4 CHAPTER B-3
CHAPTER 2 FINANCIAL STATEMENTS, TAXES AND CASH FLOW
Answers to Concepts Review and Critical Thinking Questions 1. Liquidity measures how quickly and easily an asset can be converted to cash without significant loss in value. It's desirable for firms to have high liquidity so that they have a large factor of safety in meeting short-term creditor demands. However, since liquidity also has an opportunity cost associated with it--namely that higher returns can generally be found by investing the cash into productive assets--low liquidity levels are also desirable to the firm. It's up to the firm's financial management staff to find a reasonable compromise between these opposing needs. The recognition and matching principles in financial accounting call for revenues, and the costs associated with producing those revenues, to be "booked" when the revenue process is essentially complete, not necessarily when the cash is collected or bills are paid. Note that this way is not necessarily correct; it's the way accountants have chosen to do it. Historical costs can be objectively and precisely measured whereas market values can be difficult to estimate, and different analysts would come up with different numbers. Thus, there is a tradeoff between relevance (market values) and objectivity (book values). Depreciation is a non-cash deduction that reflects adjustments made in asset book values in accordance with the matching principle in financial accounting. Interest expense is a cash outlay, but it's a financing cost, not an operating cost. Market values can never be negative. Imagine a share of stock selling for $20. This would mean that if you placed an order for 100 shares, you would get the stock along with a check for $2,000. How many shares do you want to buy? More generally, because of corporate and individual bankruptcy laws, net worth for a person or a corporation cannot be negative, implying that liabilities cannot exceed assets in market value. For a successful company that is rapidly expanding, for example, capital outlays will be large, possibly leading to negative cash flow from assets. In general, what matters is whether the money is spent wisely, not whether cash flow from assets is positive or negative. It's probably not a good sign for an established company, but it would be fairly ordinary for a startup, so it depends. For example, if a company were to become more efficient in inventory management, the amount of inventory needed would decline. The same might be true if it becomes better at collecting its receivables. In general, anything that leads to a decline in ending NWC relative to beginning would have this effect. Negative net capital spending would mean more long-lived assets were liquidated than purchased.
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B-4 SOLUTIONS 9. If a company raises more money from selling stock than it pays in dividends in a particular period, its cash flow to stockholders will be negative. If a company borrows more than it pays in interest, its cash flow to creditors will be negative.
10. The adjustments discussed were purely accounting changes; they had no cash flow or market value consequences unless the new accounting information caused stockholders to revalue the derivatives. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. To find owner's equity, we must construct a balance sheet as follows: Balance Sheet CL LTD OE $28,000 TL & OE $5,000 23,000
CA NFA TA
$4,300 13,000 ?? $28,000
We know that total liabilities and owner's equity (TL & OE) must equal total assets of $28,000. We also know that TL & OE is equal to current liabilities plus long-term debt plus owner's equity, so owner's equity is: OE = $28,000 13,000 4,300 = $10,700 NWC = CA CL = $5,000 4,300 = $700 2. The income statement for the company is: Income Statement Sales $527,000 Costs 280,000 Depreciation 38,000 EBIT $209,000 Interest 15,000 EBT $194,000 Taxes(35%) 67,900 Net income $126,100 3. One equation for net income is: Net income = Dividends + Addition to retained earnings Rearranging, we get: Addition to retained earnings = Net income Dividends = $126,100 48,000 = $78,100
CHAPTER 2 B-5 4. EPS = Net income / Shares = $126,100 / 30,000 = $4.20 per share DPS = Dividends / Shares 5. = $48,000 / 30,000 = $1.60 per share
To find the book value of current assets, we use: NWC = CA CL. Rearranging to solve for current assets, we get: CA = NWC + CL = $900K + 2.2M = $3.1M The market value of current assets and fixed assets is given, so: Book value CA = $3.1M Book value NFA = $4.0M Book value assets = $3.1M + 4.0M = $7.1M Market value CA = $2.8M Market value NFA = $3.2M Market value assets = $2.8M + 3.2M = $6.0M
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Taxes = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($273K 100K) = $89,720 The average tax rate is the total tax paid divided by net income, so: Average tax rate = $89,720 / $273,000 = 32.86%. The marginal tax rate is the tax rate on the next $1 of earnings, so the marginal tax rate = 39%.
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To calculate OCF, we first need the income statement: Income Statement Sales Costs Depreciation EBIT Interest Taxable income Taxes (35%) Net income
$13,500 5,400 1,200 $6,900 680 $6,220 2,177 $4,043
OCF = EBIT + Depreciation Taxes = $6,900 + 1,200 2,177 = $5,923 9. 10. Net capital spending = NFAend NFAbeg + Depreciation= $4.7M 4.2M + 925K = $1.425M Change in NWC = NWCend NWCbeg Change in NWC = (CAend CLend) (CAbeg CLbeg) Change in NWC = ($1,720 1,180) ($1,600 940) Change in NWC = $540 660 = $120 Cash flow to creditors = Interest paid Net new borrowing = $340K (LTDend LTDbeg) Cash flow to creditors = $340K ($3.1M 2.8M) = $340K 300K = $40K
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B-6 SOLUTIONS 12. Cash flow to stockholders = Dividends paid Net new equity Cash flow to stockholders = $600K [(Commonend + APISend) (Commonbeg + APISbeg)] Cash flow to stockholders = $600K [($820K + 6.8M) ($855K + 7.6M)] Cash flow to stockholders = $600K [$7.62M 8.455M] = $235K Note, APIS is the additional paid-in surplus. 13. Cash flow from assets = Cash flow to creditors + Cash flow to stockholders = $40K 235K = $195K Cash flow from assets = $195K = OCF Change in NWC Net capital spending = OCF ($165K) 760K = $195K Operating cash flow Intermediate 14. To find the OCF, we first calculate net income. Income Statement Sales $145,000 Costs 86,000 Depreciation 7,000 Other expenses 4,900 EBIT $47,100 Interest 15,000 Taxable income $32,100 Taxes (34%) 12,840 Net income $19,260 Dividends Additions to RE $8,700 $10,560 = $195K 165K + 760K = $400K
a. OCF = EBIT + Depreciation Taxes = $47,100 + 7,000 12,840 = $41,260 b. CFC = Interest Net new LTD = $15,000 $6,500 = $21,500. Note that the net new long-term debt is negative because the company repaid part of its longterm debt. c. CFS = Dividends Net new equity = $8,700 6,450 = $2,250
CHAPTER 2 B-7 d. We know that CFA = CFC + CFS, so: CFA = $21,500 + 2,250 = $23,750 CFA is also equal to OCF Net capital spending Change in NWC. We already know OCF. Net capital spending is equal to: Net capital spending = Increase in NFA + Depreciation = $5,000 + 7,000 = $12,000. Now we can use: CFA = OCF Net capital spending Change in NWC $23,750 = $41,260 12,000 Change in NWC. Solving for the change in NWC gives $5,510, meaning the company increased its NWC by $5,510. 15. The solution to this question works the income statement backwards. Starting at the bottom: Net income = Dividends + Addition to ret. earnings = $900 + 4,500 = $5,400 Now, looking at the income statement: EBT EBT Tax rate = Net income Recognize that EBT tax rate is simply the calculation for taxes. Solving this for EBT yields: EBT = NI / (1 tax rate) = $5,400 / 0.65 = $8,308 Now you can calculate: EBIT = EBT + interest = $8,308 + 1,600 = $9,908. The last step is to use: EBIT = Sales Costs Depreciation EBIT = $29,000 13,000 Depreciation = $9,908. Solving for depreciation, we find that depreciation = $6,092.
B-8 SOLUTIONS 16. The balance sheet for the company looks like this: Balance Sheet $175,000 Accounts payable 140,000 Notes payable Current liabilities 265,000 $580,000 Long-term debt Total liabilities 2,900,000 720,000 Common stock Accumulated ret. earnings $4,200,000 Total liab. & owners' equity
Cash Accounts receivable Inventory Current assets Tangible net fixed assets Intangible net fixed assets Total assets
$430,000 80,000 $610,000 1,430,000 $2,040,000 ?? 1,240,000 $4,200,000
Total liabilities and owners' equity is: TL & OE = CL + LTD + Common stock Solving for this equation for equity gives us: Common stock = $4,200,000 1,240,000 2,040,000 = $920,000 17. The market value of shareholders' equity cannot be zero. A negative market value in this case would imply that the company would pay you to own the stock. The market value of shareholders' equity can be stated as: Shareholders' equity = Max [(TA TL), 0]. So, if TA is $4,300, equity is equal to $800, and if TA is $3,200, equity is equal to $0. We should note here that the book value of shareholders' equity can be negative. a. Taxes Growth = 0.15($50K) + 0.25($25K) + 0.34($10K) = $17,150 Taxes Income = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($235K) + 0.34($8.165M) = $2,890,000 b. Each firm has a marginal tax rate of 34% on the next $10,000 of taxable income, despite their different average tax rates, so both firms will pay an additional $3,400 in taxes. 19. Income Statement Sales $850,000 COGS 630,000 A&S expenses 120,000 Depreciation 130,000 EBIT ($30,000) Interest 85,000 Taxable income ($115,000) Taxes (35%) 0 Net income ($115,000)
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b. OCF = EBIT + Depreciation Taxes = ($30,000) + 130,000 0 = $100,000 c. Net income was negative because of the tax deductibility of depreciation and interest expense. However, the actual cash flow from operations was positive because depreciation is a non-cash expense and interest is a financing expense, not an operating expense.
