A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being
0.25,
0.40,
and
0.35,
respectively.
A small facility is expected to earn an after-tax net present value of just
$13,000
if demand is low. If demand is average, the small facility is expected to earn
$15,000;
it can be increased to medium size to earn a net present value of
$30,000.
If demand is high, the small facility is expected to earn
$25,000
and can be expanded to medium size to earn
$70,000
or to large size to earn
$75,000.
A medium-sized facility is expected to lose an estimated
$25,000
if demand is low and earn
$130,000
if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of
$150,000;
it can be expanded to a large size for a net payoff of
$155,000.
If a large facility is built and demand is high, earnings are expected to be
$180,000.
If demand is average for the large facility, the present value is expected to be
$125,000;
if demand is low, the facility is expected to lose
$40,000.
Part 2
Choose the correct decision tree below. Note that each payoff is given in thousands ($000).
A.
Expand to lrg
Do nothing
Expand to lrg
Expand to med
Do nothing
Expand to med
Do nothing
$180
$125
−$40
$155
$150
$130
−$25
$75
$70
$25
$30
$15
$13
Low 0.25
Avg 0.40
High 0.35
Low 0.25
Avg 0.40
High 0.35
Low 0.25
Avg 0.40
High 0.35
Large
Small
Med
1234
In the diagram, 4 squares, 3 circles, and line segments connecting the squares and circles to form a decision tree are drawn. The starting point is the leftmost square labeled 1. From this square, three lines emerge to the right and each extends to a distinct branch point indicated by unlabeled circles. The upper path is labeled Large, the middle path is labeled Medium, and the lower path is labeled Small. From each of the circles, three branches continue to the right. From top to bottom, the first, the fourth, and the seventh line indicate the High path for that branch with a value of 0.35. The second, the fifth, and the eighth line indicate the Average path for that branch with a value of 0.40. The third, the sixth, and the ninth line indicate the Low path for that branch with a value of 0.25. At the end of Large High path, a square labeled 2 is drawn with 2 further branches to the right. At the end of Large Average path, a value of $ 125 is displayed. At the end of Large Low path, a value of negative $ 40 is displayed. At the end of Medium High path, a value of $ 180 is displayed. At the end of Medium Average path, a value of $ 130 is displayed. At the end of Medium Low path, a value of negative $ 25 is displayed. At the end of Small High path, a square labeled 3 is drawn with 3 further branches to the right. At the end of Small Average path, a square labeled 4 is drawn with 2 further branches to the right. At the end of Small Low path, a value of $ 13 is displayed. From top to bottom, the paths leaving square 2 are labeled Expand to large and Do nothing, respectively. At the end of the Expand to large path, a value of $ 155 is displayed; and at the end of the Do nothing path, a value of $ 150 is displayed. From top to bottom, the paths leaving square 3 are labeled Expand to large, Expand to medium, and Do nothing, respectively. At the end of the Expand to large path, a value of $ 75 is displayed; at the end of the Expand to medium path, a value of $ 70 is displayed; and at the end of the Do nothing path, a value of $ 25 is displayed. From top to bottom, the paths leaving square 4 are labeled Expand to medium and Do nothing, respectively. At the end of the Expand to medium path, a value of $ 30 is displayed; and at the end of the Do nothing path, a value of $ 15 is displayed.
B.
