Major Points
FINANCIAL STATEMENT ANALYSIS/RATIOS: PROB’S & DETAILED SOLUTIONS
(copyright © 2019 Joseph W. Trefzger)
This problem set covers all of our ratio analysis situations, with a general increase in degree of difficulty as we progress. Be sure that you have mastered the easier problems before moving ahead, because the more difficult examples tend to expand on the ideas presented in the easier ones. The last four problems are comprehensive, involving the interpretation of financial ratios that you compute or are given.
1. Compute Aurora Amalgamated Airways’ current ratio and quick ratio, based on its most recent balance sheet:
Cash $ 700,000 Accounts Payable $ 1,200,000
Marketable Securities 950,000 Notes Payable 2,500,000
Accounts Receivable 1,250,000 Long-Term Debt 1,600,000
Inventory 3,400,000 Paid-In Capital 4,250,000
Net Fixed Assets 6,550,000 Retained Earnings 3,300,000
Total Assets $12,850,000 Total Claims $12,850,000
Type: Computing liquidity ratios. In computing the current and quick ratios, we try to see whether the commitments the firm had made, as of the moment when the most recent balance sheet “snapshot” was taken, would lead to more money coming in over the subsequent year than would be paid out over the subsequent year (and by a sufficient margin). So these ratios offer insights into whether the company is “liquid” in terms of expecting to have enough money to pay its bills that will come due over the reasonably short term. An extreme interpretation of these two “snapshot”-based ratios would be as measures of the firm’s ability to pay the bills it has already agreed to pay, if it goes out of business today and never incurs another receivable or payable. A less extreme way to think about any balance sheet-based ratio is that the most recent “snapshot” figure is (unless we know it is not) a good representation of the company’s ongoing situation with regard to that asset or claim. Recall that the current ratio is computed as
Current Ratio = [pic] ,
which requires us to do some adding here because the current asset and current liability figures are not totaled in the balance sheet given. The current asset categories shown in this balance sheet are cash, marketable securities, accounts receivable, and inventory [fixed assets, such as buildings and machines, have long useful lives and thus would not be expected to be “liquidated,” or turned into cash (i.e., sold), within a “current” short time period like a year]. Current liability categories shown in this balance sheet are accounts payable and notes payable; the other right-hand side figures all involve amounts that money providers do not expect to receive until a more distant future date. So we can compute
Current Ratio = [pic] = 1.703 .
Thus it seems like the company has a reasonable cushion; the money it stands to collect over the next year (along with what it already has in cash) is 1.7 times (170% of) what it expects to pay out over the next year. But the cushion might be less than it appears on the surface if inventory ends up being hard to sell. Cash is already in the company’s checking account, and marketable securities are available with a phone call to the company’s stock broker (think of marketable securities as the company’s savings account), while accounts receivable represent dollar amounts that buyers of the company’s goods or services have already agreed to pay after a short wait. But what if inventory items the company holds for sale (or for use in producing goods for sale) end up being unsalable, perhaps because of customers’ changing desires? A more conservative measure of the company’s liquidity position (which we might pay careful attention to if inventory tends to be illiquid for firms like Aurora) is the quick ratio, computed as
Quick Ratio = [pic] .
Removing the $3,400,000 inventory from the numerator of the current ratio above, we compute
Quick Ratio = [pic] = .784 .
If we exclude inventory from the assets thought of as “current” (being readily converted to cash in a reasonably short time), then the cushion becomes negative: the money the firm stands to collect over the next year (along with what it already has in cash) is only about 78% of what it expects to have to pay out over the next year. Of course, whether a .784 quick ratio or a 1.703 current ratio suggests strong, weak, or middle-of-the-road liquidity depends on what is customary and necessary for companies in the same line of business; thus we would likely compare any computed ratio with the average current and quick ratios for a group of competing firms, or perhaps for the whole “industry” of companies that provide the types of goods or services that Aurora does.
2. Compute Belleville Building & Bulldozing’s current ratio and quick ratio, and the amount of net working capital, based on its most recent balance sheet:
Cash $ 225,000 Accounts Payable $ 750,000
Marketable Securities 300,000 Notes Payable 830,000
Accounts Receivable 575,000 Accrued Wages and Taxes 360,000
Inventory 1,550,000 Total Current Liabilities $1,940,000
Total Current Assets $2,650,000
Long-Term Debt 2,500,000
Net Fixed Assets 4,875,000 Paid-In Capital 2,000,000
Retained Earnings 1,085,000
Total Assets $7,525,000 Total Claims $7,525,000
Type: Computing liquidity ratios. The only difference from the prior problem is that the accountants who prepared this more detailed balance sheet have already provided us with current asset and current liability totals; we do not have to add the relevant values ourselves. So we can easily compute the current ratio as
Current Ratio = [pic] = 1.366 .
What about the quick ratio? Here, to get the current assets other than inventory, we could add the individual non-inventory current asset figures, as we did in the previous problem: $225,000 cash + $300,000 marketable securities + $575,000 accounts receivable = $1,100,000. But when we are already provided with a current asset total, the easy way to compute current assets other than inventory is to subtract inventory from the given total that includes inventory: $2,650,000 – $1,550,000 =$1,100,000. We thus compute the quick ratio as
Quick Ratio = [pic] = .567 .
Common mistakes made with regard to computing the current and quick ratios are to include long-term items (such as fixed assets or long-term debt) in the numerator or denominator, or (for the quick ratio specifically) to subtract the inventory value from something other than a given current asset total. The quick ratio numerator we want is current assets other than inventory; the easy way to find it is to take current assets MINUS inventory IF we know the current asset total. If we do not know the current asset total, then the easy way to find current assets other than inventory is simply to add together cash, marketable securities, and accounts receivable (and any other non-inventory current assets, perhaps prepaid expenses, that might happen to be shown).
Net working capital is defined as total current assets minus total current liabilities, which here is $2,650,000 – $1,940,000 = $710,000. One way to think of net working capital is as a liquidity measure; it is helpful to know how much more cash we expect to collect than we expect to pay out over the next several months. But a more pessimistic way to view net working capital is as the amount of short-term (“working”) assets paid for with long-term (“capital”) sources. (Here, short- term/current liabilities pay for $1,940,000 of the $2,650,000 in short-term/current assets, so the remaining $710,000 in current assets had to be paid for with long-term money sources – long term debt or else owners’ equity. While this situation has its benefits (again a liquidity issue: less time pressure on making payments), the drawback is that assets that earn low rates of return (as current assets tend to do) are financed with costlier sources of money (as long-term claims tend to be).
Again, we would have to compare each of the computed ratios to an appropriate benchmark (industry average, peer group average, earlier year figure for Belleville) to meaningfully judge the strength of the company’s liquidity position.
3. The most recently compiled balance sheet for Canton Cosmetics Corporation shows $559,475,000 in total assets, consisting of $313,306,000 in net fixed assets, $159,850,000 in inventory, and $70,437,500 in accounts receivable (along with $15,881,500 in cash & marketable securities). The most recently compiled income statement shows the year’s total sales revenue to have been $391,632,500. What are the indicated total asset turnover, fixed asset turnover, inventory turnover, and receivable turnover ratios? How many days did it take, on average, for the company’s customers to pay for their purchases from Canton (i.e., compute the days’ sales in receivables ratio)?
Type: Computing asset management ratios. Here we are given the sales and various asset values, so the asset management (utilization) ratios are quite easy to compute:
Total Asset Turnover = [pic]= .70 .
Fixed Asset Turnover = [pic]= 1.25 .
Inventory Turnover = [pic]= 2.45 .
Receivable Turnover = [pic]= 5.56 .
We compute inventory turnover as Sales/Inventory, rather than as Cost of Goods Sold/Inventory. Either is a legitimate means of addressing the “lean and mean with respect to holding inventory?” question: Cost of Goods Sold/Inventory suggests how many times the inventory physically “turns over” (is sold and replaced) each year, while Sales/Inventory suggests how much money the firm has to have tied up in inventory at any representative moment to support a year’s worth of sales. We prefer to use the latter version simply for consistency with the other asset turnover ratios; that way each of the turnover ratios we examine is just Sales/(Asset in question).
Next we can compute
Days’ Sales in Receivables =[pic],
which here gives us [pic] 65.65 days.
The days’ sales in receivables ratio provides essentially the same information as the receivable turnover (both are based on the most recent sales and accounts receivable figures), so for most purposes we can use the easier-to-compute receivable turnover to measure whether a company
is “lean and mean” with respect to receivables (i.e., whether it has too much money tied up in receivables relative to sales, such that its customers pay too slowly and owe the company more money than they should). But a useful feature of days’ sales in receivables, also known as the average collection period, is that we can easily interpret it even without an industry average or other benchmark comparison figure. If customers are expected to pay by day 45, while we see that it takes 65.65 days on average for Canton to collect, then there clearly is a problem with excess receivables, regardless of what an industry average or other comparison figure might suggest.
Because ratios can be computed in different ways (there is no universal standard), we have to be sure that whoever computed any benchmark comparison figure we use (such as an industry average) did so with the same equation that we are using in computing our ratios. We could reach some erroneous conclusions if we compared our Sales/Inventory figure with an industry average that some financial company computed with the Cost of Goods Sold/Inventory formula.
4. The most recently compiled income statement for Decatur Digital Dynamics shows $684,000 in earnings before interest and taxes (EBIT) and $106,875 in interest paid. The company’s most recent balance sheet shows total assets of $2,878,000 , paid for with $1,280,710 in debt (liabilities) financing and $1,597,290 in stockholders’ equity. What are the indicated values for the times interest earned ratio, debt ratio, debt/equity ratio, and equity multiplier?
Type: Computing debt management ratios. Here we are directly given all the needed figures for computing the requested debt management (utilization) ratios, so we can simply compute:
Times Interest Earned = [pic] = 6.400 .
Debt Ratio = [pic] = .445 .
Debt/Equity Ratio = [pic] = .802 .
Equity Multiplier = [pic] = 1.802
(by “equity” we mean total stockholders’ equity, the owners’ investment in the company). Thus, based on the most recent year’s operating results, Decatur’s EBIT is more than 6 times as high as the one expense that definitely must be met (after all operating expenses have been paid) to keep the firm out of bankruptcy court: interest to lenders. Of course, to judge whether that cushion is sufficient we would want to look at an appropriate comparison figure, such as the industry average. We can also see that the company finances its operations with about 45% borrowed money; again, to judge whether this figure is appropriate for a company like Decatur we would need a benchmark for comparison. Finally, recall that the equity multiplier must always be debt/equity + 1.0, since debt
+ equity = total assets, and thus
[pic] ( [pic] (here, .802 + 1 = 1.802).
5. The most recently compiled income statement for Effingham Electronic Enterprises shows $11,635,000 in sales; $1,287,500 in earnings before interest and taxes (EBIT); and $616,655 in net income. (The company paid income tax at a 26% average combined federal-plus-state rate.) The most recently assembled balance sheet shows total assets of $7,420,000 ; part has been paid for with $4,180,000 in owners’ equity financing (and the remaining $3,240,000 with borrowed money, or debt). What are the indicated profit margin, return on assets (ROA), return on equity (ROE), and return on invested capital (ROIC) values? If it costs Effingham 10.75% per year, on average, to provide fair financial returns to the lenders and owners who paid for the assets, what is Economic Value Added (EVA)?
