Math for Journalists: Summary of Chapters 5-8 of ‘Math Tools for Journalists’

Graphic by Marlena Chertock.

April 29, 2011

In these chapters of “Math Tools for Journalists,” Kathleen Woodruff Wickham goes over polls, surveys, math related to business and how to calculate taxes. These are essential concepts to be able to calculate and inform the public about.

Business news, taxes and polls and surveys include math and it is important for journalists to know how to use and calculate these numbers.

To read more about standards for financial accounting and reporting of information, visit the Financial Accounting Standards Board.

Definitions/Formulas:

Polls and surveys offer a glimpse of public opinion, not a fully accurate account. They can be skewed, as well. It is important for reporters to be clear when using polls and surveys in articles. Reporters must help readers understand polls and surveys and their accuracy or if they are skewed.

  • Polls: Polls are an estimate of public opinion on a single topic or question. They are based on a representative sample of the population. They are frequently used in politics.
  • Surveys: Surveys are based on representative samples of the population but include multiple questions. They are used in a wide variety of social science venues.
  • Random selection: When determining if a poll or survey is valid, a reporter must consider random selection. Random selection ensures that every person in the population had an equal opportunity to be selected. This lessens bias. Remember: The larger the sample group, the more valid the results will be. Samples help to generate a small picture of the population (since it’s impossible for researchers to contact and get responses from an entire population).

Pollsters aim for at least 400 interviews to keep the margin of error within acceptable limits.

  • Samples: There are multiple formulas to select a sample.

Census, universe or population sampling: Sampling everyone in the population. The U.S. Census is one example, since every household is queried. These samples are very expensive to conduct on a regular basis.

Cluster sampling: Sampling one area or region, identified by ZIP codes, counties or other well-defined areas.

Multistage sampling: Selecting a specific geographic area, then randomly selecting sub-groups, then individual blocks within the sub-group then a smaller block.

Systematic random sampling: Selecting a specific number and using a reference book, such as the phone book or city directory to poll every nth person. For example, if you were to use 20 as the specific number, you would poll every 20th person.

Quota sampling: Selecting the sample based on known demographic characteristics.

Probability sampling: Putting all of the potential subjects into a hat and drawing out a designated percentage. This is a time-consuming method. It is also a reliable method because everyone in the population has an equal chance to be selected.

  • Margin of error: Margin of error indicates the degree of accuracy of research or a survey, based on standard norms. It is expressed as a percentage and is based on the size of a randomly selected sample. The more people are polled, the smaller the possible error and smaller the margin of error.
  • Confidence level: The confidence level is the level or percentage that researchers have confidence in their results. It is the probability of obtaining a given result by chance, according to Wickham.  The confidence is determined in advance and usually is 90 percent, 95 percent or 98 percent. A confidence level of 90 percent explains that the results had a 10 percent probability of occurring. Confidence level is closely related to margin of error.
  • Adjusted and unadjusted figures: figures that are statistically manipulated to compensate for missing data
  • Election terms:

Electorate: the entire population of a district eligible to vote

Exit poll: a poll where voters leaving a polling station are asked how they voted

Straw poll: a nonscientific poll

Majority: more than 50 percent of votes cast

Percentage of precincts reporting: determined by dividing number of precincts that have reported results by total number of precincts

Plurality: when a candidate receives more votes than opponents, but less than 50 percent

Turnout: a percentage based on number of registered voters in district and number of voters who cast ballots, it’s determined by dividing number of voters by total number of registered voters

Winning margin: difference between highest number or percentage of votes cast and next highest number of votes or percentage cast

  • z scores: z and t scores are often used in reporting the results of studies. A z score or standard score shows how much a particular figure differs from the mean. It is used to compare figures that are hard to compare in their raw form. The standard deviation is used as the unit of measure for a z score. The mean becomes zero and the first standard deviation is 1, the second is 2 and so on.  Z scores can be negative or positive.
  • t scores: A t score or Student’s t distribution is used when the sample size is small, roughly 100 or fewer. To calculate the t score a reporter needs to look at a table of critical t values.

z score = (raw score – mean) ÷ standard deviation

  • Business reports: Businesses usually report their earnings quarterly in a report. Annual reports are more detailed. These reports help assess the financial condition of a company.
  • Financial statements: Financial statements are formal documents that are available to stakeholders who may be interested in a company’s performance. These statements make a qualitative statement of a company’s business transactions. They are usually included in an annual report. They can include profit and loss reports and balance sheets.
  • Financial terms tips:

-Numbers are often written without the last three or six zeroes. They are written in “thousands” or “millions.” This will be stated at the top of the financial statement.

-Figures in parentheses are negative.

-It is more newsworthy to show the change in time of net income, the trend. Compare net income figures over time.

