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Financial Mathematics

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Topics 10

The Time Value of Money
Understanding the concept of the time value of money, including present value, future valu...
Compound Interest
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Annuities and Perpetuities
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Net Present Value (NPV) and Internal Rate of Return (IRR)
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Bonds and Bond Valuation
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Stock Valuation
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Risk and Return
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Portfolio Management
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Capital Budgeting
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Options and Futures
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Unit Outline 45h

Learning Objectives

6 objectives
  • Understand and apply the concept of the time value of money in various financial contexts.
  • Calculate and analyze compound interest, annuities, perpetuities, and their implications on financial decisions.
  • Evaluate investment opportunities using Net Present Value (NPV) and Internal Rate of Return (IRR) methodologies.
  • Understand bond and stock valuation techniques and interpret their market implications.
  • Analyze risk and return measures and apply portfolio management principles to optimize investment outcomes.
  • Explore capital budgeting techniques and comprehend the use of derivatives such as options and futures in financial markets.

Content Outline

Preview

Unit 1198: Advanced Financial Concepts and Investment Analysis

1. The Time Value of Money

1.1 Introduction to Time Value of Money (TVM)

  • Definition and importance in finance
  • Conceptual basis: money today vs. money in the future

1.2 Present Value (PV) and Future Value (FV)

  • Present Value formula and applications
  • Future Value formula and applications

1.3 Compounding and Discounting

  • Compounding: concept and formulas
  • Discounting: concept and formulas
  • Relationship between compounding and discounting

2. Compound Interest

2.1 Compound Interest Principles

  • Definition and difference from simple interest
  • Formula for compound interest

2.2 Frequency of Compounding

  • Annual, semi-annual, quarterly, monthly, continuous compounding
  • Effect of compounding frequency on investment growth

2.3 Impact on Investments and Loans

  • Growth of investments over time
  • Loan amortization and interest accumulation

3. Annuities and Perpetuities

3.1 Types of Annuities

  • Ordinary annuity vs. annuity due

3.2 Annuity Calculations

  • Present value and future value of annuities
  • Formulas and examples

3.3 Perpetuities

  • Definition and characteristics
  • Valuation formula

4. Net Present Value (NPV) and Internal Rate of Return (IRR)

4.1 Investment Decision Criteria

  • Overview of capital budgeting

4.2 Net Present Value (NPV)

  • Definition and calculation
  • Interpretation and decision rules

4.3 Internal Rate of Return (IRR)

  • Definition and calculation methods
  • Comparing IRR with required rate of return

4.4 Comparing NPV and IRR

  • Advantages and limitations of each method

5. Bonds and Bond Valuation

5.1 Basics of Bonds

  • Definition, features, and types

5.2 Bond Pricing

  • Present value of coupon payments and face value

5.3 Yield to Maturity (YTM)

  • Concept and calculation

5.4 Relationship Between Interest Rates and Bond Prices

  • Inverse relationship explained

6. Stock Valuation

6.1 Dividend Discount Models (DDM)

  • Gordon Growth Model
  • Multi-stage growth models

6.2 Price-Earnings (P/E) Ratios

  • Definition and use in valuation

6.3 Discounted Cash Flow (DCF) Analysis

  • Estimating free cash flows
  • Discount rates and valuation

7. Risk and Return

7.1 Understanding Risk

  • Types of risk: systematic vs. unsystematic

7.2 Measuring Return

  • Expected return calculation

7.3 Risk Measures

  • Standard deviation
  • Beta coefficient
  • Sharpe ratio

7.4 Risk-Return Trade-off

  • Concept and practical implications

8. Portfolio Management

8.1 Principles of Portfolio Management

  • Diversification benefits
  • Asset allocation strategies

8.2 Efficient Frontier

  • Concept and graphical representation

8.3 Portfolio Optimization

  • Risk minimization and return maximization

9. Capital Budgeting

9.1 Overview of Capital Budgeting

  • Importance in long-term decisions

9.2 Payback Period

  • Calculation and limitations

9.3 Accounting Rate of Return (ARR)

  • Formula and usage

9.4 Discounted Cash Flow Techniques

  • NPV revisited
  • IRR revisited

10. Options and Futures

10.1 Introduction to Derivatives

  • Definition and types

10.2 Options

  • Call and put options
  • Option pricing basics (intrinsic and time value)

10.3 Futures

  • Contract features
  • Pricing and settlement

10.4 Hedging and Speculation Strategies

  • Using derivatives for risk management
  • Examples and case studies
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