Type: Computing profitability ratios. Here we are directly given all the figures needed in computing the various profitability ratios, so we can easily find
Profit Margin = [pic]= .053, or 5.3%.
Return on Assets (ROA) = [pic]= .083, or 8.3%.
Return on Equity (ROE) = [pic]= .148, or 14.8%.
Once again it is difficult for us to judge whether Effingham is delivering appropriate financial returns to its various money providers, because we do not have an industry average or other benchmark figure for making relevant comparisons. Another problem we should note is that ROA, while a widely used measure of financial performance, has a logical flaw: it is a comparison of net income (the financial return to the owners alone) with total assets (the investment made by the owners and lenders together). Thus the mere replacement of some equity financing with debt (which is sometimes, though not always, a good idea), leading to higher interest payments, will typically lead to the odd result of ROA falling even though the operation is no less well managed. We could attempt to address this flaw with a ratio that compares the financial return to the owners and lenders (after accounting for the tax authorities’ share) with the total asset base paid for by the owners and lenders together:
Return on Invested Capital (ROIC) = [pic] = .128, or 12.8%.
A dollar-based figure that relates to ROIC is EVA, which we compute as
EVA = [EBIT (1 – t)] – Cost of delivering fair returns to all money providers
= [$1,287,500 (1 – .26)] – [(.1075) ($7,420,000)]
= $952,750 – $797,650 = $155,100.
According to this measure, in the most recent year the company generated enough revenue to pay its operating costs (reflected in a positive EBIT), pay income taxes, and provide fair financial returns to the lenders and owners, and still have $155,100 left over as an economic profit (which serves as an extra return for the company’s owners).
6. The most recently compiled balance sheet for Freeport Fine Furniture shows $10,350,000 in total assets, paid for with $3,560,400 in debt financing; while the most recently compiled annual income statement shows $9,000,000 in sales, $1,600,000 in earnings before interest and taxes (EBIT), and $844,800 in net income. (The company paid income tax at a 28% average combined state + federal rate.) What are the indicated profit margin, return on assets (ROA), return on equity (ROE), and return on invested capital (ROIC) values?
Type: Computing profitability ratios. Here again we are given the net income, sales, and total asset values, so the profit margin is simply
Profit Margin = [pic]= .0939 or 9.39%,
while return on assets is simply
Return on Assets (ROA) = [pic]= .0816, or 8.16%.
But in this case return on equity is slightly more difficult to compute, because we are not “spoon-fed” the stockholders’ equity figure. But we can quickly compute it as $10,350,000 total assets – $3,560,400 total debt = $6,789,600. So return on equity is
Return on Equity (ROE) = [pic]= .1244, or 12.44%.
And again recall ROA’s logical flaw of comparing the owners’ net income to the owners’ and lenders’ combined investment in assets, which we can address by computing
Return on Invested Capital (ROIC) = [pic] = .1113, or 11.13%.
And, of course, we can draw inferences about Freeport’s strengths or weaknesses only by comparing any of these ratios to an industry average or other appropriate benchmark.
7. The most recently computed balance sheet for Galesburg Glasswork Galleries is as follows:
Cash & Mkt. Securities $ 89,000 Accounts Payable $ 113,000
Accounts Receivable 130,000 Notes Payable 250,000
Inventory 448,000 Long-Term Debt 565,000
Net Fixed Assets 1,550,000 Stockholders’ Equity 1,289,000
Total Assets $2,217,000 Total Claims $2,217,000
Compute the group of ratios (from among those we work with in class) that are based only on balance sheet figures. Why do we have to exercise caution in interpreting ratios that reflect only balance sheet information?
Type: Computing balance sheet ratios. Ratios based only on balance sheet figures are:
Current Ratio = [pic] = 1.837 .
Quick Ratio = [pic] = .603 .
Debt Ratio = [pic] = .419 .
Debt/Equity Ratio = [pic] = .720 .
Equity Multiplier = [pic] = 1.720
(as always, the equity multiplier is 1.0 more than the debt/equity ratio). These ratios relate to a company’s liquidity situation and its capital structure (mix of debt and equity financing). A problem with interpreting balance sheet-based ratios is that the balance sheet is a “snapshot” of the company’s financial situation at one instant in time, so unusual conditions that were present when the snapshot was taken (e.g., if inventory or accounts payable were at seasonally high or low levels) may leave a false impression about the company’s true circumstances.
8. The most recently computed income statement for Harrisburg Handyman’s Hardware is as follows:
Sales $12,200,000
Cost of Goods Sold (including Depreciation) 10,130,000
Earnings Before Interest and Taxes (EBIT) $ 2,070,000
Interest Expense 661,800
Earnings Before Taxes (EBT) $ 1,408,200
Income Taxes 380,200
Net Income $ 1,028,000
Compute the group of ratios (from among those we work with in class) that are based only on income statement figures. If there are 1,285,000 shares of common stock, what are earnings per share (EPS)? Why might ratios based on the income statement be less subject to interpretation problems than are balance sheet-based ratios?
Type: Computing income statement ratios. The only two ratios based solely on income statement figures are:
Times Interest Earned = [pic] = 3.128 times , and
Profit Margin = [pic] = 8.426%.
We can compute earnings per share as
Earnings per Share (EPS) = [pic] = $.80 .
Thus after collecting revenues and paying expenses, the company was able to deliver an 80¢ benefit to each stockholder, for each share owned, over the most recent year. (Part or all of that 80¢ in per-share earnings may have been retained rather than paid out as dividends; we do not have the information to determine the breakdown.)
Finally, because an income statement can be likened to a movie that shows activity over a period of time, the dollar values it shows tend to be less subject to distortion from seasonality or other unusual circumstances than are figures taken from a balance sheet (a snapshot that reflects the conditions of a specific instant). Issues like seasonal patterns lose their importance in measures that include an entire year’s worth of money flows into and out of the company. But we still have to be careful in making interpretations, because the year included in a particular income statement may not have been representative of the firm’s ongoing circumstances (we would not want to conclude that its ability to meet interest payments will continue to be strong just because we computed a high times interest earned ratio, if interest rates were especially low during the year in question). And we always have to remain mindful that financial statements present “book” values based on accrual accounting principles, which in many cases will not be good approximations of the cash flow-based true economic values on which we should make our evaluations and decisions.
9. The most recently computed balance sheet and income statement for Illiopolis Incorporated Industries are:
Cash & Mkt. Securities $ 4,875,000 Accounts Payable $ 1,972,000
Accounts Receivable 5,250,000 Notes Payable 3,225,000
Inventory 8,760,000 Long-Term Debt 9,640,000
Net Fixed Assets 15,220,000 Stockholders’ Equity 19,268,000
Total Assets $34,105,000 Total Claims $34,105,000
Sales $49,560,000
Cost of Goods Sold (including Depreciation) 44,380,000
Earnings Before Interest and Taxes $ 5,180,000
Interest Expense 1,376,000
Earnings Before Taxes $ 3,804,000
Income Taxes (24%) 913,000
Net Income $ 2,891,000
Compute the group of ratios (from among those we work with in class) that are based on both balance sheet and income statement figures. What do such ratios tell us? Why do we have to exercise some caution in interpreting these ratios? If it costs the firm 9.5% per year, on average, to provide fair financial returns to the lenders and owners who have paid for the Illiopolis asset base, what is the company’s Economic Value Added (EVA)?
Type: Computing balance sheet/income statement ratios. The ratios based on both balance sheet and income statement figures are:
Total Asset Turnover = [pic] = 1.453 .
Fixed Asset Turnover = [pic] = 3.256 .
Inventory Turnover = [pic] = 5.658 .
Receivable Turnover = [pic] = 9.440 .
Return on Assets (ROA) = [pic] = 8.477% .
Return on Equity (ROE) = [pic] = 15.004% .
Return on Invested Capital (ROIC) = [pic] = 11.543% .
These ratios compare a “snapshot” figure with a “movie” figure (in more technical terms, they compare a “stock” figure with a “flow” figure). Thus they provide insights into how much of some category of asset or financing must be present, at a representative moment, to support a year’s worth of sales or income. As before when we worked with balance sheet figures, unusual conditions can lead us to erroneous conclusions. For example, a seasonally high or low level of some asset holding (perhaps inventory) when the balance sheet “snapshot” is taken might lead us to think that the company is especially weak or strong in using that asset (or its assets in total) to support a year’s sales or generate a year’s worth of financial returns. Finally, we compute EVA (a dollar-based measure of “economic” profit, which is related to the percentage-based ROIC) as
EVA = [EBIT (1 – t)] – Cost of delivering fair returns to all money providers
= [$5,180,000 (1 – .24)] – [(.095) ($34,105,000)]
= $3,936,800 – $3,239,975 = $696,825.
10. Based on its most recently computed financial statements, Jacksonville Jellies & Jams has a receivable turnover ratio of 7.3. If annual sales shown on the company’s most recent income statement are $38,142,500, what level of accounts receivable is shown on Jacksonville’s most recent balance sheet? What is days’ sales in receivables?
Type: Computing dollar figures from ratios. Here we know that
Receivable Turnover = [pic] = 7.3 .
Therefore accounts receivable must be $38,142,500 ÷ 7.3 = $5,225,000. So holding $5,225,000
in receivables allows the company to support 7.3 times that amount in annual sales, at least as shown by the most recent balance sheet “snapshot” and income statement. We could determine whether
a receivables holding that is 1/7.3 of a year’s sales is good or bad only by looking at an appropriate benchmark, such as the average receivable turnover ratio for all firms in Jacksonville’s industry.
We get similar insights into the receivables vs. sales relationship with days’ sales in receivables:
Days’ Sales in Receivables = [pic] = 50 days.
So it takes 50 days, on average, to collect from a customer after a sale (if we think of all sales as credit sales) has been made. A nice feature of days’ sales in receivables, which is simply 365 ÷ the receivable turnover, is that its value can be useful to us even without an industry average or other benchmark comparison figure. For example, if terms of sale call for all customers to pay no later than 30 days after purchase, and days’ sales in receivables shows that they are collectively paying, on average, on day 50, then the company would seem to have a problem in collecting money it is owed (running 20 days late), regardless of what an industry average might show.
11. The debt ratio (also called total debt ratio or debt to assets ratio) for Kankakee Kitchen Kettles, based on the most recently compiled balance sheet, is 44.3%. If the firm pays for all of its assets with debt and common equity money, what is its debt/equity ratio? Its equity multiplier?
Type: Computing debt management ratios. Here the debt ratio, defined as total debt/total assets, is .443, which we can think of as 44.3/100. So lenders have contributed 44.3¢ (debt money, or liabilities) to buy assets for each 55.7¢ ($1.00 minus 44.3¢) that owners (equity money) have contributed. We can set up a simple right-hand side of a balance sheet to show these proportions:
Total Debt $ .443
Stockholders’ Equity $ .557
Total Claims (= Total Assets) $1.000
With this information we can quickly compute the debt ratio (already known), debt/equity ratio, or equity multiplier:
Debt Ratio = [pic] = .443 .
Debt/Equity Ratio = [pic] = .795 .
