1. The Tri-County Generation and Transmission Association is a nonprofit cooperative organization that provides electrical service to rural customers. Based on a faulty long-range demand forecast, Tri-County overbuilt its generation and distribution system. Tri-County now has much more capacity than it needs to serve its customers. Fixed costs, mostly debt service on investment in plant and equipment, are $82.5 million per year. Variable costs, mostly fossil fuel costs, are $25 per megawatt-hour (MWh, or million watts of power used for 1 hour). The new person in charge of demand forecasting prepared a short-range forecast for use in next year’s budgeting process. That forecast calls for Tri-County customers to consume 1 million MWh of energy next year.
2. A manufacturinglant has reached full capacity. The company must build a second plant—either small or large—at a nearby location. The demand is likely to be high or low. The probability of low demand is 0.3. If demand is low, the large plant has a present value of $5 million and the small plant, a present value of $8 million. If demand is high, the large plant pays off with a present value of $18 million, and the small plant with a present value of only $10 million. However, the small plant can be expanded later if demand proves to be high for a present value of $14 million.
Determining the Break-Even Price
Tri-County Generation and Transmission Association, a nonprofit cooperative providing electrical service to rural customers, has faced a financial challenge due to an overbuilt generation and distribution system resulting from a faulty long-range demand forecast. To evaluate their break-even price for the upcoming year, we need to consider both fixed and variable costs.
Fixed Costs: The fixed costs, primarily composed of debt service on investments in plant and equipment, amount to $82.5 million per year.
Variable Costs: Variable costs, primarily related to fossil fuel expenses, are $25 per megawatt-hour (MWh).
The new demand forecast predicts that customers will consume 1 million MWh of energy in the next year. To calculate the break-even price, we can sum the fixed and variable costs:
Total Costs = Fixed Costs + (Variable Costs per MWh * Forecasted Consumption) Total Costs = $82.5 million + ($25/MWh * 1,000,000 MWh) Total Costs = $107.5 million
Now, to determine the break-even price per MWh, we divide the total costs by the forecasted consumption:
Break-Even Price per MWh = Total Costs / Forecasted Consumption Break-Even Price per MWh = $107.5 million / 1,000,000 MWh Break-Even Price per MWh = $107.5
Answer 1: Tri-County needs to charge its customers approximately $107.5 per MWh to break even next year.
Evaluating the Impact of Customer Conservation
If customers react to this high price by conserving energy and only 95 percent of the forecasted demand materializes, we can assess the resulting surplus or loss.
Forecasted Consumption = 1,000,000 MWh Actual Consumption = 0.95 * Forecasted Consumption Actual Consumption = 0.95 * 1,000,000 MWh Actual Consumption = 950,000 MWh
To determine the financial outcome, we can recalculate the total costs for the actual consumption:
Total Costs = Fixed Costs + (Variable Costs per MWh * Actual Consumption) Total Costs = $82.5 million + ($25/MWh * 950,000 MWh) Total Costs = $107.5 million
Answer 2: If customers conserve energy, resulting in only 95 percent of forecasted demand, Tri-County will break even, with no surplus or loss. The total costs will remain at $107.5 million.
In conclusion, Tri-County needs to charge $107.5 per MWh to break even next year. If customers conserve energy, the organization will neither gain nor lose financially, maintaining a break-even point. However, the challenge lies in finding a balance between pricing and customer satisfaction to ensure long-term sustainability.
Decision Analysis for Manufacturing Plant Expansion
Creating a Decision Tree: To make an informed decision regarding the expansion of the manufacturing plant, which depends on future demand, we can construct a decision tree:
In this decision tree:
The initial decision node represents the choice between a large plant (L) and a small plant (S).
The branches from the initial decision lead to two possible future events: high demand (H) or low demand (L).
The end nodes display the present values associated with each combination of decisions and events.
Optimizing Expected Payoff
To achieve the highest expected payoff, we must consider the probabilities of each event and the associated values:
For the large plant:
If demand is low (0.3 probability):
Expected Value (EV) = 0.3 * $5 million + (1 – 0.3) * $0 = $1.5 million
If demand is high (0.7 probability):
EV = 0.7 * $18 million + (1 – 0.7) * $0 = $12.6 million
For the small plant:
If demand is low:
EV = 0.3 * $8 million + (1 – 0.3) * $0 = $2.4 million
If demand is high:
EV = 0.7 * $10 million + (1 – 0.7) * $14 million = $3.6 million
Expansion of the small plant (if demand is high):
EV = $3.6 million (no uncertainty)
Considering these expected values, the management should choose to build the large plant in anticipation of high demand. This decision yields the highest expected payoff of $12.6 million.
In summary, by analyzing the decision tree and the probabilities associated with different scenarios, management should opt for building the large plant when considering future demand to maximize the expected payoff and overall profitability.
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