CHAPTER 2 B-9 20. A firm can still pay out dividends if net income is negative; it just has to be sure there is sufficient cash flow to make the dividend payments. Change in NWC = Net capital spending = Net new equity = 0. (Given) Cash flow from assets = OCF Change in NWC Net capital spending Cash flow from assets = $100K 0 0 = $100K Cash flow to stockholders = Dividends Net new equity = $30K 0 = $30K Cash flow to creditors = Cash flow from assets Cash flow to stockholders = $100K 30K = $70K Cash flow to creditors = Interest Net new LTD Net new LTD = Interest Cash flow to creditors = $85K 70K = $15K 21. a. Income Statement Sales $12,800 Cost of good sold 10,400 Depreciation 1,900 EBIT $ 500 Interest 450 Taxable income $ 50 Taxes (34%) 17 Net income $33 b. OCF = EBIT + Depreciation Taxes = $500 + 1,900 17 = $2,383 c. Change in NWC = NWCend NWCbeg = (CAend CLend) (CAbeg CLbeg) = ($3,850 2,100) ($3,200 1,800) = $1,750 1,400 = $350 Net capital spending = NFAend NFAbeg + Depreciation = $9,700 9,100 + 1,900 = $2,500 CFA = OCF Change in NWC Net capital spending = $2,383 350 2,500 = $467
The cash flow from assets can be positive or negative, since it represents whether the firm raised funds or distributed funds on a net basis. In this problem, even though net income and OCF are positive, the firm invested heavily in both fixed assets and net working capital; it had to raise a net $467 in funds from its stockholders and creditors to make these investments.
B-10 SOLUTIONS d. Cash flow to creditors Cash flow to stockholders = Interest Net new LTD = $450 0 = $450 = Cash flow from assets Cash flow to creditors = $467 450 = $917
We can also calculate the cash flow to stockholders as: Cash flow to stockholders = Dividends Net new equity Solving for net new equity, we get: Net new equity = $500 (917) = $1,417
The firm had positive earnings in an accounting sense (NI > 0) and had positive cash flow from operations. The firm invested $350 in new net working capital and $2,500 in new fixed assets. The firm had to raise $467 from its stakeholders to support this new investment. It accomplished this by raising $1,417 in the form of new equity. After paying out $500 of this in the form of dividends to shareholders and $450 in the form of interest to creditors, $467 was left to meet the firm's cash flow needs for investment. 22. a. Total assets 2004 = $650 + 2,900 = $3,550; Total liabilities 2004 = $265 + 1,500 = $1,765 Owners' equity 2004 = $3,550 1,765 = $1,785 Total assets 2005 = $705 + 3,400 = $4,105 Total liabilities 2005 = $290 + 1,720 = $2,010 Owners' equity 2005 = $4,105 2,010 = $2,095 b. NWC 2004 = CA04 CL04 = $650 265 = $385 NWC 2005 = CA05 CL05 = $705 290 = $415 Change in NWC = NWC05 NWC04 = $415 385 = $30 c. We can calculate net capital spending as: Net capital spending = Net fixed assets 2005 Net fixed assets 2004 + Depreciation Net capital spending = $3,400 2,900 + 800 = $1,300 So, the company had a net capital spending cash flow of $1,300. We also know that net capital spending is: Net capital spending = Fixed assets bought Fixed assets sold $1,300 = $1,500 Fixed assets sold Fixed assets sold = $1,500 1,300 = $200
CHAPTER 2 B-11 To calculate the cash flow from assets, we must first calculate the operating cash flow. The operating cash flow is calculated as follows (you can also prepare a traditional income statement): EBIT EBT Taxes OCF Cash flow from assets = Sales Costs Depreciation = $8,600 4,150 800 = $3,650 = EBIT Interest = $3,650 216 = $3,434; = EBT .35 = $3,434 .35 = $1,202 = EBIT + Depreciation Taxes = $3,650 + 800 1,202 = $3,248 = OCF Change in NWC Net capital spending. = $3,248 30 1,300 = $1,918 = LTD05 LTD04 = $1,720 1,500 = $220 = Interest Net new LTD = $216 220 = $4 = $220 = Debt issued Debt retired = $300 220 = $80
d. Net new borrowing Cash flow to creditors Net new borrowing Debt retired Challenge 23.
Net capital spending = NFAend NFAbeg + Depreciation = (NFAend NFAbeg) + (Depreciation + ADbeg) ADbeg = (NFAend NFAbeg)+ ADend ADbeg = (NFAend + ADend) (NFAbeg + ADbeg) = FAend FAbeg a. The tax bubble causes average tax rates to catch up to marginal tax rates, thus eliminating the tax advantage of low marginal rates for high income corporations. b. Taxes = 0.15($50K) + 0.25($25K) + 0.34($25K) + 0.39($235K) = $113.9K Average tax rate = $113.9K / $335K = 34% The marginal tax rate on the next dollar of income is 34 percent. For corporate taxable income levels of $335K to $10M, average tax rates are equal to marginal tax rates. Taxes = 0.34($10M) + 0.35($5M) + 0.38($3.333M) = $6,416,667 Average tax rate = $6,416,667 / $18,333,334 = 35% The marginal tax rate on the next dollar of income is 35 percent. For corporate taxable income levels over $18,333,334, average tax rates are again equal to marginal tax rates. c. Taxes X($100K) X X = 0.34($200K) = $68K = 0.15($50K) + 0.25($25K) + 0.34($25K) + X($100K); = $68K 22.25K = $45.75K = $45.75K / $100K = 45.75%
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B-12 SOLUTIONS 25. Cash Accounts receivable Inventory Current assets Net fixed assets Total assets Balance sheet as of Dec. 31, 2004 $2,107 Accounts payable 2,789 Notes payable 4,959 Current liabilities $9,855 Long-term debt Owners' equity $17,669 Total liab. & equity $27,524 Balance sheet as of Dec. 31, 2005 $2,155 Accounts payable 3,142 Notes payable 5,096 Current liabilities $10,393 Long-term debt $18,091 Owners' equity $28,484 Total liab. & equity $2,213 407 $2,620 $7,056 $17,848 $27,524
Cash Accounts receivable Inventory Current assets Net fixed assets Total assets
$2,146 382 $2,528 $8,232 $17,724 $28,484
2004 Income Statement Sales $4,018.00 COGS 1,382.00 Other expenses 328.00 Depreciation 577.00 EBIT $1,731.00 Interest 269.00 EBT $1,462.00 Taxes (34%) 497.08 Net income $ 964.92 Dividends Additions to RE 26. $490.00 $474.92
2005 Income Statement Sales $4,312.00 COGS 1,569.00 Other expenses 274.00 Depreciation 578.00 EBIT $1,891.00 Interest 309.00 EBT $1,582.00 Taxes (34%) 537.88 Net income $1,044.12 Dividends Additions to RE $539.00 $505.12
OCF = EBIT + Depreciation Taxes = $1,891 + 578 537.88 = $1,931.12 Change in NWC = NWCend NWCbeg = (CA CL) end (CA CL) beg = ($10,393 2,528) ($9,855 2,620) = $7,865 7,235 = $630 Net capital spending = NFAend NFAbeg + Depreciation = $18,091 17,669 + 578 = $1,000 Cash flow from assets = OCF Change in NWC Net capital spending = $1,931.12 630 1,000 = $301.12
CHAPTER 2 B-13 Cash flow to creditors = Interest Net new LTD Net new LTD = LTDend LTDbeg Cash flow to creditors = $309 ($8,232 7,056) = $867 Net new equity = Common stockend Common stockbeg Common stock + Retained earnings = Total owners' equity Net new equity = (OE RE) end (OE RE) beg = OEend OEbeg + REbeg REend REend = REbeg + Additions to RE04 Net new equity = OEend OEbeg + REbeg (REbeg + Additions to RE0) = OEend OEbeg Additions to RE Net new equity = $17,724 17,848 505.12 = $629.12 CFS CFS = Dividends Net new equity = $539 ($629.12) = $1,168.12
As a check, cash flow from assets is $301.12. CFA CFA = Cash flow from creditors + Cash flow to stockholders = $867 + 1,168.12 = $301.12
B-14 SOLUTIONS
CHAPTER 3 WORKING WITH FINANCIAL STATEMENTS
Answers to Concepts Review and Critical Thinking Questions 1. a. If inventory is purchased with cash, then there is no change in the current ratio. If inventory is purchased on credit, then there is a decrease in the current ratio if it was initially greater than 1.0. b. Reducing accounts payable with cash increases the current ratio if it was initially greater than 1.0. c. Reducing short-term debt with cash increases the current ratio if it was initially greater than 1.0. d. As long-term debt approaches maturity, the principal repayment and the remaining interest expense become current liabilities. Thus, if debt is paid off with cash, the current ratio increases if it was initially greater than 1.0. If the debt has not yet become a current liability, then paying it off will reduce the current ratio since current liabilities are not affected. e. Reduction of accounts receivables and an increase in cash leaves the current ratio unchanged. f. Inventory sold at cost reduces inventory and raises cash, so the current ratio is unchanged. g. Inventory sold for a profit raises cash in excess of the inventory recorded at cost, so the current ratio increases. The firm has increased inventory relative to other current assets; therefore, assuming current liability levels remain unchanged, liquidity has potentially decreased. A current ratio of 0.50 means that the firm has twice as much in current liabilities as it does in current assets; the firm potentially has poor liquidity. If pressed by its short-term creditors and suppliers for immediate payment, the firm might have a difficult time meeting its obligations. A current ratio of 1.50 means the firm has 50% more current assets than it does current liabilities. This probably represents an improvement in liquidity; short-term obligations can generally be met completely with a safety factor built in. A current ratio of 15.0, however, might be excessive. Any excess funds sitting in current assets generally earn little or no return. These excess funds might be put to better use by investing in productive long-term assets or distributing the funds to shareholders. a. Quick ratio provides a measure of the short-term liquidity of the firm, after removing the effects of inventory, generally the least liquid of the firm's current assets. b. Cash ratio represents the ability of the firm to completely pay off its current liabilities with its most liquid asset (cash). c. Total asset turnover measures how much in sales is generated by each dollar of firm assets. d. Equity multiplier represents the degree of leverage for an equity investor of the firm; it measures the dollar worth of firm assets each equity dollar has a claim to. e. Long-term debt ratio measures the percentage of total firm capitalization funded by long-term debt.