Equity Multiplier = [pic] = 1.795
(recall that by “equity” we mean total stockholders’ equity, the amount the owners have contributed, as paid-in capital plus retained earnings, to pay for the firm’s assets). Here lenders provide 44.3% of the money to buy assets, which means they contribute 44.3¢ for every $1.00 – 44.3¢ = 55.7¢ the owners contribute; or think of it as the lenders’ putting up 44.3/55.7 = 79.5% as much money as the owners. As the chapter outline shows, the equity multiplier is always just 1.0 more than the debt/ equity ratio, so if we know either of those ratios we can just add or subtract 1.0 to find the other.
Without constructing Kankakee’s balance sheet, we could simply note that since debt money pays for 44.3% of the asset base (the debt ratio = total debt/total assets = .443), and since debt + equity = 100%, equity money must pay for the other 1 – .443 = .557:
[pic] = 1 – .443 = .557 .
Lenders paid for 44.3% of the company’s assets, so the common stockholders (equity) paid for the other 55.7%. And with these proportions known, we can compute
Debt/Equity Ratio = [pic] = .795 .
And knowing that stockholders’ equity/total assets = .557, we merely take its reciprocal to get total assets/stockholders’ equity:
[pic] ( [pic] = 1.795 .
As noted, it must always be the case that the debt/equity ratio + 1 = the equity multiplier, since debt/equity + equity/equity [which equals 1] = total assets/equity.
12. The debt/equity ratio for Libertyville Laminates, Ltd. based on the most recently compiled balance sheet, is 92%. What are the corresponding debt ratio and equity multiplier? If Libertyville’s return on assets (ROA) is 8.62%, and total stockholders’ equity is $6,207,000, what is the company’s return on equity (ROE)? What are the net income and total asset figures shown on the most recent financial statements?
Type: Computing debt management ratios, other figures. Here the debt/equity ratio, defined as total debt/stockholders’ equity, is .92, which we can think of as 92/100. So lenders have contributed
92¢ (debt money, or liabilities) to buy assets for each 100¢ ($1.00) that owners (equity money) have contributed. We can set up a simple right-hand side of a balance sheet to show these proportions:
Total Debt $ .92
Stockholders’ Equity $1.00
Total Claims (= Total Assets) $1.92
With this information we can quickly compute the debt ratio, debt/equity ratio (already known), or equity multiplier:
Debt Ratio = [pic] = .4792 .
Debt/Equity Ratio = [pic] = .92 .
Equity Multiplier = [pic] = 1.92 .
Here the company’s lenders provide 47.92% of the money to buy assets, which means that they put up 92% as much money as the owners do (or think of it as 47.92¢ from lenders for every $1.00 –47.92¢ = 52.08¢ the owners put up). Again, the equity multiplier is always just 1.0 more than the debt/equity ratio, so if we know either of those we can just add or subtract 1.0 to find the other.
Then, knowing ROA and the equity multiplier, we can easily compute ROE with the DuPont equation:
Return on Equity (ROE) = (Profit Margin x Total Asset Turnover) x Equity Multiplier
= ROA x Equity Multiplier
= .0862 x 1.92 = 16.55%.
Finally, knowing that total stockholders’ equity is $6,207,000 and that ROE = net income/equity = net income/$6,207,000 = 16.55%, it follows that net income = $6,207,000 x .1655 = $1,027,259. And since ROA = net income/total assets = $1,027,259/total assets is .0862, total assets has to be $1,027,259 ÷ .0862 = $11,917,158. (Or just note that if the $6,207,000 in equity constitutes 52.08% of the financing of Libertyville’s assets, then the asset total must be $6,207,000 ÷ .5208 = $11,918,203, a rounding difference from the answer computed above.)
13. The equity multiplier for Metropolis Motorcycle Manufacturing, based on the most recently compiled financial statements, is 1.481. If the company has a 6.25% profit margin and a 1.985 total asset turnover, what it its return on equity (ROE)? What are the company’s debt ratio (also called total debt ratio) and debt/equity ratio?
Type: Computing ROE, debt management ratios. Recall that, based on the DuPont breakdown,
Return on Assets (ROA) = Profit Margin x Total Asset Turnover
Return on Equity (ROE) = (Profit Margin x Total Asset Turnover) x Equity Multiplier
= ROA x Equity Multiplier
(the return on the owners’ investment is determined by the return on the company’s entire asset base, along with the degree to which the owners paid for those assets). Here we are spoon-fed all the needed components (note that ROA is .0625 x 1.985 = 12.41%):
ROE = .0625 x 1.985 x 1.481 = .1241 x 1.481 = 18.37%.
Next, we know total assets/stockholders’ equity (the equity multiplier), and want total debt/total assets (the debt ratio). So to get total assets in the denominator, take the reciprocal of each side:
[pic] = 1.481 ( [pic] = .675 .
Equity (money from the common stockholders) has been used to pay for 67.5% of Metropolis’ assets. Therefore, since equity + debt = 100%, debt (money from various lenders) must have been used to pay for the remaining 100% – 67.5% = 32.5% of the assets. And with the 32.5% debt and 67.5% equity proportions, we can easily compute
Debt/Equity Ratio = [pic] = .481 (as always, equity multiplier – 1 = debt/equity).
14. The return on equity (ROE) for Naperville Natural Nutrients, based on the most recently compiled financial statements, is 12.7%. The income statement shows sales of $3,835,000, while the balance sheet shows $3,250,000 in total assets, $564,000 in current liabilities, and $833,500 in long term debt. Compute Naperville’s debt ratio, equity multiplier, return on assets (ROA), total asset turnover, and profit margin, along with the net income level
we would expect to see on the income statement.
Type: Computing ratios and dollar amounts. Here we can compute the specified values as components of ROE in the DuPont breakdown:
Return on Equity (ROE) = [pic]
= (Profit Margin x Total Asset Turnover) x Equity Multiplier
= ROA x Equity Multiplier.
Total debt (liabilities) shown on the most recent year-end balance sheet “snapshot” was $564,000 current + $833,500 long term = $1,397,500. With total assets of $3,250,000 , the company’s debt ratio is
Debt Ratio = [pic] = 43%.
And with $1,397,500 of the $3,250,000 in assets paid for by lenders (debt), the remaining $3,250,000 – $1,397,500 = $1,852,500 had to be paid for by the owners (equity), for an equity multiplier of $3,250,000 total assets/$1,852,500 equity = 1.754 . (Or note that if debt/total assets is .43, then equity/total assets is 1 – .43 = .57, so total assets/equity must be 1/.57 = 1.754; or that debt/equity is $1,397,500/$1,852,500 = .754, so the equity multiplier must be debt/equity + 1 = 1.754.) So now we can plug in:
ROE = ROA x Equity Multiplier
.127 = ROA x 1.754
ROA = .127 ÷ 1.754 = .0724 or 7.24%.
Next we can easily compute Total Asset Turnover = [pic] = 1.18 .
Plugging figures we now know into the DuPont breakdown for return on assets (ROA), we can proceed as:
Return on Assets (ROA) = [pic]
= Profit Margin x Total Asset Turnover
.0724 = [pic]
.061356 = [pic]
Thus the Profit Margin is 6.1356%, and Net Income is .061356 x $3,835,000 = $235,300 .
Then double-check by computing
Return on Equity (ROE) = [pic]
= [pic] = .061356 x 1.18 x 1.754 = .127 or 12.7%. (
An alternative, perhaps quicker solution to Problem 3 – 14:
Step 1: Note that the DuPont breakdown of ROE is a structure that will help us analyze.
Return on Equity (ROE) = [pic]
Step 2: Plug in values we’re given (or can easily figure out).
[We also know Total Assets – Total Debt = Equity
So $3,250,000 – ($564,000 + $833,500) = $3,250,000 – $1,397,500 = $1,852,500]
So: .127 = [pic]
Step 3: Do some algebra to solve for what we don’t know.
.127 = [pic] x 1.18 x 1.754
.06136 = [pic]
So .061356, or 6.136% is the Profit Margin
.061356 x $3,835,000 = $235,300 is Net Income
1.18 is Total Asset Turnover (shown above)
1.754 is Equity Multiplier (shown above)
[pic]= .0724, or 7.24% is ROA
[pic] = .43, or 43% is Debt Ratio
15. Ottawa Ophthalmological Optics has a current ratio, as computed from the company’s most recent balance sheet, of 1.85, while the corresponding quick ratio is .975. If that most recent balance sheet shows $8,930,000 in total current liabilities, what are the total current asset and inventory figures?
Type: Computing dollar amounts from ratios. Now we know the current and quick ratios, and must use them to “work backwards” in finding various figures that make up the ratios’ numerators. Here we know that
Current Ratio = [pic] = 1.85 .
So current assets has to be $8,930,000 x 1.85 = $16,520,500. We also know that
Quick Ratio = [pic] = .975 .
Cross-multiplying, we find $16,520,500 – Inventory = $8,930,000 x .975
$16,520,500 – Inventory = $8,706,750
Inventory = $16,520,500 – $8,706,750 = $7,813,750.
Let’s double-check: Current Ratio = [pic] = 1.85 . (
Quick Ratio = [pic] = .975 . (
16. Managers at Peoria Paper & Packaging fear they are missing sales opportunities because of stock-outs. They want to buy additional inventory, which they will pay for by increasing accounts payable (borrowing from their suppliers). The most recent balance sheet shows $1,867,500 in current liabilities and $3,943,750 in current assets, $1,162,500 of which is inventory. What current and quick ratios are indicated by those values? If Peoria wants to maintain a current ratio of at least the 1.75 industry average, how much new inventory can it buy? Will the purchase leave Peoria in good standing with its bank, which requires it to have a quick ratio of at least 1.0?
Type: Computing liquidity ratios. Right now Peoria has
Current Ratio = [pic] = 2.112 and
Quick Ratio = [pic] = 1.489 .
The company does not want its current ratio to fall below 1.75. As they add equal amounts to the numerator and denominator of the current ratio formula, the quotient will get smaller (since its beginning level was greater than 1). We find the point at which it will fall from 2.112 to 1.75 by adding an unknown amount $x to both the numerator and denominator of the current ratio equation, setting the quotient equal to 1.75, and solving for $x:
[pic] = 1.75
$3,943,750 + $x = 1.75 ($1,867,500 + $x)
$3,943,750 + $x = $3,268,125 + $1.75x
$675,625 = $.75x
$900,833 = $x.
That is, if the company bought $900,833 worth of inventory and paid for it by increasing its accounts payable, its new current ratio would be
[pic] = 1.75 . (
The portion of the new $4,844,583 current asset level that is inventory would be the $1,162,500 initial amount + the added $900,833 = $2,063,333. The quick ratio at that point would be just barely greater than 1.0:
Quick Ratio = [pic] = 1.004 .
17. Compute the times interest earned (TIE) ratio for Quincy Quality Equipment, whose most recent annual income statement shows a 6.3% profit margin on sales of $11,500,000. The most recent balance sheet shows $8,560,000
in total assets, of which $5,258,000 was paid for with owners’ (equity) money. Quincy pays an 8.8% average annual interest rate on its total debt financing, and a 28% combined average state-plus-federal income tax rate.
