Question

1. A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be $400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of$450,000 and maintaining the small facility would have a net present value of $50,000. If a large facility is built and demand is high, the estimated net present value is $800,000. If demand turns out to be low, the net present value will be -$10,000. The probability that demand will be high is estimated to be .60, and the probability of low demand is estimated to be .40. a. Analyze using a tree diagram. What is your decision?

show all work, please and thank you

Answer 1

Answer:

Decision tree is a tool for decision making using the visual representation of the available decision and the associated payoffs. Create a decision tree as shown below: -S400,000 Low Demand (0.40) $50,000 No Expansion Small High Demand (0.60) Expand $450,000 Low Demand (0.40) $10,000 Large $800,000 High Demand (0.60)

Now calculate the payoffs at the decision nodes, start from the right hand side: Node-4: The payoffs for no expansion is 550.000 and payoff for Expand is $450,000. Since the payoff of expansion is higher, the payoff of node 4 is $450,000. Node 2: Calculate the expected payoff at node-2 by multiplying the payoffs with their probabilities and then adding them, as shown below. Node 2 - Probability, Payoffs -0.40% $400,000+ 0.60 $450,000 -$430,000 Node-3: Calculate the expected payoff at node-3 by multiplying the payoffs with their probabilities and then adding them, as shown below. Node-3 - Probability, Payoffs -0.40x-S10,000+ 0.60 x $800,000 -S476,000 Node 1: The payoffs for small facility is $430,000 and payoff for large facility is $476,000 Since the payoff of large facility is higher, the best decision is to open a large facility.