# DA2 – Quantitative Analysis

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#### Course Features

#### Course Details

### DA2 Quantitative Analysis

**Learning outcomes**

- Demonstrate the use of probability where risk and uncertainty exist
- Apply financial mathematical techniques
- Apply techniques for presentation and analysis of statistical data
- Apply business modelling techniques to analyse data

Topic |
Weighting |

Probability and uncertainty | 20% |

Financial mathematics techniques | 25% |

Presentation and analysis of statistical data | 25% |

Business modelling techniques | 30% |

### Content

#### 1. Probability and uncertainty

**A. Simple Probability (I)**

- Explain the most simple probability techniques used in the world of business and accounting
- Describe what probability
- Differentiate the three methods of assigning probabilities (classical, relative frequency and subjective method)
- Describe sample spaces and events for random experiments with graphs, tables, lists, or tree diagrams

**B. Addition and Multiplication Rules (I)**

- Calculate the probabilities of joint events such as unions and intersections from the probabilities of individual events
- Explain mutually exclusive and statistically independent events
- Apply the general addition and multiplication rules

**C. Conditional Probability (M)**

- Explain when two events are said to be dependent
- Apply the conditional formula to evaluate the probabilities
- Calculate conditional probabilities using Bayes’ theorem

**D. Expected Values (M)**

- Define a random variable and expectation of a random variable
- Define discrete and continuous random variables and their probability distributions
- Calculate Expected Value and Variance of a discrete probability distribution.
- Calculate and interpret expectations between random variables

**E. Risk and Uncertainty (M)**

- Explain the concept of risk and how it differs from uncertainty
- Compute risk and uncertainty and interpret the results
- Discuss different methods used to counter risk in capital expenditure planning
- State what makes risk important in the selection of projects
- Explain various techniques commonly used to measure risk in investment projects
- Use different criterions to make decisions under conditions of uncertainty (e.g maximax, maximin, minimax, Hurwicz and Laplace)

#### 2. Financial mathematics techniques

**A. Simple and Compound Interest (M)**

- Define 'simple interest' and solve problems involving this concept.
- Calculate any single variable—principal, interest rate, amount of interest, or time given the other three.
- Define the terms 'amount,' 'present value,' 'maturity value,' and 'equivalent value,' and solve problems involving these concepts.
- Define the terms 'compound interest,' 'compound amount', 'equivalent value', and 'focal date' and calculate each value given other values.

**B. Annuities and Perpetuities (M)**

- Differentiate between an Annuity and a Perpetuity
- Solve problems involving 'present value' and 'future values' and 'discounting' for loans or investments charging or earning compound interest.
- Define the term 'ordinary annuity,' and calculate the amount of an ordinary simple annuity.
- Calculate the present value of an annuity.
- Calculate, the term of an annuity, the amount of annuity, periodic payment, interest rate, or its present value, given the other factors.
- Define the term 'annuity due,' and calculate any of the components of an annuity due.

**C. Loans and Mortgages (M)**

- Solve problems involving loans and mortgages.
- Explain the concept of sinking funds and how they are used for debt retirement, and solve problems involving sinking fund principles.

**D. Net Present Value (NPV) and Internal Rate of Return (IRR) (M)**

- Define the concepts of cash flows, net present value (NPV) and internal rate of return (IRR)
- Compute the Net Present Value (NPV) of a cash flow to appraise different investment projects.
- Compute the Internal Rate of Return (IRR) to appraise different investment projects.

#### 3. Presentation and Analysis of Statistical Data

**A. Definition of data and information (I)**

- Distinguish between data and information

**B. Presentation of Data (M)**

- Present statistical data to others in graphical, tabular and chart forms for easy understanding.
- Present published graphical presentation of data.

**C. Analysis of data: Measures of central tendency and dispersion (M)**

- Explain the concepts of sample mean, sample variance, population mean, and population variance
- Compute and interpret the sample mean, mode, mean deviation, sample variance, sample standard deviation, sample median, coefficient of variation and sample range for both grouped and ungrouped data
- Summarize and analyze statistical data and interpret the analysis for others
- Make inferences about a population from a sample

**D. Frequency Distributions (M)**

- Summarise mass numbers (data) both in simple and grouped frequency tables.
- Solve problems using both the formula and the table for a number of discrete and continuous probability distributions (Binomial, Poisson, Normal)

#### 4 Business Modelling Techniques

**A. Correlation (M)**

- Apply Pearson’s formula to calculate the coefficient of correlation
- Apply Spearman’s rank correlation formula to calculate correlation as an alternative to Pearson’s correlation coefficient

**B. Regression Analysis (M)**

- Apply simple linear regression for building empirical models to business and accounting data
- Plot a scatter diagram of a given set of data
- Explain how the method of least squares is used to estimate the parameters (regression coefficients) in a linear regression model
- Apply the regression model to make a prediction of a future observation

**C. Time series Analysis (M)**

- Define the term time series
- Define and calculate four components of a time series data
- Describe appropriate model to use when forecasting: least squares method, moving average method.
- Apply basic forecasting techniques

**D. Linear Programming (M)**

- Define a linear programming problem.
- Define an objective function.
- Define a constraint.
- Formulate linear programming problems.
- Apply graphical method to solve linear programming problems.

**E. Simulation (M)**

- Explain simulation and when to use it
- Describe the simulation process
- List the advantages of simulation
- List the limitations of simulations
- List the applications of simulation
- Explain the Monte Carlo method and give the simulations where these methods are useful
- Explain the advantages and disadvantages of Monte Carlo methods
- Describe a method for generating of random numbers

**F. Replacement Analysis (M)**

- Calculate the increased operating cost, maintenance cost, forced idle time cost and cost of replacing the new equipment.

**G. Decision Trees (M)**

- Draw a decision tree from a given payoff table
- Apply several criteria such as EMV, EVPI and EOL to select alternative action to take.

#### Format of the exam

Marks | ||

Section A: | 10 compulsory multiple choice questions, 2 marks each | 20 |

Section B: | Any 4 out of 5 questions, 20 marks each | 80 |

100 |

**Recommended reading**

- ZiCA D2 Quantitative Analysis Study Manual
- Lucey, T. (2002) Quantitative Methods. 6th edition. London, Thomson Learning.
- Morris, C. (2008) Quantitative Approaches in Business Studies. 7th edition. London, FT Prentice Hall

This course does not have any sections.