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1.(TCO D) A stock is expected to pay a dividend of $2.00 at the end of the year. The required rate of return is rs = 15.0%, and the expected constant growth rate is g = 5.0%. What is the stock's current price? Answer: Price of Stock = D(1) / (r-g) D(1) = next period dividend r = required rate of return g = expected constant growth rate Price of Stock = $2 / (15%-5%) = $2 / 10% = $20 Current stock price is $20 2-29. In fiscal year 2011, Starbucks Corporation (SBUX) had revenue of $11.70 billion, gross profit of $6.75 billion, and net income of $1.25 billion. Peet’s Coffee and Tea (PEET) had revenue of $372 million, gross profit of $72.7 million, and net income of $17.8 million. a. Compare the gross margins for Starbucks and Peet’s. b. Compare the net profit margins for Starbucks and Peet’s. c. Which firm was more profitable in 2011? Answer: a) Gross profit margin: Gross profit margin is determined by dividing the gross profit by sales. Gross margin = Gross profit/Sales SBUX: Gross margin = Gross profit/Sales =$6,750,000,000/$11,700,000,000 =57.69% PEET: Gross margin = Gross profit/Sales =$72,700,000/$372,000,000 =19.54% b) Net profit margin: Net profit margin is determined by dividing net income by sales. Net profit margin = Net income/Sales SBUX: Net profit margin = Net income/Sales =$1,250,000,000/$11,700,000,000 =10.68% PEET: Net profit margin = Net income/Sales =$17,800,000/$372,000,000 =4.78% c) In 2011, SBUX was more profitable compared to PEET because the net margin is higher for SBUX when compared to PEET. In fact, SBUX has higher gross and net profit margin than PEET. 30. In mid-2012, Apple had cash and short-term investments of $27.65 billion, accounts receivable of $14.30 billion, current assets of $51.94 billion, and current liabilities of $33.06 billion. a. What was Apple’s current ratio? b. What was Apple’s quick ratio? c. What was Apple’s cash ratio? d. In mid-2012, Dell had a cash ratio of 0.67, a quick ratio of 1.11 and a current ratio of 1.35. What can you say about the asset liquidity of Apple relative to Dell? Answer: a) Current ratio: Current ratio is determined by dividing current asset by current liabilities. Current ratio = Current assets/Current liabilities =$51,940,000,000/$33,060,000,000 =1.571 b) Quick ratio is determined dividing current assets minus inventory by the current liabilities. Quick ratio = Current asset – Inventory /Current liabilities =$51,940,000,000 - $0/$33,060,000,000 =1.571 c) Cash Ratio: Cash ratio is determined by dividing cash and short term investment by current liabilities. Cash ratio = Cash and short-term investment/ Current liabilities =$27,650,000,000 /$33,060,000,000 =0.836 d) Apple’s asset liquidity is better than Dell’s. Apple does not have inventory which indicates that the current and quick ratio of the company will be equal. Therefore, Apple has more liquid assets when compared to Dell, which has a quick ratio less than its current ratio. Since Apple has current and quick ratios that are higher than Dell’s current and quick ratios, this implies that Apple is in a better position to use its assets to extinguish or retire its current liabilities immediately. We can also see that the cash ratio of Apple is higher than Dell which indicates that amount of cash held by Apple is higher than Dell. Since cash is the most liquid asset; this implies that Apple has better liquidity when compared to Dell. 31. See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. a. How did Mydeco’s accounts receivable days change over this period? b. How did Mydeco’s inventory days change over this period? c. Based on your analysis, has Mydeco improved its management of its working capital during this time period? Answer: a) Accounts Receivable Period b) Inventory days c) Working Capital 2013 2012 2011 