Expand to lrg
Do nothing
Expand to lrg
Expand to med
Do nothing
Expand to med
Do nothing
$180
$125
−$40
$155
$150
$130
−$25
$75
$70
$25
$30
$15
$13
Low 0.25
Avg 0.40
High 0.35
Low 0.25
Avg 0.40
High 0.35
Low 0.25
Avg 0.40
High 0.35
Large
Small
Med
1234
In the diagram, 4 squares, 3 circles, and line segments connecting the squares and circles to form a decision tree are drawn. The starting point is the leftmost square labeled 1. From this square, three lines emerge to the right and each extends to a distinct branch point indicated by unlabeled circles. The upper path is labeled Large, the middle path is labeled Medium, and the lower path is labeled Small. From each of the circles, three branches continue to the right. From top to bottom, the first, the fourth, and the seventh line indicate the High path for that branch with a value of 0.35. The second, the fifth, and the eighth line indicate the Average path for that branch with a value of 0.40. The third, the sixth, and the ninth line indicate the Low path for that branch with a value of 0.25. At the end of the Large High path, a value of $ 180 is displayed. At the end of the Large Average path, a value of $ 125 is displayed. At the end of the Large Low path, a value of negative $ 40 is displayed. At the end of medium High path, a square labeled 2 is drawn with 2 further branches to the right. At the end of medium Average path, a value of $ 130 is displayed. At the end of medium Low path, a value of negative $ 25 is displayed. At the end of Small High path, a square labeled 3 is drawn with 3 further branches to the right. At the end of Small Average path, a square labeled 4 is drawn with 2 further branches to the right. At the end of Small Low path, a value of $ 13 is displayed. From top to bottom, the paths leaving square 2 are labeled Expand to large and Do nothing, respectively. At the end of the Expand to large path, a value of $ 155 is displayed; and at the end of the Do nothing path, a value of $ 150 is displayed. From top to bottom, the paths leaving square 3 are labeled Expand to large, Expand to medium, and Do nothing, respectively. At the end of the Expand to large path, a value of $ 75 is displayed; at the end of the Expand to medium path, a value of $ 70 is displayed; and at the end of the Do nothing path, a value of $ 25 is displayed. From top to bottom, the paths leaving square 4 are labeled Expand to medium and Do nothing, respectively. At the end of the Expand to medium path, a value of $ 30 is displayed; and at the end of the Do nothing path, a value of $ 15 is displayed.
C.
Expand to lrg
Do nothing
Expand to lrg
Expand to med
Do nothing
Expand to med
Do nothing
$180
$125
−$40
$155
$150
$130
−$25
$75
$70
$25
$30
$15
$13
Low 0.25
Avg 0.40
High 0.35
Low 0.25
Avg 0.40
High 0.35
Low 0.25
Avg 0.40
High 0.35
Large
Small
Med
1567234
In the diagram, 7 squares and line segments connecting the squares and circles to form a decision tree are drawn. The starting point is the leftmost square labeled 1. From this square, three lines emerge to the right and each extends to a distinct branch point indicated by squares labeled 2, 3, and 4, respectively. The upper path is labeled Large, the middle path is labeled Medium, and the lower path is labeled Small. From each of these squares, three branches continue to the right. From top to bottom, the first, the fourth, and the seventh line indicate the High path for that branch with a value of 0.35. The second, the fifth, and the eighth line indicate the Average path for that branch with a value of 0.40. The third, the sixth, and the ninth line indicate the Low path for that branch with a value of 0.25. At the end of Large High path, a value of $ 180 is displayed. At the end of Large Average path, a value of $ 125 is displayed. At the end of Large Low path, a value of negative $ 40 is displayed. At the end of medium High path, a square labeled 5 is drawn with 2 further branches to the right. At the end of medium Average path, a value of $ 130 is displayed. At the end of medium Low path, a value of negative $ 25 is displayed. At the end of Small High path, a square labeled 6 is drawn with 3 further branches to the right. At the end of Small Average path, a square labeled 7 is drawn with 2 further branches to the right. At the end of Small Low path, a value of $ 13 is displayed. From top to bottom, the paths leaving square 5 are labeled Expand to large and Do nothing, respectively. At the end of the Expand to large path, a value of $ 155 is displayed; and at the end of the Do nothing path, a value of $ 150 is displayed. From top to bottom, the paths leaving square 6 are labeled Expand to large, Expand to medium, and Do nothing, respectively. At the end of the Expand to large path, a value of $ 75 is displayed; at the end of the Expand to medium path, a value of $ 70 is displayed; and at the end of the Do nothing path, a value of $ 25 is displayed. From top to bottom, the paths leaving square 7 are labeled Expand to medium and Do nothing, respectively. At the end of the Expand to medium path, a value of $ 30 is displayed; and at the end of the Do nothing path, a value of $ 15 is displayed.
D.
