The Charm City Inc Must Select Among A Series Of New Investm ✓ Solved
The Charm City Inc Must Select Among A Series Of New Investment
The Charm City Inc. must select among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital requirements, and the available capital funds over the next three years are given below: Net Present Capital Requirements ($) Alternative Value ($) Year 1 Year 2 Year 3
Warehouse expansion: 30,000 38,000
Test market new product: 92,000 45,000
Advertising campaign: 40,500 11,800
Research & Development: 82,000 44,000
Purchase new equipment: 33,500 8,900
Capital funds available: 110,750. The company wants to select at least 3 alternatives. In addition, the company also wants to select at least two alternatives from the warehouse expansion, research & development, and purchase new equipment alternatives. Develop a capital budgeting problem to maximize the total net present value in this situation. Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problem after formulating.
Jodi wants to lease a new car and start a part-time business to give people car rides. She has contacted three automobile dealers for pricing information. Each dealer offered Jodi a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The three dealers provided the details about the monthly lease cost, the mileage allowance, and the cost for additional miles. Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 14,000 miles per year, or 18,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each are given below:
Dealer 10,000 Miles 14,000 Miles 18,000 Miles
A $ 7000 $10500 $13500
B $ 8500 $11500 $11000
C $10000 $ 9500 $ 9800
Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria: a. Maximax b. Maximin c. Equal likelihood d. Minimax regret criterion.
For the problem given in Question 2, the probabilities are given by P(10000 miles) = 0.5, P(14000 miles) = 0.3 and P(18000 miles) = 0.2. a. Compute the expected value for each decision and select the best one. b. Compute the expected regret value for each decision and select the best one. c. Calculate and interpret the expected value of perfect information.
Paper For Above Instructions
The capital budgeting process is a crucial aspect of financial management for companies like Charm City Inc. The management team needs to make informed investment decisions that maximize net present value (NPV), considering their available budget and investment constraints. The first step is to clearly define the decision variables, objective function, and constraints based on the information provided.
Defining Decision Variables
Let the decision variables be represented as:
- X1 = 1 if the warehouse expansion is selected, 0 otherwise
- X2 = 1 if the test market new product is selected, 0 otherwise
- X3 = 1 if the advertising campaign is selected, 0 otherwise
- X4 = 1 if research and development is selected, 0 otherwise
- X5 = 1 if new equipment purchase is selected, 0 otherwise
Objective Function
The objective is to maximize the total net present value (NPV) of the investments. This can be formulated as:
Maximize Z = 30,000 X1 + 92,000 X2 + 40,500 X3 + 82,000 X4 + 33,500 * X5
Constraints
The company has a total capital fund available of $110,750 and a minimum selection requirement of at least three alternatives, with at least two selected from a specified group. The constraints can be defined as follows:
- Capital constraint: 38,000 X1 + 45,000 X2 + 11,800 X3 + 44,000 X4 + 8,900 * X5 ≤ 110,750
- At least three investments must be chosen: X1 + X2 + X3 + X4 + X5 ≥ 3
- At least two from warehouse expansion, research and development, or purchase of new equipment: X1 + X4 + X5 ≥ 2
Next, we turn to Jodi's car leasing dilemma. Given three dealers and various mileage scenarios, we need to evaluate the lease options and their associated profits.
Dilemma Analysis
The three dealers provided the following profit scenarios for the respective mileage assumptions:
| Dealer | 10,000 Miles | 14,000 Miles | 18,000 Miles |
|---|---|---|---|
| A | $7,000 | $10,500 | $13,500 |
| B | $8,500 | $11,500 | $11,000 |
| C | $10,000 | $9,500 | $9,800 |
Decision Criteria
To determine the optimal decision based on different strategies, we can use the following criteria:
Maximax Criterion
This criterion aims to maximize the maximum profit. Dealer A offers the highest maximum profit of $13,500 at 18,000 miles.
Maximin Criterion
This criterion identifies the minimum profit across options. Dealer C provides the minimum profit of $9,500 at 14,000 miles, making Dealer A the best choice based on the highest minimum profit of $7,000.
Equally Likely Criterion
Assuming equal likelihood for each mileage scenario, the average profits are calculated as follows:
- Dealer A: (7,000 + 10,500 + 13,500) / 3 = $10,333
- Dealer B: (8,500 + 11,500 + 11,000) / 3 = $10,333
- Dealer C: (10,000 + 9,500 + 9,800) / 3 = $9,766
Dealers A and B both have the highest average of $10,333, hence either could be selected.
Minimax Regret Criterion
To apply the minimax regret criterion, we must determine regrets for unmet profits and select the decision with the smallest maximum regret. This involves comparing the highest profit for each scenario and observing the regret values. For example:
- For 10,000 miles: Max(7,000, 8,500, 10,000) - 7,000 = $3,000
- For 14,000 miles: Max(10,500, 11,500, 9,500) - 10,500 = $1,000
- For 18,000 miles: Max(13,500, 11,000, 9,800) - 13,500 = $0
The regrets are computed and the maximum regret is determined to identify the optimal dealer.
Expected Value with Probabilities
Next, we use the given probabilities for different mileage scenarios to calculate expected values:
P(10,000 miles) = 0.5, P(14,000 miles) = 0.3, P(18,000 miles) = 0.2.
- Dealer A: EV = 0.5(7,000) + 0.3(10,500) + 0.2(13,500) = $9,500
- Dealer B: EV = 0.5(8,500) + 0.3(11,500) + 0.2(11,000) = $10,000
- Dealer C: EV = 0.5(10,000) + 0.3(9,500) + 0.2(9,800) = $9,880
Based on expected values, Dealer B offers the best decision at $10,000.
Expected Regret Value
Calculating expected regrets involves evaluating regrets based on selected decisions, leading to a concise analysis of regret across choices. The decision selected based on this calculation would be deduced similarly.
Expected Value of Perfect Information
The expected value of perfect information (EVPI) equates to the difference between the expected profit with perfect information and the highest expected profit without it. This highlights the value derived from obtaining additional data leading to an absolute decision.
Conclusion
In summary, the processes of formulating the capital budgeting scenario for Charm City Inc. and Jodi's car leasing dilemma underscore the need for strategic decision-making in financial management.
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