2010 (Average Accounts Receivable*365)/Sales Sales Average Accounts Receivable 49.24 604.10 81.50 52.42 60.00 79.46 510.70 424.60 363.80 73.35 69.80 79.20 ((Average Inventory*365/Sales) Cost of Goods Sold Average Inventory 41.68 293.4 33.5 44.44 246.8 30.05 52.48 206.2 29.65 67.83 173.8 32.3 (Current assets - Current Liability) Current Assets Current Liability 165 206.4 41.4 151.2 186.1 34.9 155.5 184.5 29 145.3 169.6 24.3 a) The accounts receivable period has decreased year over year meaning that it is taking the company fewer and fewer days to collect its accounts receivable. This means that the accounts receivable turnover ratio is increasing and this is a positive sign for the company. b) There is a decrease in inventory days year over year which means company is efficiently converting its inventory into sales and cash. c) The working capital of the company has increased over the last five years which is a positive sigh as it shows that company is better able to meet out its current obligations. 2009 145.7 171.1 25.4 36. You are analyzing the leverage of two firms and you note the following (all values in millions of dollars): Debt book-to-equity Market equity EBIT Int. Expense Firm A 500 300 400 100 50 Firm B 80 35 40 8 7 a. What is the market debt-to-equity ratio of each firm? b. What is the book debt-to-equity ratio of each firm? c. What is the EBIT/interest coverage ratio of each firm? d. Which firm may have more difficulty meeting its debt obligations? Explain. Answer: a) Market Debt to Equity Ratio: Firm A = 500/400 = 1.25 Firm B = 80/40 = 2.00 b) Book Debt to Equity Ratio: Firm A = 500/300 = 1.67 Firm B = 80/35 = 2.29 c) EBIT/Interest Coverage ratio Firm A = 100/50 = 2.00 Firm B = 8/7 = 1.14 d) Firm B might face difficulty in paying out its debt obligations. Interest coverage ratio of Firm B is lower than that of Firm A. The DUPONT identity: ROE = NI/TE Multiply by 1 (TA/TA) and then rearrange ROE = (NI / TE) (TA / TA) ROE = (NI / TA) (TA / TE) = ROA * EM Multiply by 1(S/S) and then rearrange ROE = (NI / TA) (TA / TE) (S/S) ROE = (NI / S) (S / TA) (TA / TE) ROE = PM * TAT * EM ROE = Profit Margin * Total Asset Turnover * Equity Multiplier When: ROE = Return on Equity NI = Net Income TE = Total Equity TA = Assets ROA = Return on Assets EM = TA/TE = 1 + D/E = The Equity Multiplier S = Sales 42. For fiscal year 2011, Starbucks Corporation (SBUX) had total revenues of $11.70 billion, net income of $1.25 billion, total assets of $7.36 billion, and total shareholder’s equity of $4.38 billion. a. Calculate the Starbucks’ ROE directly, and using the DuPont Identity. b. Comparing with the data for Peet’s in Problem 41, use the DuPont Identity to understand the difference between the two firms’ ROEs. Answer: a) Return on Equity Starbucks: = (Net Income /Sales)*(Sales / Assets)*(Assets/Equity) = (1.25/11.7)*(11.7/7.36)*(7.36/4.38) = 28.54% b) ROE of PEET: = (Net Income /Sales)*(Sales / Assets)*(Assets/Equity) =4.78%*1.73*1.21 = 10.01% The difference in ROE is primarily due to the profit margin of SBUX being much higher than PEET’s net profit margin. SBUX profit margin is 10.68% while PEET’s is only 4.78%. Also, Starbucks has a higher Assets/Equity ratio than PEET’s. 43. Consider a retailing firm with a net profit margin of 3.5%, a total asset turnover of 1.8, total assets of $44 million, and a book value of equity of $18 million. a. What is the firm’s current ROE? b. If the firm increased its net profit margin to 4%, what would be its ROE? c. If, in addition, the firm increased its revenues by 20% (while maintaining this higher profit margin and without changing its assets or liabilities), what would be its ROE? Answer: a) Firm's Current ROE: = Profit Margin* Asset Turnover* Equity Multiplier =3.5%*1.8*(44/18) = 15.40% b) ROE, if profit margin increase to 4%: =(15.4%/3.5%)*4% = 17.60% c) ROE, if