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CHAPTER 2 – Solutions to Assignment Problems Assignment 2.1: a. Freida, Incorporated Income Statement For the Year ending December 31, 2006 Gross sales 462,720 Less Returns and allowances (10,210) Net sales 452,510 Beginning inventory 63,210 + Materials Purchases 228,580 - Ending inventory (68,390) Cost of goods sold 223,400 Gross profit 229,110 Management salaries 17,950 Lease payments 39,270 Advertising expenditures 12,930 R&D expenditures 4,890 Repairs and maintenance costs 2,910 Depreciation 12,510 Operating profit 138,650 Interest expense 17,090 Earnings before taxes 121,560 Taxes 3,270 Net income 118,290 b. Net profit margin = net income/net sales = 118,290/452,510 = 26.14% c. Accumulated depreciation = 212,820 + 12,510 = $225,330. Assignment 2.2: a. Windcharter Company Balance Sheet For the Year ending December 31, 2006 Cash 17,600 ST bank loans 32,570 Accounts receivable, net 105,770 Accounts payable 50,830 Inventories 136,500 Accrued expenses 11,850 Current assets 259,870 Current portion LT Debt 4,080 Current liabilities 99,330 Gross fixed assets 284,950 Long-term debt 134,300 Less Accumulated depreciation (82,310) Total liabilities 233,630 Net fixed assets 202,640 Preferred stock 8,000 Common stock ($0.20 par) 60,000 Additional paid in capital 71,600 Retained earnings 89,280 Total assets 462,510 Total liabilities & net worth 462,510 b. Assume for this problem that the number given for Net income is actually Net income available to common stockholders (that is, reported Net income minus preferred dividends). Thus, Annual addition to Retained earnings = Net income available to common stockholders – Common stock dividends paid. Thus, Common stock dividends paid = Net income – Addition to (i.e., change in) Retained earnings. Common stock dividends paid = 25,400 – (89,280 – 79,880) = 16,000. Dividends per share = Dividends divided by number of shares outstanding. Number of shares outstanding = Common Stock divided by par value per share = 60,000/.20 = 300,000. Dividends per share = $0.053 or 5.3 cents per share. c. Cash spent on new plant and equipment = Depreciation for the year as listed on the income statement plus the change in net fixed assets. Thus, Cash spent on fixed assets in 1999 = 10,260 + (202,640 – 184660) = $28,240. Assignment 2.3: 1. $4,055,740 $4,100,144 Although Gross sales decreased by 2 percent, net sales (the only number reported) show an increase of 1.1 percent. Since Returns and allowances are estimates made by management, there is some chance that the growth in sales conclusion may be misleading. 2. Cost of goods sold = Beginning inventory + Purchases – Ending inventory. a. $174,300 b. $218,500 3. First solve for accumulated depreciation: 2005 2006 Gross fixed assets 3,200,000 4,620,000 Less Accumulated depreciation (1,280,000) (1,540,000) Net fixed assets 1,920,000 3,080,000 Depreciation expense = change in accumulated depreciation = $260,000. CHAPTER 2 – Answers to Additional Problems and Questions Problems: 1. Look up definitions in chapter 2. EBIT = $15,000; Net income = $6,500 3. a. $400 b. $100 c. $35 4. Gross profit = $3,120,000; Ending Inventory = 850,000. 5. Gross Sales 5,000,000 -Returns 100,000 Net Sales 4,900,000 -COGS 3,000,000 (250,000 x $12 per unit) Gross profit 1,900,000 - Operating expenses 1,000,000 - Depreciation 100,000 Operating income 800,000 - Interest 500,000 EBT 300,000 - Taxes 120,000 Net income 180,000 6. Sales 32,000 Cost of goods sold 19,200 Gross profit 12,800 Operating expenses 4,000 Depreciation 3,000 Operating profit 5,800 Interest expense 2,800 EBT 3,000 Taxes 900 Net income 2,100 7. Inventory – current asset Retained earnings - equity Accounts receivable – current asset Accounts payable – current liability Long-term debt – noncurrent liability Accrued wages and taxes – current liability Common stock (par value) - equity Notes payable (bank loans) – current liability Plant and equipment – noncurrent asset Marketable securities – current asset Cash – current asset Prepaid expenses – current asset 8. Total shareholders’ equity = $1,450,000. 9. In the following solution, the reported number for Gross fixed assets is assumed to exclude Leasehold improvements. Quest-Mar, Incorporated Balance Sheet For the Year Ending Decemebr 31, 2006 Cash 120 ST Bank loan 20 Net Accounts receivable 100 Accounts payable 90 Inventories 190 Accrued expenses 40 Current assets 410 Current portion LT Debt 60 Gross fixed assets (exc. Lease. Imp.) 900 Current liabilities 210 Leasehold improvements 300 Long-term bank loan 600 Less Accumulated depreciation (200) Total liabilities 810 Net fixed assets 1,000 Common stock ($1.00 par) 400 Retained earnings 200 Total stockholder's equity 600 Total assets 1,410 Total liabilities & net worth 1,410 10. a. $782,200 b. $54,532,500 c. $44,465,000 2004 2005 2006 11. CP LT Debt 280,000 280,000 280,000 LT Debt 2,240,000 1,960,000 1,680,000 12. a. 75,000 shares (note that all figures for this problem are in thousands). b. (10,450,000 – 8,700,000) / 75,000 = $23.33 c. $1.12 (total dividends paid by the company = NI(2006) – change in retained earnings = 700,000. Divide this by 625,000 shares outstanding to get $1.12 per share). 13. Total dividends paid = $6,000,000 ; Dividends per share = $1.20 14. a. EPS=$6.14; DPS = $1.89 b. $180,400 c. EPS=$6.01; DPS=$1.76 (assumes 3,000 shares issued – typo on problem). 15. a. 5.25 b. Price=8.25 c. 1.57 times Equity represents shareholder wealth. Book value is historical. Market value is a function of the expected future cash flows of the company. Book value is approximately what the firm’s assets are worth if liquidated. Market value is what the company is worth as a functioning entity. Thus, this company is worth approximately 1.57 times more as an operating company than if the company stopped operating and sold off all of its assets. The larger this ratio, the more successful the company is at creating value in operations. 16. a. Owners equity in 2005 = $140,000; owners equity in 2006 = $144,000 b. $10,000 c. $40,000 d. $4,000 e. $50,000 17. a. Owners equity in 2005 = $100,000; owners equity in 2006 = $110,000 b. $20,000; $24,000 c. $10,000 d. $3,000 e. $128,000 – note this merely equals the change in net fixed assets + depreciation from I/S f. +$22,000 CHAPTER 3 – Solutions to Assignment Problems Assignment 3.1: Net income 48,000 + Depreciation 30,000 + Decrease in Accounts receivable 21,000 - Increase in Inventories (10,900) - Decrease in Accounts payable (12,000) - Decrease in Accruals (14,000) Net Cash Flow from Operating Activities 62,100 Purchase of Gross fixed assets* (40,000) Net Cash Flow from Investing Activities (40,000) Increase in Notes payable 15,000 Change in LT Debt 6,000 Change in Common Stock 5,000 Increase in Capital surplus 1,000 - Payment of dividends** (33,200) Net Cash Flow from Financing Activities (6,200) Change in Cash 15,900 * Change in Net fixed assets + Depreciation ** Net income - (Change in Retained earnings) Assignment 3.2: Net income 1,800 + Depreciation 1,600 - Increase in Accounts receivable (500) - Increase in Inventories (300) + Increase in Accounts payable 1,100 + Increase in Accruals 500 Net Cash Flow from Operating Activities 4,200 Purchase of Gross fixed assets* (2,400) Net Cash Flow from Investing Activities (2,400) Change in LT Debt - Change in Common Stock - - Payment of dividends** (1,200) Net Cash Flow from Financing Activities (1,200) Change in Cash 600 * Change in