View Full Essay Words: Findings from analyzing the Arapahoe County Adopted Budgets by using the Adopted Budgets to establish a baseline for comparison The purpose of this memo is to relay to you the findings I obtained from a comprehensive analysis of the Arapahoe County Adopted Budgets through the preceding Adopted Budgets for the preceding — financial years, with the aim of developing a baseline for making comparisons.
Decision trees are a major component of many finance, philosophy and decision analysis university classes, yet many students and graduates fail to understand the purpose behind studying this topic. However, these statistical representations often play an integral role in an corporate finance and economic forecasting setting, and also have been paramount to investment theory and practice.
Decision Tree Basics The basics of decision trees are organized as follows: An individual has to make a decision such as whether or not to undertake a capital projector must chose between two competing ventures; this is often depicted with a decision node.
However, since the events indicated by end nodes will be determined in the future, their occurrence is currently uncertain. As a result, chance nodes specify the probability of a specific end node coming to fruition. Decision tree analysis involves forecasting future outcomes and assigning probabilities to those events.
As the list of potential outcomes, which are contingent on prior events, become more dynamic with complex decisions, Bayesian probability models have to be implemented to determine priori probabilities. Rather than these complicated issues, we will focus on the general purposes that decision trees serve in "the real world.
The binomial option pricing model uses discrete probabilities to determine the value of an option at expiration. The most basic binomial models assume that the value of the underlying asset will either move up or down, based on calculated probabilities, at the maturity date of the European option.
Based on these expected payoff values, the price of the option can easily be determined. The binomial tree would factor in multiple paths that the underlying asset's price can take as time progresses.
For example, the price can move up, down, down, up, up or any other combination of infinite paths. At every point in time, the future value of the option will be determined by the price path taken by the underlying security. Furthermore, the final price of the security is not limited to only two potential final values as in the above example.
As the number of nodes in the binomial decision tree increases, eventually the model converges onto the Black-Scholes formula.
Black Scholes Although the Black-Scholes formula provides an easier alternative to option pricing over decision trees, software is available which can create a binomial option pricing model with "infinite" nodes.
This type of calculation often provides more accurate pricing information, especially for Bermuda Options and dividend paying stocks. Find out how to carve your way into this valuation model niche. See Breaking Down Binomial Trees.
Using Decision Trees for Real Option Analysis Valuing real optionssuch as expansion options and abandonment optionsmust be done with the use of decision trees as their value cannot be determined via the Black-Scholes formula.
Expansion contraction options are embedded in the project. For example, an oil and gas company can purchase a piece of land today, and if drilling operations are successful, it can buy an additional lot of land for a cheap price. If drilling is unsuccessful, the company will not exercise the option and it will expire worthless.
Since real options provide significant value to corporate projects, they are an integral part of the capital budgeting decision. Real Option Analysis The decision of whether to purchase the option or not must usually be decided prior to project initiation. However, once the probabilities of success and failures are determined, decision trees can help clarify what the expected value is of potential capital budgeting decision.
Companies will often accept what initially seems like negative net present value projects, but once the real option value is considered, the NPV actually becomes positive. A primary advantage of decision tree analysis is that it provides a comprehensive overview for the alternative scenarios of a decision.
Decision Tree Applications for Competing Projects Similarly, decision trees are also applicable to marketing and business development operations.
The general setting for these types of cases is similar to that of real option pricing. Basically, companies are constantly making decisions regarding product expansion, marketing operations, international expansion, international contraction, hiring employees or even merging with another company.
Organizing all considered alternatives with a decision tree allows for a systematic means to evaluate these ideas simultaneously. This is not to suggest that when a business decides whether or not to hire an additional worker, a decision tree is used every time.
However, decision tree do provide a general framework on how to go about determining the ideal solution to a problem and can help managers realize the consequences, either positive or negative, of their decision.
For example, by formulating the issue of hiring additional staff with a decision tree, managers can determine the expected financial impact of such cases as hiring an employee who does not meet expectations and thus has to be let go.
Essentially, this type of investigation can be used as a sensitivity analysis to quantify the impact of a wide range of uncertain variables.
How can you assign a value to what a company may do with its business in the future?As you improve your forecasting accuracy, be sure to reward yourself for staying on track with your spending. Splurge a little. Upgrade the restaurant you typically go out to on Friday night to one that doesn’t use paper towels for napkins.
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Planning and Forecasting Topic Gateway Series. Planning and Forecasting also study planning in the Strategic level paper 6, Business Strategy.
Forecasting is covered in managerial level paper 1, Management Accounting Budgeting and Cash Forecasting briefly as these topics will be covered by other topic gateways.
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