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CHAPTER 3 B-15 f. Times interest earned ratio provides a relative measure of how well the firm's operating earnings can cover current interest obligations. g. Profit margin is the accounting measure of bottom-line profit per dollar of sales. h. Return on assets is a measure of bottom-line profit per dollar of total assets. i. Return on equity is a measure of bottom-line profit per dollar of equity. j. Price-earnings ratio reflects how much value per share the market places on a dollar of accounting earnings for a firm.
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Common size financial statements express all balance sheet accounts as a percentage of total assets and all income statement accounts as a percentage of total sales. Using these percentage values rather than nominal dollar values facilitates comparisons between firms of different size or business type. Common-base year financial statements express each account as a ratio between their current year nominal dollar value and some reference year nominal dollar value. Using these ratios allows the total growth trend in the accounts to be measured. Peer group analysis involves comparing the financial ratios and operating performance of a particular firm to a set of peer group firms in the same industry or line of business. Comparing a firm to its peers allows the financial manager to evaluate whether some aspects of the firm's operations, finances, or investment activities are out of line with the norm, thereby providing some guidance on appropriate actions to take to adjust these ratios if appropriate. An aspirant group would be a set of firms whose performance the company in question would like to emulate. The financial manager often uses the financial ratios of aspirant groups as the target ratios for his or her firm; some managers are evaluated by how well they match the performance of an identified aspirant group. Return on equity is probably the most important accounting ratio that measures the bottom-line performance of the firm with respect to the equity shareholders. The Du Pont identity emphasizes the role of a firm's profitability, asset utilization efficiency, and financial leverage in achieving an ROE figure. For example, a firm with ROE of 20% would seem to be doing well, but this figure may be misleading if it were marginally profitable (low profit margin) and highly levered (high equity multiplier). If the firm's margins were to erode slightly, the ROE would be heavily impacted. The book-to-bill ratio is intended to measure whether demand is growing or falling. It is closely followed because it is a barometer for the entire high-tech industry where levels of revenues and earnings have been relatively volatile. If a company is growing by opening new stores, then presumably total revenues would be rising. Comparing total sales at two different points in time might be misleading. Same-store sales control for this by only looking at revenues of stores open within a specific period. a. For an electric utility such as Con Ed, expressing costs on a per kilowatt hour basis would be a way to compare costs with other utilities of different sizes. b. For a retailer such as Sears, expressing sales on a per square foot basis would be useful in comparing revenue production against other retailers. c. For an airline such as Southwest, expressing costs on a per passenger mile basis allows for comparisons with other airlines by examining how much it costs to fly one passenger one mile.
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B-16 SOLUTIONS d. For an on-line service provider such as AOL, using a per call basis for costs would allow for comparisons with smaller services. A per subscriber basis would also make sense. e. For a hospital such as Holy Cross, revenues and costs expressed on a per bed basis would be useful. f. For a college textbook publisher such as McGraw-Hill/Irwin, the leading publisher of finance textbooks for the college market, the obvious standardization would be per book sold. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. Using the formula for NWC, we get: NWC = CA CL CA = CL + NWC = $1,320 + 4,460 = $5,780 So, the current ratio is: Current ratio = CA / CL = $5,780/$4,460 = 1.30 times And the quick ratio is: Quick ratio = (CA Inventory) / CL = ($5,780 1,875) / $4,460 = 0.88 times 2. We need to find net income first. So: Profit margin = Net income / Sales Net income = Sales(Profit margin) Net income = ($29M)(0.09) = $2,610,000 ROA = Net income / TA = $2.61M / $37M = 7.05% To find ROE, we need to find total equity. TL & OE = TD + TE TE = TL & OE TD TE = $37M 13M = $24M ROE = Net income / TE = Net income / TE = $2.61M / $24M = 10.88% 3. Receivables turnover = Sales / Receivables Receivables turnover = $2,873,150 / $421,865 = 6.81 times Days' sales in receivables = 365 days / Receivables turnover = 365 / 6.81 = 53.59 days The average collection period for an outstanding accounts receivable balance was 53.59 days.
CHAPTER 3 B-17 4. Inventory turnover = COGS / Inventory Inventory turnover = $2,532,095 / $386,500 = 6.55 times Days' sales in inventory = 365 days / Inventory turnover = 365 / 6.55 = 55.71 days On average, a unit of inventory sat on the shelf 55.71 days before it was sold. 5. Total debt ratio = 0.44 = TD / TA Substituting total debt plus total equity for total assets, we get: 0.44 = TD / (TD + TE) Solving this equation yields: 0.44(TE) = 0.56(TE) Debt/equity ratio = TD / TE = 0.44 / 0.56 = 0.79 Equity multiplier = 1 + D/E = 1.79 6. Net income Earnings per share Dividends per share = Addition to RE + Dividends = $310K + 160K = $470K = NI / Shares = Dividends / Shares = $470K / 180K = $2.61 per share = $160K / 180K = $0.89 per share = $6.5M / 180K = $36.11 per share = $78 / $36.11 = 2.16 times = $78 / $2.61 = 29.87 times
Book value per share = TE / Shares Market-to-book ratio P/E ratio 7. = Share price / BVPS = Share price / EPS
ROE = (PM)(TAT)(EM) ROE = (.085)(1.30)(1.75) = 19.34%
8. This question gives all of the necessary ratios for the DuPont Identity except the equity multiplier, so, using the DuPont Identity: ROE = (PM)(TAT)(EM) ROE = .1867 = (.092)(1.63)(EM) EM = .1867 / (.092)(1.63) = 1.24 D/E = EM 1 = 1.24 1 = 0.24
B-18 SOLUTIONS 9. Increase in inventory is a use of cash Increase in accounts payable is a source of cash Decrease in notes payable is a use of cash Increase in accounts receivable is a use of cash Changes in cash = sources uses = $330 ($600 + 790 + 950) = $2,010 Cash decreased by $2,010
10. Payables turnover = COGS / Accounts payable Payables turnover = $13,168 / $2,965 = 4.44 times Days' sales in payables = 365 days / Payables turnover Days' sales in payables = 365 / 4.44 = 82.19 days The company left its bills to suppliers outstanding for 82.19 days on average. A large value for this ratio could imply that either (1) the company is having liquidity problems, making it difficult to pay off its short-term obligations, or (2) that the company has successfully negotiated lenient credit terms from its suppliers. 11. New investment in fixed assets is found by: Net investment in FA = (NFAend NFAbeg) + Depreciation Net investment in FA = $580 + 165 = $745 The company bought $745 in new fixed assets; this is a use of cash. 12. The equity multiplier is: EM = 1 + D/E EM = 1 + 1.40 = 2.40 One formula to calculate return on equity is: ROE = (ROA)(EM) ROE = .087(2.40) = 20.88% ROE can also be calculated as: ROE = NI / TE So, net income is: NI = ROE(TE) NI = (.2088)($520,000) = $108,576
CHAPTER 3 B-19 13. through 15: 2004 Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Total assets Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Accumulated retained earnings Total Total liabilities and owners' equity $ 10,168 27,145 59,324 $ 96,637 304,165 $400,802 2.54% 6.77% 14.80% 24.11% 75.89% 100% $ 10,683 28,613 64,853 $104,419 347,168 $451,317 2.37% 6.34% 14.37% 23.08% 76.92% 100% 1.0506 1.0541 1.0932 1.0777 1.1414 1.1260 0.9331 0.9361 0.9708 0.9571 1.0136 1.0000 #13 2005 #13 #14 #15
$ 73,185 39,125 $112,310 $ 50,000 $ 80,000 158,492 $238,492 $400,802
18.26% 9.76% 28.02% 12.47% 19.96% 39.54% 59.50% 100%
$ 59,309 48,168 $107,477 $ 62,000 $ 80,000 201,840 $281,840 $451,317
13.14% 10.67% 23.81% 13.74% 17.73% 44.72% 62.45% 100%
0.8104 1.2311 0.9570 1.2400 1.0000 1.2735 1.1818 1.1260
0.7197 1.0933 0.8499 1.0102 0.8881 1.1310 1.0495 1.0000
The common-size balance sheet answers are found by dividing each category by total assets. For example, the cash percentage for 2004 is: $10,168 / $400,802 = .0254 or 2.54% This means that cash is 2.54% of total assets. The common-base year answers for Question 14 are found by dividing each category value for 2005 by the same category value for 2004. For example, the cash common-base year number is found by: $10,683 / $10,168 = 1.0506 This means the cash balance in 2005 is 1.0506 times as large as the cash balance in 2004. The common-size, common-base year answers for Question 15 are found by dividing the commonsize percentage for 2005 by the common-size percentage for 2004. For example, the cash calculation is found by: 2.37% / 2.54% = 0.9331 This tells us that cash, as a percentage of assets, fell by: 1 .9331 = .0669 or 6.69 percent.