Net fixed assets + Depreciation ** Net income - (Change in Retained earnings) Assignment 3.3: Net income 32,000 + Depreciation* 30,000 + Decrease in Accounts receivable 7,000 - Increase in Inventories (30,900) + Increase in Accounts payable 8,000 - Decrease in Accruals (1,000) Net Cash Flow from Operating Activities 45,100 Purchase of Gross fixed assets** (40,000) Net Cash Flow from Investing Activities (40,000) Change in Notes payable (3,000) Change in LT Debt 15,000 Change in Common Stock 2,000 Change in Capital surplus 4,000 - Payment of dividends*** (24,900) Net Cash Flow from Financing Activities (6,900) Change in Cash (1,800) * Change in Accumulated depreciation ** Change in Gross fixed assets *** Net income - (Change in Retained earnings) CHAPTER 3 – Answers to Additional Problems and Questions Problems: 1. Raise prices, reduce growth rate, speed up collections, hold smaller inventory levels, etc. 2. A reduction or non-payment of a dividend, the substitution of a stock dividend for a cash dividend, late payments to suppliers or other creditors, bounced payroll checks, etc. 3. July Balance Sheet Cash 15,000 Debt - Accounts receivable 35,000 Stock 40,000 Inventories 28,000 Retained earnings 38,000 Total assets 78,000 Total claims 78,000 4. The growth in sales slowed to zero percent per year. Note that outflows for this company are based on the current month’s sales level. That is, outflows in February are based on February purchases (which are based on February sales). Outflows in March are based on March purchases (which are based on March sales). And so on. Conversely, inflows are based on sales that occurred one month ago. Thus, inflows in February are based on January sales and inflows in March are based on February sales. In periods of rapid growth, this one-month lag can cause outflows to exceed inflows even though revenue exceeds costs for that period. When sales growth slows to zero, the lag effectively disappears since sales in each month are the same. In this case, inflows minus outflows are essentially the same as revenue minus cost. 5. Depreciation expense (2004) = $2,000. Depreciation expense (2005) = $4,000. Depreciation expense (2006) = $2,000. 6. Change in gross fixed assets (2004) = $20,000. Change in gross fixed assets (2005) = $40,000. Change in gross fixed assets (2006) = $20,000. 7. Change in Net fixed assets + Depreciation (2004) = 18,000 + 2,000 = $20,000. Change in Net fixed assets + Depreciation (2005) = 36,000 + 4,000 = $40,000. Change in Net fixed assets + Depreciation (2006) = 18,000 + 2,000 = $20,000. 8. Net income 26,000 + Depreciation 2,000 - Increase in Accounts receivable (4,000) - Increase in Inventories (2,000) - Decrease in Accounts payable (2,000) Net Cash Flow from Operating Activities 20,000 Purchase of Gross fixed assets (15,000) Net Cash Flow from Investing Activities (15,000) Change in Notes payable 3,000 Change in LT Debt 8,000 Change in Common Stock 15,000 - Payment of dividends (18,000) Net Cash Flow from Financing Activities 8,000 Change in Cash 13,000 9. a. Total dividend paid = NI – change in R. E. = 3200 – (4000-2800) =$2000 b. Change in GFA/purchase = change in NFA + dep = (14,900-13,300)+1800 = $3400 GFA in 2006 = GFA of 2005 + purchase =20,000+ 3400 = $23, 400 10. Net income 3,200 + Depreciation 1,800 + Decrease in Accounts receivable 500 - Increase in Inventories (600) + Increase in Accounts payable 1,800 - Decrease in Accruals (400) Net Cash Flow from Operating Activities 6,300 Purchase of Gross fixed assets (3,400) Net Cash Flow from Investing Activities (3,400) Change in Notes payable 400 Change in LT Debt (1,300) Change in Common Stock 600 - Payment of dividends (2,000) Net Cash Flow from Financing Activities (2,300) Change in Cash 600 6,300 – 3,400 – 2,300 = 600 (check) 11. Net cash flow from Operating Activities = $4,500 Net cash flow from Investing Activities = ($12,200) Net cash flow from Financing Activities = $8,200 12. Net cash flow from Operating Activities = $470,000 Net cash flow from Investing Activities = ($350,000)* Net cash flow from Financing Activities = ($110,000) *Note that Long-term investments are an investing activity. An increase in Long-term investments represents an outflow of cash. 13. a. $94,200 b. $113,500 c. $19,300 14. NCF Operating Activities = $22,900; NCF Investing Activities = ($23,200); NCF Financing Activities = $100. 15. a. $1.96 million (compute net income and then add back depreciation, since depreciation is not a cash flow). b. $400,000 (note that when depreciation increases, taxes decrease. This is why depreciation, although not a cash flow, can affect net cash flow from operations. Specifically, by changing the amount of taxes a company owes. 16. a. ($6,000) - note that change in cash and marketable securities = ($4,000) b. ($2,000) c. ($28,000) d. $26,000 The sum of these three cash flows = -$4000, which is the change in cash and marketable securities. Marketable securities, as explained in chapter 2, are an alternative form of cash. They are very short-term investments that generate a positive return; they can be converted into cash very quickly. Essentially, cash that earns a return. CHAPTER 4 – Solutions to Assignment Problems Assignment 4.1: 1. a. 2005 2006 Net sales 100.0% 100.0% Cost of goods sold 62.9% 64.1% Gross profit 37.1% 35.9% Operating expenses 27.1% 26.5% Operating income 10.0% 9.5% Income taxes 4.2% 4.1% Net income 5.8% 5.4% Note that the gross profit margin deteriorates by 1.2% and Operating profit margin deteriorates by 0.5%. Company has been able to offset some of the gross margin deterioration by controlling operating expenses – either real or manipulation of discretionary expenses. 2. (Note that some of the ratios you compute for this problem will look nonsensical. This is done on purpose to stress computation of the ratios. Hopefully you will note that a company with some of these ratios – in particular ACP and Inventory turnover, would probably be in very poor shape). 2005 2006 Current ratio 2.3 2.4 Average collection period 288.2 365 Inventory turnover ratio .40 .39 Total asset turnover ratio .28 .24 Payables ratio 488.3 491.8 Debt ratio 57% 35% Cash conversion cycle 715.5 805.1 Net profit margin 5.8% 5.4% Return on equity 3.8% 3.2% Assignment 4.2: a. Total dividends = Net income – Change in Retained earnings = 1,600,000 – 600,000 = 1,000,000. b. Number of shares = Common stock/ Par value per share = 1,500,000/.25 = 6,000,000 shares. c. Number of shares = Common stock/ Par value per share = 1,900,000/.25 = 7,600,000 shares. d. Dividends per share = Total dividends / Number of shares = 1,000,000/7,600,000 = 13 cents. e. ROE = Net income / Total Equity = 1,400,000/ (1,500,000 + 1,000,000 + 1,000,000) = 40%. f. ROE = Net income / Total Equity = 1,600,000/ (1,600,000 + 2,400,000 + 1,900,000) = 27%. g. ROE (Dupont) = Net income/Sales x Sales/Total assets x Total assets/Total equity. ROE (2002-Dupont) = .200 x 1.167 x 1.714 = .40 = 40% ROE (2003-Dupont) = .178 x 0.900 x 1.695 = .27 = 27% Net profit margin declined in 2003 by 11% (from 20% to 17.8%), Total asset turnover ratio declined by 23% (from 1.714 to 0.900) and the equity multiplier declined by 1.1%. The major reason for the deterioration in ROE is a decrease in the efficiency of asset utilization. Secondary reason is a decline in profitability. Assignment 4.3: The best approach to do these “fill in the balance sheet” type problems is to use any given values (in this case, Total assets = $1,000,000) to compute as many related values as possible. For example, given that Assets (A) = 1,000,000, then from the fact that the Debt ratio (Total liabilities/Total assets) = 60%, Total liabilities = 600,000. Since Total assets = Total liabilities + Total equity (basic accounting relationship), Total equity must be 400,000. On the given balance sheet, Total liabilities = Accounts payable + Long-term debt, and since Long-term debt is given as 180,000, Accounts payable = 420,000. Also, on the given balance sheet, since Total equity = Common stock + Retained earnings, and since Retained earnings is given as 200,000, Common stock = 200,000. Next use, Average collection period = 45 days = (Accounts receivable/Sales) x 360. From Total asset turnover = Sales/Total assets = 2.0, Sales = 2,000,000. Thus, 45 = (Accounts receivable/2,000,000) x 360, so Accounts receivable = 250,000. Then use, Inventory turnover ratio = 5 = COGS/Inventory. From Gross profit margin = 25% and Sales = 2,000,000, COGS = 1,500,000. Thus, 5 = 1,500,000/Inventory, so Inventory = 300,000. Then use Quick ratio = 1.0 = (Current assets - Inventory)/(Current liabilities). Note that Current assets for this balance sheet = Cash + Accounts receivable + Inventory, so Current assets – Inventory = Cash + Accounts receivable. Also note that for this balance sheet, Current liabilities = Accounts payable. Thus, 1 = (Cash + 250,000)/(420,000), so Cash = 170,000. Finally, Cash + Accounts receivable + Inventory + Fixed assets = Total assets. Thus, Fixed assets = 280,000. Summarizing: Cash 170,000 Accounts payable 420,000 Accounts receivable 250,000 Current liabilities 420,000 Inventories 300,000 Long-term debt 180,000 Current assets 720,000 Total liabilities 600,000 Fixed assets 280,000 Common stock 200,000 Total assets 1,000,000 Retained earnings 200,000 Total claims 1,000,000 2. Sales = 2,000,000; COGS = 1,500,000 3. CCC = Inventory conversion period + Average collection period – Payables period i. = 72 + 45 – 100.8 = 16.2 days. 4. ROE = Net profit margin x Total asset turnover ratio x (Total assets/Equity) = .10 x 2.0 x (1,000,000/400,000) = .50 = 50% CHAPTER 4 – Answers to Additional Problems and Questions Problems: 1. A grocery store. Would you want to shop at a grocery store that had an inventory turnover ratio of 2? That is, all items (fruit, meat, vegetables, etc.) turned over (i.e., sold) on average only once every 6 months! 2. High inflation can distort the relationship between book values of assets and true economic values. For example, if a firm has land on its balance sheet listed in value at $1,000 and inflation in land values in running at 40 percent annually, 5 years later the market value of the land would be worth approximately $5,400 but would only be listed on the balance sheet as being worth $1,000. A similar distortion would apply to plant and equipment. For short-term assets, however, values would, in general, adjust with inflation. If inventory turns over relatively rapidly, each turnover would adjust inventory values upward. The same would be true of accounts receivable. Thus, the relationship between the book value of short- term assets and long term assets will be distorted. Finally, since the income statement is a flow measure, high inflation usually affects all revenues and costs in a similar manner. Assume that a firm has revenue of $1,000 and costs (total) of $800 and thus profit of $200. If inflation is 50 percent and it impacts revenue and costs in a similar manner, then revenue will grow to $1,500 (due solely to inflation) and costs will increase to $1,200 causing profit to grow to $300. Thus inflation can cause a dramatic increase in net income (even more pronounced if some costs are fixed). Now consider the impact of this increase on a ratio such as ROA (recall from above that assets do not necessarily grow in line with inflation). 3. The current ratio is CA/CL. A declining ratio can either be due to a relative decline in CA or a relative increase in CL. Since the inventory turnover ratio and the ACP are constant through time, inventory and accounts receivable appear to be relatively stable. The increase in the Payables period would indicate a relatively rapidly increasing Accounts payable value, which would cause a relative increase in CL and therefore a decline in the current ratio. The analyst should investigate the causes of the increase in AP perhaps a new supplier to the firm offers more lax credit terms than the previous supplier. 4. 72%; 14.4%; 45% 5. CA = 2(CL) = 200,000. (CA - Inv)/100,000 = 1.5; thus, Inv = 50,000. 6. HINT: For problems where you are only given ratios and NO actual dollar amounts, assume that assets are $100 and solve for all other numbers - then find the answer. Thus, assume A = 100. From ROA = NI/A; .20 = NI/100; thus, NI = 20. Then, from ROE = NI/E; .50 = 20/E; thus, E = 40. Then, from the definition, A = D + E; 100 = D + 40; thus, D = 60. (NOTE: this relationship can be used for most of these types of problems). Finally, compute the debt ratio = D/A = 60/100 = .60 = 60%. 7. Assume A = 100. Then from S/A = 4, S = 400. Then from D/A = .20, D = 20. Then from A = D + E, E = 80. Then from NI/E = .10, NI = 8. Finally, compute net profit margin = NI/S = 8/400 = 2%. 8. For this problem, you are given a dollar amount, so DO NOT assume that A = 100. Instead, from ACP =(AR/S) x 360; 20 = (1,000/S) x 360; thus, S = 18,000. Then from NI/S = .05, NI = 900. Then from S/A = 2, A = 9,000. Then from D/A = .75, D = 6,750. Then from A = D + E, E = 2,250. Finally, ROE = NI/E = 900/2,250 = 40%. 9. Net profit margin = 8%; Debt ratio = 52% 10. ROA = 12.5%; ROE = 16.7% 11. Net profit margin = 8%; Debt ratio = 52% We know that if we solve for x in (1950+x)/(800+x) = 2, we get the maximum amount by which inventory = bank debt =x can increase without violating a current ratio of 2.Solving for x we get, x = 350. In this case, Inv will be 1,050. Thus, (CA-Inv)/CL = (1950+350- 1050)/(800+350), and Quick ratio = 1.087. 12. Assume A = 100. Then D = 75 and E = 25 (recall A = D + E). Thus, Equity multiplier = A/E = 100/25 = 4. 13. Answers assume a 360-day year. a. $100 b. $450 c. $150 d. 5.7% e. $400 f. $500 14. ROE = 42% (since all equity financed, equity = total assets) 15. Max Increase in debt = 1.4 16. B 17. From ACP = (ARx360)/S, 60 = (150,000x360)/S, S = 900,000. From NI/S = .04, NI = 36,000. From D/A = .64 and A = 3,000,000, D = 1,920,000. From A = D + E, E = 1,080,000. Then, ROE = NI/E = .033 = 3.3%. 18. Note that CA = Cash & Mkt. Sec. + AR + Inv. and Inventory turnover here is defined as S/Inv. From CA/CL = 3 and CA = 810,000, CL = 270,000. From (CA-Inv)/CL = 1.4 and note above and Cash & Mkt. Sec. = 120,000, AR = 258,000. From note above, now Inv = 810,000 - 120,000 - 258,000 = 432,000. From S/Inv = 6, S = 2,592,000. From ACP = (ARx360)/S, ACP = 35.8 days. 19. From NI/S = .06, NI = 120,000. From tax rate = .40 and from NI = EBT - (.40)x(EBT), EBT = 200,000. To check, note that 200,000 x .4 = taxes of 80,000 and EBT - taxes = 120,000. From EBT = EBIT - Interest, EBIT = 220,000. Thus, TIE = EBIT/Interest = 11 times. 20. Assume that currently A = 100. Then, currently, from debt ratio = .5, D = 50 and E = 50. From S/A = .25, S = 25. From NI/S = .10, NI = 2.5. Using these numbers note that ROE = 5% (they want to double the current ROE from 5% to 10%) checks out. For new, assume that S and A remain the same such that S/A will remain the same. Thus, S = 25 and A = 100. From NI/S = .14, NI = 3.5 For ROE = NI/E to be .10, E must be 35. From A = D + E, D = 65 and thus, debt ratio = D/A = 65%. 