Accounting Articles

Article / Updated 10-06-2022

After you estimate the population regression line, you can check whether the regression equation makes sense by using the coefficient of determination, also known as R2 (R squared). This is used as a measure of how well the regression equation actually describes the relationship between the dependent variable (Y) and the independent variable (X). It may be the case that there is no real relationship between the dependent and independent variables; simple regression generates results even if this is the case. It is, therefore, important to subject the regression results to some key tests that enable you to determine if the results are reliable. The coefficient of determination, R2, is a statistical measure that shows the proportion of variation explained by the estimated regression line. Variation refers to the sum of the squared differences between the values of Y and the mean value of Y, expressed mathematically as R2 always takes on a value between 0 and 1. The closer R2 is to 1, the better the estimated regression equation fits or explains the relationship between X and Y. The expression is also known as the total sum of squares (TSS). This sum can be divided into the following two categories: Explained sum of squares (ESS): Also known as the explained variation, the ESS is the portion of total variation that measures how well the regression equation explains the relationship between X and Y. You compute the ESS with the formula Residual sum of squares (RSS): This expression is also known as unexplained variation and is the portion of total variation that measures discrepancies (errors) between the actual values of Y and those estimated by the regression equation. You compute the RSS with the formula The smaller the value of RSS relative to ESS, the better the regression line fits or explains the relationship between the dependent and independent variable. Total sum of squares (TSS): The sum of RSS and ESS equals TSS. R2 is the ratio of explained sum of squares (ESS) to total sum of squares (TSS): You can also use this formula: Based on the definition of R2, its value can never be negative. Also, R2 can't be greater than 1, so With simple regression analysis, R2 equals the square of the correlation between X and Y. The coefficient of determination is used as a measure of how well a regression line explains the relationship between a dependent variable (Y) and an independent variable (X). The closer the coefficient of determination is to 1, the more closely the regression line fits the sample data. The coefficient of determination is computed from the sums of squares. These calculations are summarized in the following table. To compute ESS, you subtract the mean value of Y from each of the estimated values of Y; each term is squared and then added together: To compute RSS, you subtract the estimated value of Y from each of the actual values of Y; each term is squared and then added together: To compute TSS, you subtract the mean value of Y from each of the actual values of Y; each term is squared and then added together: Alternatively, you can simply add ESS and RSS to obtain TSS: TSS = ESS + RSS = 0.54 + 0.14 = 0.68 The coefficient of determination (R2) is the ratio of ESS to TSS: This shows that 79.41 percent of the variation in Y is explained by variation in X. Because the coefficient of determination can't exceed 100 percent, a value of 79.41 indicates that the regression line closely matches the actual sample data.

