Problem 86 - Algebra A Combined Function

Question

A company's gross profit margin \(P\) can be computed with the formula \(P=\frac{R-C}{R},\) where \(R=\) the company's revenue and \(C=\) cost of goods sold. For the fiscal year 2008 , computer company Apple had revenues of \(\$ 32.5\) billion and cost of goods sold \(\$ 21.3\) billion. (Source: Apple, Inc.) What was Apple's gross profit margin in \(2008 ?\) Express the answer as a percent, rounded to the nearest tenth of a percent.

Step-by-Step Solution

Answer

Apple's gross profit margin in 2008 was approximately 34.5%.

Step 1: Understand the Formula

The formula given for gross profit margin is \( P = \frac{R-C}{R} \). Here, \( R \) represents revenue and \( C \) represents the cost of goods sold. The gross profit margin \( P \) is expressed as a fraction of revenue, which can then be converted to a percentage.

Step 2: Substitute Values

Plug in the given values into the formula:\[ P = \frac{32.5 - 21.3}{32.5} \]Here, \( R = 32.5 \) billion dollars and \( C = 21.3 \) billion dollars.

Step 3: Perform the Calculation

Calculate the numerator first:\[ R - C = 32.5 - 21.3 = 11.2 \]Now, substitute back to find \( P \):\[ P = \frac{11.2}{32.5} \approx 0.344615 \]

Step 4: Convert to Percentage

Convert the decimal result to a percentage by multiplying by 100:\[ P = 0.344615 \times 100 \% \approx 34.4615 \% \]

Step 5: Round to the Nearest Tenth of a Percent

Round the percentage to the nearest tenth:\[ P \approx 34.5 \% \]

Key Concepts

Revenue Calculation

Revenue is the total amount of money a company earns from its business activities before any expenses are deducted. It's critical to understand that revenue is not profit, as it doesn't account for costs like the goods that were sold, salaries, and other operational expenses.
To compute revenue, tally all the income generated from the sale of goods and services provided by the business. This includes:

• Sale of products
• Provision of services
• Interest and dividends for financial companies

In the case of Apple for the fiscal year 2008, the revenue was reported as \(32.5\) billion dollars. This figure represents all incoming funds from its products and services during that year. Understanding revenue is the first step in financial analysis and helps provide an overview of how much money the business is bringing in.
Revenue calculation is foundational in business finance, as it lays the groundwork for further analysis, such as determining profitability and financial health.

Cost of Goods Sold

"Cost of goods sold" (COGS) refers to the direct costs attributable to the production of the goods sold by a company. This amount includes the cost of the materials and labor directly used to create the product but excludes indirect expenses like distribution and sales force costs.
For a business, calculating COGS is essential, as it reflects the expenses incurred in making the goods or services that were sold during a given period. For Apple, during the fiscal year 2008, the cost of goods sold was reported at \(21.3\) billion dollars. This expenditure covers all costs tied to manufacturing and delivering its products.
By analyzing COGS, businesses can gain insight into their production effectiveness and pricing strategies. This figure plays a key role in determining gross profit, which is essential for further financial decision-making and measuring competitive performance.

Percentage Conversion

Converting a fraction to a percentage is a basic yet crucial skill in financial math. It helps express results in a way that is more intuitive and easier for most people to understand. To convert a number like Apple's computed gross profit margin suggestion, first, perform the division in the formula:\[P = \frac{R-C}{R}\]For Apple, this calculation gives us a decimal. Multiplying this decimal by \(100\) converts it to a percentage.
In this case, Apple's gross profit margin started as \(0.344615\), or \(34.4615\%\), as a percentage. To present this more conveniently, it's standard to round to one decimal place. Thus, we express it as \(34.5\%\).
This process allows easier comparison and understanding of financial ratios across different companies or time periods, providing clear insight into performance measures.