Type: Computing times interest earned. Times interest earned is defined as a year’s worth of earnings before interest and taxes (EBIT), divided by a year’s worth of interest paid, or EBIT/Interest, as shown on the most recent year’s income statement. This ratio helps us see whether EBIT seems to provide a sufficient cushion (based on recent operating performance) to pay interest, which is the one expense that always must be paid, after operating expenses have been met, to keep a company out of bankruptcy court. (A lender might also require a borrower to repay a loan early, or to face other unpleasant consequences, if its TIE should fall below a specified minimum.)
To identify a year’s worth of interest payments here, we must first compute total debt financing. With $5,258,000 of the $8,560,000 in total assets paid for with owners’ (equity) money, the remaining $8,560,000 – $5,258,000 = $3,302,000 is paid for by lenders (debt). Therefore interest paid in the most recent year was just $3,302,000 in debt x the 8.8% average annual interest rate = $290,576 and net income was the 6.3% profit margin x $11,500,000 in sales = $724,500. But what was EBIT? Let’s set up the skeleton of an income statement, and plug in the numbers we know so we can solve for EBIT:
Sales $11,500,000
– Cost of Goods Sold ???
= EBIT ???
– Interest $ 290,576
= EBT ???
– Income Tax (28%) ???
= Net Income (6.3% of Sales) $ 724,500
How can we start filling in the blanks? Note that EBT must be an amount such that if 28% is taken away for income tax, the remaining net income will be $724,500:
$x – .28 $x = $724,500
.72 $x = $724,500
$x = $724,500 ÷ .72 = $1,006,250 EBT.
With 28% income tax paid on that EBT, the tax should be .28 x $1,006,250 = $281,750. And EBIT must be such that we can subtract $290,576 from it and end up with $1,006,250; thus EBIT must be $1,006,250 + $290,576 = $1,296,826. And cost of goods sold is $11,500,000 – $1,296,826 = $10,203,174, although we don’t actually need that value for our times interest earned computation. Now that we have EBIT and interest figures, we can compute
Times Interest Earned = [pic] = 4.463 .
And as always, we can use these ratios in judging Quincy’s financial strength only in the presence of an industry average or other appropriate benchmark against which to make meaningful comparisons.
18. Rockford Rotary Razors’ most recent income statement showed $4,895,000 in sales, $2,791,000 in cash-based cost of goods sold, and $970,000 in depreciation expense. Dividends paid to the company’s common stockholders totaled $230,630 in the most recent year. The most recent balance sheet showed $3,360,000 in accumulated retained earnings, while the previous year’s figure was $3,139,970. If Rockford pays income tax at a 26% combined state-plus-federal rate, what is its times interest earned (TIE) ratio ?
Type: Computing times interest earned. Once we get down to EBIT on the income statement, three general “expense” categories remain: interest, income tax, and a return for the company’s owners. Only one of these absolutely has to be met regardless of the firm’s financial circumstances: interest to lenders. (Not income tax, because if taxable income is $0 or negative no income tax is owed – whereas lenders expect to get their promised interest payments, and will sue to get them, no matter how low EBIT is.) Times interest earned, EBIT/Interest, tells how easily, once operating costs have been met, the firm can meet those required interest payments (based on figures from the most recent year’s income statement, which we treat as being representative of the company’s usual situation unless we have reason to think it would not be). Let’s plug the values we know into a simple income statement skeleton:
Sales $4,895,000
– Cash paid in producing/distributing goods 2,791,000
– Depreciation (measure of lost equipment value) 970,000
Earnings Before Interest and Taxes (EBIT) $1,134,000
– Interest (unknown)
Earnings Before Taxes (EBT) (unknown)
– Income Tax (26% of EBT) (26% of EBT)
Net Income (unknown)
Here the $1,134,000 EBIT is easy to compute, since we are given the sales and cash-related cost of goods sold and depreciation figures. But we have to “play detective” to compute the interest expense. Recall that net income, which belongs to the company’s owners, can be either paid to the owners as dividends or else retained by managers as an additional investment from the owners (on which they expect to earn financial returns in the future). Note that last year the company earned enough income to pay total dividends of $230,630. At the same time, accumulated retained earnings shown on the balance sheet rose from $3,139,970 to $3,360,000, for an increase of $220,030 (the amount of earnings retained in the most recent year). So net income had to be enough to allow for both of these amounts, or $230,630 + $220,030 = $450,660. The taxable income (EBT) on which the $450,660 net income was based had to be high enough that the company could pay 26% of the EBT in income tax and still have $450,660 left; thus we can compute EBT as
EBT – .26 EBT = $450,660
EBT (1 – .26) = $450,660
EBT (.74) = $450,660
EBT = $450,660 ÷ .74 = $609,000 ,
with 26% of that amount (.26 x $609,000 = $158,340) paid as income tax. Now let’s plug the newly computed figures into our income statement skeleton:
Sales $4,895,000
– Cash paid in producing/distributing goods 2,791,000
– Depreciation (measure of lost equipment value) 970,000
Earnings Before Interest and Taxes (EBIT) $1,134,000
– Interest (unknown)
Earnings Before Taxes (EBT) $ 609,000
– Income Tax (26% of EBT) 158,340
Net Income $ 450,660
We can see that interest must be the difference between the $1,134,000 EBIT and the $609,000 EBT: $1,134,000 – $609,000 = $525,000. With $1,134,000 EBIT and $525,000 interest, we compute
Times Interest Earned = [pic] = 2.16 .
Whether a TIE of 2.16 indicates a strong or weak position for Rockford depends on the TIE level maintained by similar firms, as evidenced by an industry average or other appropriate benchmark.
19. The total asset turnover, return on assets (ROA), and return on equity (ROE) for Springfield Spring & Sprocket, based on its most recent financial statements, are 2.13 times, 9.9045%, and 23.57%, respectively. What are the company’s profit margin and debt ratio? Base your analysis on the DuPont equation.
Type: DuPont analysis. Any time we think about return on assets (ROA) or return on equity (ROE), we should think in terms of the DuPont equation:
Return on Assets (ROA) = [pic]
= Profit Margin x Total Asset Turnover
Return on Equity (ROE) = [pic]
= (Profit Margin x Total Asset Turnover) x Equity Multiplier
= ROA x Equity Multiplier
DuPont allows us to break important measures (ROA and, especially, ROE) into component parts that can be compared individually against industry averages or other useful benchmarks, to give insights into the areas most in need of improvement. In this case, we know that ROA is 9.9045%, such that
9.9045% = Profit Margin x 2.13
So Profit Margin = 9.9045% ÷ 2.13 = 4.65% .
And we know that ROE is 23.57%, such that
23.57% = 4.65% x 2.13 x Equity Multiplier
So Equity Multiplier = 23.57% ÷ (4.65% x 2.13) = 23.57% ÷ 9.9045% = 2.38 .
With an equity multiplier (total assets/equity) of 2.38, equity/total assets must be 1/2.38 = 42%, so debt/total assets is the other 58% (while debt/equity is 58/42 = 1.38, such that 1 + debt/equity = 1 + 1.38 = the 2.38 equity multiplier).
20. The most recent annual income statement for Taylorville Tachometric Tools shows $71,600,000 in sales and
$9,100,675 in EBIT. The most recent balance sheet shows $61,196,600 in total assets, financed in part with $33,705,000 in debt financing, on which the company pays a 7.5% annual interest rate. Taylorville pays income tax at a 27% combined average state-plus-federal rate. Using the DuPont equation, compute the company’s profit margin, total asset turnover, return on assets (ROA), and return on equity (ROE). What would Taylorville’s return on invested capital (ROIC) be?
Type: DuPont analysis. Here we could do our computations without the DuPont breakdown. However, a benefit of using DuPont is that it allows us to analyze the various components of ROA and ROE individually, to see where the firm’s specific strengths and weaknesses lie (so we can devote the greatest attention to areas most in need of improvement). Under DuPont we compute
Return on Assets (ROA) = [pic]
= Profit Margin x Total Asset Turnover
Return on Equity (ROE) = [pic]
= (Profit Margin x Total Asset Turnover) x Equity Multiplier.
First, we have to compute net income. With EBIT of $9,100,675 and interest expense of .075 x $33,705,000 = $2,527,875, EBT is $9,100,675 – $2,527,875 = $6,572,800. After paying 27% in income tax, TTT is left with the remaining 73% as net income: .73 x $6,572,800 = $4,798,144 (the tax itself is .27 x $6,572,800 = $1,774,656). The profit margin therefore is
Profit Margin = [pic] = .06701 or 6.701%.
The total asset turnover here can be computed with the given values simply as
Total Asset Turnover = [pic] = 1.17 .
With these figures we can compute ROA as that profit margin times the total asset turnover:
ROA = .06701 x 1.17 = .0784 or 7.84%.
With total assets of $61,196,600 and $33,705,000 in debt financing, stockholders’ equity must be $61,196,600 – $33,705,000 = $27,491,600, and thus the equity multiplier is:
Equity Multiplier = [pic] = 2.226 .
So now, with these figures, we can compute ROE as the profit margin times the total asset turnover times the equity multiplier:
ROE = .06701 x 1.17 x 2.226 = .17453 or 17.453%.
Finally, we would compute the company’s return on invested capital (actually we could have computed it first, since all the needed values are directly given in the problem) as
Ret. on Invested Capital (ROIC) = [pic] = 10.856%.
We could judge whether Taylorville is strong or weak financially, and what its problems might be, only if we had industry average or other benchmark values against which to compare the company’s profit margin (measure of cost control), total asset turnover (measure of efficiency in using assets to support sales), and equity multiplier (measure of effective use of debt in paying for assets).
21. After analyzing the most recent financial statements for Urbana United Utilities, you have computed a 6.5% profit margin, a 47.06% debt/equity ratio, and a 12.24% return on equity (ROE). If total assets were $6,300,000, what were the sales and net income figures shown on the most recent income statement, and the stockholders’ equity figure shown on the most recent balance sheet?
Type:DuPont analysis. Here again we want to work with the DuPont breakdown for ROE. Let’s first use the known debt/equity ratio to compute the equity multiplier. If debt/equity is .4706 (which we can represent as .4706/1), then lenders put up 47.06¢ for every $1.00 put up by the owners. So for every $.4706 + $1.00 = $1.4706 in assets, lenders put up $.4706/$1.4706 = 32% (debt ratio), while owners (equity investors) paid for the other $1.00/$1.4706 = 68%. Then we take the reciprocal: with equity/total assets = 68%, total assets/equity must be 1/68% = 1.4706. (Or just add 1 to the debt/equity ratio.) Now we know:
Return on Equity (ROE) = [pic]
= Profit Margin x Total Asset Turnover x Equity Multiplier
= [pic] = .1224
[pic] = .1224 ÷ (.065 x 1.4706) = 1.281
Sales = 1.281 x $6,300,000 = $8,070,300 .
And with a profit margin (net income/sales) of 6.5% on $8,070,300 in sales, Net Income had to be .065 x $8,070,300 = $524,570. Finally, knowing the $6,300,000 total asset figure and the equity multiplier, we can compute
[pic] = 1.4706
Equity = $6,300,000 ÷ 1.4706 = $4,284,000
(or just note that equity money paid for 68% of the $6,300,000 in assets = $4,284,000).
