25. Describe how to use break-even analysis.
Break-even analysis entails the calculation and examination of the margin of safety for an entity based on the revenues collected and associated costs. Analyzing different price levels relating to various levels of demand, an entity uses break-even analysis to determine what level of sales are needed to cover total fixed costs. A demand-side analysis would give a seller greater insight regarding selling capabilities.
BREAKING DOWN 'Break-Even Analysis'
Break-even analysis is useful in the determination of the level of production or in a targeted desired sales mix. The analysis is for management’s use only as the metric and calculations are often not required to be disclosed to external sources such as investors, regulators or financial institutions. Break-even analysis looks at the level of fixed costs relative to the profit earned by each additional unit produced and sold. In general, a company with lower fixed costs will have a lower break-even point of sale. For example, a company with $0 of fixed costs will automatically have broken even upon the sale of the first product assuming variable costs do not exceed sales revenue. However, the accumulation of variable costs will limit the leverage of the company as these expenses are incurred for each item sold.
Contribution Margin
The concept of break-even analysis deals with the contribution margin of a product. The contribution margin is the excess between the selling price of the good and total variable costs. For example, if a product sells for $100, total fixed costs are $25 per product and total variable costs are $60 per product, the product has a contribution margin of the product is $40 ($100 - $60). This $40 reflects the amount of revenue collected to cover fixed costs and be retained as net profit. Fixed costs are not considered in calculating the contribution margin.
Formulas for Break-Even Analysis
The calculation of break-even analysis may be performed using two formulas. First, the total fixed costs are divided the unit contribution margin. In the example above, assume total company fixed costs are $20,000. With a contribution margin of $40, the break-even point is 500 units ($20,000 divided by $40). Upon the sale of 500 units, all fixed costs will be paid for, and the company will report a net profit or loss of $0.
Alternatively, the break-even point in sales dollars is calculated by dividing total fixed costs by the contribution margin ratio. The contribution margin ratio is the contribution margin per unit divided by the sale price. Using the example above, the contribution margin ratio is 40% ($40 contribution margin per unit divided by $100 sale price per unit). Therefore, the break-even point in sales dollars is $50,000 ($20,000 total fixed costs divided by 40%). This figured may be confirmed as the break-even in units (500) multiplied by the sale price ($100) equals $50,000.
26. Explicate decision trees or problem solving and decision making.
A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm.
Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning.
A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represents classification rules.
In decision analysis a decision tree and the closely related influence diagram are used as a visual and analytical decision support tool, where the expected values (or expected utility) of competing alternatives are calculated.
A decision tree consists of 3 types of nodes:
Decision nodes - commonly represented by squares
Chance nodes - represented by circles
End nodes - represented by triangles
Decision trees are commonly used in operations research and operations management. If in practice decisions have to be taken online with no recall under incomplete knowledge, a decision tree should be paralleled by a probability model as a best choice model or online selection model algorithm. Decision trees, influence diagrams, utility functions, and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods.
Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). Therefore, used manually, they can grow very big and are then often hard to draw fully by hand. Traditionally, decision trees have been created manually — as the aside example shows — although increasingly, specialized software is employed.
Decision making is the process of choosing a solution from available alternatives.
Rational decision making is a systematic process in which managers define problems, evaluate alternatives, and choose optimal solutions that provide maximum benefits to their organizations.
