# Decision trees

Useful quantitative tool to analyze decisions that involve a progression of decision

Decision trees are a useful way to analyze hiring, marketing, investment, equipment purchases, pricing, and similar decisions that involve a progression of decisions. They’re called decision trees because, when diagrammed they look a lot like a tree with branches. Typical decision trees encompass expected value analysis by assigning probabilities to each possible outcome and calculating payoffs for each decision path.

Exhibit illustrates a decision facing Sangeeta Bakshi who wants to relocate her fashion clothing outlet. The lease on her store in Greater Kailash, New Delhi, is expiring and she has decided not to renew it. Her property consultant has identified an excellent site in a nearby shopping mall on Saket. The mall owner has offered two comparable locations: one with 12,000 square feet (the same as she has now) and the other a larger, 20,000 square foot space. Sangeeta has an initial decision to make about whether to rent the larger or smaller location. If she chooses the larger space and the economy is strong she estimates the store will make a Rs 320,000 profit. However, if the economy is poor the high operating costs of the larger store will mean that profit will be only Rs 50,000. With the smaller store, she estimates the profit at Rs 240,000 with a good economy and Rs 130,000 with a poor one.

As you can see from Exhibit, the expected value for the larger store is Rs239,000 [(.70 x 320) + ( .30 x 50)] . The expected value for the smaller store is Rs 207,000 [(70 x 240) + (.30 x 130)] . Given these projections, Sangeeta is planning to recommend the rental of the larger store space. What if Sangeeta wants to consider the implications of initially renting the smaller space and then and then expanding if the economy picks up? She can extend the decision tree to include this second decision point. She ahs calculated three options: no expansion, adding 4,000 square feet, and adding 8,000 square feet. Following the approach used for Decision Point 1, he could calculate the profit potential by extending the branches on the tree and calculating expected values for the various options.

Break even analysis:

A technique or identifying the point to which total revenue is just sufficient to cover total costs.

How many units of a product must an organization sell in order to break even — that is, to have neither profit nor loss? A manager might want to know the minimum number of units that must b sold to achieve his or her profit objective or whether a current product should continue to be sold or should be dropped from the organization’s product line. Breakeven analysis is a widely used technique foe helping managers make profit projections.

Break even analysis is a simplistic formulation, yet it is valuable to managers because it points out the relationship among revenues, costs and profits. To compute the break even point (BE) the manager needs to know the unit price of the product being sold (P) the variable cost per unit (CV) and the total fixed costs (TFC).

An organization’s break even when its total revue is just to equal its total costs. But total cost has two parts; a fixed component and a variable component. Fixed costs are expenses that do not change, regardless of volume, such as insurance premiums and property taxes. Fixed costs, of course are fixed only in the short term because, in the long run commitments terminate and are, thus subject to variation. Variable costs change in proportion to output and include raw materials, labor costs, and energy costs.

The break even point can be computed graphically or by using the following formula:

BE = [TFC /(P – VC)]

This formula tells us that (1) total revenue will equal total cost when we sell enough units at a price that covers all variable unit costs, and (2) the difference between price and variable costs, when multiplied by the number of units sold, equals the fixed costs.

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