Expand to lrg
Do nothing
Expand to lrg
Expand to med
Do nothing
Expand to med
Do nothing
$180
$125
$40
$155
$150
$130
$25
$75
$70
$25
$30
$15
$13
Low 0.35
Avg 0.40
High 0.25
Low 0.35
Avg 0.40
High 0.25
Low 0.35
Avg 0.40
High 0.25
Large
Small
Med
1234
In the diagram, 4 squares, 3 circles, and line segments connecting the squares and circles to form a decision tree are drawn. The starting point is the leftmost square labeled 1. From this square, three lines emerge to the right and each extended to separate branch points indicated by circles. The upper path is labeled Large, the middle path is labeled Medium and the lower path is labeled Small. From each circle three branches continue to the right. From top to bottom, the first, the fourth, and the seventh line indicate the High path with a value of 0.25. The second, the fifth, and the eighth line indicate the Average path with a value of 0.40. The third, the sixth, and the ninth line indicate the Low path with a value of 0.35. At the end of Large High path, a value of $ 180 is displayed. At the end of Large Average path, a value of $ 125 is displayed. At the end of Large Low path, a value of $ 40 is displayed. At the end of Medium High path, a square labeled 2 is drawn with 2 further branches to the right. At the end of Medium Average path, a value of $ 130 is displayed. At the end of Medium Low path, a value of $ 25 is displayed. At the end of Small High path, a square labeled 3 is drawn with 3 further branches to the right. At the end of Small Average path, a square labeled 4 is drawn with 2 further branches to the right. At the end of Small Low path, a value of $ 13 is displayed. From top to bottom, the paths leaving square 2 are labeled Expand to large and Do nothing, respectively. At the end of the Expand to large path, a value of $ 155 is displayed; and at the end of the Do nothing path, a value of $ 150 is displayed. From top to bottom, the paths leaving square 3 are labeled Expand to large, Expand to medium, and Do nothing, respectively. At the end of the Expand to large path, a value of $ 75 is displayed; at the end of the Expand to medium path, a value of $ 70 is displayed; and at the end of the Do nothing path, a value of $ 25 is displayed. From top to bottom, the paths leaving square 4 are labeled Expand to medium and Do nothing, respectively. At the end of the Expand to medium path, a value of $ 30 is displayed; and at the end of the Do nothing path, a value of $ 15 is displayed.
Part 3
What should management do to achieve the highest expected payoff?
The management should build a
in order to achieve the highest expected payoff of
$enter your response here.
(Enter your response as a whole number.)
In the realm of business, strategic decision-making plays a pivotal role in determining success. When faced with multiple choices and uncertain outcomes, decision analysis tools like decision trees become invaluable. In this context, we explore a decision tree scenario to determine the optimal course of action for a manager deciding on facility expansion. The goal is to maximize expected payoffs while considering probabilities associated with different demand levels.
Understanding the Decision Tree
The decision tree, as presented in option B, provides a visual representation of the decision-making process. It starts with the initial decision of choosing between a small, medium, or large facility, influenced by the expected demand levels: low, average, and high. Each branch of the tree leads to different outcomes, and the associated probabilities guide the decision-making process.
Evaluating the Outcomes
The decision tree systematically evaluates potential outcomes based on varying demand scenarios. For instance, if demand is low, building a small facility results in a $13,000 payoff. On the other hand, if demand is high, constructing a large facility yields a substantial payoff of $180,000. The tree also accounts for expansion options, allowing for further refinement of decisions.
Optimizing the Expected Payoff
To optimize the expected payoff, the following strategies emerge:
Demand is Low: In this scenario, building a small facility is the preferred choice, offering a $13,000 payoff.
Demand is Average: When demand is anticipated to be average, the optimal decision is building a large facility, which leads to an expected payoff of $125,000.
Demand is High: Under high demand conditions, building a large facility remains the best strategy, with an expected payoff of $180,000.
Conclusion
Effective decision-making in the business world requires a careful consideration of all available options, probabilities, and potential outcomes. Decision trees, as illustrated in option B, provide a structured approach to this complex process. In this particular scenario, the optimal strategy to achieve the highest expected payoff involves building a large facility under all demand scenarios.
By following this decision analysis, management can enhance their ability to make informed choices, ultimately maximizing profitability and ensuring the long-term success of the organization. The systematic evaluation of options, as demonstrated in this decision tree, serves as a valuable tool in the arsenal of any manager seeking to navigate uncertain waters and secure the best possible outcome for their company.
Incorporating decision analysis methodologies into business strategies empowers managers to make data-driven decisions that not only optimize payoffs but also mitigate risks. As the business landscape continues to evolve, the ability to make informed, calculated decisions becomes a cornerstone of sustainable success.
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