Chapter 12

• Quantitative Analysis

  Problem solver attempts to formulate decision problem in mathematical terms.
• Quantitative Analysis requires:

  1. Specification of complete list of variable factors relevant to the problem at hand
  2. Specific quantifiable relationship among those variables
• Quantitative Analysis helps:

  1. Make choice which is compatible with his goals
  2. Enable him to consider variables which relevant in making appropriate decision
• Accountant using quantitative analysis

  • Must acquaint himself with objectives, assumptions and requirements of the decision employed
  • Tool that decision maker use in addition to other inputs in arriving at decisions.
  • Ensure alternatives are logically evaluated
• 2 types of decision making under Probability

  1. Decision making under certainty
  2. Decision making under Uncertainty
• Decision making under certainty

  • Each decision action only one event and single outcome for each action
• Decision making under certainty 


  100% chance of occurrence and probability 1.0
• Decision making under Uncertainty 


  common in reality, each action with it's probability of occurence
• Two bases of Probability of occurrence

  1. Mathematical proofs
  2. Historical evidence

  In absence: Subjective to assignment of probabilities
• Payoff


  Value assigned to different outflow.es from a decision and may be positive or negative
• Information economics 


  Process of deciding whether cost benefit criterion has been met
• Information deemed to meet cost benefit test


  Expected value of decision exceed result obtaining additional information
• Decision maker normally deal with in uncertainty rather than certainty
• Probability Distribution 


  Describes chance or likelihood of each of the collectively exhaustive and mutually exclusive set of events
• Probability event varies

  • Probability of 0 = events cannot occur
  • Probability of 1 = events is certain to occur
  • Probability between 0 and 1 = likelihood events will occur
• Types of Probabilities

  • Objective probabilities - calculated either LOGIC or ACTUAL EXPERIENCE
  • Subjective probabilities - estimates based on JUDGEMENT and PAST EXPERIENCES f likelihood of future events
• Basic terms of probability

  • Mutually exclusive - events cannot occur simultaneously
  • Joint Probability - both events will occur
  • Conditional Probability - Events will likely to occur since other events already occured
  • Independent - occurence of one does not effect other
  • Dependent - occurence of one have an effect to other
  • Independent - Joint prob = single prob
  • Independent - conditional prob = unconditional prob
• Rules in combining Probabilities

  Joint probability for two events = Probability of first event (Pr1) x Conditional probability of second events (Pr2)
• Rules in combining Probabilities

  Probability either one or both two events occur = sum of seperate probabilities - joint probability
• Rules in combining Probabilities 


  Probabilities for all possible mutually exclusive outcomes = single experiment must be add up to one.

  Ex: 4 variables/ 1 = 0.25

  V1=0.25, V2= 0.25, V3= 0.25, V4= 0.25

  = 1
• Discrete Distribution

  1. Uniform Distribution - All outcomes are equally likely
  2. Binomial Distribution - Each trial has only two possible outcomes ( accept or reject)
  3. Bernoulli Distribution - Involves in one trial where it deals with many as necessary
  4. Hypergeometric distribution - It used sampling without replacement
  5. Poison Distribution - Event being studied may happen more than once with random frequency
• Continuous Distribution

  1. Normal Distribution - most important and useful of all probability distribution, describe many physical phenomena.
  2. Exponential Distribution - Probability of zero occurence in a time period
  3. T-distribution ( student distribution) - used small samples of population, less than 30
  4. Chi square distribution - Test goodness of fit between actual data and theoretical distribution
• Unknown population variance of T distribution

  • Large sample sizes - almost identical to standard normal distribution
  • Small sample size - only the standard deviation is known
• T- distribution provides :

  • Reasonable estimate for test of population mean
  • Provides best estimates of variance than normal distribution
• payoff decision tables


  Identify best solution given several decision choices and future condition involves risk
• Payoff table 


  Present outcomes of specific decision when certain states of nature occur
• Perfect information 


  Knowledge of future state of nature will occur with certainty
• Expected Value of Perfect Information ( EVPI)


  EVPI = Expected value w/o perfect information - Return of best action taken given perfect information
• Expected Value of Perfect Information 


  Amount of company is willing to pay for the market analyst errorless advice.
• Decision Tree 


  Analytical tool which series of decision has to be made at various time intervals influenced by information available at the time it is made
• Event of each act 


  Several decisions or acts and possible consequence that decision tree diagram show
• Steps in making decisions tree

  1. Identification of points and decision and alternatives available
  2. Determination points of uncertainty and types of range on outcomes
  3. Estimate . probabilities of different events
  4. Estimates cost and gains of various events
  5. Analysis of alternative value in chosing course of action.
• Learning curves 


  Reflects increase of rates at which people Performed task as they gained experience, only applicable on each stage of production
• Leaning Curves

  • Time requires is reduced by 20% to 40%, 20% is the most common
• Simulation 


  Technique for experimenting with logical and mathematical models using a computer
• Simulation Techniques 


  Experimentation is neither new nor uncommon in business. It is organized trial and error using model of the rela world to obtain information prior full time implementation
• Simulation Techniques 


  Models classified into two:

  1. Physical Models
  2. Abstract Models - maybe pictorial, logical mathematics that is time consuming calculations and eliminated much of costly drudgery lead to grow of interest
• Simulation procedure

  1. Define objectives - they serve as a guideline, aid in understanding existing System and estimate behavior of some new system. What if questions whether to modify models.
• Simulation Procedure 


  2. Formulate the model - include individual behavior and interrelationship must be define in precise logic mathematical terms.

  2 KINDS OF MODEL

  1. Controllable - decision maker influence
  2. Probabilistics - involve circumstances beyond their control
• Simulation procedure

  3. Validate the model - Assurance that experiment be realistic require validation often using historical data