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Chapter 20: Problem 7

Keepsake Gifts, Inc. has decided to use the high-low method to estimate the total cost and the fixed and variable cost components of the total cost. The data for the highest and lowest levels of production are as follows: \begin{tabular}{lrc} & Units Produced & Total Costs \\ \hline Highest level & 15,000 & \(\$ 432,500\) \\ Lowest level & 5,000 & \(\$ 237,500\) \end{tabular} a. Determine the variable cost per unit and the fixed cost. b. Based on (a), estimate the total cost for 12,000 units of production.

Short Answer

Expert verified
Variable cost per unit is $19.5, fixed cost is $140,000; estimated cost for 12,000 units is $374,000.

Step by step solution

01

Identify high and low values

Firstly, identify the highest and lowest levels of production and the corresponding total costs from the data provided. The highest level of production is 15,000 units at a cost of $432,500, and the lowest level of production is 5,000 units at a cost of $237,500.
02

Calculate the variable cost per unit

To determine the variable cost per unit, use the formula: \[ \text{Variable Cost per Unit} = \frac{\text{Cost at High Level} - \text{Cost at Low Level}}{\text{Units at High Level} - \text{Units at Low Level}} \]Substitute the values in: \[ \frac{432,500 - 237,500}{15,000 - 5,000} = \frac{195,000}{10,000} = 19.5 \]Thus, the variable cost per unit is $19.5.
03

Calculate the fixed cost

Once the variable cost is calculated, use one of the data points to find the fixed cost. Use the formula: \[ \text{Fixed Cost} = \text{Total Cost at High Level} - (\text{Variable Cost per Unit} \times \text{Units at High Level}) \]Substitute the known values: \[ \text{Fixed Cost} = 432,500 - (19.5 \times 15,000) = 432,500 - 292,500 = 140,000 \]Therefore, the fixed cost is $140,000.
04

Estimate total cost for 12,000 units

Using the calculated variable cost per unit and fixed cost, estimate the total cost for 12,000 units with the following formula: \[ \text{Total Cost} = (\text{Variable Cost per Unit} \times \text{Units}) + \text{Fixed Cost} \]Substitute the values: \[ \text{Total Cost} = (19.5 \times 12,000) + 140,000 = 234,000 + 140,000 = 374,000 \]Thus, the estimated total cost for producing 12,000 units is $374,000.

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Key Concepts

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

Variable Cost Calculation
Calculating the variable cost is a crucial step when estimating costs using the high-low method. Variable costs are those costs that change with the level of production activity. To find out the cost per unit, you start by identifying the difference in total cost and the difference in production quantity between the highest and lowest levels of activity.

Here's how you can do it in simple steps:
  • First, identify the cost and production levels at the highest and lowest points.
  • Calculate the change in costs by subtracting the total cost at the low level from the total cost at the high level.
  • Similarly, calculate the change in units by subtracting the units at the low level from the units at the high level.
  • Finally, divide the change in costs by the change in units. This gives you the variable cost per unit.
For example, if the cost difference is $195,000 and the unit difference is 10,000, the variable cost per unit would be \( \frac{195,000}{10,000} = 19.5 \). Understanding this helps break down the cost behavior into more manageable parts.
Fixed Cost Calculation
Once you have determined your variable cost per unit, the next step is finding the fixed costs. Fixed costs are those that do not change with the level of production, such as rent or salaries, and they remain the same regardless of how many units you produce.

To calculate fixed costs using the high-low method:
  • Pick either the high or low production level data point. It doesn't matter which one since the formula will yield the same fixed cost from either point.
  • Start with the total cost from your chosen data point.
  • Subtract the total variable costs from this, which you get by multiplying the variable cost per unit by the number of units produced at the selected level.
  • The remaining number is the fixed cost.
For instance, using the high level data: if the total cost is $432,500 and variable cost for 15,000 units is \( 19.5 \times 15,000 = 292,500 \), then the fixed cost is \( 432,500 - 292,500 = 140,000 \). Knowing this helps in budgeting as these costs must be covered regardless of output.
Cost Estimation
Estimating the total cost is often the goal of using the high-low method. By understanding how variable and fixed costs work, you can forecast costs for different production levels, which is crucial for making reliable business decisions.

To estimate total costs:
  • Multiply your calculated variable cost per unit by the number of units you want to estimate for.
  • Add the fixed cost to this product.
  • The sum gives you the total estimated cost for the desired production levels.
For instance, to find the total cost for 12,000 units, calculate \( 19.5 \times 12,000 = 234,000 \), then add the fixed cost of \(140,000. This results in a total estimated cost of \)374,000.

Using these cost estimation techniques helps businesses to plan their finances effectively, predicting how different levels of production impact total costs.

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Most popular questions from this chapter

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