Problem 93 - Algebra A Combined Function

Question

Solve. See Example 22. A negative net income results when a company spends more money than it brings in. Johnson Outdoors Inc. had the following quarterly net incomes during its 2009 fiscal year. (Source: Yahoo Finance) $$ \begin{array}{|c|c|} \hline \text { Quarter of Fiscal 2009 } & \text { Net Income (in millions) } \\\ \hline \text { First } & 2.5 \\ \hline \text { Second } & 9 \\ \hline \text { Third } & -14.2 \\ \hline \text { Fourth } & -4.2 \\ \hline \end{array} $$ What was the total net income for fiscal year \(2009 ?\)

Step-by-Step Solution

Answer

The total net income for fiscal year 2009 is -6.9 million.

Step 1: Identify the Net Incomes

List the net income for each quarter as given in the problem: First quarter: 2.5 million, Second quarter: 9 million, Third quarter: -14.2 million, Fourth quarter: -4.2 million.

Step 2: Sum the Net Incomes

Calculate the total net income by summing up the net incomes for each quarter: \(2.5 + 9 - 14.2 - 4.2\).

Step 3: Simplify the Equation

Perform the addition and subtraction: \(2.5 + 9\) yields 11.5, then \(11.5 - 14.2\) yields -2.7, and finally \(-2.7 - 4.2\) yields -6.9.

Step 4: Conclude the Total Net Income

The total net income for the fiscal year 2009 is -6.9 million.

Key Concepts

Understanding Addition and Subtraction in Net Income Calculation

When calculating a company's net income, it's essential to understand basic arithmetic operations: addition and subtraction. These operations help in determining whether a business has made a profit or a loss over a period.
Given the net income data for each quarter, you start with the first value. If it's positive, it indicates a profit. If negative, it reflects a loss. From there, you perform sequential additions and subtractions for each following quarter.

• Start by adding any positive net incomes to accumulate the total profits.
• Subtract negative net incomes, which represent losses.

Determining the total net income involves summing these values to either a positive or negative result, indicating a profit or loss for the period.

Solving Step-by-Step: A Simple Approach

Breaking down problems into steps can make them more manageable. Here's how to apply a step-by-step approach to calculating net income:
Start by listing the net incomes provided.

• First quarter: 2.5 million (profit).
• Second quarter: 9 million (profit).
• Third quarter: -14.2 million (loss).
• Fourth quarter: -4.2 million (loss).

Next, calculate the total net income by summing these values. Begin by adding the two positive net incomes: \(2.5 + 9 = 11.5\). This is your intermediate total.

• Subtract the third quarter loss: \(11.5 - 14.2 = -2.7\).
• Then subtract the fourth quarter loss: \(-2.7 - 4.2 = -6.9\).

Each step brings you closer to the final result. By understanding and simplifying each step, you'll find that the total net income for fiscal year 2009 is -6.9 million.

Fiscal Year Analysis: Insights from Quarterly Performances

A fiscal year analysis allows businesses to assess their financial health. Johnson Outdoors Inc.'s fiscal year comprised four quarters, each contributing to the final net income:
The sum of quarterly profits and losses gives a snapshot of the company's financial trajectory.

• Positive quarters (Q1 and Q2) added to the potential for a profitable year.
• However, significant losses in Q3 and Q4 reversed this potential.

Evaluating each quarter's performance can reveal trends, such as cyclical business patterns or seasonal impacts. These insights can guide strategic decisions to optimize future financial outcomes.
An overall negative net income, as seen in 2009, might prompt a company to investigate underlying reasons behind losses and strategize corrective measures.