22. Vernon Hills Vulcanized Valves’ most recently compiled income statement shows a 5.8% profit margin on sales of $27,766,500. If you have computed the company’s total asset turnover to be 1.07, what were total assets? If assets were to remain at that level, how much would sales have to increase to raise the total asset turnover to 1.3 ?
Type: Computing dollar values from ratios. Here we are dealing only with the relationship between sales and total assets, which is total asset turnover (the 5.8% profit margin figure here is superfluous information, provided just to see if you would try to use it). The asset level is computed as
Total Asset Turnover = [pic] = 1.07 .
Total Assets = $27,766,500 ÷ 1.07 = $25,950,000 .
Then we consider: how high would sales have to be if assets were to remain at $25,950,000 and the total asset turnover were to rise to 1.3? Management evidently feels that Vandalia should be able to generate more in sales with its asset base (recall that “assets are bad,” in that we should acquire assets only if they will help to enhance the firm’s sales activities). Specifically, the most recent year’s worth of sales was only 1.07 times the $25,950,000 in assets held at the representative moment when the most recent balance sheet “snapshot” was taken. If the coming year’s sales is to be 1.3 times the $25,950,000 asset level, sales will have to be 1.3 x $25,950,000 = $33,735,000.
23. Waukegan Waterproofing & Weatherseal operates with $4,822,069 in total assets, all of which has been paid for with stockholders’ equity (there is no debt financing at this time). The company has an annual return on invested capital (ROIC), based on the most recently computed financial statements, of 11.6%, and it pays a 24% average state plus federal combined annual income tax rate. What is Waukegan’s return on equity (ROE) under its current financing arrangement? What would ROE be if the company moved to a debt ratio of 30% (at which it would pay a 10% annual interest rate) or 60% (with a 16% annual interest rate)?
Type: Computing ROE under various scenarios. Here ROIC = [EBIT (1 – t)]/Total Assets is 11.6%. First we can compute EBIT with the formula
Return on Invested Capital (ROIC) = [pic] = .116
EBIT (.76) = .116 x $4,822,069
EBIT (.76) = $559,360
EBIT= $736,000
Now we can compute Net Income under each of the three levels of debt financing:
No Debt1 30% Debt2 60% Debt3
EBIT $736,000 $736,000 $736,000
– Interest 0 144,662 462,919
= EBT $736,000 $591,338 $273,081
– Income Tax (24%) 176,640 141,921 65,539
= Net Income $559,360 $449,417 $207,542
ROE = [pic] ( [pic] [pic] [pic]
= .1160 = .1331 = .1076
1) With no debt financing there would be no interest to pay, and the entire $4,822,069 in assets would be paid for with stockholders’ equity.
2) With 30% of $4,822,069 = $1,446,621 in debt financing, the company would pay .10 x $1,446,621 = $144,662 in interest. The remaining $4,822,069 – $1,446,621 = $3,375,448 would be financed with stockholders’ equity.
3) With 60% of $4,822,069 = $2,893,241 in debt financing, the company would pay .16 x $2,893,241= $462,919 in interest. The remaining $4,822,069 – $2,893,241 = $1,928,828 would be financed with stockholders’ equity.
Here is what happens. If the entire asset base (all the invested capital) is paid for with equity money, then stockholders’ equity = invested capital, and ROE = ROIC. With a moderate amount (30%) of the assets paid for with debt financing, the smaller remaining equity position gets a higher percentage return. (ROE is increased through the use of “financial leverage” because the after-tax interest rate of .10 x .76 = 7.6% is lower than the 11.6% ROIC, with an income tax savings as an added bonus.) But paying for a substantial amount (60%) of the assets with debt financing leads to a high interest rate and a lower percentage return on equity, even though the equity position is even smaller. (Now ROE is reduced through “financial leverage,” because the .16 x .76 = 12.16% after-tax interest rate paid on the borrowed money exceeds the 11.6% ROIC – which is the same as saying that the 16% before-tax interest rate exceeds the Basic Earning Power [BEP] ratio of EBIT/total assets = $736,000/$4,822,069 = 15.26%.)
24. Financial analysts are forecasting some key ratios for the first year of newly-formed Exeter Executive X-Rays’ operations. The planned capital structure is 49% debt, 51% equity (49% of Exeter’s assets are to be paid for with debt financing; 51% with equity financing). Sales are expected to be $21,250,000, with cost of goods sold of $20,000,000 and a total asset turnover of 3.4. Exeter is expected to pay a 10.2% annual interest rate on borrowed money, and its combined federal-plus-state average income tax rate is expected to be 28%. What should the analysts expect Exeter’s first-year times interest earned (TIE), return on assets (ROA), return on equity (ROE), return on invested capital (ROIC), and economic value added (EVA) to be?
Type: Computing ratios. This is another good “detective” problem. For each of the desired ratios, we have to know expected net income (or at least EBIT). First, we might note that
Total Asset Turnover = [pic] = 3.4 ,
so total assets are expected to be $21,250,000 ÷ 3.4 = $6,250,000. Then with 51% of that asset base paid for with equity financing, we have expected equity = .51 x $6,250,000 = $3,187,500, while expected debt is .49 x $6,250,000 = $3,062,500. With 10.2% annual interest to be paid on borrowed money, total interest payments are expected to be .102 x $3,062,500 = $312,375.
Now we can plug the numbers we know into the skeleton of an expected income statement:
Sales $21,250,000
– Cost of Goods Sold 20,000,000
EBIT $ 1,250,000
– Interest 312,375
= EBT $ 937,625
– Income Tax (28%) 262,535
= Net Income $ 675,090
So now we can compute all of the indicated expected ratios:
Times Interest Earned = [pic] = 4.002 .
Return on Assets (ROA) = [pic] = 10.8014%.
Return on Equity (ROE) = [pic] = 21.179%.
Or we could compute net income as we did, and note that if Equity/Total Assets = 51%, then Total Assets/Equity = 1 ÷ 51% = 1.96078 (the equity multiplier), and use the given total asset turnover of 3.4 to compute ROE with DuPont:
ROE = [pic]= .031769 x 3.4 x 1.96078 = 21.179%.
Recall that a problem with ROA is that it relates the company owners’ financial returns to the investment made by the lenders and owners combined. ROIC, on the other hand, relates the money left for the lenders and owners together, after all other parties (including income taxes) have been paid, to the investment made by the lenders and owners combined:
Return on Invested Capital = [pic] = 14.4%.
Judging strengths or weaknesses by these ratios would require comparisons with industry averages or other appropriate benchmarks, of course.
Finally, in EVA we relate a year’s worth of the money expected to remain for the lenders and owners to what it costs the company annually to deliver fair returns to the lenders and owners. Here the company plans to pay its lenders a 10.2% interest rate, but it will save 28% in income tax on any interest it pays, leaving an after-tax cost of .102 (1 – .28) = 7.344% for debt. With $3,062,500 in debt financing, the cost in dollar terms should be .07344 x $3,062,500 = $224,910. And let’s assume that the owners’ minimum required return on equity is 18%. With $3,187,500 in equity financing, the cost in dollar terms is .18 x $3,187,500 = $573,750; the total expected after-tax cost of delivering fair returns to the lenders and owners thus is $224,910 + $573,750 = $798,660. Thus we can compute
EVA = [EBIT (1 – t)] – Cost of delivering fair returns to all money providers
= [$1,250,000 (1 – .28)] – $798,660
= $900,000 – $798,660 = $101,340
So Exeter is expected to generate enough money in its first year of operations to provide fair financial returns to its lenders and owners, and to have an additional $101,340 as an extra return for the owners (as any residual belongs to the company’s owners).
25. Analysts examining Yorkville Yacht Yard’s most recent financial statements have computed a quick ratio of
.79, current ratio of 1.94, and receivable turnover of 6.8 times. The balance sheet shows $14,000,000 in total assets ($1,160,000 of which is cash & marketable securities) and $3,420,000 in current liabilities. Compute Yorkville’s annual sales, total asset turnover, fixed asset turnover, and inventory turnover.
Type: Computing ratios from dollar figures. This is a nice detective-type problem. It will seem less overwhelming if we take it one step at a time. Because we know that
Current Ratio = [pic] = 1.94 ,
the Current Asset total has to be $3,420,000 x 1.94 = $6,634,800. And because we know that
Quick Ratio = [pic] = .79 ,
it has to be (based on cross-multiplying) that
$6,634,800 – Inventory = .79 x $3,420,000
$6,634,800 – Inventory = $2,701,800
Inventory = $3,933,000 .
Then, because (cash + marketable securities) + accounts receivable + inventory = current assets, which means that $1,160,000 + accounts receivable + $3,933,000 = $6,634,800, accounts receivable must be $6,634,800 – $3,933,000 – $1,160,000 = $1,541,800. And because current assets + fixed assets = total assets, which means that $6,634,800 + fixed assets = $14,000,000, fixed assets must be $14,000,000 – $6,634,800 = $7,365,200.
Next, because Receivable Turnover = [pic] = 6.8
(such that days’ sales in receivables would be 365 ÷ 6.8 = 53.68 days), it has to be that Sales = 6.8 x $1,541,800 = $10,484,240. So with $14,000,000 in total assets we can compute
Total Asset Turnover = [pic] = .749 ,
Fixed Asset Turnover = [pic] = 1.423 ,
and Inventory Turnover = [pic] = 2.666 . Whew!!
26. The following figures were taken, or computed, from Zion Zinc & Zirconium’s most recent financial statements:
Accrued Wages & Taxes $2,140,000 Quick Ratio 1.25
Long Term Debt $3,000,000 Total Asset Turnover 1.85
Paid-In Capital $6,000,000 Inventory Turnover 7.85
Total Assets $15,875,000 Receivable Turnover 12.15
Avg. Income Tax Rate 27.5% Debt/Equity Ratio 88.7%
Times Interest Earned 3.6 Profit Margin 5.2%
Use this information to recreate Zion’s balance sheet and income statement. Treat cash and marketable securities as one combined account, and treat accounts and notes payable as one combined account. There is no separate paid-in capital in excess of par value; paid-in capital consists of a single account (could be called “common stock” since the company is a corporation).
Type: Computing dollar figures from ratios. The best way to attack a problem like this one is to write down the “skeletons” for the balance sheet and income statement, plug in the figures we are given, and solve to fill in the missing pieces. The balance sheet and income statement should ultimately appear as below. Explanations are provided in the footnotes that follow.
Cash & Mkt. Securities 7 $ 3,159,382 Accrued Wages & Taxes (Given) $ 2,140,000
Accounts Receivable 6 2,417,181 Accounts and Notes Payable 2 2,321,250
Inventory 5 3,741,242 Long Term Debt (Given) 3,000,000
Fixed Assets 8 6,557,195 Paid-In Cap. (Common stock, Given) 6,000,000 Retained Earnings 3 2,413,750
Total Assets (Given) $15,875,000 Total Claims 1 $15,875,000
Sales 4 $29,368,750
Cost of Goods Sold 14 26,452,130
Earnings Before Interest and Taxes (EBIT) 13 $ 2,916,620
Interest 12 810,172
Earnings Before Taxes (EBT) 10 $ 2,106,448
Income Taxes (27.5%) 11 579,273
Net Income 9 $ 1,527,175
1) If total assets are $15,875,000 , then total claims have to be $15,875,000 as well.
