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Automatic Transmissions, Inc., has the following estimates for its new gear assembly project: price \(=\$ 1,280\) per unit; variable costs \(=\$ 340\) per unit; fixed costs \(=\$ 5.5\) million; quantity \(=80,000\) units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?

Short Answer

Expert verified
In the best-case scenario, the company should use the following variable values: - Price per unit: $1,472 - Variable cost per unit: $289 - Fixed cost: $4,675,000 - Quantity of units: 92,000 While in the worst-case scenario, the company should use the following variable values: - Price per unit: $1,088 - Variable cost per unit: $391 - Fixed cost: $6,325,000 - Quantity of units: 68,000

Step by step solution

01

Calculate the best-case scenario values

In the best-case scenario, we want to maximize the profits. To do this, we'll increase the price per unit, decrease the variable cost per unit, decrease the fixed costs, and increase the quantity of units, as follows: 1. Price per unit (increase by 15%): Price = \(1,280 * (1 + 0.15) = \)1,472$ 2. Variable cost per unit (decrease by 15%): Variable cost = \(340 * (1 - 0.15) = \)289$ 3. Fixed cost (decrease by 15%): Fixed cost = \(5,500,000 * (1 - 0.15) = \)4,675,000$ 4. Quantity of units (increase by 15%): Quantity = \(80,000 * (1 + 0.15) = 92,000\) units In the best-case scenario, the company should use the following variable values: - Price per unit: $1,472 - Variable cost per unit: $289 - Fixed cost: $4,675,000 - Quantity of units: 92,000
02

Calculate the worst-case scenario values

In the worst-case scenario, we'll do the opposite to minimize profits. We'll decrease the price per unit, increase the variable cost per unit, increase the fixed costs, and decrease the quantity of units, as follows: 1. Price per unit (decrease by 15%): Price = \(1,280 * (1 - 0.15) = \)1,088$ 2. Variable cost per unit (increase by 15%): Variable cost = \(340 * (1 + 0.15) = \)391$ 3. Fixed cost (increase by 15%): Fixed cost = \(5,500,000 * (1 + 0.15) = \)6,325,000$ 4. Quantity of units (decrease by 15%): Quantity = \(80,000 * (1 - 0.15) = 68,000\) units In the worst-case scenario, the company should use the following variable values: - Price per unit: $1,088 - Variable cost per unit: $391 - Fixed cost: $6,325,000 - Quantity of units: \(68,000\) With these values, the company can perform its best-case and worst-case scenario analysis and plan for different possibilities.

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Key Concepts

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

Fixed Costs
Fixed costs are the expenses that do not change based on the level of production or sales. No matter how many units you produce, these costs remain constant. For a company like Automatic Transmissions, Inc., some examples of fixed costs could be
  • rent for manufacturing space,
  • salaries of permanent employees, and
  • the cost of equipment used in production.
In the context of scenario analysis, it's crucial to understand how these costs impact profitability. If the sales volume drops, the company still has to cover fixed costs, which could lead to lower profit margins or even losses.
Consider that in the worst-case scenario, fixed costs increased by 15% to a total of $6,325,000. This increase translates directly to a higher overall expense regardless of how many units are sold. Understanding fixed costs helps managers make more informed decisions about pricing and production levels.
Variable Costs
Variable costs fluctuate with the level of production. Unlike fixed costs, these expenses increase or decrease based on the amount produced. For each additional unit manufactured by Automatic Transmissions, Inc., there are variable costs such as
  • raw materials,
  • labor directly involved in production, and
  • utilities based on usage.
When performing scenario analysis, determining how changes in variable costs can impact the overall cost structure is essential. For instance, in the best-case scenario, the company reduces its variable costs by 15%, bringing them down from $340 to $289 per unit.
This reduction means that for every unit sold, the cost of production is lower, increasing the potential margin. On the flip side, a 15% increase, as seen in the worst-case scenario, pushes variable costs up to $391 each. This would reduce their profit per unit sold, making it more challenging to achieve financial goals with the same sales volumes.
Price Per Unit
Price per unit is the amount a company charges each customer for a single unit of a product. It serves as a primary revenue driver for manufacturers. For Automatic Transmissions, Inc., this price is set at $1,280 per unit in normal scenarios.
Adjusting the price per unit is a powerful lever in scenario analysis. Increasing the price can lead to higher revenues per unit, but may also deter potential buyers if the price becomes too high. Conversely, lowering the price might increase sales volume but could reduce profit margins. In the best-case scenario described above, the price per unit increased by 15% to $1,472. This elevation increases revenue, assuming sales volume remains unaffected. If a decrease occurs, such as in the worst-case scenario where it's set at $1,088, the company may need to sell more units to maintain the same level of revenue.
Strategically managing the price per unit is essential for balancing profitability and market competitiveness. Companies must evaluate how price changes affect consumer demand and adjust their production strategies accordingly.

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Most popular questions from this chapter

A proposed new investment has projected sales of \(\$ 860,000\). Variable costs are 60 percent of sales, and fixed costs are \(\$ 195,000\) depreciation is \(\$ 86,000\). Prepare a pro forma income statement assuming a tax rate of 35 percent. What is the projected net income?

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