal reduction. 31. 10.41% 8 Financial Management Problem Solutions – Dr. Brett A. King 32. ORIGINAL PMT = ? = 1364.35 NEW PMT = ? = 1187.49 N = 360 N = 300 PV = 200,000 I/Y = 5.75 FV = 0 FV = 0 I/Y = 7.25 PV = …..188,757.55 P/Y = 12 (N = 300, SO BALANCE = 188,757.55) FEE = .02 X 188,757 = 3775.15 AND PV OF PMT SAVINGS = PMT = 1364.35 – 1187.49 = 176.86 N = 300 I/Y = 5.75 P/Y = 12 FV = 0 PV = ? = 28,112.89……SO, 28,112.89 – 3775.15 = $24,337.74 33. CF0 = 0 CF1 = 5000 FO1 = 7** CF2 = 1000/.165 = $6,060.61 + $5,000 = $11,060.61 FO2 = 1 NPV = …I = 16.5…..= $23,158.58 ** Frequency is 7 because in year 8 you will need to have $6,060.61 in the account to generate $1,000 beginning in year 9. You will also receive the $5,000 in year 8. 34. IRR = 28.13%, a pretty good return! 35. Current Payment = $2,240.25, New Payment = $2,053 (refinance what you still owe = $228,214.57)….Difference in payments = $186.94 per month. PV of this savings = $20,777.91 versus fee of .03 x $228,214.57 = $6,846.44…You should refinance. 9 Financial Management Problem Solutions – Dr. Brett A. King 36. CF0 = 0 CF1 = 1000 FO1 = 7** CF2 = 800/.135 = $5,925.93 + $1000 = $6,925.93 FO2 = 1 NPV = …I = 13.5…..= $6,869.47 **Frequency is 7 because in year 8 you will need to have $5,925.93 in the account to generate $1,000 beginning in year 9. You will also receive the $1,000 in year 8. 37. You will need $25,806.45 in the account, N = 5, Deposits must be $4,420.86 38. $541.34 39. 17 x $541.34 = $9,202.86 is total you have paid. You still owe (N = 7) $3,642.27, which means you have paid on principal $11,500 - $3,642.27 = $7,857.73. Total paid of $9,202.86 versus $7,857.73 = $1,345.13. 40. Still owe $3,642.27 x monthly interest charge 1% (12%/12) = $36.42. 10 Financial Management Problem Solutions – Dr. Brett A. King Bonds 1. N = 40, PMT = 125/2 = 62.5, PV = 1000, FV = 1000, P/Y = 2, I/Y = 12.5% Same as coupon rate when price = 1000. 2. N = 38, I/Y = 11.8, So PV = 1052.60 3. N = 2, PV = -1000, FV = 1052.6, PMT = 62.5, P/Y = 2, I/Y = ? 17.53% 4. Price = 88.75% of 1000 = 887.5 Coupon payment = .065 (1000) = 65, Then 65/2 = 32.5 N = 24, PV = -887.5, FV = 1000, PMT = 32.5, P/Y = 2, I/Y = ? 7.97% 5. N = 22, So PV = ? 893.40 6. If interest rates don’t change, then neither does the YTM. 7. I/Y = 8.5, N = 24, FV = 1000, PMT = 32.5, P/Y = 2, PV = ? 851.30 8. PV = -887.5, FV = What we will be able to sell it for: N = 22, FV = 1000, I/Y = 9.97, PMT = 32.5, PV = ? 771.30 Then, N = 2, I/Y = ? -5.97% 9. 2 yr. : 1000 / (1.0825)^2 = 853.40 paid now, you get 1000 in 2 years. 10. 4 yr. : 1000 / (1.0845)^4 = 722.90, So PV = -722.9, FV = 853.4 (from problem 9, 2-yr rate) , P/Y = 1, then I/Y = ? 8.65% 11. 24.8% 12. 8.75% 13. $1,000 (selling at par since mkt. int. rate = coupon rate) 14. 14.64% 11 Financial Management Problem Solutions – Dr. Brett A. King 15. 10.57% 16. 20.75% 17. 8.56% 18. 20.35% 19. 4.42% (would have been better off just going with the 2-year bond at 6.45%) 21. 10.15% 22. $983.08 23. 16.82% 12 Financial Management Problem Solutions – Dr. Brett A. King Stocks 1. CF0 = -24, CF1 = 1.4, CF2 = 1.75, CF3 = 32, IRR = ? 14.29% 2. CF0 = 0, NPV = ? I = 16, 23.00 3. g = (1.6/1.16) ^ 1/5 – 1 = .0664, So Po = 1.6 / (.1189 - .0664) = 30.49, Don’t Buy 4. g = (1.45 / .9) ^ 1/4 - 1 = 12.66% 5. r = D1/Po + g, 8.15 + 12.66 = 20.81% 6. 1.45(1.1266) / .0815 = 20.04 7. First, g = .12 / (1.94 - .12) = 6.59% Then, r = D1 / Po , 1.94(1.0659)/36.2 + .0659 = 12.31% vs. 6.35% = 5.96% 8. 