21. Assume A = 100. From D/A = .35, D = 35 and E = 65. From NI/E = .15, NI = 9.75. From S/A = 2.8, S = 280 Thus, NI/S = .0348 = 3.48%. 22. For these conversion type problems, note that if D = D/E and E = 1, D/E will be the stated amount. Thus, for the first one, if D = 2.5 and E = 1, then D/E = 2.5. From A = D + E, A = 2.5 + 1 = 3.5. Then, D/A = 2.5/3.5 = .714 = 71.5% and A/E (the equity multiplier) = 3.5/1 = 3.5 times. For the second one, let D = 1 and E = 1 (thus, D/E = 1). Then A = D + E and A = 2. Thus, D/A = .5 and A/E = 2. For the third one, let D = .6 and E = 1. Then, A = 1.6. Thus, D/A = .375 = 37.5% and A/E = 1.6 times. 23. From NI/S = .075, NI = 150,000. From NI/E = .24, E = 625,000 From NI/A = .15, A = 1,000,000 Thus, Total liabilities = NP + AP + LT Debt = 375,000. From S = 2,000,000 and Gross profit = 400,000, COGS = 1,600,000. From COGS/Inv = 4, Inv = 400,000. From (APx360)/COGS = 20, AP = 88,889. From ACP = (ARx360)/S = 40, AR = 222,222. From CA/CL = 3.8 and CA = AR + Inv = 622,222, CL = 163,743. From CL = Notes payable + AP, Notes payable = 74,854. Thus, long-term debt = 375,000 - 74,854 - 88,889 = 211,257. Finally, A = 1,000,000 = AR + Inv + Fixed Assets. Thus, Fixed assets = 377,778. Summarizing, AR = 222,222; Inv = 400,000; Fixed assets = 377,778; Total assets = 1,000,000; Notes payable = 74,854; AP = 88,889; Long-term debt = 211, 257; Equity = 625,000; Total liab & eq. = 1,000,000. 24. See if you can derive the following answer on your own. Hint, compute Accounts receivable first, and then use the Quick ratio and Current ratio to compute Current liabilities and Inventories. Accounts receivable 400 Current liabilities 400 Inventories 800 Long-term debt 2000 Fixed assets 2800 Equity 1600 Total assets 4000 Total claims 4000 CHAPTER 5 – Solutions to Assignment Problems Assignment 5.1: Balance Sheet FreshFish, Inc. Years ending December 31, 2006 and 2007 2006 2007 Cash $ 20,000 $ 30,000 Accounts receivable 10,000 15,000 Inventory 80,000 120,000 Total Current Assets $110,000 165,000 Net plant and equipment $430,000 645,000 Total assets $540,000 $810,000 Notes payable 15,000 15,000 Accounts payable to suppliers 50,000 75,000 Accruals 5,000 7,500 Total current liabilities $ 70,000 97,500 Long-term debt 190,000 190,000 Common stock ($2.00 par value) 20,000 20,000 Capital surplus 150,000 150,000 Retained earnings 110,000 138,350 Total Liabilities and Equity $540,000 $595,850 2. OFN = $810,000 – $595,850 = $214,150 3. 540,000(.50) – 55,000(.50) – 900,000(1.50)(.035)(.60) = 270,000 – 27,500 – 28,350 = $214,150 Assignment 5.2: You can answer this question for all parts using the OFN equation. Note that in that equation, the last part is the change in retained earnings due to projected profit that is reinvested back into the firm. This part of the equation is given as: [(S0 + (g)(S0)](NPM) – Div0] The first part of this equation is projected net income. With some minor mathematical rearrangement, it can be written as (S0)(1+g)(NPM). The last term in the equation is the amount of net income that is paid out in dividends. In the equation, it is given as a constant. For Assignment 6.2, it is stated as a percent of net income (i.e., “Tabler pays out 40 percent of all its annual profit in dividends”). If 40% of profit is paid out, then the remainder (i.e., 60%) must be retained. Mathematically, this can be written as: (S0)(1+g)(NPM)(.60) Thus, the OFN equation becomes: OFN = (TA0)(g) – [(L0)(g) + (S0)(1+g)(NPM)(.60)] And filling in all other given values: OFN = (1,220,000)(g) – [(500,000)(g) + (4,000,000)(1+g)(.05)(.60)] = 1,220,000g – 500,000g – 120,000g – 120,000 = 600,000g – 120,000. a. For g = 0% = 0, OFN = -120,000 b. For g = 10% = .10, OFN = -60,000 c. For g = 20% = .10, OFN = 0 d. For g = 30% = .10, OFN = 60,000 e. For g = 40% = .10, OFN = 120,000 f. For g = 50% = .10, OFN = 180,000 2. OFN = 0 when g = 20% (see c above). Assignment 5.3: a. Earnings per share = Net income divided by number of shares of common stock outstanding. Net income = (.05)(90,000) = 4,500. Number of shares = Common stock value of balance sheet divided by par value per share = 60,000/2 = 30,000. Thus, Earnings per share = 4,500/30,000 = .15 = 15% b. Dividends = Net income – Change in retained earnings = 4,500 – (30,000 – 28,200) = 2,700. Dividend payout ratio = Dividends divided by Net income (that is, the ratio measures the percent of net income that is paid out in dividends). Dividend payout ratio = 2,700/4,500 = .60 = 60%. c. Use the equation: OFN = (TA0)(g) – [(L0)(g) + [(S0 + (g)(S0)](NPM) – Div0]. OFN = (200,000)(.40) – [(60,000)(.40) + [(90,000 + (.40)(90,000)](.05) – 4,000] = 80,000 – 24,000 – 2,300 = 53,700. 2. Construct the proforma income statement: Sales $330,000 Operating Costs (70%) 231,000 Fixed costs 60,000 EBIT 39,000 Interest 10,000 EBT 29,000 Taxes (40%) 11,600 Net income 17,400 Dividends 9,000 Addition to Retained earnings 8,400 Now, construct the proforma balance sheet: Current assets 110,000 Notes payable 20,000 Net fixed assets 55,000 Accounts payable 22,000 Total assets 165,000 Accruals 11,000 Long-term debt 50,000 Equity 58,400 Total claims 161,400 OFN = 165,000 – 161,400 = 3,600. CHAPTER 5 – Answers to Additional Problems and Questions Problems: 1. Reduce the dividend payout rate or increase the net profit margin. 2. a. and b. Apr May Jun Jul Aug Sep Cash Collections 75,000 100,000 300,000 500,000 900,000 500,000 Cash Expenses 350,000 350,000 350,000 350,000 350,000 350,000 Net Cash Flow (NCF) (275,000) (250,000) (50,000) 150,000 550,000 150,000 Begin. Cash + NCF 75,000 (175,000) - 150,000 600,000 625,000 Ending ST Loan Balance - 225,000 275,000 125,000 - - Ending Cash Balance 75,000 50,000 50,000 50,000 475,000 625,000 NOTE: If ending cash balance is greater than 50,000, the ST loan is zero. If ending cash balance is less than 50,000, the ST loan will grow so as to make ending cash equal to 50,000. c. Accounts receivable balance (Apr) = 100,000 Accounts receivable balance (May) = 300,000 Accounts receivable balance (Jun) = 500,000 Accounts receivable balance (Jul) = 900,000 Accounts receivable balance (Aug) = 500,000 Accounts receivable balance (Sep) = 200,000 3. Annual Inventory Related Interest Cost (current) = 25 x 500 x .10 = $1,250 Annual Inventory Related Interest Cost (proposed) = 15 x 500 x .10 = $750 So, reduction in annual inventory related interest cost = $750. Reduction in Rent = $5,000 annual savings. So, total benefit of proposed change = $5,750 Number of Inventory orders per year (current) = 12 Number of Inventory orders per year (proposed) = 36 Increase in Inventory order cost = (36)($250) = $6,000 Thus, benefit – cost = $5,750 - $6,000 = ($250) – DO NOT CHANGE POLICY. 4. COFFYS Proforma Balance Sheet For the Year Ending June 30, 2004 Cash $14,000 Notes payable $10,000 Accounts receivable 11,200 Accounts payable 35,000 Inventories 100,800 Accruals 7,000 Current Assets 126,000 Current Liabilities 52,000 Gross fixed assets 1,148,000 Long term bank loan 400,000 Accumulated dep. (84,000) Common stock 200,000 Net fixed assets 1,064,000 Retained earnings 226,000 Total assets 1,190,000 Total Liab. & equity 878,000 All asset accounts grow by 40% and accounts payable and accruals (i.e., spontaneous liabilities) grow by 40%. Financing variable (i.e., Notes payable, Long-term bank loan and Common stock) values stay fixed. The change in Retained earnings is due to net income that is not paid in dividends. Specifically, Change in RE = (2003 Sales)(1 + Projected growth rate)(Net profit margin) – Dividends = (800,000)(1.4)(.05) – 40,000 = 16,000 And thus proforma Retained earnings = 210,000 + 16,000 = 226,000. Outside funds needed = 1,190,000 – 878,000 = 312,000. Check: OFN = (TA0)(g) – [(L0)(g) + [(S0 + (g)(S0)](NPM) – Div0] = (850,000)(.40) – [(30,000)(.40) + [(800,000 + (.40)(800,000)](.05) – 40,000 = 340,000 – [12,000 + 16,000] = 312,000. 