Article / Updated 09-22-2022

You can use the Central Limit Theorem to convert a sampling distribution to a standard normal random variable. Based on the Central Limit Theorem, if you draw samples from a population that is greater than or equal to 30, then the sample mean is a normally distributed random variable. To determine probabilities for the sample mean the standard normal tables requires you to convert to a standard normal random variable. The standard normal distribution is the special case where the mean equals 0, and the standard deviation equals 1. For any normally distributed random variable X with a mean and a standard deviation you find the corresponding standard normal random variable (Z) with the following equation: For the sampling distribution of the corresponding equation is As an example, say that there are 10,000 stocks trading each day on a regional stock exchange. It's known from historical experience that the returns to these stocks have a mean value of 10 percent per year, and a standard deviation of 20 percent per year. An investor chooses to buy a random selection of 100 of these stocks for his portfolio. What's the probability that the mean rate of return among these 100 stocks is greater than 8 percent? The investor's portfolio can be thought of as a sample of stocks chosen from the population of stocks trading on the regional exchange. The first step to finding this probability is to compute the moments of the sampling distribution. Compute the mean: The mean of the sampling distribution equals the population mean. Determine the standard error: This calculation is a little trickier because the standard error depends on the size of the sample relative to the size of the population. In this case, the sample size (n) is 100, while the population size (N) is 10,000. So you first have to compute the sample size relative to the population size, like so: Because 1 percent is less than 5 percent, you don't use the finite population correction factor to compute the standard error. Note that in this case, the value of the finite population correction factor is: Because this value is so close to 1, using the finite population correction factor in this case would have little or no impact on the resulting probabilities. And because the finite population correction factor isn't needed in this case, the standard error is computed as follows: To determine the probability that the sample mean is greater than 8 percent, you must now convert the sample mean into a standard normal random variable using the following equation: To compute the probability that the sample mean is greater than 8 percent, you apply the previous formula as follows: Because these values are substituted into the previous expression as follows: You can calculate this probability by using the properties of the standard normal distribution along with a standard normal table such as this one. Standard Normal Table — Negative Values Z 0.00 0.01 0.02 0.03 –1.3 0.0968 0.0951 0.0934 0.0918 –1.2 0.1151 0.1131 0.1112 0.1093 –1.1 0.1357 0.1335 0.1314 0.1292 –1.0 0.1587 0.1562 0.1539 0.1515 The table shows the probability that a standard normal random variable (designated Z) is less than or equal to a specific value. For example, you can write the probability that (one standard deviation below the mean) as You find the probability from the table with these steps: Locate the first digit before and after the decimal point (–1.0) in the first (Z) column. Find the second digit after the decimal point (0.00) in the second (0.00) column. See where the row and column intersect to find the probability: Because you're actually looking for the probability that Z is greater than or equal to –1, one more step is required. Due to the symmetry of the standard normal distribution, the probability that Z is greater than or equal to a negative value equals one minus the probability that Z is less than or equal to the same negative value. For example, This is because are complementary events. This means that Z must either be greater than or equal to –2 or less than or equal to –2. Therefore, This is true because the occurrence of one of these events is certain, and the probability of a certain event is 1. After algebraically rewriting this equation, you end up with the following result: For the portfolio example, The result shows that there's an 84.13 percent chance that the investor's portfolio will have a mean return greater than 8 percent.

Article / Updated 09-15-2022

Financial statement fraud, commonly referred to as "cooking the books," involves deliberately overstating assets, revenues, and profits and/or understating liabilities, expenses, and losses. When a forensic accountant investigates business financial fraud, she looks for red flags or accounting warning signs that indicate suspect business accounting practices. These red flags include the following: Aggressive revenue recognition practices, such as recognizing revenue in earlier periods than when the product was sold or the service was delivered Unusually high revenues and low expenses at period end that can't be attributed to seasonality Growth in inventory that doesn't match growth in sales Improper capitalization of expenses in excess of industry norms Reported earnings that are positive and growing but operating cash flow that's declining Growth in revenues that's far greater than growth in other companies in the same industry or peer group Gross margin or operating margins out of line with peer companies Extensive use of off–balance sheet entities based on relationships that aren't normal in the industry Sudden increases in gross margin or cash flow as compared with the company's prior performance and with industry averages Unusual increases in the book value of assets, such as inventory and receivables Disclosure notes so complex that it's impossible to determine the actual nature of a particular transaction Invoices that go unrecorded in the company's financial books Loans to executives or other related parties that are written off A business that engages in such fraudulent practices stands to lose a tremendous amount of money when penalties and fines, legal costs, the loss of investor confidence, and a tarnished reputation are taken into account.

Cheat Sheet / Updated 09-02-2022

As a business manager or owner, taking care of your company’s accounting needs is a top priority. Correctly preparing financial statements, financial analyses, and accounting reports involves knowing all the financial data and information that needs to appear in these items. Making a profit helps keep you in business, while maintaining a strong balance sheet ensures you can stay in business. So, make sure you understand the financial statements, record adjustments if needed, and follow some basic rules for presenting accounting information to your business’s managers, owners, investors, and creditors.