  • Profit and loss: Profit and loss statements, or P&L, shows if a company is making money or not. Different methods can be used to produce these reports. But the basis is calculating a business’ profit by subtracting expenses from income.
  • Cost of goods sold: This business term refers to direct expense a business incurs in making or buying its products. If a company buys finished products for resale then the cost of goods sold is called the “wholesale” cost. When all the subtractions have been made, what is left is “net profit,” “net earnings” or “net income.”
  • Overhead: Overhead is a term that refers to expenses not directly related to the product being made. It can include salaries of employees, rent, utilities and insurance.
  • Gross margin: The gross margin is determined by calculating the difference between the “cost of goods sold” and the selling price. It can also be called “markup.”

Gross margin = selling price – cost of goods sold

Net profit = gross margin – overhead

  • EBITDA: EBITDA or “earnings before interest, taxes, depreciation and amortization” is important to calculate and understand. It shows how much cash a company is earning, not taking into account items that are unrelated to current business. It is often called “operational cash flow” because it measures how much cash the business has available to operate with. Banks who may be offering a business a loan may want to know how a company looks and its finances on paper. So the EBITDA must be calculated.

Gross profit = gross margin x number of items sold

  • Balance sheet: A balance sheet is a written financial statement of a company’s assets, liabilities and equity. The assets side of a balance sheet always equals the liabilities and equity side. It shows the financial stability of the company. Different companies can use different terms in their balance sheets.

Assets = liabilities + equity

  • Balance sheet definitions:

Assets: resources owned by a company. They have some economic value. For example, a company’s real estate, equipment and cash. Current assets include cash investments and other liquid items of value. Long-term assets include buildings and office furniture.

Liabilities: money the company owes, obligations that need to be paid at some later date. For example, loans.

Equity: what the company is really worth

Accounts receivable: money owed to the company by customers

Accumulated depreciation: the decline of the value of an asset

Inventory: a record of goods on hand, raw materials and work in progress

Intangible assets: copyrights, patents and research with legal and economic value

Investments in other corporations: stock owned or influence acquired  in other companies for economic gain

Fixed assets: property, plants, equipment and deferred charges

Short-term investments: stocks and bonds

Pre-paid expenses: rent and insurance

Uncollected accounts receivable: write-offs for bad debts and an allowance for potential bad debts

Equity: value of the company, owners’ and/or shareholders’ investments in company, capital accounts and other related assets

Dividends: payments to shareholders that represent distribution of company’s assets

Retained earnings: earnings set aside for future business purposes

Accounts payable: bills that need to be paid

Accrued liabilities: liabilities that have occurred but are not yet paid

Current or short-term liabilities: money owed to suppliers, interest on debt, taxes and wages

Long-term liabilities: debt, deferred taxes and leases

  • Ratio analysis: Ratios are calculations that analysts and business owners use to evaluate a company’s financial status, such as cash situation, profitability, operating efficiency and market value. Ratios examine trends throughout a company’s life. They can be used to compare companies in the same field. Ratios are indicators of a company’s strengths and weaknesses, but are not a complete picture. When reporting company ratios, include industry standards so readers can compare. Industry standards are reported in different publications, including Dunn & Bradstreet’s Industry Norms and Key Business Ratios.
  • Current ratio: a liquidity ratio that measures the ability of a company to meet its liabilities. It is a common ratio.

Current ratio = current assets ÷ current liabilities

  • Quick ratio: a liquidity ratio that measures the ability of a company to meet its current liabilities with cash on hand

Quick ratio = cash ÷ current liabilities

  • Debt-to-asset ratio: similar to current ratio, this ratio includes all assets and all liabilities. (Note: debt can be used interchangeably with liabilities). It is a better indicator of a company’s long-term health.

Debt-to-asset ratio = total debt ÷ total assets

  • Debt-to-equity ratio: this ratio indicates how deeply a company is leveraged by comparing what is owed to what is owned

Debt-to-equity = total debt ÷ equity

  • Return on assets: a profitability ratio that measures the return on investment on all assets

Return on assets = net income ÷ total assets

  • Return on equity: a profitability ratio that measures the return on investment made in equity

Return on equity = net income ÷ equity

  • Price-earnings ratio: a value ratio that measures the return of investment based on stock price

Price-earnings = market price/share ÷ earnings/share

  • Stocks and bonds are two ways businesses raise money.
  • Stocks: Companies and corporations sell stocks to raise cash. People buy stocks for investments. When a person buys a share of stock in a company, he or she becomes a part owner of the company. Each share represents a tiny portion of ownership. The value of a stock varies over time, based on demand. The more people who want to buy a stock, the higher the price. The conditions that change a stock’s demand are business conditions, publicity, future expectations and others. In a published stock table, the stock is given a name that is usually a shortened version of the company name. Div is the most recent annual dividend the company paid to shareholders, per share. P/E is the price/earnings ratio (stock is divided by per-share earnings reported in last 12 months). Last is the price of one share at the end of the previous day. Change is how much the stock price went up or down that day.
  • Mutual funds: an alternative way to invest in stocks. Mutual fund companies sell shares of funds and use the money to buy stock in other companies.
  • Bonds: A bond is a loan from an investor to the government or organization selling the bond. Bonds are used by governments to raise money. Bonds earn interest at a set rate, are generally low-interest investments, have set dates for interest payments and maturity. “Face value” of a bond is the amount the owner will receive at maturity. There can be a catch: investors often sell bonds on the open market before they mature. Even though the face value and interest rate remain the same, the value of the bond on the open market fluctuates with supply and demand. The bond’s “current yield,” the return on the investment, also fluctuates.