5. COFFYS Proforma Balance Sheet For the Year Ending June 30, 2004 Cash $14,000 Notes payable $ 8,400 Accounts receivable 11,200 Accounts payable 35,000 Inventories 100,800 Accruals 7,000 Current Assets 126,000 Current Liabilities 50,400 Gross fixed assets 1,148,000 Long term bank loan 400,000 Accumulated dep. (84,000) Common stock 200,000 Net fixed assets 1,064,000 Retained earnings 226,000 Total assets 1,190,000 Total Liab. & equity 876,400 All asset accounts grow by 40% and accounts payable and accruals (i.e., spontaneous liabilities) grow by 40%. To solve for Notes payable, use the fact that the current ratio will be 2.5. Since you have projected current assets = 126,000, this implies that projected current liabilities will be 50,400. With Accounts payable = 35,000 and Accruals = 7,000 (due to spontaneous liabilities grow by 40%), Notes payable = 52,000 – 35,000 – 7,000 = 8,400. The remaining financing variable (i.e., Long-term bank loan and Common stock) values stay fixed. The change in Retained earnings is due to net income that is not paid in dividends. Specifically, Change in RE = (2003 Sales)(1 + Projected growth rate)(Net profit margin) – Dividends = (800,000)(1.4)(.05) – 40,000 = 16,000 And thus proforma Retained earnings = 210,000 + 16,000 = 226,000. Long term outside funds needed = 1,190,000 – 876,400 = 313,600. (This money will come from some combination of additional long-term debt and additional common stock). 6. COFFYS Proforma Balance Sheet For the Year Ending June 30, 2004 Cash $14,000 Notes payable $21,000 Accounts receivable 11,200 Accounts payable 35,000 Inventories 100,800 Accruals 7,000 Current Assets 126,000 Current Liabilities 63,000 Gross fixed assets 1,148,000 Long term bank loan 413,000 Accumulated dep. (84,000) Common stock 200,000 Net fixed assets 1,064,000 Retained earnings 226,000 Total assets 1,190,000 Total Liab. & equity 902,000 All asset accounts grow by 40% and accounts payable and accruals (i.e., spontaneous liabilities) grow by 40%. To solve for Notes payable, use the fact that the current ratio will be 2.0. Since you have projected current assets = 126,000, this implies that projected current liabilities will be 63,000. With Accounts payable = 35,000 and Accruals = 7,000 (due to spontaneous liabilities grow by 40%), Notes payable = 63,000 – 35,000 – 7,000 = 21,000. To solve for Long-term bank loan, use the fact that the debt ratio will be 40 percent. The debt ratio = total liabilities divided by total assets. With total assets projected to be 1,190,000, total liabilities will be (.40)(1,190,000) = 476,000. Since Current liabilities = 63,000, Long-term bank loan must be 476,000 – 63,000 = 413,000. The remaining financing variable (i.e., Common stock) value stay fixed. The change in Retained earnings is due to net income that is not paid in dividends. Specifically, Change in RE = (2003 Sales)(1 + Projected growth rate)(Net profit margin) – Dividends = (800,000)(1.4)(.05) – 40,000 = 16,000 And thus proforma Retained earnings = 210,000 + 16,000 = 226,000. Money needed from selling additional common stock = 1,190,000 – 902,000 = 288,000. 7. a. $101,000 b. - $24,000 (TA = 1250000*1.15 =1437,500, 60% of which is debt, Total equity needed = 0.4 of 1437,500 = 575,000. Now addition to R. E = 49,000. Total R. E = 300,000+49,000 = 349,000. Total equity fund available = (50,000+200,000+349,000) = 599,000. Therefore, common stock needed (575,000-599,000) = -24,000 8. $130,400 9. $112,500 10. a. $150,000 b. $137,400 c. $124,800 11. (a) 2003 Actual 2004 Proforma Cash 400,000 500,000 Acc. receivable 900,000 1,125,000 Inventory 1,200,000 1,500,000 Net Prop. & Plant 2,500,000 3,125,000 Total Assets 5,000,000 6,250,000 Acc. payable 800,000 1,000,000 Long term debt 1,500,000 1,500,000 Common Stock 1,800,000 1,800,000 Retain earnings 900,000 1,140,000 Tot. Liab. & Equity 5,000,000 5,440,000 Total Outside Funds Needed = 810,000 (b) 2003 Actual 2004 Proforma Cash 400,000 500,000 Acc. receivable 900,000 1,125,000 Inventory 1,200,000 1,500,000 Net Prop. & Plant 2,500,000 3,125,000 Total Assets 5,000,000 6,250,000 Acc. payable 800,000 1,000,000 Long term debt 1,500,000 2,750,000 Common Stock 1,800,000 1,800,000 Retain. earnings 900,000 1,140,000 Tot. Liab. and Equity 5,000,000 6,690,000 Additional Common Stock Needed =(440,000) 12. a. Total Outside Funds Needed = 2,235,000 b. Total Outside Funds Needed = 885,000 CHAPTER 6 – Solutions to Assignment Problems Assignment 6.1: 1. FV = PV (1+r). Let FV = 2 and PV =1. Thus, 2 = 1(1+r). When you solve for r, you get r=1. Expressed as a percent, the interest rate is 100%. 2. FV = PV (1+r); 7397 = PV(1+.0439) or PV = 7297/1.0439; Solve PV = 7,085.93. 3. FV = PV (1+r); 13000 = PV(1.08) or PV = 13000/1.08; Solve for PV = 12,037.04. 4. Note that you will only need 25000 – 4500 = 20,500 one year from today. Thus, FV = PV (1+r); 20500 = PV(1.075) or PV = 20500/1.075; Solve for PV = 19,069.77 5. FV = PV (1+r); 14739 = PV(1.12) or PV = 14739/1.12; Solve for PV = 13,159.82. Assignment 6.2: 1. FVn = PV (1+r)n. Let FV = 2 and PV =1. Thus, 2 = 1(1+r)2 or 2½ = (1+r). When you solve for r, you get r=.4142. Expressed as a percent, the interest rate is 41.42%. 2. PV = FV1(1/1+r)1 + FV2(1/1+r)2 ; PV = 3200(1/1.06)1 + 7300(1/1.06)2 ; PV = 3018.87 + 6496.97 = 9,515.84. 3. Note that the first deposit will grow for one year – that is, it will grow to become 7448 (1.07) = 7969.36. When you add the extra 2476, you will have a total of 10,445.36 in your account. 4. Continuing from #3, the 10,445.36 will grow again by 7 percent to be 10445.367(1.07) = 11,176.54. 5. 15000 = X(1.12)2 + X(1.12)1 = X [(1.12)2 + (1.12)1] = X[2.3744]. Thus, X = 6,317.39. Assignment 6.3: 1. FV2 = Deposit0 (1+r)2 + Deposit1 (1+r)1. (Note that the deposit made today (at t=0) will earn interest for 2 years and the deposit made one year from today will earn interest for 1 year). Thus, 4000 = 8000(1.04)2 + Deposit (1.04)1; 4000 = 8652 + Deposit (1.04). Solve for Deposit and you get Deposit = -4,473.85. The negative sign implies that you will withdraw this amount at the end of year one. 2. The question is what is the present value of the investment. That is, what is the present value of 6500 one year from today + 5000 two years from today. We then compare the value of the investment with the cost. If value > cost, you should buy. If value < cost, you should not buy. PV = FV1(1/1+r)1 + FV2(1/1+r)2 ; PV = 6500(1/1.12)1 + 5000(1/1.12)2 ; PV = 5803.57 + 3958.97 = 9,789.54. Do not make investment. 3. 538 = 500 (1+r)1; 1.0760 = 1+r; r = .0760 = 7.6% 4. (1 + rnominal) = (1 + rreal) x (1 + i); (1 + rnominal) = (1.08) x (1.04) = 1.1232. rnominal = .1232 = 12.32%. 5. (1 + rnominal) = (1 + rreal) x (1 + i); (1.122) = (1 + rreal) x (1.036); (1 + rreal) = 1.083. rreal = .083 = 8.3%. 6. (1 + rnominal) = (1 + rreal) x (1 + i); (1.086) = (1.047)(1 + i); (1 + i) = 1.0372. i = .0372 = 3.72% CHAPTER 6 – Answers to Additional Problems and Questions Problems: 1. 10.24% 2. 8.112% 3. 5.77% 4. 5.15% 5. 