/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 Reisen Travel offers helicopter ... [FREE SOLUTION] | 91Ó°ÊÓ

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Reisen Travel offers helicopter service from sub-urban towns to John F. Kennedy International Airport in New York City. Each of its 10 helicopters makes between 1,000 and 2,000 round-trips per year. The records indicate that a helicopter that has made 1,000 round-trips in the year incurs an average operating cost of \(\$ 350\) per round-trip, and one that has made 2,000 round- trips in the year incurs an average operating cost of \(\$ 300\) per round-trip. 1\. Using the high-low method, estimate the linear relationship \(y=a+b X\), where \(y\) is the total annual operating cost of a helicopter and \(X\) is the number of round-trips it makes to JFK airport during the year. 2\. Give examples of costs that would be included in a and in \(b\). 3\. If Reisen Travel expects each helicopter to make, on average, 1,200 round- trips in the coming year, what should its estimated operating budget for the helicopter fleet be?

Short Answer

Expert verified
The linear relationship between the total annual operating cost (y) and the number of round-trips (X) is given by \(y = \$100,000 + \$250X\). Fixed costs (a) include depreciation, hangar fees, and insurance, while variable costs (b) include fuel, pilot wages, and maintenance. If each of Reisen Travel's 10 helicopters makes 1,200 round-trips in the coming year, the estimated operating budget for the helicopter fleet should be \$4,000,000.

Step by step solution

01

Identify the high and low points

In this step, we're going to identify the high and low points from the given data. The high point is when a helicopter makes the most round-trips, 2,000, and the low point is when it makes the least, 1,000. High Point (2,000 round-trips): Operating cost per round-trip is \(\$300\) Low Point (1,000 round-trips): Operating cost per round-trip is \(\$350\)
02

Calculate the variable cost per unit (b) using the high-low method

Using the high-low method formula, we will now calculate the variable cost per unit, \(b\), in our equation \(y = a + bX\). The formula is: \(b = \frac{(Total\, Cost\, at\, High\, Point - Total\, Cost\, at\, Low\, Point)}{(Units\, at\, High\, Point - Units\, at\, Low\, Point)}\) Total cost at High Point = 2,000 round-trips * \(\$300\) per round-trip = \(\$600,000\) Total cost at Low Point = 1,000 round-trips * \(\$350\) per round-trip = \(\$350,000\) \(b = \frac{(\$600,000 - \$350,000)}{(2,000 - 1,000)} = \frac{\$250,000}{1,000} = \$250\) per round-trip
03

Calculate the fixed cost (a)

Now that we have the variable cost per unit (b) calculated, we can plug this value back into the equation to find the fixed cost (a). Using the Low Point data, we get: Total cost at Low Point = a + b * (number of round-trips at Low Point) \(\$350,000 = a + \$250 * 1,000\) \(\$350,000 = a + \$250,000\) a = \(\$350,000 - \$250,000) = \(\$100,000\) The fixed cost a is \$100,000.
04

Write the linear relationship

Now we have both fixed cost and variable cost values, so we can write the linear relationship as follows: \(y = a + bX\) \(y = \$100,000 + \$250X\)
05

Give examples of costs included in a and b

Examples of costs included in the fixed cost (a): - Depreciation of helicopter - Hangar rental fees - Insurance expense Examples of costs included in the variable cost (b): - Fuel consumption per round-trip - Pilot wages per round-trip - Maintenance costs per round-trip
06

Calculate the estimated operating budget for the fleet at 1,200 round-trips

Lastly, using the predicted average of 1,200 round-trips for each helicopter, we will calculate the estimated operating budget for the entire fleet of 10 helicopters: Operating Cost per Helicopter = \(\$100,000 + \$250(1,200)\) Operating Cost per Helicopter = \(\$100,000 + \$300,000 = \$400,000\) Total Operating Budget for Fleet = Operating Cost per Helicopter * Number of Helicopters Total Operating Budget for Fleet = \(\$400,000 * 10 = \$4,000,000\) The estimated operating budget for the helicopter fleet, considering an average of 1,200 round-trips per helicopter, should be \$4,000,000.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cost Behavior Analysis
When companies endeavor to analyze their operating costs, they need a method to categorize each type of expense. Cost behavior analysis is this necessary cornerstone of management accounting, as it provides insights into how costs change in relation to the company's level of activity. For instance, in the context of Reisen Travel, cost behavior analysis helps distinguish between costs that remain constant regardless of the number of round-trips made by their helicopters and those that vary with this activity level.