Article / Updated 08-19-2022

You can compare reading a business’s financial report with shucking an oyster: You have to know what you’re doing and work to get at the meat. You need a good reason to pry into a financial report. The main reason to become informed about the financial performance and condition of a business is because you have a stake in the business. The financial success or failure of the business makes a difference to you. Get in the right frame of mind You don’t have to be a math wizard or rocket scientist to extract the essential points from a financial report. You can find the bottom line in the income statement and compare this profit number with other relevant numbers in the financial statements. You can read the amount of cash in the balance sheet. If the business has a zero or near-zero cash balance, you know that this is a serious — perhaps fatal — problem. Get in the right frame of mind. Don’t let a financial report bamboozle you. Locate the income statement, find bottom-line profit (or loss!), and get going. You can do it! Decide what to read Suppose you want more financial information than you can get in news articles. The annual financial reports of public companies contain lots of information: a letter from the chief executive, a highlights section, trend charts, financial statements, extensive footnotes to the financial statements, historical summaries, and a lot of propaganda. In contrast, the financial reports of most private companies are significantly smaller; they contain financial statements with footnotes and not much more. You could read just the highlights section and let it go at that. This might do in a pinch. You should read the chief executive’s letter to shareowners as well. Ideally, the letter summarizes in an evenhanded and appropriately modest manner the main developments during the year. Be warned, however, that these letters from the top dog often are self-congratulatory and typically transfer blame for poor performance on factors beyond the control of the managers. Read them, but take these letters with a grain of salt. Many public businesses release a condensed summary version in place of their much longer and more detailed annual financial reports. The scaled-down, simplified, and shortened versions of annual financial reports are adequate for average stock investors. They aren’t adequate for serious investors and professional investment managers. These investors and money managers should read the full-fledged financial report of the business, and they perhaps should study the company’s annual 10-K report that is filed with the Securities and Exchange Commission (SEC). Improve your accounting savvy Financial statements — the income statement, balance sheet, and statement of cash flows — are the core of a financial report. To make sense of financial statements, you need at least a rudimentary understanding of financial statement accounting. You don’t have to be a CPA, but the accountants who prepare financial statements presume that you’re familiar with accounting terminology and financial reporting practices. If you’re an accounting illiterate, the financial statements probably look like a Sudoku puzzle. There’s no way around this demand on financial report readers. After all, accounting is the language of business. Judge profit performance A business earns profit by making sales and by keeping expenses less than sales revenue, so the best place to start in analyzing profit performance is not the bottom line but the top line: sales revenue. Here are some questions to focus on: How does sales revenue in the most recent year compare with the previous year’s? What is the gross margin ratio of the business? Based on information from a company’s most recent income statement, how do gross margin and the company’s bottom line (net income, or net earnings) compare with its top line (sales revenue)? One last point: Put a company’s profit performance in the context of general economic conditions. Test earnings per share (EPS) against change in bottom line As you know, public companies report net income in their income statements. Below this total profit number for the period, public companies also report earnings per share (EPS), which is the amount of bottom-line profit for each share of its stock. Strictly speaking, therefore, the bottom line of a public company is its EPS. Private companies don’t have to report EPS; however, the EPS for a private business is fairly easy to calculate: Divide its bottom-line net income by the number of ownership shares held by the equity investors in the company. The market value of ownership shares of a public company depends mainly on its EPS. Individual investors obviously focus on EPS, which they know is the primary driver of the market value of their investment in the business. The book value per share of a private company is the closest proxy you have for the market value of its ownership shares. The higher the EPS, the higher the market value for a public company. And the higher the EPS, the higher the book value per share for a private company. Now, you would naturally think that if net income increases, say, 10 percent over last year, then EPS would increase 10 percent. Not so fast. EPS — the driver of market value and book value per share — may change more or less than 10 percent: