Problem 22 - Accounting

Question

Southwest Blue Airways provides air transportation services between Seattle and San Diego. A single Seattle to San Diego round-trip flight has the following operating statistics: \(\begin{array}{lr}\text { Fuel } & \$ 7,000 \\ \text { Flight crew salaries } & 5,400 \\ \text { Airplane depreciation } & 2,600 \\ \text { Variable cost per passenger-business class } & 50 \\ \text { Variable cost per passenger- economy class } & 40 \\ \text { Round-trip ticket price—business class } & 550 \\ \text { Round-trip ticket price-economy class } & 290\end{array}\) It is assumed that the fuel, crew salaries, and airplane depreciation are fixed, regardless of the number of seats sold for the round-trip flight. a. Compute the break-even number of seats sold on a single round-trip flight for the overall product. Assume that the overall product is \(20 \%\) business class and \(80 \%\) economy class tickets. b. How many business class and economy class seats would be sold at the break- even point?

Step-by-Step Solution

Answer

Sell 50 seats: 10 business class and 40 economy class.

Step 1: Define Fixed Costs

The fixed costs for a single round-trip flight include fuel, flight crew salaries, and airplane depreciation. These remain constant and are calculated as follows:\[\text{Fixed Costs} = 7000 + 5400 + 2600 = 15000.\]

Step 2: Calculate Average Variable Cost per Passenger

For the average variable cost per passenger, we utilize the given percentages of ticket sales. With 20% business and 80% economy, the average variable cost is:\[\text{Average Variable Cost} = 0.2 \times 50 + 0.8 \times 40 = 42.\]

Step 3: Determine Average Revenue per Passenger

Similarly, we calculate the average ticket price by proportionally weighting the business and economy class prices:\[\text{Average Revenue} = 0.2 \times 550 + 0.8 \times 290 = 342.\]

Step 4: Calculate Contribution Margin per Passenger

The contribution margin per passenger is the difference between the average revenue per passenger and the average variable cost:\[\text{Contribution Margin} = 342 - 42 = 300.\]

Step 5: Calculate Break-even Number of Seats

The break-even point in terms of seats sold is found by dividing the total fixed costs by the contribution margin per passenger:\[\text{Break-even Seats} = \frac{15000}{300} = 50.\]

Step 6: Distribute Seats Between Classes

The break-even seats need to be distributed according to the percentage of business and economy class tickets:- Business class seats: \(0.2 \times 50 = 10\).- Economy class seats: \(0.8 \times 50 = 40\).

Key Concepts

Fixed Costs

Fixed costs are expenses that remain constant, regardless of the number of products or services produced. For a business like Southwest Blue Airways, these costs are stable and do not fluctuate with the number of passengers. In the context of a flight from Seattle to San Diego, fixed costs include:

• Fuel expenses
• Flight crew salaries
• Airplane depreciation

These costs total $15,000 per round-trip flight. This stability allows the airline to plan and forecast expenses without worrying about variations caused by fluctuating passenger numbers. Understanding fixed costs is crucial for break-even analysis, as they form the baseline amount that needs to be covered by revenue before a business starts making a profit.

Variable Costs

Variable costs differ from fixed costs because they change based on the level of production or number of services provided. For an airline, variable costs are directly linked to the number of passengers. In this exercise, we focus on:

• Variable cost per passenger for business class: $50
• Variable cost per passenger for economy class: $40

To find the average variable cost per passenger, we consider the distribution of ticket sales—20% business class and 80% economy class. By calculating a weighted average, we find the average variable cost per passenger to be $42. Variable costs are essential for determining the contribution margin, which helps in analyzing profitability.

Contribution Margin

The contribution margin is a key component in profit analysis, as it reveals how much money from each sale is available to cover fixed costs and contribute to profit. It is calculated by subtracting the average variable cost from the average revenue per passenger. In our scenario, the average revenue per passenger is \(342, while the average variable cost is \)42. Hence, the contribution margin is:\[\text{Contribution Margin} = 342 - 42 = 300.\]This means each passenger contributes $300 towards covering the fixed costs. A higher contribution margin indicates that a company can cover its fixed costs more quickly and start generating profit with fewer sales. The contribution margin is pivotal in calculating the break-even point.

Profit Analysis

Profit analysis involves examining how various elements contribute to a company's profitability, particularly in relation to the break-even point. The break-even point is where total revenue equals total costs, resulting in no net profit or loss. In this analysis, we take the fixed costs and divide them by the contribution margin to ascertain the number of seats that must be sold to break even:\[\text{Break-even Seats} = \frac{15000}{300} = 50.\]This indicates that 50 seats must be sold on a given flight to cover all costs. At this point, the airline makes neither profit nor loss. By distributing these seats into 10 business class and 40 economy class per the given percentages, the airline can strategically understand and manage its pricing and capacity decisions. Profit analysis empowers airlines to gauge the effectiveness of their pricing strategies and adjust forecasts for better financial performance.