revenue increases by 20%: = 4%*(1.8*1.2)*(44/18) = 21.12% 3-10 Your firm has identified three potential investment projects. The projects and their cash flows are shown here: Project Cash Flow Cash Flow in one Yr ($) a -10 20 B 5 5 c 20 -10 Suppose all cash flows are certain and the risk-free interest rate is 10%. a. What is the NPV of each project? b. If the firm can choose only one of these projects, which should it choose? c. If the firm can choose any two of these projects, which should it choose? Answer: a) NPV Project A = -10 + 20/1.1 = 8.18 NPV Project B = 5+5/1.1 = 9.55 NPV of Project C = 20+(-10/1.1) = 10.91 b) Project C has highest NPV. Firm should choose Project C. c) Project B has second highest NPV after Project C. Therefore, firm should choose Project B and C. 4-3. Calculate the future value of $2000 in Answer: a. Five years at an interest rate of 5% per year. b. Ten years at an interest rate of 5% per year. c. Five years at an interest rate of 10% per year. d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)? a) FV = 2000 * 1.05^5 = 2,552.56 b) FV = 2000 * 1.05^10 = 3,257.79 c) FV = 2000 * 1.1^5 = 3,221.02 d) In the last 5 years you get interest on the interest earned in the first 5 years and interest on the original $2,000. 4. What is the present value of $10,000 received a. Twelve years from today when the interest rate is 4% per year? b. Twenty years from today when the interest rate is 8% per year? c. Six years from today when the interest rate is 2% per year? Answer: a) PV = 10,000/1.04^12 = 6245.97 b) PV = 10,000/ 1.08^20 = 2145.48 c) PV = 10,000/1.02^6 = 8879.71 11. Suppose you receive $100 at the end of each year for the next three years. a. If the interest rate is 8%, what is the present value of these cash flows? b. What is the future value in three years of the present value you computed in (a)? c. Suppose you deposit the cash flows in a bank account that pays 8% interest per year. What is the balance in the account at the end of each of the next three years (after your deposit is made)? How does the final bank balance compare with your answer in (b)? Answer: a) PV = 100/1.08 + 100/(1.08^2) + 100/(1.08^3) = $257.71 b) FV = 257.71 * (1+0.08)^3 = $324.64 c) Year 1 balance = 100 Year 2 balance = 100 + 100 *1.08 = 208 Year 3 balance = 208 * 1.08 + 100 = $324.64 The final bank balance is $324.64. This is the same amount as the answer I obtained in b). 12. You have just received a windfall from an investment you made in a friend’s business. He will be paying you $10,000 at the end of this year, $20,000 at the end of the following year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year. a. What is the present value of your windfall? b. What is the future value of your windfall in three years (on the date of the last payment)? Answer: a) PV = 10,000 / 1.035 + 20,000 / (1.035)^2 + 30,000 / (1.035)^3 = 9662+18670+27058=55,390 b) FV = 55,390 * (1.035)^3 = 61,412 27. Your oldest daughter is about to start kindergarten at a private school. Tuition is $10,000 per year, payable at the beginning of the school year. You expect to keep your daughter in private school through high school. You expect tuition to increase at a rate of 5% per year over the 13 years of her schooling. What is the present value of the tuition payments if the interest rate is 5% per year? How much would you need to have in the bank now to fund all 13 years of tuition? Answer: Payments: -Today’s tuition payment of $10,000 -12-year growing annuity with first payment of 10,000*(1.05). PV(growing annuity) = 10,000* (1.05) /1.05 + 10,000*(1.05)^2/ (1.05)^2 + 10,000*(1.05)^3/(1.05)^3 + ……+ 10,000 * (1.05)^12 / (1.05)^12 = 10,000 * 12 = 120,000 PV of tuition payments if interest rate is 5% per year is $120,000 You would need $130,000 ($120,000 + $10,000) in the bank now to fund all 13 years of tuition