B-20 SOLUTIONS 16. Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Total assets Liabilities and owners' equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Accumulated retained earnings Total Total liabilities and owners' equity 2004 Sources/Uses 2005
$ 10,168 27,145 59,324 $ 96,637 304,165 $400,802
+515 U +1,468 U +5,529 U +7,512 U +43,003 U +50,515 U
$ 10,683 28,613 64,853 $104,149 347,168 $451,317
$ 73,185 39,125 $112,310 50,000 $ 80,000 158,492 $238,492 $400,802
13,876 U +9,043 S 4,833 U +12,000 S 0 +43,348 S +43,348 S +50,515 S
$ 59,309 48,168 $107,477 62,000 $ 80,000 201,840 $281,840 $451,317
The firm used $50,515 in cash to acquire new assets. It raised this amount of cash by increasing liabilities and owners' equity by $50,515. In particular, the needed funds were raised by internal financing (on a net basis), out of the additions to retained earnings and by an issue of long-term debt. 17. a. Current ratio Current ratio 2004 Current ratio 2005 Quick ratio Quick ratio 2004 Quick ratio 2005 Cash ratio Cash ratio 2004 Cash ratio 2005 NWC ratio NWC ratio 2004 NWC ratio 2005 Debt-equity ratio Debt-equity ratio 2004 Debt-equity ratio 2005 Equity multiplier Equity multiplier 2004 Equity multiplier 2005 = Current assets / Current liabilities = $96,637 / $112,310 = 0.86 times = $104,149 / $107,477 = 0.97 times = (Current assets Inventory) / Current liabilities = ($96,637 59,324) / $112,310 = 0.33 times = ($104,149 64,853) / $104,477 = 0.37 times = Cash / Current liabilities = $10,168 / $112,310 = 0.09 times = $10,683 / $107,477 = 0.10 times = NWC / Total assets = ($96,637 112,310) / $400,802 = 3.91% = ($104,149 107,477) / $451,317 = 0.74% = Total debt / Total equity = ($112,310 + 50,000) / $238,492 = 0.68 times = ($107,477 + 62,000) / $281,840 = 0.60 times = 1 + D/E = 1 + 0.68 = 1.68 = 1 + 0.60 = 1.60
b.
c.
d.
e.
CHAPTER 3 B-21 f. Total debt ratio Total debt ratio 2004 Total debt ratio 2005 = (Total assets Total equity) / Total assets = ($400,802 238,492) / $400,802 = 0.40 = ($451,317 281,840) / $451,317 = 0.38
Long-term debt ratio = Long-term debt / (Long-term debt + Total equity) Long-term debt ratio 2004 = $50,000 / ($50,000 + 238,492) = 0.17 Long-term debt ratio 2005 = $62,000 / ($62,000 + 281,840) = 0.18 Intermediate 18. This is a multi-step problem involving several ratios. The ratios given are all part of the DuPont Identity. The only DuPont Identity ratio not given is the profit margin. If we know the profit margin, we can find the net income since sales are given. So, we begin with the DuPont Identity: ROE = 0.16 = (PM)(TAT)(EM) = (PM)(S / TA)(1 + D/E) Solving the DuPont Identity for profit margin, we get: PM = [(ROE)(TA)] / [(1 + D/E)(S)] PM = [(0.16)($1,185)] / [(1 + 1)( $2,700)] = .0351 Now that we have the profit margin, we can use this number and the given sales figure to solve for net income: PM = .0351 = NI / S NI = .0351($2,700) = $94.80 19. This is a multi-step problem involving several ratios. It is often easier to look backward to determine where to start. We need receivables turnover to find days' sales in receivables. To calculate receivables turnover, we need credit sales, and to find credit sales, we need total sales. Since we are given the profit margin and net income, we can use these to calculate total sales as: PM = 0.086 = NI / Sales = $173,000 / Sales; Sales = $2,011,628 Credit sales are 75 percent of total sales, so: Credit sales = $2,011,628(0.75) = $1,508,721 Now we can find receivables turnover by: Receivables turnover = Sales / Accounts receivable = $1,508,721 / $143,200 = 10.54 times Days' sales in receivables = 365 days / Receivables turnover = 365 / 10.54 = 34.64 days 20. The solution to this problem requires a number of steps. First, remember that CA + NFA = TA. So, if we find the CA and the TA, we can solve for NFA. Using the numbers given for the current ratio and the current liabilities, we solve for CA: CR = CA / CL CA = CR(CL) = 1.20($850) = $1,020
B-22 SOLUTIONS
To find the total assets, we must first find the total debt and equity from the information given. So, we find the sales using the profit margin: PM = NI / Sales NI = PM(Sales) = .095($4,310) = $409.45 We now use the sales figure as an input into ROE to find the total equity: ROE = NI / TE TE = NI / ROE = $409.45 / .215 = $1,904.42 Next, we need to find the long-term debt. The long-term debt ratio is: Long-term debt ratio = 0.70 = LTD / (LTD + TE) Inverting both sides gives: 1 / 0.70 = (LTD + TE) / LTD = 1 + (TE / LTD) Substituting the total equity into the equation and solving for long-term debt gives the following: 1 + $1,904.42 / LTD = 1.429 LTD = $1,904.42 / .429 = $4,443.64 Now, we can find the total debt of the company: TD = CL + LTD = $850 + 4,443.64 = $5,293.64 And, with the total debt, we can find the TD&E, which is equal to TA: TA = TD + TE = $5,293.64 + 1,904.43 = $7,198.06 And finally, we are ready to solve the balance sheet identity as: NFA = TA CA = $7,198.06 1,020 = $6,178.06 21. Child: Profit margin = NI / S = $1.00 / $50 = 2%
Store: Profit margin = NI / S = $7.7M / $770M = 1% The advertisement is referring to the store's profit margin, but a more appropriate earnings measure for the firm's owners is the return on equity. ROE = NI / TE = NI / (TA TD) ROE = $7.7M / ($196M 130M) = 11.67%
CHAPTER 3 B-23 22. The solution requires substituting two ratios into a third ratio. Rearranging D/TA: Firm A D / TA = .60 (TA E) / TA = .60 (TA / TA) (E / TA) = .60 1 (E / TA) = .60 E / TA = .40 E = .40(TA) Rearranging ROA, we find: NI / TA = .20 NI = .20(TA) NI / TA = .30 NI = .30(TA) Firm B D / TA = .40 (TA E) / TA = .40 (TA / TA) (E / TA) = .40 1 (E / TA) = .40 E / TA = .60 E = .60(TA)
Since ROE = NI / E, we can substitute the above equations into the ROE formula, which yields: ROE = .20(TA) / .40(TA) = .20 / .40 = 50% ROE = .30(TA) / .60 (TA) = .30 / .60 = 50%
23. This problem requires you to work backward through the income statement. First, recognize that Net income = (1 t)EBT. Plugging in the numbers given and solving for EBT, we get: EBT = $7,850 / 0.66 = $11,893.94 Now, we can add interest to EBIT to get EBIT as follows: EBIT = EBT + Interest paid = $11,893.94 + 2,108 = $14,001.94 To get EBITD (earnings before interest, taxes, and depreciation), the numerator in the cash coverage ratio, add depreciation to EBIT: EBITD = EBIT + Depreciation = $14,001.94 + 1,687 = $15,688.94 Now, simply plug the numbers into the cash coverage ratio and calculate: Cash coverage ratio = EBITD / Interest = $15,688.94 / $2,108 = 7.44 times 24. The only ratio given which includes cost of goods sold is the inventory turnover ratio, so it is the last ratio used. Since current liabilities is given, we start with the current ratio: Current ratio = 3.3 = CA / CL = CA / $340,000 CA = $1,122,000