Less than 10 percent: The business may have issued additional stock shares during the year, or it may have issued additional management stock options that get counted in the number of shares used to calculate diluted EPS. The profit pie may have been cut up into a larger number of smaller pieces. How do you like that? More than the 10 percent: The business may have bought back some of its own shares, which decreases the number of shares used in calculating EPS. This could be a deliberate strategy for increasing EPS by a higher percent than the percent increase in net income. Compare the percent increase/decrease in total bottom-line profit over last year with the corresponding percent increase/decrease in EPS. Why? Because the percent changes in EPS and profit can diverge. For a public company, use its diluted EPS if it’s reported. Otherwise, use its basic EPS. Tackle unusual gains and losses Many income statements start out normally: sales revenue less the expenses of making sales and operating the business. But then there’s a jarring layer of unusual gains and losses on the way down to the final profit line. This could be the result of a flooded building or a lawsuit. What’s a financial statement reader to do when a business reports such unusual, nonrecurring gains and losses in its income statement? There’s no easy answer to this question. You could blithely assume that these things happen to a business only once in a blue moon and should not disrupt the business’s ability to make profit on a sustainable basis. Think of this as the earthquake mentality approach: When there’s an earthquake, there’s a lot of damage, but most years have no serious tremors and go along as normal. Unusual gains and losses are supposed to be nonrecurring in nature and recorded infrequently. In actual practice, however, many businesses report these gains and losses on a regular and recurring basis — like having an earthquake every year or so. Check cash flow from profit The objective of a business is not simply to make profit but to generate cash flow from making profit as quickly as possible. Cash flow from making profit is the most important stream of cash inflow to a business. A business could sell off some assets to generate cash, and it can borrow money or get shareowners to put more money in the business. But cash flow from making profit is the spigot that should always be turned on. A business needs this cash flow to make cash distributions from profit to shareowners, to maintain liquidity, and to supplement other sources of capital to grow the business. The income statement does not — this bears repeating, does not — report the cash inflows of sales and the cash outflows of expenses. Therefore, the bottom line of the income statement is not a cash flow number. The net cash flow from the profit-making activities of the business (its sales and expenses) is reported in the statement of cash flows. When you look there, you’ll undoubtedly discover that the cash flow from operating activities (the official term for cash flow from profit-making activities) is higher or lower than the bottom-line profit number in the income statement. Look for signs of financial distress A business can build up a good sales volume and have very good profit margins, but if the company can’t pay its bills on time, its profit opportunities could go down the drain. Solvency refers to a business’s prospects of being able to meet its debt and other liability payment obligations on time, in full. Solvency analysis looks for signs of financial distress that could cause serious disruptions in the business’s profit-making operations. Even if a business has a couple billion bucks in the bank, you should ask, “How does its solvency look? Is there any doubt it can pay its bills on time?” Recognize the possibility of restatement and fraud When a business restates its original financial report and issues a new version, it doesn’t make restitution for any losses that investors suffered by relying on the originally reported financial statements. In fact, few companies even say they’re sorry when they put out revised financial statements. All too often, the reason for the restatement is that someone later discovered that the original financial statements were based on fraudulent accounting. Frankly speaking, CPAs don’t have a very good track record for discovering financial reporting fraud. What it comes down to is this: Investors take the risk that the information in the financial statements they use in making decisions is subject to revision at a later time. Remember the limits of financial reports There’s a lot more to investing than reading financial reports. Financial reports are an important source of information, but investors also should stay informed about general economic trends and developments, political events, business takeovers, executive changes, technological changes, and much more. When you read financial statements, keep in mind that these accounting reports are somewhat tentative and conditional. Accountants make many estimates and predictions in recording sales revenue and income and recording expenses and losses. Some soft numbers are mixed in with hard numbers in financial statements. In short, financial statements are iffy to some extent. There’s no getting around this limitation of accounting.

