Chapter 4: Introduction to Valuation - The Time Value of Money

4.1 Chapter Overview

• Key Concepts Covered:

  • Future Value and Compounding

  • Present Value and Discounting

  • Further exploration of Present and Future Values

4.2 Understanding Time Value of Money (TVM)

• Financial managers must ascertain the present value of future cash flows.

• Example: Investment worth £100 in one year is not equivalent to £100 today because of potential investment growth.

• Conclusion: The value of money increases over time due to potential earnings through investment.

4.3 Future Value (FV) & Compounding

4.3.1 Future Value Defined

• 

  Future Value: Amount an investment grows to after one or more periods.

• Example Calculation:

  • Year 0: Invest £100 at 10%

  • Year 1: £100 + 10% = £110

4.3.2 Compounding Process

• Compounding: Accumulation of interest on an investment, leading to earning interest on interest.

• Compound Interest vs. Simple Interest:

  • Compound Interest: Interest calculated on initial principal and also on accumulated interest.

  • Simple Interest: Calculated only on the principal amount.

    

4.4 Investments Over Multiple Periods

4.4.1 Timeline Representation

• Timeline helps visualize cash flows, determining if money is received at the beginning, end, or spread over periods.

• Cash Flows:

  • Inflows (positive) and Outflows (negative) indicated on a timeline.

4.4.2 Calculating Future Value

• FV Formula:

  • Formula: FV = £1 × (1 + r)^t

  • Utilization of Future Value Interest Factor.

4.5 Example of Compound Interest

• Investment Scenario: €400 at 12% annual interest.

  • 3-Year Future Value: €561.97

  • 7-Year Future Value: €884.27

4.6 Present Value (PV) & Discounting

4.6.1 Present Value Explained

• Present Value: Current value of future cash flows discounted at a specified rate.

• Formula:

  • PV = FV / (1 + r)^t

4.6.2 Example Calculation

• Receiving £1 in Year 1 at a 10% interest rate:

  • Year 0 PV = £1 / 1.1 = £0.909

4.7 Lump Sum Present Value

• Calculation for €400 needed next year, with 7% interest:

  • Today’s investment = €373.83 (which will grow to €400 in a year)

4.8 Present Value of Cash Flow Streams

• Example: Cash flows of £100, £200, £300, and £400 over four years discounted at 10%:

  • Total Present Value = £754.80

4.9 Solving for Interest Rate

• Reverse calculation to find interest rate with both FV and PV known:

  • Formula: r = [FV / PV]^1/n - 1

4.10 Compounding Periods Calculation

• To find how many periods it takes for an investment to grow:

  • Use logarithmic properties to simplify calculations.

4.11 Spreadsheet Applications for TVM

• Excel Formulas:

  • FV: =FV(rate,nper,pmt,pv)

  • PV: =PV(rate,nper,pmt,fv)

  • RATE, NPER for discount rate and number of periods respectively.

4.12 Application of Discounted Cash Flow (DCF)

4.12.1 DCF Overview

• DCF valuation: Valuing an investment based on future cash flows discounted to present value.

• If DCF value exceeds investment cost, it is a viable opportunity.

4.12.2 DCF Formula

• Formula: DCF = CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CF_n/(1+r)^n

4.13 Purpose of DCF Analysis

• Estimates actual cash received from an investment, reflecting the time value of money.

• Determining investment worth based on required return rate.

4.14 Applications of DCF Valuation Models

• To value businesses, projects, bonds, shares, and income-producing properties.