# DA2 – Quantitative Analysis

No access plans exist. ### DA2 Quantitative Analysis

Learning outcomes

On successful completion of DA2, students should be able to:
1. Demonstrate the use of probability where risk and uncertainty exist
2. Apply financial mathematical techniques
3. Apply techniques for presentation and analysis of statistical data
4. 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)

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
• 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
Time allowed: 3 hours, plus 15 minutes reading time