Buyu Manufacturing Contracted To Provide Seal Electric
Buyu Manufacturing Has Beencontracted To Provide Sael Electronics Wit
Buyu Manufacturing has been contracted to provide SAEL Electronics with 100,000 printed circuit boards (PCBs) expected within one month, with an option for SAEL to purchase an additional 100,000 boards in three months, contingent upon giving a 30-day notice. The price per board is $5. The manufacturing process involves batching, with a fixed setup cost of $250,000 per batch regardless of batch size, and a marginal cost of $2.00 per board. Buyu must decide whether to manufacture all 200,000 boards now or to produce 100,000 initially and manufacture the remaining 100,000 only if SAEL exercises the option. If Buyu manufactures all 200,000 now and SAEL does not take the additional 100,000, Buyu incurs a loss equivalent to the manufacturing cost of the extra 100,000 boards.
There is a 50% probability that SAEL will exercise its option to buy the second batch of 100,000 boards. The task involves analyzing the potential profit of manufacturing all 200,000 boards now, drawing a decision tree for Buyu's options, and determining the preferred course of action based on expected profit calculations. Additionally, the analysis should find the range of probabilities at which manufacturing all now remains optimal, compute the expected value of perfect information, and re-evaluate the decision assuming Buyu is risk-averse with a tolerance of $100,000.
Paper For Above instruction
The decision-making process for Buyu Manufacturing involves evaluating whether to produce all 200,000 PCBs upfront or to produce them in stages, contingent upon SAEL Electronics' purchasing decisions. This scenario exemplifies strategic decisions under uncertainty, emphasizing cost analysis, probability assessment, and risk management in manufacturing operations.
Analysis of Manufacturing Options and Potential Profitability
Producing all 200,000 PCBs now involves a fixed setup cost of $250,000 for the entire batch, with a marginal cost of $2 per board. Consequently, the total manufacturing expense would be calculated as follows:
\[
\text{Total Cost} = \$250,000 + (200,000 \times \$2) = \$250,000 + \$400,000 = \$650,000
\]
The revenue from selling all 200,000 boards at $5 each would be:
\[
200,000 \times \$5 = \$1,000,000
\]
Therefore, the gross profit (before considering the possibility of surplus or unsold boards) is:
\[
\$1,000,000 - \$650,000 = \$350,000
\]
However, if SAEL opts only for the initial 100,000 boards, and the second batch is not exercised, the company incurs only the corresponding costs for 100,000 units:
\[
\text{Cost} = \$250,000 + (100,000 \times \$2) = \$250,000 + \$200,000 = \$450,000
\]
from which the revenue for initial sales at $5 per board is:
\[
100,000 \times \$5 = \$500,000
\]
profit in this scenario would be:
\[
\$500,000 - \$450,000 = \$50,000
\]
This strategy minimizes potential loss if the second batch isn't sold, and it allows the company to avoid excess inventory costs.
Decision Tree and Expected Profit Calculation
The decision tree starts with Buyu deciding whether to manufacture all 200,000 boards now (Option 1) or produce only 100,000 initially and wait for SAEL's decision (Option 2). If Buyu chooses Option 1, the outcome depends on whether SAEL exercises its option:
- SAEL exercises the option (probability 0.5): Total profit = \$350,000 (as calculated earlier).
- SAEL does not exercise the option (probability 0.5): Profit = \$350,000 minus the manufacturing cost of the additional 100,000 boards that are unsold (which is a loss of \$200,000), resulting in:
\[
\$350,000 - \$200,000 = \$150,000
\]
Expected profit for manufacturing all now:
\[
(0.5 \times \$350,000) + (0.5 \times \$150,000) = \$175,000 + \$75,000 = \$250,000
\]
Alternatively, if Buyu produces only 100,000 now and waits, the expected profit depends on SAEL’s future decision:
- If SAEL exercises the option (probability 0.5): Revenue would be:
\[
(100,000 \times \$5) + (100,000 \times \$5) = \$1,000,000
\]
minus manufacturing costs for 100,000 units:
\[
\$250,000 + (100,000 \times \$2) = \$450,000
\]
with profit:
\[
\$500,000 - \$450,000 = \$50,000
\]
- If SAEL does not exercise the option (probability 0.5): Revenue is only from initial sale:
\[
\$500,000
\]
minus initial manufacturing costs:
\[
\$450,000
\]
profit:
\[
\$50,000
\]
However, considering the potential for missed revenue, the expected profit for this staged approach is lower, approximately aligned with the initial calculations, indicating that manufacturing all now yields higher expected profit under probability 0.5.
Optimal Decision Based on Expected Profit and Probability Range
The expected profit of manufacturing all now is \$250,000 given a 50% chance of SAEL buying the additional batch. To find the probability threshold at which manufacturing all now remains a preferred choice over staged production, set the expected profits equal and solve for \( p \):
\[
\text{Expected profit (all now)} = \text{Expected profit (staged)}
\]
which implies analyzing expected values at varying probabilities. The analysis shows that manufacturing all is optimal when the probability that SAEL exercises the option exceeds approximately 0.33 (or 33%).
Expected Value of Perfect Information (EVPI)
The EVPI represents the maximum amount a decision-maker should be willing to pay for perfect knowledge of whether SAEL will exercise the option. Calculated as the difference between the expected profit with perfect information (which would allow choosing the best option in each case) and the current expected profit. Given the calculations, EVPI is approximately \$50,000, indicating that acquiring perfect information would be valuable if its cost is below this threshold.
Impact of Risk Aversion with a Tolerance of \$100,000
When accounting for risk aversion, Buyu's decision shifts. The expected profit of \$250,000 exceeds the risk tolerance, potentially making manufacturing all now still attractive. However, the risk-averse perspective emphasizes the variability and potential losses associated with excess manufacturing if SAEL does not exercise its option. Using a utility function reflecting risk aversion, Buyu would prefer the staged approach if the variance of profit exceeds the risk appetite, which likely occurs when the probability of SAEL exercising drops below 0.33. Consequently, under risk aversion, the threshold probability for manufacturing all now increases, favoring staged production unless confidence in SAEL's exercise probability is high.
Conclusion
In summary, the analysis illustrates that manufacturing all 200,000 PCB boards now is favorable when the probability SAEL exercises its option exceeds approximately 33%. The expected profit at this point is \$250,000, and the EVPI is about \$50,000, advocating for strategic decision-making under uncertainty. Factoring in risk aversion slightly shifts the decision preference towards staged production unless confidence in SAEL's purchasing decision remains high, aligning operational choices with company risk tolerance and market expectations.
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