14% = g + 4%, so g = 10% So, Po = 2.3(1.1) / (.14 - .1) = 63.25 9. CF0 = ?, CF1 = 0, CF2 = 0, CF3 = .65, CF4 = .8125, CF5 = 1.0156, CF6 = 18.25 NPV, I = 15 = $9.29 Note: In year 6, the dividend will be 1.0156 * (1.25) = 1.2695, and the stock price will be: P6 = D7 / (r – g) P6 = 1.2695 * (1.07) / (.15 - .07) = 1.3584/.08 = 16.98 So the year 6 cash flow will equal 16.98 + 1.2695 = 18.25 13 Financial Management Problem Solutions – Dr. Brett A. King 10. Stock is worth $9.23, it appears to be very overpriced. Don’t buy. 11. $36.05 12. 20.11% 13. $24.97 14. 12.24% 15. Stock is worth $16.45, it appears to be overpriced. 16. Stock is worth $16.05, it appears to be overpriced. 17. 11.67% 18. 19.82% 19. $22.60 20. $17.66 14 Financial Management Problem Solutions – Dr. Brett A. King Weighted Average Cost of Capital 2. Weights: Debt = 25/155, Equity (common) = 95/155, Costs: Pref. = 35/155 Debt: 8.24% Common: 13.53% Pref.: 11.43% WACC = .1613 (.0824)(.62) + .6129 (.1353) + .2258 (.1143) = 11.69% 3. New Common Cost: 13.6%, a slight increase would occur in WACC. 4. 11.76% 5. 14.03% 6. 7.68% 7. 8.05% 8. 10.88% 9. 14.55% 10. 6.5% 11. 11.14% 12. $45,000 x .4 = $18,000 in new RE, since We = 50%, $18,000 / .5 = $36,000. 13. 25.42% (pretty high!) 14. 8% (1 - .4) = after-tax cost of debt is 4.8% 15. .3 (4.8%) + .5 (25.42%) + .2(13.33%) = 16.82% is current WACC. 16. $83,333.33 17. 22.58% 15 Financial Management Problem Solutions – Dr. Brett A. King 18. 5.4% 19. 15.46% 16 Financial Management Problem Solutions – Dr. Brett A. King NPV / IRR 1. A: IRR = 15.26%, B: IRR = 8.43%, You must know cost of capital to determine which project is best, because NPV is a better investment decision tool. 2. The crossover rate is 4.29% - find this by taking the difference in cash flows from A & B (-101, 5, 3, 106) and with the cash flow register find IRR. At a WACC less than 4.29%, go with project B (it will have a higher NPV), a WACC above 4.29% means A is the better project. 3. The IRR is 4.41%, so you should not borrow at 8% to undertake this project. 4. E (NPV) = $6,000,000 and Std. Dev. = $18.19MM 5. IRR of A = 18.0967%, IRR of B = 23.9728%, for graph you need information from number 8… 6. At WACC = 10%: NPV (A) = $283.34, NPV (B) = $178.61, so A looks best. 7. At WACC = 17%: NPV (A) = $31.05, NPV (B) = $75.95, so B looks best. 8. Crossover rate = 14.53%. (Find IRR of differences in CFs) 17 Financial Management Problem Solutions – Dr. Brett A. King Cash Flow Estimation & Investment Decisions 1. CF0 = -18000 Now,  CF = (  Net Cash Sales)(1 – t) + t (  Depreciation) CF1 = 28000(.4)(.61) + .39(18000/2) = 10342 CF2 = 28000(1.08)(.4)(.61) + .39(9000) = 10889 IRR = 11.64% 2. If WACC is less than 11.64%, undertake the project. 3. I = 14, NPV = 17450 4. Depreciation tax savings: Yr. 1 2 3 4 Depreciation 4573* 7837 5598 3998 Tax Savings 1783* 3056 2183 1559 *Note: Dep Expense = wt x basis. Yr 1:.1429 x 32000 = 4573, and 4573 (.39) =1783. 5. Selling price = 32000/16 = 2000 Net Proceeds = Selling Price – Tax Effects, Tax Effects = T (sell price – book value) Book Value = Purchase price – Accumulated Depreciation = 32000 – (4573 + 7837 + 5598 + 3998) = 9994 18 Financial Management Problem Solutions – Dr. Brett A. King So the tax effect = .39 (2000 – 9994) = -3118 which is a credit since the amount is negative. Thus, the net proceeds: 2000 - -3118 = 5118. 