Understanding cost behavior is critical for effective budgeting, forecasting, and strategic decision-making. In the Reisen Travel example, managers can predict the financial impact of increasing or decreasing round-trips and optimize their services accordingly. They can also use this information to set pricing strategies that cover costs and generate profit.
Fixed and Variable Costs
The high-low method used in the exercise simplifies the complexity of cost behaviors into two main categories: fixed costs and variable costs. Fixed costs, or 'a' in the linear equation, are expenses that do not change with the level of activity. These could include items like the depreciation of helicopters or insurance, as highlighted in the example. These are costs that Reisen Travel will incur regardless of how many round-trips their helicopters are making.

On the other hand, variable costs, denoted 'b' in the equation, change in direct proportion to the level of activity. When a helicopter makes more trips to JFK airport, costs like fuel, maintenance, and pilot wages naturally increase. Conversely, with fewer trips, these costs decrease. Variable costs are significant in the travel industry as they can greatly impact the profitability of each trip and hence the entire operation.
Operating Cost Estimation
Operating cost estimation is vital for any business that aims to be sustainable, as it influences both short-term and long-term financial planning. The high-low method provides a quick estimation of the linear relationship between operating costs and the level of activity, which is examined using 'fixed' and 'variable' cost categorizations.

As seen in Reisen Travel's case, the estimated operating budget is calculated by combining fixed costs with the variable costs projected at an expected level of activity. Utilizing the high-low method resulted in an estimated budget of $4,000,000 for 1,200 trips per helicopter. This approach is straightforward yet effective for businesses needing quick cost projections. However, it's important to incorporate a margin of error when relying on such estimates, as they assume a perfectly linear relationship and do not account for potential changes in cost behaviors beyond the high and low activity levels observed.

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Most popular questions from this chapter

What are the four key assumptions examined in specification analysis in the case of simple regression?

Dr. Young, of Young and Associates, LLP, is examining how overhead costs behave as a function of monthly physician contact hours billed to patients. The historical data are as follows: $$\begin{array}{cc}\text { Total 0verhead costs } & \text { Physician Contact Hours Billed to Patients } \\ \hline \$ 90,000 & 150 \\\105,000 & 200 \\\111,000 & 250 \\\125,000 & 300 \\\137,000 & 350 \\\150,000 & 400\end{array}$$ 1\. Compute the linear cost function, relating total overhead costs to physician contact hours, using the representative observations of 200 and 300 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed overhead costs of Young and Associates? Why? 2\. What would be the predicted total overhead costs for (a) 150 hours and (b) 400 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 150 and 400 hours. 3\. Dr. Young had a chance to do some school physicals that would have boosted physician contact hours billed to patients from 200 to 250 hours. Suppose Dr. Young, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin of \(\$ 9,000\), before deducting the predicted increase in total overhead cost, \(\$ 10,000\). What is the total contribution margin actually forgone?

"All the independent variables in a cost function estimated with regression analysis are cost drivers." Do you agree? Explain.

Discuss four frequently encountered problems when collecting cost data on variables included in a cost function.

Hankuk Electronics started production on a sophisticated new smartphone running the Android operating system in January \(2017 .\) Given the razor-thin margins in the consumer electronics industry, Hankuk's success depends heavily on being able to produce the phone as economically as possible. At the end of the first year of production, Hankuk's controller, Inbee Kim, gathered data on its monthly levels of output, as well as monthly consumption of direct labor-hours (DLH). Inbee views labor-hours as the key driver of Hankuk's direct and overhead costs. The information collected by Inbee is provided below: 1\. Inbee is keen to examine the relationship between direct labor consumption and output levels. She decides to estimate this relationship using a simple linear regression based on the monthly data. Verify that the following is the result obtained by Inbee: Regression 1: Direct labor-hours \(=a+(b \times 0 \text { utput units })\) 2\. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line. 3\. Inbee estimates that Hankuk has a variable cost of \(\$ 17.50\) per direct labor-hour. She expects that Hankuk will produce 650 units in the next month, January 2018 . What should she budget as the expected variable cost? How confident is she of her estimate?

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