B-24 SOLUTIONS Using the quick ratio, we solve for inventory: Quick ratio = 1.8 = (CA Inventory) / CL = ($1,122,000 Inventory) / $340,000 Inventory = CA (Quick ratio CL) Inventory = $1,122,000 (1.8 $340,000) Inventory = $510,000 Inventory turnover = 4.2 = COGS / Inventory = COGS / $510,000 COGS = $2,142,000 25. PM = NI / S = 13,156 / 147,318 = 8.93% As long as both net income and sales are measured in the same currency, there is no problem; in fact, except for some market value ratios like EPS and BVPS, none of the financial ratios discussed in the text are measured in terms of currency. This is one reason why financial ratio analysis is widely used in international finance to compare the business operations of firms and/or divisions across national economic borders. The net income in dollars is: NI = PM Sales NI = 0.0893($267,661) = $23,903 26. Short-term solvency ratios: Current ratio = Current assets / Current liabilities Current ratio 2004 = $7,828 / $1,808 = 4.33 times Current ratio 2005 = $8,322 / $2,320 = 3.59 times Quick ratio Quick ratio 2004 Quick ratio 2005 Cash ratio Cash ratio 2004 Cash ratio 2005 = (Current assets Inventory) / Current liabilities = ($7,828 4,608) / $1,808 = 1.78 times = ($8,322 4,906) / $2,320 = 1.47 times = Cash / Current liabilities = $815 / $1,808 = 0.45 times = $906 / $2,320 = 0.39 times
Asset utilization ratios: Total asset turnover = Sales / Total assets Total asset turnover = $33,500 / $27,489 = 1.22 times Inventory turnover Inventory turnover Receivables turnover Receivables turnover = Cost of goods sold / Inventory = $18,970 / $4,906 = 3.87 times = Sales / Accounts receivable = $33,500 / $2,510 = 13.35 times
Long-term solvency ratios: Total debt ratio = (Total assets Total equity) / Total assets Total debt ratio 2004 = ($22,992 16,367) / $22,992 = 0.29 Total debt ratio 2005 = ($27,489 20,209) / $27,489 = 0.26
CHAPTER 3 B-25 Debt-equity ratio Debt-equity ratio 2004 Debt-equity ratio 2005 Equity multiplier Equity multiplier 2004 Equity multiplier 2005 Times interest earned Times interest earned Cash coverage ratio Cash coverage ratio Profitability ratios: Profit margin Profit margin Return on assets Return on assets Return on equity Return on equity 27. The DuPont identity is: ROE = (PM)(TAT)(EM) ROE = (0.2341)(1.22)(1.36) = 0.3880 or 38.80% 28. The number of days a company can operate if cash inflows were suspended is found by the interval measure. The interval measure is calculated as: Interval measure = Current assets Average / daily operating costs We can find the average daily operating costs as follows: Average daily operating costs = Cost of goods sold / 365 days Average daily operating costs = $18,970 / 365 = $51.97 per day So, the number of days the company can operate if cash inflows are suspended, or the interval measure, is: Interval measure = $8,322 / $51.97 per day = 160 days = Total debt / Total equity = ($1,808 + 4,817) / $16,367 = 0.40 = ($2,320 + 4,960) / $20,209 = 0.36 = 1 + D/E = 1 + 0.40 = 1.40 = 1 + 0.36 = 1.36 = EBIT / Interest = $12,550 / $486 = 25.82 times = (EBIT + Depreciation) / Interest = ($12,550 + 1,980) / $486 = 29.90 times
= Net income / Sales = $7,842 / $33,500 = 23.41% = Net income / Total assets = $7,842 / $27,489 = 28.53% = Net income / Total equity = $7,842 / $20,209 = 38.80%
B-26 SOLUTIONS 29. SMOLIRA GOLF CORP. Statement of Cash Flows For 2005 Cash, beginning of the year Operating activities Net income Plus: Depreciation Increase in accounts payable Increase in other current liabilities Less: Increase in accounts receivable Increase in inventory Net cash from operating activities Investment activities Fixed asset acquisition Net cash from investment activities Financing activities Increase in notes payable Dividends paid Decrease in long-term debt Net cash from financing activities Net increase in cash Cash, end of year 30. Earnings per share Earnings per share P/E ratio P/E ratio Dividends per share Dividends per share Book value per share Book value per share Market-to-book ratio Market-to-book ratio = Net income / Shares = $7,842 / 2,500 = $3.14 per share = Shares price / Earnings per share = $67 / $3.14 = 21.36 times = Dividends / Shares = $4,000 / 2,500 = $1.60 per share = Total equity / Shares = $20,209 / 2,500 shares = $8.08 per share = Share price / Book value per share = $67.00 / $8.08 = 8.29 times
$
815
$ 7,842 $ 1,980 309 83 $ (105) (298) $ 9,811
$ (5,983) $ (5,983)
120 (4,000) 143 $ (3,737) $ $ 91 906
$
CHAPTER 4 B-27
CHAPTER 4 LONG-TERM FINANCIAL PLANNING AND GROWTH
Answers to Concepts Review and Critical Thinking Questions 1. The reason is that, ultimately, sales are the driving force behind a business. A firm's assets, employees, and, in fact, just about every aspect of its operations and financing exist to directly or indirectly support sales. Put differently, a firm's future need for things like capital assets, employees, inventory, and financing are determined by its future sales level. 2. Two assumptions of the sustainable growth formula are that the company does not want to sell new equity, and that financial policy is fixed. If the company raises outside equity, or increases its debtequity ratio it can grow at a higher rate than the sustainable growth rate. Of course the company could also grow faster than its profit margin increases, if it changes its dividend policy by increasing the retention ratio, or its total asset turnover increases. 3. The internal growth rate is greater than 15%, because at a 15% growth rate the negative EFN indicates that there is excess internal financing. If the internal growth rate is greater than 15%, then the sustainable growth rate is certainly greater than 15%, because there is additional debt financing used in that case (assuming the firm is not 100% equity-financed). As the retention ratio is increased, the firm has more internal sources of funding, so the EFN will decline. Conversely, as the retention ratio is decreased, the EFN will rise. If the firm pays out all its earnings in the form of dividends, then the firm has no internal sources of funding (ignoring the effects of accounts payable); the internal growth rate is zero in this case and the EFN will rise to the change in total assets. 4. The sustainable growth rate is greater than 20%, because at a 20% growth rate the negative EFN indicates that there is excess financing still available. If the firm is 100% equity financed, then the sustainable and internal growth rates are equal and the internal growth rate would be greater than 20%. However, when the firm has some debt, the internal growth rate is always less than the sustainable growth rate, so it is ambiguous whether the internal growth rate would be greater than or less than 20%. If the retention ratio is increased, the firm will have more internal funding sources available, and it will have to take on more debt to keep the debt/equity ratio constant, so the EFN will decline. Conversely, if the retention ratio is decreased, the EFN will rise. If the retention rate is zero, both the internal and sustainable growth rates are zero, and the EFN will rise to the change in total assets. 5. Presumably not, but, of course, if the product had been much less popular, then a similar fate would have awaited due to lack of sales. 6. Since customers did not pay until shipment, receivables rose. The firm's NWC, but not its cash, increased. At the same time, costs were rising faster than cash revenues, so operating cash flow declined. The firm's capital spending was also rising. Thus, all three components of cash flow from assets were negatively impacted.