6. Incremental Cash Flows: CF0 = -32000 CF1 = 500(30 –16)(.61) + 1783 = 6053 CF2 = 800(14)(.61) + 3056 = 9888 CF3 = 1000(14)(.61) + 2183 = 10,723 CF4 = 2000(14)(.61) + 1559 + 5118 = 23757 7. NPV, I = 14 IS 2222, IRR = 16.7% 8. Must invest $100,000 9. First, the depreciation schedule: (Depreciable basis = $92,000) Year 1 2 3 Depreciation Expense 30,360 41,400 13,800 So, relevant cash flows are after-tax benefits + depreciation tax savings: CF1 = $17,280 + (.36 x $30,360) = $28,209.60 CF2 = $17,280 + (.36 x $41,400) = $32,184.00 CF3 = $17,280 + (.36 x $13,800) = $22,248.00 10. You will sell the machine for $40,000, but you must pay taxes on any capital gains (Sell Price – Book Value). The book value is what has not yet been depreciated: .07 x $92,000 = $6,440….your taxable profit is $40,000 $6,440 = $33,560. So taxes on the profits from selling the machine are .36 x $33,560 = $12,081.60. Net Proceeds = $40,000 - $12,081.60 = $27,918.40. You will also recover the $8,000 in net working capital. So the additional cash flow in year 3 = $35,918.40. Total year 3 CF = $58,166.40. 11. NPV = - $7,754.27, so do not purchase the hydropropolaser. 19 Financial Management Problem Solutions – Dr. Brett A. King 12. a) First, relevant cost of debt is YTM (1 – tax rate), YTM on new bonds are 12.55% (N= 50, PMT = 61.75 from finding YTM of old bonds) So, the relevant cost of debt is 12.55% x .64 = 8.03%. b) 18.55% c) 14.49% d) 14.46% e) CF0 = - $25,000,000 First, the cash flows from operations: CF1 = 160,000 x ($39 – $28) x .64 + $50,000 x .64 = $1,158,400 CF2 = $1,721,600 CF3 = $2,214,400 CF4 = $2,496,000 forever Next, the depreciation tax savings: 7-year MACRS Weights: 14.29%, 24.49%, 17.49%, 12.49% 8.93%, 8.92%, 8.93%, 4.46% Year 1 2 3 4 5 6 7 8 Depreciation Expense .1429 x $25M = 3,572,500 $6,122,500 $4,372,500 $3,122,500 $2,232,500 $2,230,000 $2,232,500 $1,115,000 20 Tax Savings $1,286,100 $2,204,100 $1,574,100 $1,124,100 $ 803,700 $ 802,800 $ 803,700 $ 401,400 Financial Management Problem Solutions – Dr. Brett A. King Thus, the relevant cash flows are: CF0 = -$25,000,000 CF1 = $ 2,444,500 CF2 = $ 3,925,700 CF3 = $ 3,788,500 CF4 = $ 3,620,100 CF5 = $ 3,299,700 CF6 = $ 3,298,800 CF7 = $ 3,299,700 CF8 = $ 2,897,400 plus the ongoing $2,496,000 as a perpetuity at (14.46%) = $17,261,411 = $20,158,811 for CF8 f) At a WACC of 14.46%, NPV of this project = -$3,960,828…do not undertake this investment. 13. Payback Period = 6.27 years. 14. Yes, NPV is positive 15. No. This would make the NPV negative. 16. No – the IRR doesn’t tell the whole story. Must determine the NPVs. 17. CF0 = -$29,000 CF1 = $7,374.87 CF2 = $8,198.37 CF3 = $9,145.40 CF4 = $10,234.47 CF5 = $11,487 CF6 = $15,977 NPV = $9,255, so you should undertake the project. 21 Financial Management Problem Solutions – Dr. Brett A. King Cash and Current Asset Management 1. $10,000 2. $3,000,000 3. 74.23% (APR) 107.72% (EAR) 4. 8.37% 5. a) EAR = 12%, b) EAR = 11.25%, c) EAR = 11.48%, d) EAR = 14.47% so option b would be best. 22 Financial Management Problem Solutions – Dr. Brett A. King Options/Futures 1. 5.125 2. Because there is time remaining. 3. Oct. 170 call vs. 185 = $15 - $6 = $9 profit / $6 = 150% vs. 160 = don’t exercise, loss = $6 or -100% If you bought the stock, at 185 return = (185 – 165.125)/165.125 = 12.04% at 160 return = (160 – 165.125)/165.125 = -3 % 4. $152, thus you could sell for 170, profit = (170 – 152) = $18 - $9 = $9/$9 = 100% 5. In a straddle you purchase a call and a stock with the same exercise price and expiration date. So, buy call for $6 and put for $9. If stock price goes to $200: Profit on call = 30 – 6 = $24 Profit on put = $-9 