Article / Updated 08-11-2022

In cost accounting, the cost of goods available for sale represents the product’s total costs. Total costs have two components — joint costs and separable costs. When possible, you want to reduce separable costs, but first take a look at your company’s joint costs. Assume you manufacture leaf blowers. Your two products are heavy-duty blowers and yardwork blowers. The separable costs are $1,200,000 for the heavy-duty blower and $912,000 for the yardwork blower. If you know the separable costs and the cost of goods available for sale, you can compute the joint cost allocation. This table shows the process. Joint Cost Allocation Heavy-Duty Yardwork Total Cost of goods available for sale $1,751,163 $1,260,837 $3,012,000 Less separable costs $1,200,000 $912,000 $2,112,000 Equals joint cost allocation $551,163 $348,837 $900,000 Each company division provides the separable costs. So altogether, this table gives you a joint cost allocation. Now assume that the heavy-duty blower division is able to sharply reduce its separable costs to an amazingly low $500,000. The first table listed heavy-duty separable costs of $1,200,000. Consider what now happens to heavy-duty’s joint cost allocation. Take a look at the next table. Cost Allocation — Less Heavy Duty Separable Costs Heavy-Duty Yardwork Total Cost of goods available for sale $1,751,163 $1,260,837 $3,012,000 Less separable costs $500,000 $912,000 $1,412,000 Equals joint cost allocation $1,251,163 $348,837 $1,600,000 Heavy-duty’s joint cost allocation increases to $1,251,163 (from $551,163). That doesn’t seem right. The goal is to analyze costs to reduce or eliminate them. If you do, supposedly you increase your profits. In this case, the heavy-duty division’s reducing separable costs increased its joint cost allocation. There doesn’t seem to be a benefit to operating more efficiently. Here’s an explanation: The gross margin percentage method (calculated as gross margin ÷ total sales value x 100) locks in total costs as a percentage of sales value. If the gross margin is about 12.5 percent of sales value, it means that costs must be about 87.5 percent of sales value. For heavy-duty, that 87.5 percent total cost number is $1,751,163. Those costs are either separable or joint costs. If one increases, the other decreases. The heavy-duty manager may have a problem with this process. The manager works hard (using good old cost accounting) to lower the separable costs. The manager’s “reward” is a higher joint cost allocation. The heavy-duty division has lowered costs but doesn’t get any savings in total costs. The constant gross margin percentage method clarifies the revenue and profit calculations company-wide. This method eliminates some of the variation between company divisions. Although some managers may complain, each division has the same gross margin percentage. The process makes managing company profit easier. This is one of those “Here’s why the chief financial officer (CFO) makes the big bucks” moments. As CFO, you explain the gross margin percentage method to the heavy-duty division manager. The goal is to allocate joint costs so that each product maintains the same gross margin percentage of about 12.5 percent. If a division reduces separable costs, it must get a bigger joint cost allocation — otherwise, the gross margin percentage would increase. Now heavy-duty’s manager should be evaluated based on the successful cost reduction. The manager had a success, and you want to encourage more cost savings. Although the gross margin percentage process requires a bigger joint cost allocation, that must not take away from the manager’s good performance.

Article / Updated 08-11-2022

In cost accounting, the cost of goods available for sale represents the product’s total costs. Total costs have two components — joint costs and separable costs. Assume the cost of goods available for sale are $1,751,163 and $1,260,837 for the heavy-duty blower and the yardwork blower. Say the separable costs are $1,200,000 and $912,000. If you know the separable costs and the cost of goods available for sale, you can compute the joint cost allocation. The first table shows the process. Joint Cost Allocation Heavy-Duty Yardwork Total Cost of goods available for sale $1,751,163 $1,260,837 $3,012,000 Less separable costs $1,200,000 $912,000 $2,112,000 Equals joint cost allocation $551,163 $348,837 $900,000 Each company division provides the separable costs. So altogether, the table gives you a joint cost allocation. Now calculate the gross margin percentage. Say your sales values are $2,000,00 and $1,440,000 for heavy-duty and yardwork blowers. The total cost is the cost of goods available for sale from the first table. The gross margin percentage is the gross margin divided by the sales value. For each product, the gross margin percentage is the same (12.442 percent) as the company’s overall gross margin. Verifying Gross Margin Percentage Heavy-Duty Yardwork Total Sales value (A) $2,000,000 $1,440,000 $3,440,000 Total cost (B) $1,751,163 $1,260,837 $3,012,000 Gross margin (A – B) $248,837 $179,163 $428,000 Gross margin percentage 12.442 12.442 Here’s the point of this table: it uses the traditional formula to compute gross margin and gross margin percentage. The table verifies that the calculations are correct. If the heavy-duty product has the higher sales value, it ends up with a higher gross margin in dollars than the yardwork product. However, both sale values are multiplied by the same gross margin percentage. Both products have a gross margin of about 12.5 percent (rounded). That means that about 87.5 percent of sales value represents cost of goods available for sale.

