91Ó°ÊÓ

The Digital Arts Company manufactures color laser printers. Model A200 presently sells for \(\$ 300\) and has a total product cost of \(\$ 240\), as follows: \begin{tabular}{lr} Direct materials & \(\$ 170\) \\ Direct labor & 40 \\ Factory overhead & 30 \\ Total & \(\$ 240\) \\ \hline \end{tabular} It is estimated that the competitive selling price for color laser printers of this type will drop to \(\$ 285\) next year. Digital Arts has established a target cost to maintain its historical markup percentage on product cost. Engineers have provided the following cost reduction ideas: 1\. Purchase a plastic printer cover with snap-on assembly. This will reduce the amount of direct labor by 6 minutes per unit. 2\. Add an inspection step that will add 3 minutes per unit direct labor but reduce the materials cost by \(\$ 5\) per unit. 3\. Decrease the cycle time of the injection molding machine from 4 minutes to 3 minutes per part. Twenty-five percent of the direct labor and \(40 \%\) of the factory overhead is related to running injection molding machines. The direct labor rate is \(\$ 20\) per hour. a. Determine the target cost for Model A200. b. Determine the required cost reduction. c. Evaluate the three engineering improvements to determine if the required cost reduction (drift) can be achieved.

Step by step solution

01

Calculate Current Markup Percentage

First, find the current markup percentage. The current selling price is \\(300, and the current cost is \\)240.Calculate the markup percentage using:\[\text{Markup Percentage} = \left(\frac{\text{Selling Price} - \text{Cost}}{\text{Cost}}\right) \times 100 = \left(\frac{300 - 240}{240}\right) \times 100 \%\]This gives a markup percentage of \(25\%\).

02

Determine Target Price and Cost

The target price for next year is \\(285. The target cost must maintain the same 25% markup.Calculate the target cost using:\[\text{Target Cost} = \frac{\text{Target Price}}{1 + \left(\frac{\text{Markup Percentage}}{100}\right)} = \frac{285}{1 + 0.25} = \\)228\]

03

Calculate Required Cost Reduction

The current cost is \\(240, and the target cost is \\)228.Calculate the required cost reduction:\[\text{Required Cost Reduction} = \text{Current Cost} - \text{Target Cost} = 240 - 228 = \$12\]

04

Evaluate Improvement 1: Snap-on Assembly

This improvement reduces direct labor by 6 minutes per unit. At \\(20 per hour, the labor cost reduction is:\[\text{Labor Cost Reduction} = \frac{6}{60} \times 20 = \\)2\]So, the cost reduction from this improvement is \$2.

05

Evaluate Improvement 2: Add Inspection Step

This improvement adds 3 minutes of labor (cost increase) but reduces material cost by \\(5.Labor cost increase at \\)20 per hour is:\[\text{Labor Cost Increase} = \frac{3}{60} \times 20 = \\(1\]Net cost impact is: \(-\\)5 + \\(1 = -\\)4\).

06

Evaluate Improvement 3: Injection Molding Machine Cycle Time

Decrease in cycle time affects labor and overhead. Labor is 25% and overhead is 40% of total costs related to injection molding.Current labor cost from injection = \(40 \times 0.25 = \\(10\)Labor cost with cycle reduction = \(10 \times \frac{3}{4} = \\)7.50\)Current overhead for injection = \(30 \times 0.4 = \\(12\)Overhead cost with cycle reduction = \(12 \times \frac{3}{4} = \\)9\)Total cost savings from this change = \( (10 - 7.5) + (12 - 9) = \$5.50\).

07

Calculate Total Cost Reduction from Improvements

Add up cost reductions from all improvements:Total cost reduction = \( 2 + 4 + 5.50 = \\(11.50\).Compare this to the required cost reduction of \\)12.

08

Conclusion on Achieving Target Cost

The total cost reduction from improvements is \\(11.50, which is slightly below the required \\)12 reduction.Thus, the improvements nearly achieve the target, but a shortfall of \$0.50 remains.

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Key Concepts

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

Cost Reduction

In manufacturing, cost reduction is crucial for maintaining profitability when market conditions change. For the Digital Arts Company, cost reduction involves bringing down the total product cost of their Model A200 color laser printer. This is necessary because the expected market price is going to decrease from $300 to $285. For the company to continue profiting with its historical markup, the cost needs to be targeted at $228. To achieve this, the company can employ various strategies as suggested by engineers. These include optimizing direct labor, reducing material costs, and enhancing machine efficiency. Lowering costs by focusing on production efficiencies and technological innovations ensures competitiveness in pricing without sacrificing profit margins. Overall, it's essential to evaluate whether these proposed changes effectively close the gap between current costs and target costs. In this case, the sum of potential cost savings from changes nearly meets the required target, needing just a tiny additional saving of $0.50 to fully bridge the cost reduction gap.

Markup Percentage

Markup percentage is an essential concept in pricing strategy. It tells us how much more the selling price is compared to the cost of the product, in percentage terms. For Digital Arts Company's Model A200, the present markup percentage on its product is calculated using the formula:\[\text{Markup Percentage} = \left(\frac{\text{Selling Price} - \text{Cost}}{\text{Cost}}\right) \times 100\]By plugging in the values: \(\text{Selling Price} = \(300\) and \(\text{Cost} = \)240\), the markup is determined to be 25%. This means the company sells the printer at 25% above its production cost.To maintain this markup while adapting to a lower market price of \(285, Digital Arts needs to adjust its cost down to \)228. It’s a delicate balancing act to lessen costs appropriately and still keep the markup level that ensures desired profit margins. This underlines the importance of strategic cost management and efficiency improvements.

Direct Labor Calculations

Direct labor plays a pivotal role in the production cost and subsequently impacts the pricing strategy. Calculating labor cost accurately is key since it affects the overall cost structure significantly. The wage rate for direct labor is given as \(20 per hour, which translates every labor activity, measured in minutes, into its equivalent cost.For instance, reducing labor time by 6 minutes per unit using a snap-on assembly directly decreases the labor cost. This reduction is calculated as:\[\text{Labor Cost Reduction} = \frac{6}{60} \times 20 = \\)2\]However, not all changes imply savings. Additional inspection that increases labor time by 3 minutes incurs an added cost of $1, though it brings about a material cost saving.Moreover, reducing the injection molding cycle time from 4 to 3 minutes per unit influences both labor and factory overhead costs owned mainly to these activities. This results in notable savings in direct labor expense, essential to approach the target cost efficiently. Proper calculation and management of direct labor can significantly help in achieving overall cost targets in a competitive market.