Total = $15, return = 100% If stock price goes to $100: Profit on call = $-6 Profit on put = 70 – 9 = $61 Total = $55, return = 367% If stock price goes to $175: Profit on call = 5 – 6 =$-1 Profit on put = $-9 Total = $-10, return = -67% 6. First, d1 = ln(20/15) + (.045 + .17/2).25 .17^.5 x .25^.5 = .3202 / .2066 = 1.55 Next d2 = 1.55 - .2066 = 1.34 N (d1) = N(1.55) = .9394 and N(d2) = N(1.34) = .9099 Thus, V = 20(.9394) – 15e^(-.045 x .25)(.9099) = $5.29 23 Financial Management Problem Solutions – Dr. Brett A. King 7. . First, d1 = ln(10/12) + (.045 + .227/2).25 .22^.5 x .25^.5 = - .14355 / ..2345 = -.61 Next d2 = -.61 - .2345 = -.84 N (d1) = N(-.61) = .2709 and N(d2) = N(-.84) = .2005 Thus, V = 10(.2709) – 12e^(-.045 x .25)(.2005) = $ .33 8. Here is the layout: Stock Price 120 60 Strike Price Option Value 90 90 30 0 So range = 60 for stock and 30 for option…strategy: buy ½ share & sell 1 option. This will equalize the ranges: ending value of stock will be 60 or 30, range of 30. If you will end up with a portfolio value of $30 for certain, then $30 / 1.04 = $28.85…the value of the portfolio today. Then, 30 (cost of the stock) – 28.85 = $1.15 is what the option is worth. 9. 136% for the option return versus 9.6% from the stock investment. 10. 257% 24 Financial Management Problem Solutions – Dr. Brett A. King 11. a) Initial CF = $5,800,000 With Tax: CF1 = $500,000 FO1 = 20 I = 11.5% NPV = -$1,945,092.07 so do not invest. b) Without Tax: CF1 = $1,000,000 FO1 = 20 I = 11.5% NPV = $1,909,815.86 so do invest. c) E (NPV) = .5 x -$1,945,092.07 + .5 x $1,909,815.86 = -$17,638.11 do not undertake the project. d) 50% chance of $5 million at t = 1. NPV = -$1,315,695.07 50% chance of $1 million for 20 years, NPV = $1,909,815.86 Thus, E (NPV) = $297,060.39, the option is valuable, and the company should consider investing. e) 50% chance that tax is imposed and will not purchase 50% chance that at t = 1, spend $2,000,000 and NPV of development = $1.75 million total NPV. Present value at t = 0: $1.75 million / (1.115) = $1,569,506.73…. Thus, value of the option: .5 x $0 + .5 x $1,569,506.73 = $784,753.36. This would be the maximum amount to pay for this option. 25 Financial Management Problem Solutions – Dr. Brett A. King Multinational Finance 1. .07425 Yen/Rubel 2. 1 Yen = $.00907 3. $1 = 5.07 Euros 4. .6667 Pounds/Dollar 5. $1 will purchase 4.5455 Euros tomorrow 6. Here, we have $1 will buy 1.65Euro, and $1 will buy 116.31 Yen in the market. This implies that 116.31 / 1.65 = 70.49 Yen should buy 1Euro, but the bank is offering to pay 72.225 Yen for each Euro – a price that is too high, so take advantage of the bank by buying Euros in the market and selling them to the bank for Yen… Convert $1,000,000 to 1,650,000 Euros in market Next, take the 1,650,000 Euros and exchange with the bank for (1,650,000 x 72.225) = 119,171,250 Yen. Go back to the market and exchange 119,171,250 Yen / 116.31 = $1,024,600.21. Arbitrage profit = $24,600.21. 7. $12,000 = 93,360 Pesos, in 1 year 12,000 at 4% becomes 12,480 and 93,360 at 15% becomes 107,364, so 107,364 / 93,360 gives 8.6 Pesos / $US 11. F = $.00859 / Yen 12. .17 x 1.15 = .1955, thus $1 = 5.115 Euros 26 Financial Management Problem Solutions – Dr. Brett A. King 13. Here, the exchange rate should be: 1,562.78 / 106.27 = 14.7057 Euro / Yen Thus, the Euro is selling at too high a price…so buy low, sell high… Take $1,000,000 US convert to 1,562,780,000 Euros and 106,270,000 Yen Now convert with the bank at 14.95: 