2) If the debt/equity ratio is 88.7%, then the lenders have invested 88.7¢ for every $1.00 the owners invested. Therefore the debt ratio is $.887/$1.887 = 47%, so total debt must be .47 x $15,875,000 = $7,461,250. If the long term component
of that $7,461,250 is $3,000,000 and accrued wages and taxes total $2,140,000, then accounts & notes payable must be the remaining $7,461,250 – $2,140,000 – $3,000,000 = $2,321,250.
3) So the only missing value on the balance sheet’s right-hand side is retained earnings, which must be $15,875,000 – $7,461,250 – $6,000,000 = $2,413,750. (Or just note that owners’ equity must be 53% of $15,875,000 = $8,413,750, so if paid-in capital is $6,000,000 the remaining $8,413,750 – $6,000,000 = $2,413,750 must be retained earnings.)
4) Total asset turnover = Sales/Total Assets = Sales/$15,875,000 = 1.85. So Sales = 1.85 x $15,875,000 = $29,368,750.
5) Inventory turnover = Sales/Inventory = $29,368,750/Inventory = 7.85. So Inventory = $29,368,750 ÷ 7.85 = $3,741,242.
6) Receivable turnover = Sales/Accounts Receivable = $29,368,750/Accounts Receivable = 12.15. So Accounts Receivable = $29,368,750 ÷ 12.15 = $2,417,181.
7) Quick Ratio = (Cash & Mkt. Sec. + Accounts Receivable)/(Accounts & Notes Payable + Accruals) = (Cash & Mkt. Sec.
+ $2,417,181)/($2,321,250 + $2,140,000) = 1.25. So Cash & Mkt. Sec. + $2,417,181 must equal 1.25 x ($2,321,250 + $2,140,000) = 1.25 x $4,461,250 = $5,576,563. Thus Cash & Mkt. Sec. = $5,576,563 – $2,417,181 = $3,159,382.
8) So Fixed Assets has to be the “plug” figure to make the left-hand side equal to $15,875,000: $15,875,000 – $3,159,382 – $2,417,181 – $3,741,242 = $6,557,195.
9) Since the profit margin = Net Income/Sales = Net Income/$29,368,750 = .052, it must be that Net Income = .052 x $29,368,750 = $1,527,175.
10) If EBT minus 27.5% of EBT = $1,527,175, then 72.5% of EBT = $1,527,175, so EBT = $1,527,175 ÷ .725 = $2,106,448.
11) So income tax is just .275 x $2,443,480 = $579,273.
12) EBIT/INT (times interest earned) is 3.6, so EBIT = 3.6 INT. And EBIT – INT = $2,106,448, so if we restate EBIT as 3.6 INT, then 3.6 INT – INT = $2,106,448. Thus 2.6 INT = $2,106,448, so INT = $2,106,448 ÷ 2.6 = $810,172.
13) And EBIT = 3.6 x $810,172 = $2,916,620 (or just take $2,106,448 + $810,172 = $2,916,620).
14) Finally, Cost of Goods Sold must be the difference between the $29,368,750 in sales and the $2,916,620 EBIT = $26,452,130.
27. The most recent balance sheet and income statement for Illinois Industrial Imports are as follows:
Cash $ 101,000 Accounts Payable $ 1,350,000
Marketable Securities 130,000 Notes Payable 650,000
Accounts Receivable 810,000 Accrued Wages & Taxes 300,000
Inventory 4,820,000 Total Current Liabilities $ 2,300,000
Total Current Assets $ 5,861,000
Long-Term Debt $11,380,000
Total Debt $13,680,000
Gross Plant & Equipment $38,830,000 Paid-In Capital (Common Stock) $ 1,000,000
Less Accum. Depreciation 17,180,000 Paid-in Capital in Excess of Par 10,000,000
Net Plant & Equipment $21,650,000 Retained Earnings 2,831,000
Total Stockholders’ Equity $13,831,000
Total Assets $27,511,000 Total Claims $27,511,000
Sales $35,571,480
Cost of Goods Sold 25,145,400
Depreciation 5,080,000
Earnings Before Interest & Taxes (EBIT) $ 5,346,080
Interest paid 1,422,720
Earnings Before Taxes (EBT) $ 3,923,360
Income Tax (28%) 1,098,541
Net Income $ 2,824,819
Industry average figures for some key ratios are as follows:
Current ratio 2.040
Quick ratio .544
Receivable turnover 43.867
Inventory turnover 10.797
Fixed asset turnover 1.641
Total asset turnover 1.359
Times interest earned 3.735
Debt ratio .499
Debt/equity ratio .997
Equity multiplier 1.997
Profit margin .076
Return on assets (ROA) .104
Return on equity (ROE) .207
Return on invested capital (ROIC) .142
Compute the relevant ratios for Illinois (include the DuPont breakdown), and comment on the company’s strengths and weaknesses.
Type: Comprehensive/interpretation. Relevant ratios to compute are those for which we have meaningful benchmarks against which to make comparisons. Each ratio is shown followed by the industry average in parentheses:
Current Ratio = [pic] = 2.548 (2.040)
Quick Ratio = [pic] = .453 (.544)
Receivable Turnover = [pic] = 43.915 (43.867)
(Days’ sales in receivables would be 365 ÷ 43.915 = 8.31 days for Illinois, 365 ÷ 43.867 = 8.32 days for the industry, so buyers of this type of product seem to pay fairly quickly on average.)
Inventory Turnover = [pic] = 7.380 (10.797)
Fixed Asset Turnover = [pic] = 1.643 (1.641)
Total Asset Turnover = [pic] = 1.293 (1.359)
Times Interest Earned = [pic] = 3.758 (3.735)
Debt Ratio = [pic] = .497 (.499)
Debt/Equity Ratio = [pic] = .989 (.997)
Equity Multiplier = [pic] = 1.989 (1.997)
Profit Margin = [pic] = .079 (.076)
Return on Assets (ROA) = [pic] = .103 (.104)
Return on Equity (ROE) = [pic] = .204 (.207)
Return on Invested Capital (ROIC) = [pic] = .140 (.142)
We can gain further insights into ROA and ROE by looking at their component parts through the DuPont breakdown:
Return on Assets (ROA) = [pic]
= Profit Margin x Total Asset Turnover
= [pic]
= .079412 x 1.292991 = .102680 , or 10.3%
(vs. .076 x 1.359 = 10.4% for the industry on average); and
Return on Equity (ROE) = [pic]
= (Profit Margin x Total Asset Turnover) x Equity Multiplier
= ROA x Equity Multiplier
= [pic]
= .079412 x 1.292991 x 1.989082 = .204238 , or 20.4%
(vs. .076 x 1.359 x 1.997 = 20.7% for the industry on average).
The beauty of DuPont is that it lets us quickly gain insights into a range of issues facing a company by breaking an important problem (understanding ROA or ROE) into smaller parts that can be analyzed and dealt with separately. After completing the DuPont breakdown we can compare each individual ratio that contributes to ROA or ROE with its industry average, or other appropriate benchmark, to better understand what the company is doing well or poorly. For example, if managers want to improve a low ROA, where should they begin?
In the case at hand, the profit margin is slightly higher than the industry average, while total asset turnover is somewhat below the industry average figure. So Illinois would seem to display effective cost control (as suggested by the favorable profit margin), but its excessive holding of assets to support sales (as evidenced by low total asset turnover) keeps ROA just below the industry average. Because the problems relate to holding excessive assets relative to sales, it would be unproductive to try to raise ROA by focusing on cost control issues. This below-average ROA could possibly be transformed into an above-average ROE if Illinois made greater-than-average use of debt financing (for an above-average equity multiplier). But its proportional use of debt financing is actually slightly below the industry average, so the firm is slightly below-average on the ROE measure, as well. Of course, raising ROE with a high equity multiplier is not necessarily a good thing. A company taking this approach would risk future financial problems if, for example, a slight downturn in sales left too few dollars, after operating costs were met, to make the high interest payments owed to lenders under a high-debt capital structure. (The after-tax interest rate that would be paid on the higher amount of borrowed money would have to be less than the company’s ROIC for ROE to rise.)
After using DuPont to gain some general insights, what more specific inferences might we draw by looking at the entire list of ratios? The high current ratio suggests that Illinois’ liquidity position is stronger than that of its competitors, but the low quick ratio suggests a weak liquidity position. A high current ratio coupled with a low quick ratio suggests that the company is heavy in its holding of inventory. (The ratio with inventory in its numerator has a high relative quotient, while the ratio that excludes inventory from its numerator has a low relative quotient.) The idea of too-high inventory is strongly supported by an inventory turnover ratio considerably below the industry average (although the firm is a tiny bit more efficient than average in holding receivables and fixed assets in support of sales, as evidenced by receivable and fixed asset turnovers slightly above the industry averages). With especially heavy holdings in a major asset category (inventory), and only slight relative advantages in the holdings of other assets (receivables, fixed), it is not surprising that the company shows as not being “lean and mean” overall, based on a low total asset turnover.
As noted in the DuPont discussion, Illinois makes slightly less proportional use of debt financing than do its competitors, on average, as shown by debt ratio, debt/equity ratio, and equity multiplier figures that are slightly below the respective industry averages (along with a times interest earned ratio that is, not surprisingly, also slightly higher). And as we saw above, the company must also be efficient at controlling operating expenses, because its profit margin is slightly above the industry average. But return on assets is low; recall that ROA is the product of the profit margin and the total asset turnover, and here the firm’s low total asset turnover holds ROA lower than it would otherwise be. After all, if you hold too much in assets (investors’ money is tied up in things, notably inventory, that just sit around collecting dust) your return on assets (and the more logical return on invested capital, or ROIC, measure) will be low. And ROE can not be above the industry average if ROA and the proportional use of debt financing are both below the industry average.
So overall (and to the extent that the financial statement figures are good representations of economic realities), we have a company that manages its operating expenses well, and that is “lean and mean” (at least as good as its competitors are, in fact a tiny bit better than they are, on average) in its holding of accounts receivable and fixed assets. But it has far too much of investors’ money tied up in inventory for the level of sales it generates. This excessive holding of assets (even though it is just one category) keeps ROA and ROIC below the industry average. ROE for the year in question was also below the industry average, because of the below-average use of debt financing and the accompanying below-average equity multiplier.
28. The most recent balance sheet and income statement for Land of Lincoln Landscaping are as follows:
Cash & Mkt. Securities $ 5,780,000 Accounts Payable $ 2,875,000
Accounts Receivable 8,500,000 Notes Payable 5,650,000
Inventory 10,852,000 Accrued Wages & Taxes 478,000
Total Current Assets $25,132,000 Total Current Liabilities $ 9,003,000
Net Plant & Equipment $29,850,000 Long-Term Debt $11,750,000
Total Stockholders’ Equity $34,229,000
Total Assets $54,982,000 Total Claims $54,982,000
Sales $43,000,000
Cost of Goods Sold (including Depreciation) 34,300,000
Earnings Before Interest & Taxes (EBIT) $ 8,700,000
Interest paid 2,158,312
Earnings Before Taxes (EBT) $ 6,541,688
Income Tax (27%) 1,766,256
Net Income $ 4,775,432
Industry average figures for some key ratios are as follows:
Current ratio 2.314
Quick ratio 1.558
Receivable turnover 4.882
Inventory turnover 6.579
Fixed asset turnover 1.520
Total asset turnover .890
Times interest earned 4.576
Debt ratio .343
Debt/equity ratio .522
Equity multiplier 1.522
Profit margin .103
Return on assets (ROA) .092
Return on equity (ROE) .140
Return on invested capital (ROIC) .118
Compute the relevant ratios for Land of Lincoln (include the DuPont breakdown), and comment on its strengths and weaknesses.