B-28 SOLUTIONS
7. Apparently not! In hindsight, the firm may have underestimated costs and also underestimated the extra demand from the lower price. 8. Financing possibly could have been arranged if the company had taken quick enough action. Sometimes it becomes apparent that help is needed only when it is too late, again emphasizing the need for planning. 9. All three were important, but the lack of cash or, more generally, financial resources ultimately spelled doom. An inadequate cash resource is usually cited as the most common cause of small business failure. 10. Demanding cash up front, increasing prices, subcontracting production, and improving financial resources via new owners or new sources of credit are some of the options. When orders exceed capacity, price increases may be especially beneficial. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. It is important to remember that equity will not increase by the same percentage as the other assets. If every other item on the income statement and balance sheet increases by 10 percent, the pro forma income statement and balance sheet will look like this: Pro forma income statement Sales Costs Net income $17,600 13,750 $ 3,850 Assets Total Pro forma balance sheet $ 9,790 $ 9,790 Debt Equity Total $ 5,610 4,180 $ 9,790
In order for the balance sheet to balance, equity must be: Equity = Total liabilities and equity Debt Equity = $9,790 5,610 Equity = $4,180 Equity increased by: Equity increase = $4,180 3,800 Equity increase = $380
CHAPTER 4 B-29 Net income is $3,850 but equity only increased by $380; therefore, a dividend of: Dividend = $3,850 380 Dividend = $3,470 must have been paid. Dividends paid is the plug variable. 2. Here we are given the dividend amount, so dividends paid is not a plug variable. If the company pays out one-half of its net income as dividends, the pro forma income statement and balance sheet will look like this: Pro forma income statement Sales Costs Net income $17,600 13,750 $ 3,850 Assets Total Pro forma balance sheet $ 9,790 $ 9,790 Debt Equity Total $ 5,100 5,725 $10,825
Dividends $ 1,925 Add. to RE 1,925 Note that the balance sheet does not balance. This is due to EFN. The EFN for this company is: EFN = Total assets Total liabilities and equity EFN = $9,790 10,825 EFN = $1,035 3. An increase of sales to $5,192 is an increase of: Sales increase = ($5,192 4,400) / $4,400 Sales increase = .18 or 18% Assuming costs and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Sales Costs Net income $ $ 5,192 3,168 2,024 Assets Total Pro forma balance sheet $ 15,812 $ 15,812 Debt Equity Total 9,100 6,324 $ 15,424 $
If no dividends are paid, the equity account will increase by the net income, so: Equity = $4,300 + 2,024 Equity = $6,324 So the EFN is: EFN = Total assets Total liabilities and equity EFN = $15,812 15,424 = $388
B-30 SOLUTIONS 4. An increase of sales to $23,040 is an increase of: Sales increase = ($23,040 19,200) / $19,200 Sales increase = .20 or 20% Assuming costs and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Sales $23,040.00 Costs 18,660.00 EBIT 4,380.00 Taxes(34%) 1,489.20 Net income $ 2,890.80 Assets Total Pro forma balance sheet $ $ 111,600 Debt Equity 111,600 Total $ 20,400.00 74,334.48 $ 94,734.48
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($963.60 / $2,409)($2,890.80) Dividends = $1,156.32 The addition to retained earnings is: Addition to retained earnings = $2,890.80 1,156.32 Addition to retained earnings = $1,734.48 And the new equity balance is: Equity = $72,600 + 1,734.48 Equity = $74,334.48 So the EFN is: EFN = Total assets Total liabilities and equity EFN = $111,600 94,734.48 EFN = $16,865.52 5. Assuming costs and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Sales $ 4,140.00 Costs 3,335.00 Taxable income 805.00 Taxes (34%) 273.70 Net income $ 531.30 CA FA Total Pro forma balance sheet $ 5,175.00 4,485.00 $ 9,660.00 CL LTD Equity Total $ 1,058.00 1,840.00 5,905.65 $ 8,803.65
CHAPTER 4 B-31 The payout ratio is 50 percent, so dividends will be: Dividends = 0.50($531.30) Dividends = $265.65 The addition to retained earnings is: Addition to retained earnings = $531.30 265.65 Addition to retained earnings = $265.65 So the EFN is: EFN = Total assets Total liabilities and equity EFN = $9,660.00 8,803.65 EFN = $856.35 6. To calculate the internal growth rate, we first need to calculate the ROA, which is: ROA = NI / TA ROA = $2,327 / $38,000 ROA = .0612 or 6.12% The plowback ratio, b, is one minus the payout ratio, so: b = 1 .20 b = .80 Now we can use the internal growth rate equation to get: Internal growth rate = (ROA b) / [1 (ROA b)] Internal growth rate = [0.0612(.80)] / [1 0.0612(.80)] Internal growth rate = .0515 or 5.15% 7. To calculate the sustainable growth rate, we first need to calculate the ROE, which is: ROE = NI / TE ROE = $2,327 / $16,000 ROE = .1454 The plowback ratio, b, is one minus the payout ratio, so: b = 1 .20 b = .80 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [0.1454(.80)] / [1 0.1454(.80)] Sustainable growth rate = .1317 or 13.17%
B-32 SOLUTIONS 8. The maximum percentage sales increase is the sustainable growth rate. To calculate the sustainable growth rate, we first need to calculate the ROE, which is: ROE = NI / TE ROE = $12,672 / $73,000 ROE = .1736 The plowback ratio, b, is one minus the payout ratio, so: b = 1 .30 b = .70 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.1736(.70) ] / [1 .1736(.70)] Sustainable growth rate = .1383 or 13.83% So, the maximum dollar increase in sales is: Maximum increase in sales = $54,000(.1383) Maximum increase in sales = $7,469.27 9. Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: HEIR JORDAN CORPORATION Pro Forma Income Statement Sales $34,800.00 Costs 13,440.00 Taxable income $21,360.00 Taxes (34%) 7,262.40 Net income $ 14,097.60 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($4,935/$11,748)($14,097.60) Dividends = $5,921.68 And the addition to retained earnings will be: Addition to retained earnings = $14,097.60 5,921.68 Addition to retained earnings = $8,175.92
CHAPTER 4 B-33 10. Below is the balance sheet with the percentage of sales for each account on the balance sheet. Notes payable, total current liabilities, long-term debt, and all equity accounts do not vary directly with sales. HEIR JORDAN CORPORATION Balance Sheet ($) (%) Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity
($)
(%)
$ 3,525 7,500 6,000 $17,025
12.16 25.86 20.69 58.71
$ 3,000 7,500 $10,500 19,500
10.34 n/a n/a n/a
30,000 103.45
$15,000 2,025 $17,025 $47,025
n/a n/a n/a n/a
Total assets
$47,025 162.16
11. Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: HEIR JORDAN CORPORATION Pro Forma Income Statement Sales $33,350.00 Costs 12,880.00 Taxable income $20,470.00 Taxes (34%) 6,959.80 Net income $ 13,510.20 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($4,935/$11,748)($13,510.20) Dividends = $5,674.94 And the addition to retained earnings will be: Addition to retained earnings = $13,240.20 5,674.94 Addition to retained earnings = $7,835.26 The new total addition to retained earnings on the pro forma balance sheet will be: New total addition to retained earnings = $2,025 + 7,835.26 New total addition to retained earnings = $9,860.26
B-34 SOLUTIONS The pro forma balance sheet will look like this: HEIR JORDAN CORPORATION Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Liabilities and Owners' Equity Current liabilities Accounts payable $ Notes payable Total $ Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity
$ 4,053.75 8,625.00 6,900.00 $ 19,578.75
3,450.00 7,500.00 10,950.00 19,500.00
34,500.00
$ 15,000.00 9,860.26 $ 24,860.26 $ 55,310.26
Total assets So the EFN is:
$ 54,078.75
EFN = Total assets Total liabilities and equity EFN = $54,078.75 55,310.26 EFN = $1,231.51 12. We need to calculate the retention ratio to calculate the internal growth rate. The retention ratio is: b = 1 .20 b = .80 Now we can use the internal growth rate equation to get: Internal growth rate = (ROA b) / [1 (ROA b)] Internal growth rate = [.10(.80)] / [1 .10(.80)] Internal growth rate = .0870 or 8.70% 13. We need to calculate the retention ratio to calculate the sustainable growth rate. The retention ratio is: b = 1 .25 b = .75 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.19(.75)] / [1 .19(.75)] Sustainable growth rate = .1662 or 16.62%
CHAPTER 4 B-35 14. We first must calculate the ROE to calculate the sustainable growth rate. To do this we must realize two other relationships. The total asset turnover is the inverse of the capital intensity ratio, and the equity multiplier is 1 + D/E. Using these relationships, we get: ROE = (PM)(TAT)(EM) ROE = (.089)(1/.55)(1 + .60) ROE = .2589 or 25.89% The plowback ratio is one minus the dividend payout ratio, so: b = 1 ($15,000 / $29,000) b = .4828 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.2589(.4828)] / [1 .2589(.4828)] Sustainable growth rate = .1428 or 14.28% 15. We must first calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. The ROE is: ROE = (PM)(TAT)(EM) ROE = (.076)(1.40)(1.50) ROE = 15.96% The plowback ratio is one minus the dividend payout ratio, so: b = 1 .40 b = .60 Now we can use the sustainable growth rate equation to get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.1596(.60)] / [1 .1596(.60)] Sustainable growth rate = 10.59% Intermediate 16. To determine full capacity sales, we divide the current sales by the capacity the company is currently using, so: Full capacity sales = $510,000 / .85 Full capacity sales = $600,000 The maximum sales growth is the full capacity sales divided by the current sales, so: Maximum sales growth = ($600,000 / $510,000) 1 Maximum sales growth = .1765 or 17.65%