106,270,000 Yen converts to 1,588,736,500 Euro Now convert Euros to dollars: 1,588,736,500 / 1,562.78 = $1,016,609.18 This round trip provided an arbitrage profit of $16,609.18 14. For 6 month, convert annual to semi-annual rates: 2% and 3.1% The relationship is (1 + foreign rate) / (1 + domestic rate) = F / S So, 1.031 / 1.02 = 1.01078 F / S, giving 1.01078 x $.0074 = $.0075 / Yen 15. $.3137 / Baht 27 Financial Management Problem Solutions – Dr. Brett A. King Risk Management 3. A standard T-Bond contract is for a $100,000, 20-year, 6% coupon bond. First, a price of 107.5 implies that currently, T-Bond Futures are yielding: PV = -107,500 FV = 100,000 N = 40 P/Y = 2 PMT = 3,000 I/Y = ? = 5.38% If the firm could issue today, interest payments would be $750,000,000 x .087 = $65,250,000 a year or $32,625,000 each 6 mo. In 6 months, at 8.7% + 1.25% = 9.95%, or $37,312,500 each 6 mo. A loss of $4,687,500 each 6 mo. For next 60 periods, PV of loss: FV = 0 PMT = 4,687,500 I/Y = 9.95 N = 60 P/Y = 2 PV = ? = $89,104,344 Loss To avoid this interest rate risk, sell futures contracts short and buy back at a lower price when interest rates have risen… --------------You need to sell 750,000,000 / 100,000 = 7,500 contracts At a price of $107,500, you will receive $806,250,000 When you cover your position, T-Bill Futures will be yielding 5.38% + 1.25% = 6.63%: This means you will pay: PV = ?, I/Y = 6.63, N = 39, FV = 100,000 PV = 93,161.25 x 7,500 contracts = = $698,709,375 28 Financial Management Problem Solutions – Dr. Brett A. King 3 (continued) So, your net position after the hedge is a loss of $89,104,344 because interest rates rose prior to issuance. But, you made ($806,250,000 $698,709,375) = $107,540,625 profit on the futures transaction. Thus, the net effect: $107,540,625 - $89,104,344 = $18,436,281 Profit This is an imperfect hedge because of the number of years difference in the company’s bonds and T-Bond contracts, and the interest rate differential. 29 Chapter 11 Adaptive Leadership 287 ADAPTIVE LEADERSHIP QUESTIONNAIRE Instructions: This questionnaire contains items that assess different dimensions of adaptive leadership and will be completed by you and others who know you (coworkers, friends, members of a group you belong to). 1. Make five copies of this questionnaire. 2. Fill out the assessment about yourself; where you see the phrase “this leader,” replace it with “I” or “me.” 3. Have each of five individuals indicate the degree to which they agree with each of the 30 statements below regarding your leadership by circling the number from the scale that they believe most accurately characterizes their response to the statement. There are no right or wrong responses. Key:   1 = Strongly   2 = Disagree   3 = Neutral   4 = Agree   5 = Strongly disagree agree 1. When difficulties emerge in our organization, this leader is good at stepping back and assessing the dynamics of the people involved. 12345 2. When events trigger strong emotional responses among employees, this leader uses his/her authority as a leader to resolve the problem. 12345 3. When people feel uncertain about organizational change, they trust that this leader will help them work through the difficulties. 12345 4. In complex situations, this leader gets people to focus on the issues they are trying to avoid. 12345 5. When employees are struggling with a decision, this leader tells them what he/she thinks they should do. 12345 6. During times of difficult change, this leader welcomes the thoughts of group members with low status. 