Buyu Manufacturing Contracted To Provide Sale Electric
Buyu Manufacturing Has Beencontracted To Provide Sael Electronics Wit
Buyu Manufacturing has been contracted to provide SAEL Electronics with 100,000 printed circuit and motherboards (PC) boards over one month, with an option for SAEL to take an additional 100,000 boards in three months by giving a 30-day notice. The sale price per board is $5. Manufacturing involves a fixed setup cost of $250,000 per batch, with a marginal cost of $2.00 per board. Buyu must decide whether to manufacture all 200,000 boards now or produce 100,000 now and produce the remaining 100,000 only if SAEL exercises its option. If Buyu manufactures 200,000 boards now and SAEL does not exercise its option, Buyu incurs a loss on the extra 100,000 boards equal to the manufacturing cost. There is a 50% probability SAEL will exercise its option. The decision involves analyzing potential profits, constructing a decision tree, evaluating expected profits, and considering risk aversion with a $100,000 risk tolerance.
Paper For Above instruction
The contractual arrangement between Buyu Manufacturing and SAEL Electronics presents a complex decision-making scenario rooted in production planning, probabilistic outcomes, and risk management principles. The core dilemma involves whether Buyu should produce all 200,000 PC boards immediately or stage production based on SAEL's decision to exercise its option for an additional 100,000 units. Analyzing this problem requires comprehensive understanding of cost structures, expected profits, decision trees, and risk preferences.
Cost Structure and Revenue Profile
Manufacturing costs are characterized by a significant fixed setup cost of $250,000 per batch, regardless of batch size. The marginal production cost is $2.00 per board. Consequently, the total manufacturing cost for a batch of \(Q\) units is:
\[
\text{Total Cost} = \text{Setup Cost} + \text{Marginal Cost} \times Q = 250,000 + 2Q
\]
The sale price per board is fixed at $5, providing a revenue of:
\[
\text{Revenue} = 5 \times Q
\]
Profit from producing \(Q\) units is then:
\[
\text{Profit} = \text{Revenue} - \text{Total Cost} = 5Q - (250,000 + 2Q) = 3Q - 250,000
\]
Decision Alternatives
Buyu faces two principal options:
1. Produce all 200,000 boards now:
The profit for this scenario is:
\[
\text{Profit}_{200,000} = 3 \times 200,000 - 250,000 = 600,000 - 250,000 = \$350,000
\]
However, if SAEL does not exercise the option, Buyu bears a loss equivalent to the manufacturing cost of the extra 100,000 boards:
\[
\text{Additional Cost for extra 100,000} = 250,000 + 2 \times 100,000 = 250,000 + 200,000 = \$450,000
\]
revenue from the initial 100,000 boards:
\[
5 \times 100,000 = \$500,000
\]
profit on the initial set:
\[
3 \times 100,000 - 250,000 = \$300,000 - 250,000 = \$50,000
\]
if SAEL does not exercise the option, valuation with the initial 100,000 boards is:
\[
\text{Profit} = \$50,000 - \text{cost of extra} = \$50,000 - \$200,000 - 250,000
\]
but since the extra batch isn't sold, the loss on the additional 100,000 boards is 450,000, leading to a net profit of:
\[
\$50,000 - 200,000 - 250,000 = -\$400,000
\]
2. Produce 100,000 now and 100,000 later if SAEL exercises its option:
Initial profit:
\[
3 \times 100,000 - 250,000 = \$50,000
\]
If SAEL exercises the option (probability 50%), profit from the additional 100,000 boards:
\[
3 \times 100,000 - 250,000 = \$50,000
\]
The overall expected profit:
\[
0.5 \times (\$50,000 + \$50,000) + 0.5 \times \$50,000 = \$100,000
\]
Note that the initial production is profitable, and the optional batch only proceeds if SAEL exercises its option, which has a 50% chance.
Constructing the Decision Tree
The decision tree begins with two main branches:
- Manufacture all 200,000 immediately:
- SAEL exercises option (probability 50%): Profit = \$350,000
- SAEL does not exercise (probability 50%): Profit = -\$400,000
- Manufacture 100,000 now, and wait:
- SAEL exercises option (probability 50%): Profit = \$50,000 (initial) + \$50,000 (additional) = \$100,000
- SAEL does not exercise (probability 50%): Profit = \$50,000 (initial only)
Expected values are calculated for each decision to assess the optimal choice.
Expected Profit Analysis
- When manufacturing all at once:
\[
\text{Expected Profit} = 0.5 \times \$350,000 + 0.5 \times (-\$400,000) = \$175,000 - \$200,000 = -\$25,000
\]
indicating a negative expected profit.
- When staging manufacturing:
\[
\text{Expected Profit} = 0.5 \times \$100,000 + 0.5 \times \$50,000 = \$50,000 + \$25,000 = \$75,000
\]
which is positive and hence preferable.
Decision and Probabilistic Thresholds
Given analysis, producing 100,000 now and waiting appears favorable with an expected profit of \$75,000, which exceeds the negative expected profit of manufacturing entirely now.
Furthermore, one can determine the probability threshold of SAEL exercising its option (\(p\)) where the expected profits of the two strategies are equal:
\[
p \times \$350,000 + (1 - p) \times (-\$400,000) = p \times \$50,000 + (1 - p) \times \$50,000
\]
Simplifying yields a threshold probability where production decisions would be indifferent.
Expected Value of Perfect Information (EVPI)
Knowing with certainty whether SAEL will exercise its option would allow buyu to optimize production, avoiding negative payoffs. The EVPI quantifies this additional value, computed as the difference between the expected profit with perfect information and the expected profit under current uncertainty.
Impact of Risk Aversion
Considering buyu's risk aversion with a tolerance of \$100,000, decision-making shifts toward strategies that maximize expected utility rather than expected monetary gains. Applying utility functions or risk measures like Value at Risk or Conditional Value at Risk adjusts the decision, possibly favoring staged production to mitigate potential losses.
Conclusion
The analysis indicates that staged production—manufacturing 100,000 now and waiting for the option exercise—is optimal under the probabilistic model and expected profit calculations. Meanwhile, incorporating risk aversion slightly favors conservative staging, emphasizing the importance of flexible production planning in uncertain contractual arrangements. Accurate valuation of these options hinges on detailed probabilistic modeling and risk preference assessments, which are essential for strategic manufacturing decisions in supply chain management contexts.
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