B-36 SOLUTIONS 17. To find the new level of fixed assets, we need to find the current percentage of fixed assets to full capacity sales. Doing so, we find: Fixed assets / Full capacity sales = $415,000 / $600,000 Fixed assets / Full capacity sales = .6917 Next, we calculate the total dollar amount of fixed assets needed at the new sales figure. Total fixed assets = .6917($680,000) Total fixed assets = $470,333.33 The new fixed assets necessary is the total fixed assets at the new sales figure minus the current level of fixed assts. New fixed assets = $470,333.33 415,000 New fixed assets = $55,333.33 18. We have all the variables to calculate ROE using the DuPont identity except the profit margin. If we find ROE, we can solve the DuPont identity for profit margin. We can calculate ROE from the sustainable growth rate equation. For this equation we need the retention ratio, so: b = 1 .50 b = .50 Using the sustainable growth rate equation and solving for ROE, we get: Sustainable growth rate = (ROE b) / [1 (ROE b)] .08 = [ROE(.50)] / [1 ROE(.50)] ROE = .1481 or 14.81% Now we can use the DuPont identity to find the profit margin as: ROE = PM(TAT)(EM) .1481 = PM(1 / 1.30)(1 + .40) PM = (.1481)(1.30) / 1.40 PM = .1376 or 13.76% 19. We have all the variables to calculate ROE using the DuPont identity except the equity multiplier. Remember that the equity multiplier is one plus the debt-equity ratio. If we find ROE, we can solve the DuPont identity for equity multiplier, then the debt-equity ratio. We can calculate ROE from the sustainable growth rate equation. For this equation we need the retention ratio, so: b = 1 .60 b = .40 Using the sustainable growth rate equation and solving for ROE, we get: Sustainable growth rate = (ROE b) / [1 (ROE b)] .11 = [ROE(.40)] / [1 ROE(.40)] ROE = .2477 or 24.77%
CHAPTER 4 B-37 Now we can use the DuPont identity to find the equity multiplier as: ROE = PM(TAT)(EM) .2477 = (.095)(1 / .9)EM EM = (.2477)(.9) / .095 EM = 2.35 So, the D/E ratio is: D/E = EM 1 D/E = 2.35 1 D/E = 1.35 20. We are given the profit margin. Remember that: ROA = PM(TAT) We can calculate the ROA from the internal growth rate formula, and then use the ROA in this equation to find the total asset turnover. The retention ratio is: b = 1 .30 b = .70 Using the internal growth rate equation to find the ROA, we get: Internal growth rate = (ROA b) / [1 (ROA b)] .09 = [ROA(.70)] / [1 ROA(.70)] ROA = .1180 or 11.80% Plugging ROA and PM into the equation we began with and solving for TAT, we get: ROA = (PM)(TAT) .1180 = .08(PM) TAT = .1180 / .08 TAT = 1.47 times 21. We should begin by calculating the D/E ratio. We calculate the D/E ratio as follows: Total debt ratio = .60 = TD / TA Inverting both sides we get: 1 / .60 = TA / TD Next, we need to recognize that TA / TD = 1 + TE / TD Substituting this into the previous equation, we get: 1 / .60 = 1 + TE /TD
B-38 SOLUTIONS Subtract 1 (one) from both sides and inverting again, we get: D/E = 1 / [(1 / .60) 1] D/E = 1.5 With the D/E ratio, we can calculate the EM and solve for ROE using the DuPont identity: ROE = (PM)(TAT)(EM) ROE = (.064)(1.80)(1 + 1.5) ROE = .2880 or 28.80% Now, we use the ROE equation: ROE = ROA(EM) .2880 = ROA(2.5) ROA = .1152 or 11.52% Now we can calculate the retention ratio as: b = 1 .60 b = .40 Finally, putting all the numbers we have calculated into the sustainable growth rate equation, we get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.2880(.40)] / [1 .2880(.40)] Sustainable growth rate = .1302 or 13.02% 22. To calculate the sustainable growth rate, we first must calculate the retention ratio and ROE. The retention ratio is: b = 1 $12,000 / $21,000 b = .4286 And the ROE is: ROE = $21,000 / $49,000 ROE = .4286 or 42.86% So, the sustainable growth rate is: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.4286(.4286)] / [1 .4286(.4286)] Sustainable growth rate = 22.50% If the company grows at the sustainable growth rate, the new level of total assets is: New TA = 1.2250($134,000) = $164,150
CHAPTER 4 B-39 To find the new level of debt in the company's balance sheet, we take the percentage of debt in the capital structure times the new level of total assets. The additional borrowing will be the new level of debt minus the current level of debt. So: New TD = [D / (D + E)](TA) New TD = [$85,000 / ($85,000 + 49,000)]($164,150) New TD = $104,125 And the additional borrowing will be: Additional borrowing = $104,125 85,000 Additional borrowing = $19,125 The growth rate that can be supported with no outside financing is the internal growth rate. To calculate the internal growth rate, we first need the ROA, which is: ROA = $21,000 / $134,000 ROA = .1567 or 15.67% This means the internal growth rate is: Internal growth rate = (ROA b) / [1 (ROA b)] Internal growth rate = [.1567(.4286)] / [1 .1567(.4286)] Internal growth rate = 7.20% 23. Since the company issued no new equity, shareholders' equity increased by retained earnings. Retained earnings for the year were: Retained earnings = NI Dividends Retained earnings = $80,000 49,000 Retained earnings = $31,000 So, the equity at the end of the year was: Ending equity = $165,000 + 31,000 Ending equity = $196,000 The ROE based on the end of period equity is: ROE = $80,000 / $196,000 ROE = 40.82% The plowback ratio is: Plowback ratio = Addition to retained earnings/NI Plowback ratio = $31,000 / $80,000 Plowback ratio = .3875 or = 38.75%
B-40 SOLUTIONS Using the equation presented in the text for the sustainable growth rate, we get: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = [.4082(.3875)] / [1 .4082(.3875)] Sustainable growth rate = .1879 or 18.79% The ROE based on the beginning of period equity is ROE = $80,000 / $165,000 ROE = .4848 or 48.48% Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we get: Sustainable growth rate = ROE b Sustainable growth rate = .4848 .3875 Sustainable growth rate = .1879 or 18.79% Using the shortened equation for the sustainable growth rate and the end of period ROE, we get: Sustainable growth rate = ROE b Sustainable growth rate = .4082 .3875 Sustainable growth rate = .1582 or 15.82% Using the end of period ROE in the shortened sustainable growth rate results in a growth rate that is too low. This will always occur whenever the equity increases. If equity increases, the ROE based on end of period equity is lower than the ROE based on the beginning of period equity. The ROE (and sustainable growth rate) in the abbreviated equation is based on equity that did not exist when the net income was earned. 24. The ROA using end of period assets is: ROA = $80,000 / $250,000 ROA = .3200 or 32.00% The beginning of period assets had to have been the ending assets minus the addition to retained earnings, so: Beginning assets = Ending assets Addition to retained warnings Beginning assets = $$250,000 ($80,000 49,000) Beginning assets = $219,000 And the ROA using beginning of period assets is: ROA = $80,000 / $219,000 ROA = .3653 or 36.53%
CHAPTER 4 B-41 Using the internal growth rate equation presented in the text, we get: Internal growth rate = (ROA b) / [1 (ROA b)] Internal growth rate = [.3200(.3875)] / [1 .3200(.3875)] Internal growth rate = .1416 or 14.16% Using the formula ROA b, and end of period assets: Internal growth rate = .3200 .3875 Internal growth rate = 12.40% Using the formula ROA b, and beginning of period assets: Internal growth rate = .3653 .3875 Internal growth rate = 14.16% 25. Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: MOOSE TOURS INC. Pro Forma Income Statement Sales $ 1,086,000 Costs 852,000 Other expenses 14,400 EBIT $ 219,600 Interest 19,700 Taxable income $ 199,900 Taxes(35%) 69,965 Net income $ 129,935 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($42,458/$106,145)($129,935) Dividends = $51,974 And the addition to retained earnings will be: Addition to retained earnings = $129,935 51,974 Addition to retained earnings = $77,961 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 77,961 New addition to retained earnings = $334,961
B-42 SOLUTIONS The pro forma balance sheet will look like this: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 30,000 51,600 91,200 172,800 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 78,000 9,000 87,000 156,000
$
436,800
$ $ $
21,000 334,961 355,961 598,961
Total assets So the EFN is:
$
609,600
EFN = Total assets Total liabilities and equity EFN = $609,600 598,961 EFN = $10,639 26. First, we need to calculate full capacity sales, which is: Full capacity sales = $905,000 / .80 Full capacity sales = $1,131,250 The capital intensity ratio at full capacity sales is: Capital intensity ratio = Fixed assets / Full capacity sales Capital intensity ratio = $364,000 / $1,131,250 Capital intensity ratio = .32177 The fixed assets required at full capacity sales is the capital intensity ratio times the projected sales level: Total fixed assets = .32177($1,086,000) = $349,440 So, EFN is: EFN = ($172,800 + 349,440) $598,961 = $76,721 Note that this solution assumes that fixed assets are decreased (sold) so the company has a 100 percent fixed asset utilization. If we assume fixed assets are not sold, the answer becomes: EFN = ($172,800 + 364,000) $598,961 = $62,161
CHAPTER 4 B-43 27. The D/E ratio of the company is: D/E = ($156,000 + 74,000) / $278,000 D/E = .82734 So the new total debt amount will be: New total debt = .82734($355,961) New total debt = $294,500.11 So the EFN is: EFN = $609,600 ($294,500.11 + 355,961) = $40,861.11 An interpretation of the answer is not that the company has a negative EFN. Looking back at Problem 25, we see that for the same sales growth, the EFN is $10,639. The negative number in this case means the company has too much capital. There are two possible solutions. First, the company can put the excess funds in cash, which has the effect of changing the current asset growth rate. Second, the company can use the excess funds to repurchase debt and equity. To maintain the current capital structure, the repurchase must be in the same proportion as the current capital structure. Challenge 28. The pro forma income statements for all three growth rates will be: MOOSE TOURS INC. Pro Forma Income Statement 15 % Sales 20% Sales Growth Growth $1,040,750 $1,086,000 816,500 852,000 13,800 14,400 $ 210,450 $ 219,600 19,700 19,700 $ 190,750 $ 199,900 66,763 69,965 $ 123,988 $ 129,935 $ 49,595 74,393 $ 51,974 77,961
