Homework Assignment Three

DECISION TREE: The Widget-san Company is considering opening a new location. Management is trying to decide whether to build a small, medium, or large facility. The level of demand for the new facility can be described as poor, moderate, or good, with the probability for poor of 0.30, for moderate of 0.55, and for good of 0.15.

If a large facility is built and demand is good, the net present worth of the after-tax earnings is calculated to be $175,000. If demand is moderate for the large facility, the PW will be $100,000; and if demand is poor, the facility will lose a PW of $50,000.

A medium-sized facility will lose a PW of $20,000 if demand is poor and will make a PW of $110,000 if demand is moderate. If demand is good, the medium-sized facility is expected to earn a PW of $120,000, or it can be enlarged at a cost of $50,000 to earn a PW of $165,000 before the cost of the expansion is deducted.

A small facility is estimated to earn a PW of $25,000 if demand is poor. If demand is moderate, the small facility is expected to earn a PW of $90,000, or it can be enlarged moderately at a cost of $40,000 to earn a PW of $110,000 before the cost of the enlargement is deducted. If demand is good, the small facility will earn a PW of $90,000, or it can be enlarged moderately at a cost of $40,000 to earn $110,000 (as above), or greatly enlarged at a cost of $60,000 to earn a PW of $175,000 before the cost of the expansion is deducted.

1. Construct a decision tree manually or have TreePlan draw and solve (for EMV) the decision tree for this problem. Clearly show all the relevant monetary values on the tree.
2. State in words what the company should do to achieve the highest EMV.
   A-1 Given the following conditional value table, determine the appropriate decision under uncertainty using:
   1. Maximax
   2. Maximin
   3. Equally likely

States of Nature

Alternatives Very favorable market Average Market Unfavorable Market

Build new plant $350,000 $240,000 -$300,000

Subcontract $180,000 $90,000 -$20,000

Overtime $110,000 $60,000 -$10,000

Do nothing $0.00 $0.00 $0.00

A-7 The following payoff table provides profits based on various possible decision alternatives and various levels of demand at Amber Gardner’s software firm:

Demand

Low High

Alternative 1 $10,000 $30,000

Alternative 2 $5,000 $40,000

Alternative 3 -$2,000 $50,000

The probability of low demand is 0.4, whereas the probability of high demand is 0.6

1. What is the highest possible expected monetary value?
2. What is the expected value under certainty?
3. Calculate the expected value of perfect information for this situation.

A-9 Chung Manufacturing is considering the introduction of a family of new products. Long-term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of choosing a process that is inappropriate. Chen Chung is VP of operations. He can choose among batch Manufacturing or custom manufacturing, or he can invest in-group technology. Chen won’t be able to forecast demand accurately until after he makes the process choice. Demand will be classified into four compartments: poor, fair, good and excellent. The table below indicates the payoffs (profits) associated with each process/demand combination, as well as the probabilities of each long-term demand level.

Poor Fair Good Excellent

Probability .1 .4 .3 .2

Batch -$200,000 $1,000,000 $1,200,000 $1,300,000

Custom $1,000,000 $3,000,000 $7,000,000 $8,000,000

Group Technology -$1,000,000 -$5,000,000 $5,000,000 $2,000,000

1. Based on expected value, what choice offers the greatest gain?
2. What would Chen Chung be willing to pay for a forecast that would accurately determine the level of demand in the future?

Price: $14.62

Solution: The downloadable solution consists of 7 pages, 762 words and 1 charts.
Deliverable: Word Document