Current yield = (interest rate x face value) ÷ price

  • Investment reports: companies publish commonly these

Form 8-K: companies are required to file an 8-K when a special event occurs (bankruptcy, major assets are bought or sold)

Form 10-K: official audited annual report public companies are required to file, shows assets, liabilities, revenue and more

Form 10-Q: quarterly reports of financial information

Proxy statement: a document sent to shareholders about matters that shareholders will vote about

  • Bond cost: calculating the actual cost of a bond issued by a municipality

Bond cost (interest) = amount x rate x years

  • Market indexes: market indexes and averages are used to measure action on exchanges. Stock indexes track prices of certain groups of stocks. This gives a snapshot of the overall market conditions. Popular indexes are the Dow Jones Industrial Average, NASDAQ, Russell 2000 and S&P 500. Bonds are tracked by J.P. Morgan Government Bond Index and Down Jones Corporate Bond Index.

Dow Jones Industrial Average: Dow is one popular index, the total value of one share each of 30 select stocks divided by a figure called the divisor. The divisor takes into account stock dividends, splits, spinoffs and other corporate actions. Find the current divisor here. Dow monitors the value of key stocks and is thus able to provide a snapshot of the entire stock market.

NASDAQ: NASDAQ, the National Association of Securities Dealers Automated Quotations, is another popular index, it’s monitored by the Securities and Exchange Commission. It is an automated quotation system that reports on trading of domestic stocks and bonds not listed on regular stock markets. It lists more than 5,000 securities. NASDAQ publishes two composite price indexes daily.

  • Property taxes: the largest single source of income for local government, school districts and other municipal organizations. Property taxes pay for supplies, salaries, maintenance costs and other day-to-day expenses. Property tax rate is determined by taking the local amount of money the governing body needs and dividing that among property owners in the taxing district. How much each owner pays is based on the value of his or her property. Most taxing districts take into account real property (real estate, homes, buildings). They are measured in units called mills. A mill is 1/10 of a cent or $0.001. Property taxes are expressed in terms of mills levied for each dollar of assessed valuation of property. One mill per dollar is 10 cents per $100 assessed valuation or $1 per $1,000 valuation. Property taxes are usually applied to assessed valuations, not the actual price a home would sell for on the open market. Assessed value is a percentage of market value. Each community and state uses a different property tax formula. Property is often taxed by more than one governing body. In some areas property owners will only pay county taxes or city taxes, but in others they pay both. The percentage used to calculate assessed value might differ based on the type of property.

Reappraisal: A reappraisal updates real property values to reflect current market value of all taxable properties within a taxing district. Neighborhoods can improve and decline in value over time. How often an area is reappraised varies.

Mill levy = taxes to be collected by government body assessed ÷ assessed valuation of all property in taxing district

  • Appraisal value: based on property’s use (residential , business, vacant land, farm, business, commercial), property’s characteristics (location, square footage or total living area, number of stories, exterior wall type, age and year of construction, quality of construction, amenities such as number of bathrooms and bedrooms, garage, deck, porch, fireplace or pool), current market conditions determined by sales in immediate area over specific number of years, visual inspection of property by trained appraisers
  • Assessed value: mill levy is applied to assessed valuation. Assessed value of a property depends on local policies.

Assessed value = appraisal value x rate

Calculating tax:

tax owed = tax rate x (assessed value of property ÷ $100)

Note: Divide assessed value by $1,000, rather than $100, if rate is based on amount per $1,000 of assessed value.

Math problems:

1. Gross margin:

If Bill Nye makes $357,989 for each science video he makes and sells them for $859,675, what is his gross margin?

$859,675 – $357,989 = $501,686

So his gross margin is $501,686.

2. Current ratio:

Blueberries & Pies Inc. has $570.4 million in current assets. The company also has $65.8 million in current liabilities. What is the current ratio for Blueberries & Pies Inc.?

570,400,000 ÷ 65,000,000 = $8.78 million

So the current ratio is $8.78 million.

3. Debt-to-asset ratio:

Manischewitz wine has a total debt of $32.6 million. The company has $480.5 million in total assets. What is its debt-to-asset ratio?

32,600,000 ÷ 480,500,000 = 0.678 million

The debt-to-asset ratio of Manischewitz wine is 0.678 million.

4. Bond cost:

Emmie Gyre was issued $7.8 million worth of 35-year bonds to pay for a new medical facility. If the coupon is 7 percent how much will Emmie have to pay in interest over the life of the bonds?

7,800,000 x .07 x 35 = $19,110,000

The bond cost is $19,110,000.

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About Marlena Chertock

Marlena Chertock's first collection of poetry, On that one-way trip to Mars, is available from Bottlecap Press. Her articles have appeared in The Washington Post, Marketplace, and WTOP. Her poems and fiction has appeared in The Deaf Poets Society, Moonsick Magazine, and Paper Darts.

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