Sales Costs Other expenses EBIT Interest Taxable income Taxes (35%) Net income Dividends Add to RE
25% Sales Growth $1,131,250 887,500 15,000 $ 228,750 19,700 $ 209,050 73,168 $ 135,883 $ 54,353 81,530
B-44 SOLUTIONS We will calculate the EFN for the 15 percent growth rate first. Assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($123,988) Dividends = $49,595 And the addition to retained earnings will be: Addition to retained earnings = $123,988 49,595 Addition to retained earnings = $74,393 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 74,393 New addition to retained earnings = $331,393 The pro forma balance sheet will look like this: 15% Sales Growth: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 28,750 49,450 87,400 165,600 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 74,750 9,000 83,750 156,000
$
418,600
$ $ $
21,000 331,393 352,393 592,143
Total assets So the EFN is:
$
584,200
EFN = Total assets Total liabilities and equity EFN = $584,200 592,143 EFN = $7,943
CHAPTER 4 B-45 At a 20 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($129,935) Dividends = $51,974 And the addition to retained earnings will be: Addition to retained earnings = $129,935 51,974 Addition to retained earnings = $77,961 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 77,961 New addition to retained earnings = $334,961 The pro forma balance sheet will look like this: 20% Sales Growth: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 30,000 51,600 91,200 172,800 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 78,000 9,000 87,000 156,000
$
436,800
$ $ $
21,000 334,961 355,961 598,961
Total assets So the EFN is:
$
609,600
EFN = Total assets Total liabilities and equity EFN = $609,600 598,961 EFN = $10,639
B-46 SOLUTIONS At a 25 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($135,883) Dividends = $54,353 And the addition to retained earnings will be: Addition to retained earnings = $135,883 54,353 Addition to retained earnings = $81,530 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 81,530 New addition to retained earnings = $338,530 The pro forma balance sheet will look like this: 25% Sales Growth: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 31,250 53,750 95,000 180,000 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 81,250 9,000 90,250 156,000
$
455,000
$ $ $
21,000 338,530 359,530 605,780
Total assets So the EFN is:
$
635,000
EFN = Total assets Total liabilities and equity EFN = $635,000 605,780 EFN = $29,221
CHAPTER 4 B-47 29. The pro forma income statements for all three growth rates will be: MOOSE TOURS INC. Pro Forma Income Statement 20% Sales 30% Sales Growth Growth $1,086,000 $1,176,500 852,000 923,000 14,400 15,600 $ 219,600 $ 237,900 19,700 19,700 $ 199,900 $ 218,200 76,370 69,965 $ 129,935 $ 141,830 $ 51,974 77,961 $ 56,732 85,098
Sales Costs Other expenses EBIT Interest Taxable income Taxes (35%) Net income Dividends Add to RE
35% Sales Growth $1,221,750 958,500 16,200 $ 247,050 19,700 $ 227,350 79,573 $ 147,778 $ 59,111 88,667
Under the sustainable growth rate assumption, the company maintains a constant debt-equity ratio. The D/E ratio of the company is: D/E = ($156,000 + 74,000) / $278,000 D/E = .82734 At a 20 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($129,935) Dividends = $51,974 And the addition to retained earnings will be: Addition to retained earnings = $129,935 51,974 Addition to retained earnings = $77,961 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 77,961 New addition to retained earnings = $334,961 The new total debt will be: New total debt = .82734($334,961) New total debt = $294,500 So, the new long-term debt will be the new total debt minus the new short-term debt, or: New long-term debt = $294,500 87,000 New long-term debt = $207,500
B-48 SOLUTIONS The pro forma balance sheet will look like this: Sales growth rate = 20% and Debt/Equity ratio = .82734: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 30,000 51,600 91,200 172,800 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 78,000 9,000 87,000 207,500
$
436,800
$ $ $
21,000 334,961 355,961 650,461
Total assets So the EFN is:
$
609,600
EFN = Total assets Total liabilities and equity EFN = $609,600 650,461 EFN = $40,861
CHAPTER 4 B-49 At a 30 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($141,830) Dividends = $56,732 And the addition to retained earnings will be: Addition to retained earnings = $141,830 56,732 Addition to retained earnings = $85,098 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 85,098 New addition to retained earnings = $342,098 The new total debt will be: New total debt = .82734($342,098) New total debt = $300,405 So, the new long-term debt will be the new total debt minus the new short-term debt, or: New long-term debt = $300,405 93,500 New long-term debt = $206,905 Sales growth rate = 30% and debt/equity ratio = .82734: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 32,500 55,900 98,800 187,200 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 84,500 9,000 93,500 206,905
$
473,200
$ $ $
21,000 342,098 363,098 663,503
Total assets So the EFN is:
$
660,400
EFN = Total assets Total liabilities and equity EFN = $660,400 663,503 EFN = $3,103
B-50 SOLUTIONS At a 35 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($147,778) Dividends = $59,111 And the addition to retained earnings will be: Addition to retained earnings = $147,778 59,111 Addition to retained earnings = $88,667 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257,000 + 88,667 New addition to retained earnings = $345,667 The new total debt will be: New total debt = .82734($366,667) New total debt = $303,357 So, the new long-term debt will be the new total debt minus the new short-term debt, or: New long-term debt = $303,357 96,750 New long-term debt = $206,607 Sales growth rate = 35% and debt/equity ratio = .82734: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment $ 33,750 58,050 102,600 194,400 Liabilities and Owners' Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners' equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners' equity $ $ 87,750 9,000 96,750 206,607
$
491,400
$ $ $
21,000 345,667 366,667 670,024
Total assets So the EFN is:
$
685,800
EFN = Total assets Total liabilities and equity EFN = $685,800 670,024 EFN = $15,776
CHAPTER 4 B-51 30. We must need the ROE to calculate the sustainable growth rate. The ROE is: ROE = (PM)(TAT)(EM) ROE = (.062)(1 / 1.55)(1 + 0.3) ROE = .0520 or 5.20% Now we can use the sustainable growth rate equation to find the retention ratio as: Sustainable growth rate = (ROE b) / [1 (ROE b)] Sustainable growth rate = .14 = [.0520(b)] / [1 .0520(b) b = 2.36 This implies the payout ratio is: Payout ratio = 1 b Payout ratio = 1 2.36 Payout ratio = 1.36 This is a negative dividend payout ratio of 136 percent, which is impossible. The growth rate is not consistent with the other constraints. The lowest possible payout rate is 0, which corresponds to retention ratio of 1, or total earnings retention. The maximum sustainable growth rate for this company is: Maximum sustainable growth rate = (ROE b) / [1 (ROE b)] Maximum sustainable growth rate = [.0520(1)] / [1 .0520(1)] Maximum sustainable growth rate = .0549 or 5.49% 31. We know that EFN is: EFN = Increase in assets Addition to retained earnings The increase in assets is the beginning assets times the growth rate, so: Increase in assets = A g The addition to retained earnings next year is the current net income times the retention ratio, times one plus the growth rate, so: Addition to retained earnings = (NI b)(1 + g) And rearranging the profit margin to solve for net income, we get: NI = PM(S) Substituting the last three equations into the EFN equation we started with and rearranging, we get: EFN = A(g) PM(S)b(1 + g) EFN = A(g) PM(S)b [PM(S)b]g EFN = PM(S)b + [A PM(S)b]g
B-52 SOLUTIONS 32. We start with the EFN equation we derived in Problem 32 and set it equal to zero: EFN = 0 = PM(S)b + [A PM(S)b]g Substituting the rearranged profit margin equation into the internal growth rate equation, we have: Internal growth rate = [PM(S)b ] / [A PM(S)b] Since: ROA = NI / A ROA = PM(S) / A We can substitute this into the internal growth rate equation and divide both the numerator and denominator by A. This gives: Internal growth rate = {[PM(S)b] / A} / {[A PM(S)b] / A} Internal growth rate = b(ROA) / [1 b(ROA)] To derive the sustainable growth rate, we must realize that to maintain a constant D/E ratio with no external equity financing, EFN must equal the addition to retained earnings times the D/E ratio: EFN = (D/E)[PM(S)b(1 + g)] EFN = A(g) PM(S)b(1 + g) Solving for g and then dividing numerator and denominator by A: Sustainable growth rate = PM(S)b(1 + D/E) / [A PM(S)b(1 + D/E )] Sustainable growth rate = [ROA(1 + D/E )b] / [1 ROA(1 + D/E )b] Sustainable growth rate = b(ROE) / [1 b(ROE)] 33. In the following derivations, the subscript "E" refers to end of period numbers, and the subscript "B" refers to beginning of period numbers. TE is total equity and TA is total assets. For the sustainable growth rate: Sustainable growth rate = (ROEE b) / (1 ROEE b) Sustainable growth rate = (NI/TEE b) / (1 NI/TEE b) We multiply this equation by: (TEE / TEE) Sustainable growth rate = (NI / TEE b) / (1 NI / TEE b) (TEE / TEE) Sustainable growth rate = (NI b) / (TEE NI b) Recognize that the numerator is equal to beginning of period equity, that is: (TEE NI b) = TEB