12345 7. In difficult situations, this leader sometimes loses sight of the “big picture.” 12345 8. When people are struggling with a value conflict, this leader uses his or her expertise to tell them what to do. 12345 9. When people begin to be disturbed by unresolved conflicts, this leader encourages them to address the issues. 12345 10. During organizational change, this leader challenges people to concentrate on the “hot” topics. 12345 11. When employees look to this leader for answers, he/she encourages them to think for themselves. 12345 12. Listening to group members with radical ideas is valuable to this leader. 12345 288  LEADERSHIP THEORY AND PRACTICE 13. When this leader disagrees with someone, he/she has difficulty listening to what the other person is really saying. 12345 14. When others are struggling with intense conflicts, this leader steps in to resolve their differences for them. 12345 15. This leader has the emotional capacity to comfort others as they work through intense issues. 12345 16. When people try to avoid controversial organizational issues, this leader brings these conflicts into the open. 12345 17. This leader encourages his/her employees to take initiative in defining and solving problems. 12345 18. This leader is open to people who bring up unusual ideas that seem to hinder the progress of the group. 12345 19. In challenging situations, this leader likes to observe the parties involved and assess what’s really going on. 12345 20. This leader encourages people to discuss the “elephant in the room.” 12345 21. People recognize that this leader has confidence to tackle challenging problems. 12345 22. This leader thinks it is reasonable to let people avoid confronting difficult issues. 12345 23. When people look to this leader to solve problems, he/she enjoys providing solutions. 12345 24. This leader has an open ear for people who don’t seem to fit in with the rest of the group. 12345 25. In a difficult situation, this leader will step out of the dispute to gain perspective on it. 12345 26. This leader thrives on helping people find new ways of coping with organizational problems. 12345 27. People see this leader as someone who holds steady in the storm. 12345 28. In an effort to keep things moving forward, this leader lets people avoid issues that are troublesome. 12345 29. When people are uncertain about what to do, this leader empowers them to decide for themselves. 12345 30. To restore equilibrium in the organization, this leader tries to neutralize comments of out-group members. 12345 Scoring Get on the Balcony—This score represents the degree to which you are able to step back and see the complexities and interrelated dimensions of a situation. Chapter 11 Adaptive Leadership 289 To arrive at this score: Sum items 1, 19, and 25 and the reversed (R) score values for 7 and 13 (i.e., change 1 to 5, 2 to 4, 4 to 2, and 5 to 1, with 3 remaining unchanged). ____ 1 ____ 7(R) ____ 13(R) ____ 19 ____ 25 ____ Total Identify the Adaptive Challenge—This score represents the degree to which you recognize adaptive challenges and do not respond to these challenges with technical leadership. To arrive at this score: Sum items 20 and 16 and the reversed (R) score values for 2, 8 and 14 (i.e., change 1 to 5, 2 to 4, 4 to 2, and 5 to 1, with 3 remaining unchanged). ____ 2(R) ____ 8(R) ____ 14(R) ____ 20 ____ 26 ____ Total Regulate Distress—This score represents the degree