A Manager Must Decide How Many Machines Of A Certain Type To

A Manager Must Decide How Many Machines Of A Certain Type To Buy T

A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buying one machine or buying two. If only one machine is purchased initially and demand exceeds its capacity, a second machine can be purchased later. However, the cost per machine is lower if both are purchased at the same time. The estimated probability of low demand is 0.30, and the probability of high demand is 0.70.

The net present value (NPV) associated with purchasing two machines immediately is $75,000 if demand is low and $130,000 if demand is high. The NPV for purchasing one machine under low demand is $90,000. If demand is high, there are three options: doing nothing (NPV of $90,000), subcontracting (NPV of $110,000), or purchasing a second machine (NPV of $100,000).

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In the strategic decision-making process for capital investments, managers routinely face complex choices under uncertainty. The decision regarding how many machines to purchase—either one or two—entails analyzing potential costs, benefits, and risks associated with each alternative, factoring in the probabilistic nature of demand. This decision is vital because it influences operational capacity, costs, and long-term profitability, especially for a business experiencing increased demand for a new product line.

Understanding the implications of each option involves evaluating their respective expected values, considering the probabilities of high and low demand scenarios. The decision analysis incorporates the concept of expected monetary value (EMV), a common decision-making tool used in managerial finance and operations management. EMV helps quantify the expected outcomes by weighting the net present values (NPVs) of each scenario by their probabilities, thus aiding managers in making more informed decisions under risk and uncertainty.

Evaluating the Options: One vs. Two Machines

The first option involves purchasing a single machine. If demand remains low, the NPV is $90,000. However, if demand turns out to be high, the manager faces three potential courses of action: doing nothing, subcontracting production, or purchasing an additional machine. Doing nothing with high demand yields an NPV of $90,000, which is equivalent to low demand conditions, but may be insufficient to meet actual production requirements. Subcontracting offers a higher NPV of $110,000, although it might involve higher costs or less control over production quality. Purchasing a second machine under high demand results in an NPV of $100,000, but entails an upfront investment and associated risks.

The second alternative involves purchasing two machines simultaneously. This strategy has an initial net present value of $75,000 under low demand and $130,000 under high demand, reflecting economies of scale and potential cost savings when buying in bulk. Although the upfront investment is higher, it offers increased operational capacity and potentially higher profitability, especially if demand materializes as expected.

Expected Monetary Value Analysis

Calculating EMV for the single machine option under high demand involves considering the three possible actions:

• Do nothing: NPV = $90,000
• Subcontract: NPV = $110,000
• Buy second machine: NPV = $100,000

Given the probabilities and NPVs, the EMV for high demand can be computed by selecting the action with the highest expected payoff or, more precisely, combining with the low demand scenario. The overall EMV for purchasing one machine involves weighing the potential of each action and its probability.

The probabilistic evaluation suggests that purchasing two machines upfront might provide strategic advantages by reducing operational uncertainties, although at higher initial costs. Conversely, purchasing one machine adds flexibility, allowing the company to respond to demand changes over time. Decision-makers might also consider factors such as financing options, capacity planning, and long-term strategic goals in their final judgment.

Conclusion

Ultimately, the optimal choice hinges on the company's risk appetite, financial capacity, and demand forecast accuracy. If the company prefers minimizing upfront costs and maintaining flexibility, purchasing one machine and possibly expanding later aligns with risk management strategies. Alternatively, if the forecast indicates robust demand and cost savings are prioritized, buying two machines initially could yield higher profitability. Employing decision analysis tools like EMV facilitates making rational choices under uncertainty, providing a quantitative foundation that complements qualitative considerations.

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