1. 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
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Warehouse expansion 30,850 32,000 12,000 38,000
Test market new product 92,300 58,000 41,000 45,000
Advertising campaign 40,000 25,000 12,500 11,800
Research & Development 82,000 53,000 13,000 44,000
Purchase new equipment 33,000 12,500 4,500 8,900
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Capital funds available 110,500 65,000 88,750
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.
2. 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 10000 Miles 14000 Miles 18000 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.
3. 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.