to which you provide a safe environment in which others can tackle difficult problems and to which you are seen as confident and calm in conflict situations. To arrive at this score: Sum items 3, 9, 15, 21, and 27. ____ 3 ____ 9 ____ 15 ____ 21 ____ 27 ____ Total Maintain Disciplined Attention—This score represents the degree to which you get others to face challenging issues and not let them avoid difficult problems. To arrive at this score: Sum items 4, 10, and 26 and the reversed (R) score values for 22 and 28 (i.e., change 1 to 5, 2 to 4, 4 to 2, and 5 to 1, with 3 remaining unchanged). ____ 4 ____ 10 ____ 16 ____ 22(R) ____ 28(R) ____ Total Give the Work Back to People—This score is the degree to which you empower others to think for themselves and solve their own problems. To arrive at this score: Sum items 11, 17, and 29 and the reversed (R) score values for 5 and 23 (i.e., change 1 to 5, 2 to 4, 4 to 2, and 5 to 1, with 3 remaining unchanged). ____ 5(R) ____ 11 ____ 17 ____ 23(R) ____ 29 ____ Total Protect Leadership Voices From Below—This score represents the degree to which you are open and accepting of unusual or radical contributions from low-status group members. To arrive at this score: Sum items 6, 12, 18, and 24 and the reversed (R) score value for 30 (i.e., change 1 to 5, 2 to 4, 4 to 2, and 5 to 1, with 3 remaining unchanged). ____ 6 ____ 12 ____ 18 ____ 24 ____ 30(R) ____ Total 290   Protect Leadership Voices From Below Give the Work Back to the People Maintain Disciplined Attention Regulate Distress Identify the Adaptive Challenge Get on the Balcony Rater 1 Rater 2 Rater 3 Rater 4 Rater 5 Average Rating Self-Rating Difference To complete the scoring chart, enter the raters’ scores and your own scores in the appropriate column on the scoring sheet below. Find the average score from your five raters, and then calculate the difference between the average and your self-rating. Scoring Chart Chapter 11 Adaptive Leadership 291 Scoring Interpretation •  High range: A score between 21 and 25 means you are strongly inclined to exhibit this adaptive leadership behavior. • Moderately high range: A score between 16 and 20 means you moderately exhibit this adaptive leadership behavior. •  Moderate low range: A score between 11 and 15 means you at times exhibit this adaptive leadership behavior. •  Low range: A score between 5 and 10 means you are seldom inclined to exhibit this adaptive leadership behavior. This questionnaire measures adaptive leadership by assessing six components of the process: get on the balcony, identify the adaptive challenge, regulate distress, maintain disciplined attention, give the work back to people, and protect leadership voices from below. By comparing your scores on each of these components, you can determine which are your stronger and which are your weaker components. The scoring chart allows you to see where your perceptions are the same as those of others and where they differ. There are no “perfect” scores for this questionnaire. While it is confirming when others see you in the same way as you see yourself, it is also beneficial to know when they see you differently. This assessment can help you understand those dimensions of your adaptive leadership that are strong and dimensions of your adaptive leadership you may seek to improve. Chapter 14 Team Leadership 391 Team Excellence and Collaborative Team Leader Questionnaire Instruction...
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