Type: Comprehensive/interpretation. The relevant ratios to compute are those for which we have industry averages or other meaningful benchmarks against which to make comparisons. Each ratio is shown followed by the industry average in parentheses:
Current Ratio = [pic] = 2.792 (2.314)
Quick Ratio = [pic] = 1.586 (1.558)
Receivable Turnover = [pic] = 5.059 (4.882)
Inventory Turnover = [pic] = 3.962 (6.579)
Fixed Asset Turnover = [pic] = 1.441 (1.520)
Total Asset Turnover = [pic] = .782 (.890)
Times Interest Earned = [pic] = 4.031 (4.576)
Debt Ratio = [pic] = .377 (.343)
Debt/Equity Ratio = [pic] = .606 (.522)
Equity Multiplier = [pic] = 1.606 (1.522)
Profit Margin = [pic] = .111 (.105)
Return on Assets (ROA) = [pic] = .087 (.093)
Return on Equity (ROE) = [pic] = .140 (.142)
Return on Invested Capital (ROIC) = [pic] = .116 (.119)
We can gain further insights into ROA and ROE by looking at their component parts through the DuPont breakdown:
Return on Assets (ROA) = [pic]
= Profit Margin x Total Asset Turnover
= [pic]
= .111057 x .782074 = .086854 , or 8.7%
(vs. .105 x .890 = 9.3% for the industry on average); and
Return on Equity (ROE) = [pic]
= (Profit Margin x Total Asset Turnover) x Equity Multiplier
= ROA x Equity Multiplier
= [pic]
= .111057 x .782074 x 1.606299 = .139514 , or 14.0%
(vs. .105 x .890 x 1.522 = 14.2% for the industry on average).
Let’s get some initial insights into Land of Lincoln by looking at DuPont, and then proceed with individual ratios in more detail than we attempted in question 27 above. A peek at the DuPont breakdown shows that the company is well managed in terms of having somewhat better expense control than do its competitors, on average (based on a higher-than-average profit margin); but poorly managed in terms of requiring proportionally more in assets to support its sales level than its competitors do, on average. With overall ROA a bit lower than the industry average, it takes a higher-than-average proportional use of debt financing (evidenced here by the higher-than-average equity multiplier) to end up with ROE right at about the industry average. And note that the greater use of debt financing places the company in a riskier position, since a greater number of borrowed dollars must be “serviced” with interest payments each year to keep Land of Lincoln out of bankruptcy court. [Two additional caveats here: we are assuming that the values shown on the company’s most recent balance sheet and income statement are decent representations of true ongoing economic realities (market values, cash flows), and that an industry-wide average is an appropriate benchmark to use in our comparisons.]
Now let’s take a detailed look at individual ratios. Land of Lincoln’s liquidity position is stronger than that of its competitors, on average, as evidenced by the high current and quick ratios. And because both the current and quick ratios are above the industry average, it might not initially seem that inventory is a current asset held excessively. However, note that the current ratio is 2.792/2.314 = 1.21 times the industry average, whereas the quick ratio is only 1.586/1.558 = 1.02 times the industry average; thus the holding of inventory seems to be somewhat high (the company holds more inventory than it should need to support its sales figure). [The ratio with inventory in its numerator has a high relative quotient, whereas the ratio that excludes inventory from its numerator has a lower relative quotient, just a tiny bit above the benchmark.] The idea of too-high inventory is also supported by an inventory turnover ratio that is only 3.962/6.579 = 60% of the industry average. The company holds slightly less in receivables, relative to sales, than do its competitors on average, as shown by a receivable turnover 5.059/4.882 = 1.04 times the industry average; but also holds slightly more in fixed assets, relative to sales, than competing companies do on average, as shown by a fixed asset turnover just 1.441/1.520 = 95% of the industry average (though these fairly small percentage differences might not seem overly troubling to an analyst). With high inventory holding and a slightly excessive holding of fixed assets, it is not surprising that the firm shows as not being “lean and mean” overall, based on a total asset turnover just .782/.890 = 88% of the benchmark.
Proportional use of debt financing, as shown by a comparison of debt ratios, is .377/.343 = 1.10 times (or 10% higher than) the industry average. (The debt/equity ratio and equity multiplier are, of course, also slightly higher than the respective industry averages.) It is therefore not surprising that times interest earned is only 4.031/4.576 = 88% of the industry average.
At the same time, the company must be fairly efficient at controlling operating expenses, because its profit margin is .111/.105 = 1.06 times (6% higher than) the industry average. Return on assets is a bit low, however; only .087/.093 = 94% of the industry average. Recall that ROA is the product of the profit margin and the total asset turnover, and here the firm’s low total asset turnover holds ROA below the average level. After all, if you hold too much in assets (investors’ money is tied up in things that just sit around collecting dust) your return on assets will be low. And therefore ROIC, which is another asset-based measure, is less than the industry average (though it is .116/.119 = 97% of the average, because ROIC does not directly penalize debt financing). But the company seems to pick up some ground when we look at its return on equity, which is .140/.142 = 99% of the industry average, because with proportionally more debt financing than the average for the industry, Land of Lincoln’s equity multiplier is slightly higher than average.
So overall (and, again, to the extent that the financial statement figures are good representations of economic realities), we have a firm that manages its operating expenses well, and that is a bit more “lean and mean” than are similar firms, on average, in its holding of accounts receivable. But it has too much of investors’ money tied up in (perhaps) fixed assets and (definitely) inventory, for the level of sales it generates, thereby bringing ROA down below the industry benchmark despite the high profit margin. ROE for the year in question was very close to the benchmark only because of the higher relative use of debt financing, which places the company in a risky situation. Recall that
Land of Lincoln’s times interest earned ratio is markedly (approximately 12%) lower than the average for similar firms, meaning that a decline in sales revenue (or upturn in operating costs) could leave the company with too little in EBIT to pay all the interest owed to lenders, possibly leading to bankruptcy. A higher equity multiplier actually results in a higher ROE only if the after-tax rate of return the company earns on its investments (ROIC) exceeds the after-tax interest rate it pays its lenders – arguably a tougher standard to meet as the proportional use of debt financing increases, causing lenders to perceive more risk and demand higher interest rates.
29. Some key ratios computed from Prairie State Precision Pencils’ most recent year’s financial statements, and the corresponding average ratios for Prairie State’s industry, are as follows. What inferences can we draw regarding Prairie State’s recent financial performance?
Ratio Prairie State Industry Average
Current Ratio 2.255 2.243
Quick Ratio 1.459 1.257
Receivable Turnover 8.525 8.469
Inventory Turnover 7.927 6.311
Fixed Asset Turnover 1.970 1.961
Total Asset Turnover 1.156 1.149
Times Interest Earned 6.522 6.286
Debt Ratio .409 .406
Debt/Equity Ratio .692 .682
Equity Multiplier 1.692 1.682
Profit Margin .100 .132
Return on Assets .115 .152
Return on Equity .195 .255
Return on Invested Capital .136 .180
Type: Interpretation. By this stage we can assume that computing ratios is not especially difficult, and can concentrate on interpreting a group of given ratios. Again we assume that the dollar figures shown in the balance sheet are reasonable approximations of true economic/market values, and that the dollar figures shown in the income statement are reasonable approximations of the company’s cash flows. We can start with a DuPont breakdown to get some general insights:
Return on Assets (ROA) = Profit Margin x Total Asset Turnover
.115 = .100 x 1.156
(vs. industry average .152 = .132 x 1.149)
Return on Equity (ROE) = Profit Margin x Total Asset Turnover x Equity Multiplier
.195 = .100 x 1.156 x 1.692
(vs. industry average .255 = .132 x 1.149 x 1.682)
We see that the company ranks low on the ROA and ROE measures. Prairie State is slightly more efficient in using assets to support sales than its competitors are, on average. But it appears to be very inefficient in controlling costs, as shown by the low profit margin (only .100/.132 = 76% of the industry average). This very low profit margin holds ROA down considerably below the industry average, and even ROE is far below average despite an equity multiplier slightly above average.
Looking at specific ratios, we see that Prairie State’s current and quick ratios are both above the industry average figures. So there is no initial indicator that inventory is being held excessively. In fact, the current ratio is only 2.255/2.243 = 1.005 times the industry average, whereas the quick ratio is a much higher 1.459/1.257 = 1.161 multiple of the benchmark. Thus Prairie State’s inventory holding would seem to be unusually low. In fact, the inventory turnover ratio is quite a bit higher than average: 7.927/6.311 = 1.256 times the average for similar firms. A concern might be that Prairie State’s inventory holdings are actually too low, leading to lost sales. But the company does seem to be efficient, overall, in using assets in support of sales.
Then we might ask: with relatively low asset holdings (including the current asset categories of accounts receivable and inventory), how could the current and quick ratios be high? With inventory and accounts receivable both low (the receivable turnover is slightly above average also), a possible explanation for high liquidity ratios would be above average cash and marketable securities holdings (which would contribute to a lower ROA and ROIC, since cash and marketable securities generate very low returns but the investors whose money pays for them have to be compensated). Another possible explanation would be for the company’s holding of current liabilities to be relatively low.
However, since the debt ratio is slightly higher than average, if short term debt is low it must be that Prairie State uses a comparatively high level of long term debt financing. But with higher than average use of debt financing, how could the times interest earned ratio be a little higher than the industry benchmark, especially in light of the low profit margin (suggesting a high cost of goods sold and thus low EBIT)? This outcome could be consistent with Prairie State’s being a heavy user of long term debt financing, and having gotten a comparatively low rate of interest on its long term debt by borrowing at some point in previous years when interest rates were especially low.
30. 21st State Stainless Steel was long viewed as the strongest company in its industry. However, over the past year it has been plagued by complaints from customers, investors, and suppliers; and both its managers and some outside analysts are trying to understand what has gone wrong. What seems to have happened to 21st State?
Ratio Most Recent Year Prior Year
Current Ratio 1.986 2.222
Quick Ratio 1.000 1.111
Receivable Turnover 7.447 8.000
Inventory Turnover 5.000 5.333
Fixed Asset Turnover 1.989 2.000
Total Asset Turnover 1.104 1.143
Times Interest Earned 3.067 3.846
Debt Ratio .514 .464
Debt/Equity Ratio 1.058 .867
Equity Multiplier 2.058 1.867
Profit Margin .054 .065
Return on Assets .060 .074
Return on Equity .123 .138
Return on Invested Capital .088 .100
Type: Interpretation. Here we are using not industry averages, but rather the company’s own past performance, as our benchmark for comparisons. We are assuming that:
• the values shown on the accrual accounting-based financial statements are reasonably representative of the economic realities the company faces (cash flows, market values), and
• we need not be concerned with issues such as inventory treatment or seasonal highs/lows in inventory or receivables, since the balance sheets on which the two years’ ratios have been based are from the same company, and were computed at the same time each year,and thus the ratios are useful decision tools.