1.92% 6. 10.04% 7. 1294.80 8. 4108.90 9. 237.60 10. 4917.12 11. 969.31 12. 1696.25 13. 3752.35 14. 612.83 15. E(R) [i.e., Expected Return] on first = 11.5%;E(R) on second = 12.1% Choose both since Expected Return > Required Return. NOTE: This problem implicitly assumes that these two investments are of equal risk. Unless otherwise explicitly stated, for all problems in this book, we will assume that all comparable investments are of equal risk. 16. E(R) on first = 10.2%; E(R) on second = 7.48% Choose neither since for both E(R) < Required Return. 17. (d) is correct. For (a), PV must be less than 432 since interest rate is greater than 0.for (b), the FV (t=1) must be greater than the PV (t=0) value since interest rate is greater than 0.for (c), you would never pay more than the simple sum of all future cash flows (i.e., 2,300+2,300 = 4,600 < 6,600) 18. 70,661.16 19. 1,680.00; 1,915.20 20. In the following equation, solve for X (note that ^2 means raised to the second power, or int this case, squared): 10,000 = 7,000 (1/1.13)^1 + X(1/1.13)^2 ==> X = 4,859 21. In the following equation, solve for r: 4,100 = 3,500 (1+r)^2 ==> r = 8.233% 22. Buy the two year subscription because the PV of buying a one year subscription today and another one year subscription one year from today = 48 + 48(1/1.10) = 91.64 which is greater than the two year subscription price of 70. This answer of course assumes that you actually want to read this magazine for two years! 23. Assume that the two payments are due one month from today and 2 months from today. Payoff = 791.09 24. Compare 20,000 - 2,850 = 17,150 to the PV of 20,000 two years from today. 20,000(1/1.08)^2 = 17,146.78. Since 17,150 > 17,146.78, choose (b) because it is "cheaper." CHAPTER 7 – Solutions to Assignment Problems Assignment 7.1: 1. PV = -30000, FV = 49000, n = 5, Compute I/Y = 10.31%. PV = -73000, FV = 128000, n = 7, Compute I/Y = 8.35%. 2. Use cash flow register: CF0 = 0, C01 = 22000, F01 = 1, C02 = 27500, F02 = 1, C03 = 33000, F03 = 1, C04 = 35000, F04 = 1; Compute NPV (with I = 6%) = 100,660.33 3. Use cash flow register to find NPV. Then find FV of this amount. Thus, CF0 = 11000, C01 = 13000, F01 = 1, C02 = 17400, F02 = 1, C03 = 12800, F03 = 1, C04 = 9600, F04 = 1; C05 = 17200, F05 = 1; Compute NPV (with I = 8%) = 66878.10. Now find the future value of this amount 10 years from today. PV = 66878.10, I = 8, n = 10, Compute FV = 144,384.81. Assignment 7.2: 1. PV = -28000, fv = 30000, I = 6, n = 10, Compute PMT = 1,528.26. 2. First find F of deposits. PMT = 2500, I = 8, n = 20, Compute FV20 = 114404.91. Now find withdrawals. PV = 114404.91, n = 25, I = 8, Compute PMT = 10,717.31 3. First find NPV of all cash flows with the unknown cash flow assumed to be 0. That is, CF0 = 5000, C01 = 0, F01 = 10, C02 = -60000, F02 = 1, C03 = 0, F03 = 2, C04 = 25000, F04 = 1, C05 = 0, F05 = 11, C06 = -1500000, F06 = 25; Compute NPV (with I = 7%) = 335884.60. Now find PMT. PV = 335884.60, I = 7, n = 25, Compute PMT = 28,822.43. 4. First find PV20 of perpetuity = 30000/.12 = 250000 (note this is value in year 20). CF0 = 0, C01 = 12000, F01 = 3, C02 = 17000, F02 = 4, C03 = 21000, F03 = 8, C04 = 24000, F04 = 4; C05 = 274000, F05 = 1; Compute NPV (with I = 12%) = 154,486.56. Assignment 7.3: 1. PV = -1, FV = 2, I = 7/2 = 3.5, Compute n = 20.1488 semi-annual periods = 10.07 years. 2. Bank A: 10.00%; Bank B: 10.04%; Bank C: 9.95%; Bank D: 9.93%; Bank E: 9.86%. 3. PMT = 140000, n = 10, I = 9, Compute PV = 898472.08. This is value need at the end of year 20. Since first deposit will be made today, set calculator in BEGIN mode. Now, FV = 898472.08, I = 9, n = 20, Compute PMT = 16,111.89. 4. Annual payment = $8,652.62. Beginning Ending Year Balance Interest Payment Balance 1 40,000.00 3,200.00 $8,652.62 34,547.38 2 34,547.38 2,763.79 $8,652.62 28,658.56 3 28,658.56 2,292.68 $8,652.62 22,298.63 4 22,298.63 1,783.89 $8,652.62 15,429.90 5 15,429.90 1,234.39 $8,652.62 8,011.68 6 8,011.68 640.93 $8,652.62 0.00 CHAPTER 7 – Answers to Additional Problems and Questions Problems: 1. a – more compounding periods per year creates a larger effective interest rate. 2. e 3. 17 years 4. 4.45% 5. $10,962.37 6. d 7. a 8. 19.56% 9. $704 10. e 11. e 12. This question is misleading. This is not an annuity problem. For example, n=10, PMT=0, r = 10, FV = 5,000, PV = ?1,927.72 n=10, PMT=0, r= 10, PV = 5,000, FV = ? 12, 968.71 Rate PV FV 0 5,000.00 5,000.00 5 3,069.57 8,144.47 10 1,927.72 12,968.71 15 1,235.92 20,227.79 20 807.53 30,958.68 25 536.87 46,566.13 30 362.69 68,929.25 35 248.68 100,532.78 40 172.86 144,627.33 45 121.70 205,423.45 50 86.71 288,325.20 Plot of Present Values 6,000.00 5,000.00 Present Value 4,000.00 3,000.00 Series1 2,000.00 1,000.00 - 0 5 10 15 20 25 30 35 40 45 50 Interest Rate Plot of Future Values 350,000.00 300,000.00 250,000.00 Future Value 200,000.00 Series1 150,000.00 100,000.00 50,000.00 - 0 5 10 15 20 25 30 35 40 45 50 Interest Rate 13. $15,129.38 14. $45,349.14 15. $26.97 16. $889.23 17. 2.74% 18. 4.47% 19. $96,969.53 20. 7.10%; 7.23% 21. $31,265.66 22. 8.654% 23. $7,669.12; $18,419.93 24. $76,175.84 25. $6,714.27 Alternative 1: I do not think solution manual gave right answer, I did in two different method and this is what I get CF1 = 20,000, CF1 = 0, F1= 10 (assume that t = 12 means ending of year 11) CF2 = -25,000, F2 = 4, (ending at t = 14 or beginning at t = 15) Cf3 = 0, f3 = 2 (assume that t = 18 means ending of year 17) Cf4= -33,000, f4 = 4 I = 8%, NPV = - 50,257.52 (this is the spending at t =0) You have to save for this for 10 yrs Pv = - 70,257.52, FV = 0, N = 10, 1/Y = 8, PMT = ? 7,489.85 Alternative 2: Pv1) PMT= 33,000; n=4; FV=0; PV=-118, 044.2006; 1/y= 8, (Solved as ANN Due) at the end of t =17 Pv2) PMT=0; n=7; 1/y=8; FV= 118, 044.2006, PV=- 68,877.65 at the end of t = 10 PV3) PMT= 25000; n=4; i/y= 8; FV=0; Pv= -89,427.42468 (Solved as ANN Due) at the end of t =11 PV4) Fv= 89,427.42468; n=1; 1/y= 8, PMT=0, PV= -82,803.171 at the end of t = 10 Pt 5) Pv= -20,000, n=10, FV= (68,877.65 +82,803.171), 1/y=8, PMT= -7,489.85 26. $4,520,178.42 today; $2,883,820.96 (5,082,277.89 is correct answer) in five years. 27. $263.80 28. $59,739.98 29. $9.50 30. $482.09 When PMT = 0, it does not matter if you use END or BGN mode. But I suggest you always keep your calculator at end mode, just to avoid problems. Cf0 = 0, cf1 = 0, f1 = 59 (beg of t = 60 implies end of t = 59) Cf2 = -2500, f2=16, I = 1.25, NPV = - 17,322.37 PV = - 17,322.37, N = 48, 1/y = 1.25, FV = 0, PMT = ? 482.09 31. Amount of payment that goes to principal = 7757.16; Amount that goes to interest = 1,698.84 32. $925,764 33. $86,303.09 34. $17,954.13 Correct method for the solution in END mode is as follows: PV= -3000, PMT= -3000, n=4, I/y=9, FV= 17, 954. 13 35. $276.21 36. $167,790.24 37. $5,468.21 38. $61,534.10 39. $165,918.32 40. $71,474.07 41. $871.47 As a first step, calculate the PV of the cash flows (at 10.5%): cf0 = 0, Cf1=1700, f1 = 1, Cf2=1800, f2 = 1, cf3 = 0, f3 =1, cf4 = 2000, f4 = 1, NPV =4354. 1026 Therefore, you are 5000-4354. 1026=645.897 “short” of the 5000. This represents the PV of the missing cash flow. To calculate the actual cash flow, calculate the FV of the 645.897: PV=645.897, N=3; I=10.5; PMT = 0; FV=??