Article / Updated 08-02-2022

Everything that makes up a corporation and everything a corporation owns, including the building, equipment, office supplies, brand value, research, land, trademarks, and everything else, are considered assets. Believe it or not, when you start a corporation, that company’s assets aren’t just included in a Welcome Letter; you have to go out and acquire them. Generally speaking, you start off with cash, which you then use to purchase other assets. For most new companies, this cash consists of a combination of the following: The owner’s own money: This money is considered equity because the owner can still claim full possession over it. Small loans, such as business and personal loans from banks, business and personal lines of credit, and government loans: The money obtained through loans is considered a liability because the corporation has to pay it back at some point. In other words, these loans are a form of debt. The combination of these two funding sources leads to the explanation of the most fundamental equation in corporate finance: Assets = Liabilities + Equity The total value of assets held by a company is equal to the total liabilities and total equity held by the company. Because the total amount of debt a company incurs goes into purchasing equipment and supplies, increasing debt through loans increases a company’s liabilities and total assets. As an owner contributes his own funding to the company’s usage, the total amount of company equity increases along with the assets. Note: Capital, assets, money, and cash are basically all the same thing at this point; after a company raises the original capital, or cash, it exchanges that cash for more useful forms of capital, such as erasable markers. Unlike liabilities, equity represents ownership in the company. So if a company owns $100,000 in assets and $50,000 was funded by loans, then the owner still holds claim over $50,000 in assets, even if the company goes out of business, requiring the owner to give the other $50,000 in assets back to the bank. For corporations, the equity funding varies a bit, however, because the owners of a corporation are the stockholders. The equity funding of corporations comes from the initial sale of stock, which exchanges shares of ownership for cash to be used in the company.

Article / Updated 08-01-2022

In cost accounting, two types of capacity focus on production: theoretical capacity and practical capacity. Consider how much you could produce if customer demand was unlimited. Select a capacity method that makes sense to you, and use that as a tool to plan production and spending. Theoretical capacity assumes that nothing in your production ever goes wrong. Accountants describe this capacity as working at full efficiency all the time. Consider what your pie-in-the-sky or perfect-world capacity would be. It’s a world in which everything runs perfectly and no machines or equipment ever break down. It’s utopia where no worker ever makes a mistake. That would be great, wouldn’t it? That’s theoretical capacity, and you can’t reach it. It seems silly, but you need to see this level of capacity to understand the others. Say you own a business that makes athletic running shorts and other clothing. At maximum capacity, you can make 200 pairs of shorts per shift. You run three 8-hour shifts per day, 365 days a year. Based on those numbers, here is your theoretical capacity: Theoretical capacity = shorts x shifts x 365 days Theoretical capacity = 200 x 3 x 365 days Theoretical capacity = 219,000 Unfortunately, this level of capacity isn’t attainable. You need to take into account the unavoidable. That gets you to practical capacity. Practical capacity is the level of capacity that includes unavoidable operating interruptions. Another description is unavoidable losses of operating time. Consider maintenance on equipment, employee vacations, and holidays. You’re willing to accept a good, rather than perfect, capacity level. The people in your company can help you determine your practical capacity. Your production and engineering staff can answer questions about machine capacity and repair time. Your human resources staff can forecast employee availability, based on vacations and holidays. You determine that 250 days is a more realistic number of production days, given unavoidable operating interruptions. Also, you decide that two shifts per day are realistic. Here’s the practical capacity calculation: Practical capacity = shorts x shifts x days Practical capacity = 200 x 2 x 250 Practical capacity = 100,000 The practical capacity is 100,000 units (pairs of shorts) per year.

Cheat Sheet / Updated 04-07-2022

A great bookkeeper cares that the financial statements make sense and gets upset when something doesn’t balance or stuff goes missing. They also feel responsible when it comes to getting customers to pay on time. A good bookkeeper, in other words, is worth their weight in gold. This Cheat Sheet summarizes what you need to know to be an excellent bookkeeper.