We might try to get some general initial insights by looking first at a DuPont breakdown:
Return on Assets (ROA) = Profit Margin x Total Asset Turnover
.060 = .054 x 1.104
(vs. prior year figures .074 = .065 x 1.143)
Return on Equity (ROE) = Profit Margin x Total Asset Turnover x Equity Multiplier
.123 = .054 x 1.104 x 2.058
(vs. prior year figures .138 = .065 x 1.143 x 1.867)
Here we can see that the company has become less efficient both in keeping its costs in check (note the lower profit margin) and in using assets to support sales (as evidenced by the lower total asset turnover). The most recent ROE is also lower than the company’s longer-term experience, despite the greater proportional use of debt financing. We should note that, even though the simple algebra of DuPont shows ROE increasing with a greater use of debt financing, it actually increases only if ROA is not too adversely affected. A higher proportional use of debt financing would, by itself, be expected to reduce the profit margin (and thus ROA), because of the greater number of borrowed dollars on which interest must be paid. Aggravating this problem is that the interest rate is likely to be higher as lenders pay for more of the firm’s asset base, because they perceive more risk. More debt could also be consistent with a lower total asset turnover (thus hurting ROA), if the added borrowing is used to buy unneeded assets. So we seem to have a company that has become inefficient of late, and found it necessary to borrow more money.
Our next step might be to look at percentage changes in all of the ratios since the prior year (looking at proportional differences can be useful no matter what type of benchmark we use):
Ratio Most Recent Year ÷ Prior Year = Ratio as % of Prior Year’s
Current Ratio 1.986 2.222 .894
Quick Ratio 1.000 1.111 .900
Receivable Turnover 7.447 8.000 .931
Inventory Turnover 5.000 5.333 .938
Fixed Asset Turnover 1.989 2.000 .994
Total Asset Turnover 1.104 1.143 .966
Times Interest Earned 3.067 3.846 .798
Debt Ratio .514 .464 1.107
Debt/Equity Ratio 1.058 .867 1.221
Equity Multiplier 2.058 1.867 1.103
Profit Margin .054 .065 .833
Return on Assets .060 .074 .805
Return on Equity .123 .138 .887
Return on Invested Capital .088 .100 .883
Here 21st State’s liquidity position has become less secure, even though the company holds more in some short term assets, relative to sales, than it did in earlier years (the receivable and inventory turnovers are both lower than the representative figures from the previous year). So it must be that cash and marketable security holdings have become quite low, and/or that short term liabilities have risen by an even greater proportion than have short term assets. With the current and quick ratios below the historic figures by similar proportions (each about 10%), it does not seem that inventory holdings have become disproportionately high relative to other asset holdings. Rather, the fact that all the turnovers are below their benchmarks by a few percentage points suggests that the company is a bit heavy in all its asset holdings.
With a profit margin only 83% as high as the benchmark and a total asset turnover only 97% as high, it should not be surprising that ROA is only .83 x .97 = .805 times the historical figure. (The higher proportional holding of assets also causes the asset-based return on invested capital, or ROIC, ratio to be low, although it is a higher 88% of the prior year’s standard. ROIC treats interest as a return to investors rather than as a cost, so its value does not change materially simply because a firm replaces owners’ money with lenders’ money.) And with ROA about 20% lower than the benchmark while the equity multiplier is only about 10% higher, it should not be surprising that ROE is only .805 x 1.103 = .887 times as high as the figure that reflects the company’s longer term experience. (The higher use of debt financing is shown in debt ratio, debt/equity ratio, and equity multiplier figures higher than those seen historically, and a lower times interest earned.)
So here it seems that we have a company with more money tied up in assets than it should need based on its sales. It has paid for part of the asset buildup by increasing its proportional use of debt financing (shown in the higher debt ratio and lower times interest earned). It has also faced increased costs (shown in the lower profit margin), part of which probably reflects higher interest costs on the additional money borrowed to pay for the unneeded increase in assets. And part of these added costs may still be owed (as shown in the buildup of short term liabilities that help bring about the lower current and quick ratios – consistent with complaints from suppliers, who are being paid less quickly than they would like). Perhaps 21st State invested in additional assets to support a higher expected sales level, and then the sales growth never materialized. Stagnant sales would be consistent with problems like product defects, which would lead to complaints from customers.
31. Mississippi-Ohio-Wabash (MOW) Lawn Products’ income statement and balance sheet for the year just ended are as follows:
Income Statement: For Most Recent Year ($ thousands)
Sales $8,850
Cost of Producing & Distributing Goods 6,372
Operating Income $2,478
Minus Interest 885
Taxable Income $1,593
Minus Income Tax (26% average rate) 414
Net Income $1,179
Dividends Paid $ 602
Earnings Retained $ 577
Balance Sheet: As of End of Most Recent Year ($ thousands)
Cash & Marketable Securities $ 708
Accounts Receivable 1,062
Inventory 2,124
Net Fixed Assets (plant & equipment) 5,487
Total Assets $9,381
Accounts Payable & Accruals $1,416
Notes Payable 1,200
Long-term Debt 2,000
Paid-In Capital 4,000
Retained Earnings 765
Total Claims $9,381
Sales in the coming year are forecast to be $10,089. Use the percentage of sales approach to compute additional (or external) financing needed (called AFN or EFN). Assume that all costs, all assets, and accounts payable & accruals vary directly with sales. Also assume that the average income tax rate and the dividend payout ratio (the proportion of income paid to common stockholders as dividends) are expected to be the same each year.
Type: Forecasting with Percentage of Sales Method. In the percentage of sales method, we assume that several key financial values vary directly, from year to year, with the company’s sales level. It makes sense to assume that most costs, and at least some assets (cash, receivables, inventory), will tend to vary with sales, and that accounts payable & accruals will as well. (We assume that other “right-hand side” values will not vary directly with sales, since other sources of financing require explicit negotiation with investors and do not simply increase spontaneously in the ordinary course of doing more business.) If we assume that net fixed assets will also change proportionally with sales, then we are implicitly making two additional assumptions: that fixed assets are already being used
to capacity (such that we could not produce more goods or services without holding more in fixed assets), and that fixed assets can be added in exactly the desired proportions (rather than the “lumpy” additions that would sometimes be necessary; for example, if sales increased by 10% it might be difficult to add exactly 10% more building or machinery capacity). Let’s look first at the percentages indicated by the most recent year’s activities:
Income Statement: For Most Recent Year ($ thousands)
Sales $8,850
Cost of Producing & Distributing Goods 6,372 (72% of Sales)
Operating Income $2,478
Minus Interest 885 (10% of Sales)
Taxable Income $1,593
Minus Income Tax (26% average rate) 414 (26% of Taxable Income)
Net Income $1,179
Dividends Paid $ 602 (51% of Net Income)
Earnings Retained $ 577 (49% of Net Income)
Balance Sheet: As of End of Most Recent Year ($ thousands)
Cash & Marketable Securities $ 708 ( 8% of Sales)
Accounts Receivable 1,062 (12% of Sales)
Inventory 2,124 (24% of Sales)
Net Fixed Assets (plant & equipment) 5,487 (62% of Sales)
Total Assets $9,381
Accounts Payable & Accruals $1,416 (16% of Sales)
Notes Payable 1,200
Long-term Debt 2,000
Paid-In Capital 4,000
Retained Earnings 765
Total Claims $9,381
If the indicated percentages remain intact as we move to the expected higher $10,089 level of sales, then our financial statements a year from now should show:
Income Statement: Projected (“Pro Forma”) For Coming Year ($ thousands)
Sales $10,089
Cost of Producing & Distributing Goods 7,264 (72% of Sales)
Operating Income $2,825
Minus Interest 1,009 (10% of Sales)
Taxable Income $1,816
Minus Income Tax (26% average rate) 472 (26% of Taxable Income)
Net Income $1,344
Dividends Paid $ 685 (51% of Net Income)
Earnings Retained $ 659 (49% of Net Income)
Balance Sheet: Projected (“Pro Forma”) for End of Coming Year ($ thousands)
Cash & Marketable Securities $ 807 ( 8% of Sales)
Accounts Receivable 1,211 (12% of Sales)
Inventory 2,421 (24% of Sales)
Net Fixed Assets (plant & equipment) 6,255 (62% of Sales)
Total Assets $10,694
Accounts Payable & Accruals $1,614 (16% of Sales)
Notes Payable (preliminary) 1,200 (assuming no change)
Long-term Debt (preliminary) 2,000 (assuming no change)
Paid-In Capital (preliminary) 4,000 (assuming no change)
Retained Earnings 1,424 (initial $765 + new $659)
Total Claims (preliminary) $10,238
Sales are expected to rise to $10,089/$8,850 = 1.14 times, or 14% greater than, the most recent year’s level. Thus the coming year’s expected asset total must be 1.14 times the most recent year’s $9,381 level, or 1.14 x $9,381 = $10,694. However, the preliminary figure for total claims is not $10,694; it is lower (by $10,694 – $10,238 = $456). Recall that we made an initial assumption that notes payable, long-term debt, and paid-in capital would remain at the earlier year’s level. Why? Because we have to go out and negotiate for funds from these sources, so it makes sense initially to treat these categories as unchanging. But now we can see that spontaneous internal sources of money (increases in accounts payable & accruals as we place more orders from suppliers and have our employees working more hours, plus new earnings that will be retained) will not provide enough financing to fully pay for the higher asset total needed. The remaining $456 is additional (or external) financing needed, money we have to negotiate with new lenders or owners to provide.
So here is what is expected to happen. If sales rise, then MOW will have to hold more in assets to support that higher level of business activity. But we won’t have to go begging investors for enough money to pay for the entire addition to the asset base. First, the increase in one type of asset (raw material inventory) should be paid for, initially, with a spontaneous increase in accounts payable: our promise to pay higher amounts to our suppliers at a later date. Second, the higher level of sales should lead spontaneously to our earning a higher net income; we will retain part (here, 49%) of that higher income level and use it to pay for some more of the asset growth. What is not paid for through these spontaneous sources is additional financing needed (AFN), an extra amount that MOW must obtain from external sources located through the financial marketplace.
MOW will borrow this $456 from short-term lenders (such as banks), borrow it from long-term lenders (bondholders), or obtain it from new owners (obtaining additional paid-in capital by selling new shares of common stock). Or it could use some combination of these potential financing sources. (It would actually have to raise slightly more than $456,000 so it would be left with $456,000 after providing the new money providers with their first year’s interest and/or dividend payments.) The type(s) of financing chosen would reflect capital structure (debt/equity) issues, market conditions (such as interest rate levels), and practical considerations (firms usually raise small amounts by borrowing from local lenders, because the complex formal process of creating new bonds or shares of stock is expensive and thus typically reserved for really large transactions).
Finally, those analyzing MOW’s performance would use the projected income statement and balance sheet to compute various ratios to see whether the expected changes would leave the firm with problems in its liquidity, asset utilization, debt utilization, or profitability.
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