=871.47 To verify your answer, enter the 871.47 as Cf3 and calculate the PV (it works out to 5,000) CHAPTER 9 ASSIGNMENT 9.1 1. a. Treat as a perpetuity. P = Coupon/Interest Rate = 82.50/0.08 = $1,031.25 b. P = 1000/(1.0815) = $315.24 c. N = 20; PMT = 70; I/Y = 8; FV = 1000; CPT PV. P = $901.82 2. a. N = 60; FV = 1000; PMT = 35; I/Y = 4.5; CPT PV. P = $793.62 b. N = 80; FV = 1000; PMT = 25; I/Y = 2.25; CPT PV. P = $1,092.37 3. PV = -978; FV = 1000; PMT = 90; N = 14; CPT I/Y. Cost of Debt = YTM = 9.29% 4. N = 68; (i.e. 17x4 quarters) PV = -1020; FV = 1000; PMT = 20; CPT I/Y; I/Y = 1.9467; Thus, Cost of Debt = YTM = 1.9467 x 4 = 7.79% ASSIGNMENT 9.2 1. Preferred should be treated as a perpetuity as it pays a perpetual stream of preferred dividends. Price = 2.25/0.11 = $20.45 QWE’s estimate of the required rate of return is higher than the actual required rate of return investors are using to value the preferred stock. The actual rate = 2.25/24 = 9.375% 2. Since the common stock pays constant dividends forever, the present value of the dividends is obtained using the perpetuity formula, as in 1 above. P = 1.50/0.09 = $16.67 3. P0 = D1 / (k-g) = 2.50/(0.10-0.03) = $35.71 4. First find P5 = D6 / (k-g) = $1(1.05)/(0.12-0.05) = 1.05/0.07 = $15. Now P0 = 1/1.12 + 1/1.122 + 1/1.123 + 1/1.124 + (1+15)/1.125 = $12.12. Alternative Solution: After finding P5 note that the cash flow lends itself to the use of the third row keys on your calculator. Thus we can use our usual setup to find the present value. PMT = 1; FV = 15; N = 5; I/Y = 12; CPT PV. P = $12.12 ASSIGNMENT 9.3 1. P0 = D1/(k-g) = D0(1+g)/(k-g). We can make k the subject of this equation. k = g + D0(1+g)/P0 = 0.04 + 2(1.04)/38 = 0.04 + 0.0547 = 9.47% 2. First determine D4 = D3(1+g) = 3(1.06) = $3.18 Then P3 = D4/(k-g) = 3.18/(0.14-0.06) = $39.75 Now, P0 = 2/1.14 + 1/1.142 + (3+39.75)/1.143 = $31.38 You can also use the CF (cash flow) procedure to do the calculations in the last step: C01 = 2; F01 =1; C02 = 1; F02 =1; C03 = 42.75 (3+39.75); F03 = 1; I=14. 3. D1 = 1.75(1.5) = 2.625; D2 = 1.7591.5)2 = 3.9375; D3 =1.75(1.52)(1.3) = 5.11875 D4 = 1.75(1.52)(1.32) = 6.654375; D5 = 1.75(1.52)(1.32)(1.2) = 7.98525; D6 = 1.75(1.52)(1.32)(1.2)(1.07) = 8.5442175. P5 = D6/(k-g) = 8.5442175/(0.15-0.07) = $106.80 Then P0 = 2.625/1.15 + 3.9375/1.152 + 5.11875/1.153 + 6.654375/1.154 + (7.98525+106.8027)/1.155 = $69.50. Again, you can use the CF procedure (probably easier) for the last step. 4. D1 = $1(1.35) = 1.35; D2 = 1(1.352) = 1.8225; D3 = 1(1.353) = 2.460375; D4 = 2.460375(1.2) = 2.95245; D5 = 2.95245(1.2) = 3.54294; D6 = 3.54294(1.2) = 4.251528; D7 = D8 = D9 = …… = D∞ = 4.251528. After this, it is probably best to use the cash flow procedure for the last step: C01 = 1.35; F01 = 1; C02 = 1.8225; F02 = 1; C03 = 2.460375; F03 = 1; C04 = 2.95245; F04 =1; C05 = 3.54294; F05 = 1; C06 = 4.251528; F06 = 999. Use I = 15. Then the (NPV) Price = $21.71 Alternatively, the last step can be done using the analytical method: First find P6 = D7/k = 4.251528/0.15 = $28.34. P0 = 1.35/1.15 + 1.8225/1.152 + 2.460375/1.153 + 2.95245/1.154 + 3.54294/1.155 + (4.251528+28.34)/1.156 = $21.71 ADDITIONAL PROBLEMS 1. PV = -1100; N = 25; PMT = 90; FV =1000; CPT I/Y. Market interest rate = YTM = 8.06% 2. To be indifferent between calling the bond and not calling the bond, the call price of $1,075 must be equal to the present value of the remaining payments. Thus: PV = -1075; PMT = 80; N = 25; FV = 1000; CPT 1/Y. 7.34% 3. Use the usual procedure for finding the price of a bond. Just be careful to use the appropriate YTM for I/Y for the various times. a. $1,000 b. $1,087.45; c. $873.08; d. $974.69; e. $972.97 4. FV = 1000; PV = -1092; PMT = 50; N=40; CPT I/Y. I/Y = 4.5%. Thus YTM = 9% 5. FV=1000; N=8; PMT = 0; I/Y = 4. CPT PV. Price = $730.69 6. FV=1000; N=34; PMT = 40; I/Y = 3.625; CPT PV. P = $1,072.62 7. FV = 1000; N = 30; PMT = 35; PV = -825; CPT I/Y. I/Y = 4.585. YTM = 9.17% 8. YTM = 9.09% 9. P = $859.16 10. First find the yield to maturity of the zero coupon bonds. N = 30; FV =1000; PV = -99.38; PMT = 0; CPT I/Y . YTM = 8%. Now, the yield to maturity of the coupon bond is also 8%. Thus for the coupon bond: N = 60; FV = 1000; PV = -886.88; I/Y = 4; CPT PMT. PMT = 35. Coupon Rate = 7%. 11. Price per share = 20000000/1000000 = $2. D = P x k = 2x0.11 = $2.20 per share. 12. P0 = D0(1+g)/(k-g) = 1.50(1.04)/(0.12-0.04) = 1.56/0.08 = $19.50 13. P0 = D0(1+g)/(k-g) = 4(1-0.05)/(0.20--0.05) = 4(0.95)/0.25 = $15.20 14. P0 = D0(1+g)/(k-g); 15 = 1(1+g)/(0.12-g); 1.80 -15g = 1+g; g = 0.8/16 = 5% 15. P0 = D0(1+g)/(k-g); 72.25 = 5.12(1.06)/(k-0.06); k = 13.51% 16. The first dividend that begins the constant growth forever is D5. Thus, we can find P4 using: P4 = D4 (1+g)/(k-g) = 3.5(1.08)/(0.14-0.08) = $63. Now, either use he cash flow procedure or the analytical method to solve for P0. P0 = 2/1.14 + 1.50/1.142 + 2.50/1.143 + (3.50+63)/1.144 = $43.97 17. First let’s find the discount rate, k. 24 = 3/k. Thus k = 12.5%. Now, with the 3 percent expected growth, the dividend one year from now, D1 = 3(1.03) = $3.09. Therefore, P0 = 3.09/(0.125-0.03) = $32.53. 18. g = 2.14/2 – 1 = 7%. P0 = 2.14/(0.26-0.07) = $11.26 Take note of the fact that the question gave some pieces of information that were irrelevant to solving the problem. 19. First determine k, the investors required rate of return. k = 2.10/15 = 14%. Then P0 = 2.10(1.04)/(0.14-0.04) = $21.84. 20. D1 = 4(0.75) = 3; D2 3(0.86) = 2.58; D3 = 2.58(0.94) = 2.4252. P3 = 2.4252(1.044)/(0.184-0.044) = 18.09. P0 = 3/1.184 + 2.58/1.1842 + (2.4252+18.09)/1.1843 = 2.534 +1.8404 + 12.36 =16.73 CHAPTER 10 ASSIGNMENT 10.1 1. Payback Discounted NPV IRR PI Period Payback Per. A $3,456.40 22.58% 1.38 2.8 years 3.22 years B $3,885.38 20.66 1.35 3.09 3.59 C $5,583.82 19.48 1.24 3.11 3.44 Never Pays D -$2,536.31 2.62 0.80 4.84 Back (∞) 2. PMT = $26,000,000; FV = 20,000,000; N = 10; I/Y = 12; CPT PV. PV (Benefits) = $153,345,263.50. Thus, NPV = PV (Benefits) – PV (Costs) = 153,345,263.50 – 200,000,000 = - $ 46,654,736.50 IRR = 6.25% PI = PV (Benefits)/PV (Costs) = 153,345,263.5/200,000,000 = 0.77 3. P0 = 10,000,000/(0.14-0.05) = $111,111,111.11 NPV = 111,111,111.11 – 100,000,000 = $11,111,111.11 The IRR is the discount rate that will make the present value of the benefits equal to the initial cost (that is the discount rate that will make the NPV equal to zero). 100,000,000 = 10,000,000/(k-0.05); k = IRR = 15% PI = 111,111,111.11/100,000,000 = 1.11 ASSIGNMENT 10.2 1. R NPV 0 -300 10 86.78 20 250 30 275.15 40 214.29 50 100 60 -46.86 70 -212.80 80 -388.89 2. NPV Profile for Project A 400 300 200 100 0 NPV -100 0 10 20 30 40 50 60 70 80 90 -200 -300 -400 -500 Discount Rate The IRRs estimated from the graph are 7% and 57% ASSIGNMENT 10.3 1. The net cash flow per month is 12x600 – 1800 = $5400. Thus, PMT = $5400; FV = $500,000; N =120; I/Y = 1; CPT PV. PV = $527,880.21 2. The net cash flow per year = 20x6000 – 33000 = $87,000. Thus, PMT = 87000; N = 12; FV = 400000; I/Y = 12; CPT PV. PV = $641,580.59. The offer of $675,000 exceeds the present value of cash flows from the property. Therefore SELL. 3. YTM = 8.5% = Pretax cost of debt. After tax cost of debt = (1-0.3)x(8.5%) = 5.95%. For common stock: 20=1.5(1.05)/(k-0.05). Solve this equation for k, the investors required rate of return. k = 0.05 + 0.07875 = 12.875% Cost of capital = 0.25(5.95) + 0.75(12.875) = 11.14% 4. Bond. FV = 1000; N =50; PMT = 27.5; PV = -695; CPT I/Y. I/Y = 4.2249%. Since coupons are paid semiannually, the YTM = 2x4.2249 = 8.45% After tax cost of debt = (1-0.3)(8.45) = 5.915% Stock. 