Dench manufacturing has received a special order from Sands to produce 225 components to be incorporated into Sand's product. The components have a high cost, due to the expertise required for their manufacture. Dench produces the components in batches of 15, and as the ones required are to be custom made to Sands' specifications, a 'prototype' batch was manufactured with the following costs:
Materials $
4kg of A, $ 7.50/kg 30
2kg of B, $ 15kg 30
Labour
20 hrs skilled, $ 15/hr 300
5 hrs semi-skilled, $8/hr 40
Variable overhead 100
25 labour hours, $ 4/hr 500
Additional information with respect to the workforce is noted below:
Skilled : Virtually a permanent workforce' that has been employed by Dench for a long period of time. These workers have a great deal of experience in manufacturing components similar to those required by Sands, and turnover is virtually non-existent.
Semi-Skilled: Hired by Dench on an 'as needed' basis. These workers would have had some prior experience, but Dench management believe the level to be relatively insignificant Past experience shows turnover rate to be quite high, even for short employment periods.
Dench's plans are to exclude the prototype batch from Sands' order. Management believes a 80% learning rate effect is experienced in this manufacturing process, and would like a cost estimate for the 225 components prepared on that basis. „
Required
a) Prepare the cost estimate, assuming an 80% learning rate is experienced. (10 Marks)
b) Briefly discuss some of the factors that can limit the use of learning curve. (5 Marks)
please we need solution to this
To prepare the cost estimate for the 225 components assuming an 80% learning rate, we need to understand the concept of a learning curve and how it affects costs.
A learning curve is a mathematical concept that describes how the amount of time or cost required to perform a task decreases as workers gain experience or expertise. It suggests that with each doubling of output, there will be a certain percentage reduction in time or cost required. In this case, an 80% learning curve effect means that with each doubling of output, the cost will decrease by 80%.
Let's break down the cost estimate calculation:
1. Calculate the learning curve percentage: 80% learning curve effect implies that with each doubling of output, the cost decreases by 80%. Therefore, the learning curve percentage is calculated as 100% - 80% = 20%.
2. Calculate the cumulative average time or cost reduction: The learning curve formula states that the cumulative average reduction in time or cost (R) can be calculated using the following formula: R = log(LC) / log(2), where LC is the learning curve percentage in decimal form. In this case, LC = 20%, so R = log(0.2) / log(2) = -0.322.
3. Calculate the average time or cost per unit for the prototype batch: The prototype batch is not included in the 225 components order, so we need to calculate the cost estimate for the prototype batch separately. Based on the given costs for materials, labor, and variable overheads, the total cost for the prototype batch is $30 (materials) + $340 (labor) + $100 (variable overheads) = $470. Since the prototype batch is a batch of 15 components, the average cost per component is $470 / 15 = $31.33.
4. Calculate the average time or cost per unit for the subsequent batches: Using the cumulative average reduction value (R) calculated earlier, we can calculate the average time or cost per unit for the subsequent batches. Since the learning curve effect is based on doubling of output, we can calculate the number of doublings required to reach the desired quantity of 225 components by solving the equation 2^x = 225, where x is the number of doublings. Solving this equation, we find that x ≈ 7.81. Therefore, we need to round up to the nearest whole number, which gives us 8 doublings. This means that the cost per unit for the 225 components will be reduced by 8 times the cumulative average reduction value (R).
Let's calculate the average cost per unit for the 225 components:
Cost per unit for subsequent batches = Cost per unit for prototype batch * (1 - R)^x
= $31.33 * (1 - 0.322)^8
= $31.33 * 0.554
= $17.33 (rounded to 2 decimal places)
Therefore, the estimated cost per unit for the 225 components is $17.33.
b) Factors that can limit the use of learning curve:
1. Changes in technology or processes: If there are significant changes in technology or processes, the learning curve effect may not be applicable or may be less effective. New methods or technologies may require different skills or approaches that cannot benefit from previous experience.
2. Variations in product design: The learning curve assumes a consistent product design and process. If there are frequent changes in product design or customization, it can disrupt the learning curve effect as workers have to adapt to each new design, reducing the efficiency gains from previous experience.
3. High turnover rate: The learning curve effect assumes a stable and experienced workforce. If there is a high turnover rate among workers, it can disrupt the accumulation of experience and expertise, limiting the effectiveness of the learning curve.
4. Limited production volumes: The learning curve effect is most significant in high-volume production scenarios. If the production volume is low or sporadic, it may be difficult to achieve the full benefits of the learning curve.
5. Skills and expertise required: The learning curve effect may be limited if highly specialized skills or expertise are required for the task. In such cases, the learning curve may not significantly reduce the time or cost required as the tasks remain complex and challenging regardless of experience.
Overall, while the learning curve can be a useful tool for estimating costs and understanding how experience impacts efficiency, it is important to consider these limiting factors to assess its applicability in a specific situation.