26.5 = 2.1(1.055)/(k-0.055). Solving for k, we have: k= 13.86% Cost of capital = 0.6(5.915) + 0.4(13.86) = 9.09% Additional Questions and Problems 1. PROJECT NPV IRR PI Payback Period Disc. Payback Period A $603.58 31.79% 1.60 2.5 yrs 3.07 yrs B -$456.15 7.93% 0.92 4 yrs Infinity C -$3974.15 6.54% 0.86 3.67 yrs Infinity D $3807.59 16.43% 1.22 3.70 yrs 4.22 yrs 2. The project has 2 IRRs because the cash flows change signs two times. The IRRs are 48.18% and -50.55%. To solve for the IRR, you need to solve the following equation for r. 1996/(1+r) – 740/(1+r)2 -1010 = 0. You can use trial and error or you can solve using the quadratic formula. For the quadratic, first multiply the equation through by (1+r)2 and simplify to obtain a quadratic equation. Then use the quadratic formula. If the cost of capital is 20%, the project should be accepted because it has a positive NPV. NPV = $139.44. 3. a. $100,000 b. $65,738.04 c. 18% 4. NPV = PV(Benefits) – PV (costs). 6,900 = PV(Benefits) – 15000. Therefore PV (Benefits) = $21,900. Use cash flow keys to find IRR = 24.95%. PI = PV (benefits)/ PV(costs) = 21900/15000 = 1.46 Cost of capital (or discount rate). Since we know that the present value of the benefits equals $21,900, we can solve for the discount rate. PMT = 4500; N = 8; PV = -21,900; FV = 0; CPT I/Y. I/Y = cost of capital = 12.59%. 5. PI = PV (Benefits)/ PV (Costs). Thus we have 0.96 = PV (Benefits)/1000000. So, PV(Benefits) = $960,000. NPV = PV(Benefits) – PV(Costs) = 960000 – 1000000 = -$40,000. 6. b. 7. e 8. a 9. NPV = $9,298.81; IRR = 19.63%; PI = 1.116. Accept Project as NPV is positive. 10. B. It has the highest NPV. 11. A,B,C,D (ALL). They all have positive NPV. 12. NPV = $54.85 13. Bonds: PV = -1095; FV = 1000; PMT = 116; N =24; CPT I/Y. I/Y = Pretax cost of debt = 10.50%. After-tax cost of debt = (1-0.3) (10.5) = 7.35% Stock. k = 0.07+5.25(1.07)/68.25 = 15.23% Cost of capital = 0.5(7.35) + 0.5(15.23) = 11.29% 14. Bonds: PV = -8785; N = 60; FV = 10000; PMT = 390; CPT I/Y. I/Y = 4.487%. Thus the YTM = Pre-tax cost of debt = 2(4.487) = 8.97%. After-tax cost of debt = (1-0.30)(8.97%) = 6.28%. Stocks: 33.75 = 2.90(1.0375)/(k-0.0375). Solving for k we get k = 12.66%, the cost of equity. Thus, cost of capital = 0.8(6.28) + 0.2 (12.66) = 7.56%. CHAPTER 11 Assignment 11.1: 1. Determine Net Cash Flow: NCF = (2,000,000 – Depreciation)(1 – T) + Depreciation NCF = (2,000,000 – 1,000,000)(.7) + 1,000,000 = 1,700,000. CF0 = -10000000; C01= 1700000; F01=10; Compute NPV (with I = 13) = -775,386.09. 2. Project A: CF0 = -80000; C01=18000; F01=8; Compute NPV (with I = 10) = 16,028.67. With same figures in CF register, compute IRR = 15.29% Project B: CF0 = -40000; C01=10000; F01=8; Compute NPV (with I = 10) = 13,349.26. With same figures in CF register, compute IRR = 18.62% Note that NPV indicates that we should accept Project A and IRR indicates that we should accept Project B. ALWAYS CHOOSE THE PROJECT WITH THE HIGHEST NPV, so choose Project A. 3. Enter all values in cash flow register and compute: NPV (A) = 4497.54; IRR(A) = 19.31% NPV (B) = 7937.38; IRR(B) = 28.97% Choose Project B because higher NPV. 4. If you construct graph correctly, you should find that the two lines cross at a discount rate of approximately 16.25%. Note that with I = 16.25, NPV (P) = 1249.76 and NPV (Q) = 1249.77. At rates above 16.25%, NPV(P) > NPV(Q) At rates above 16.25%, NPV(P) < NPV(Q). Assignment 11.2: 1. (Assume tax rate = 0). First compute the NPV of cost of each machine. X100: CF0=-45000; C01=-5000; F01=4; C02=-5000+6000=1000; F02=1; Compute NPV (I=12) = - 59619.32. Note that this is NPV of costs. X1300: CF0=-65000; C01=-2000; F01=6; C02=-2000+10000=8000; F02=1; Compute NPV (I=12) = -69604.02. Note that this is NPV of costs. Because these two projects have different lives, to compare we must now compute EAC. EAC(X100): PV = -59619.32; N=5 (i.e., project life); I/Y=12, CPT PMT = 16,538.98. EAC(X1300): PV = -69604.02; N=7 (i.e., project life); I/Y=12, CPT PMT = 15,251.48. Thus EAC (X100) = 16,538.98. EAC (X1300) = 15,251.48. Choose X1300 because it has a lower equivalent annual cost. 2. Initial Cash Outflow: Buy Machine -31M Decrease in NWC + 2M CF0 -29M Note that annual depreciation = (31-3)/20 = 1.4M Annual Operating NCF = (Rev – Costs – Dep)(1-T) + Dep = [(5)(.9) – (.6)(5)(.9) - .6 – 1.4](.7) + 1.4 = 1.26M per year for 20 years Final Year Non-Operating Cash Flow: Sell Machine for Scrap Value 3M Replace NWC -2M Total 1M To Compute NPV: CF0 = -29, C01 = 1.26; F01 = 19; C02 = 2.26; F02 = 1; CPT NPV (with I = 11) = -18.842M Assignment 11.3: Q36: CF0 = -3M; C01 = .6M; F01 = 8; CPT NPV = 200,955.72. Z96: CF0 = -4M; C01 = .7M; F01 = 10; CPT NPV = 301,196.97. Since these projects have different lives, to compare, must compute Equivalent Annual Annuity. EAA(Q36): PV = 200955.72; I = 10; N = 8; CPT PMT = EAA = 37,667.95. EAA(Z96): PV = 301196.97; I = 10; N = 10; CPT PMT = EAA = 49018.42. Choose Z96, since it has higher EAA. Problems: 1. Must compute EAA of each project. Rank of EAA: D, C, A, B. 2. Relevant – Opportunity cost Not relevant – Sunk cost Relevant – Initial cost Not relevant – Sunk cost Relevant – Incremental expense Not relevant – Sunk cost The incremental revenue of 93% of $2 million is relevant. The tax savings associated with depreciation is relevant. Specifically, 36% of incremental depreciation. Relevant – Incremental expense Not relevant – No incremental cost Relevant – Incremental Not relevant – must be paid regardless of whether project is accepted or rejected. Therefore, not incremental. 3. The easiest way to do this problem is to assume the company can sell radiators for $150 per radiator. Then: NPV (Buy from Supplier) = 13,477,081. NPV (Manufacture) = 9,439,730. ??? Project Buy: CF0=0, CF1=(150-120)*100,00*(1-0.3)=2.1 million, F1=10, NPV=13,477,081 Project Manufacture: (150-80)*100,000=7 mil , 7 mil – 0.5m (depreciation)=6.5 million, 6.5*(1-0.3)=4.55 mil 4.55 mil + 0.5 mil (depreciation)=5.05 mil CF0=-5 million, CF1=5.05 mil, F1=10, NPV= 27,409,171 So make the radiators. 4. EAC(A) = 1160.76; EAC(B) = 1813.90 – Choose project with lower equivalent annual cost. 5. NPV(Superior) = 17,802.68; NPV (Peerless) = 16,816.12 – Choose project with highest NPV. 6. IRR(A) = 34.90%; NPV(A) = 5,849.33 IRR(B) = 31.61%; NPV(B) = 10,490.40 7. Crossover rate = 7.167%; NPV(X) = NPV(Y) = 6720.60. 8. a. Yes – incremental; b. No – Sunk; c. No – financing cost (captured in NPV analysis); d. Yes – incremental; e. Yes – incremental. 9. Note that annual NCF = Net income + Depreciation = 700,000 per year. NPV = 227,462.17. 10. 3,690.93 11. Note that annual NCF = Net income + Depreciation = 6.55M per year. NPV = -5.879M. 12. CF0 = (12,000,000); CF1 through CF10 = 2,880,000; No final year non-operating cash flow. NPV = 1,919,695. 13. CF0 = (26,800,000); Operating net cash flow = 26,800,000; Final year non-operating cash flow = 2,200,000. NPV = 97,762,829. 14. (56,004.33) 15. For this problem, assume that the cost of capital is 14%. Then, NPV = (320,096). Reject. 16. Step 1: Initial Investment in the Project Opportunity cost of the land -8M Buy knives, blades, etc. -5.7M New Building construction -70M Increase in Net Working capital -10M Total Year 0 Cash Flow -93.7M Step 2: Annual Operating Cash Flow Note that Incremental revenue = (3000)(300)(30) = 27M and Depreciation = (5.7-.7)/25 + 70/25 = 3.0M NCF = (27M - 3.2M - 4.5M - 2.3M - 3.0M)(.6) + 3.0M = 11.4M for 25 years. Step 3: Final Year non-operating Cash Flow Sell land 8M Sell equipment .7M Recover NWC 10M Total 18.7M To compute NPV: CF0=-93.7; C01 = 11.4; F01=24; C02=11.4+18.7=30.1; F02 = 1; CPT NPV = -14.642M.