Notes_Time Value of Money Regularities

Investment Policy

  • Understanding the basics of investment policy in the context of cash flow valuation.

Discounted Cash Flow Valuation

  • Essential tool for determining the value of an investment based on its expected future cash flows.

  • Present Value (PV): Value today of a future cash flow, considering a specific rate of return.

Time Value of Money: Fundamentals

  • Concept: Money available today is worth more than the same amount in the future due to its potential earning capacity.

  • Formula:

    • Future Value (FV) = C₀ × (1 + r)ᵀ

    • Where:

      • C₀ = Cash flow today

      • r = rate of return

      • T = time period

Calculating Future Value

Example: Tuition Investment

  • Needed for tuition in 12 years: $50,000.

  • Investment today: $5,000.

  • Required Rate of Return:

    • FV = C₀ × (1 + r)ᵀ

    • $50,000 = $5,000 × (1 + r)¹²

    • Solving gives: r ≈ 21.15%.

Retirement Savings Calculation

  • Goal: $1,000,000 for retirement.

  • Current savings: $500,000 at 10% interest.

  • Years until retirement:

    • FV = PV × (1 + r)ⁿ

    • ln formula is used to solve for T:

    • T = ln(FV/PV) / ln(1+r)

    • Result: approximately 7.27 years.

Rule of 72

  • Quick method to estimate the number of years required to double an investment.

  • Formula: Years to double ≈ 72 / Interest Rate.

    • Example: For an interest rate of 10%, it is approximately 7.2 years.

Present Value Calculations

  • PV of cash flows can be computed as:

    • PV = CF₀*(1) + CF₁*(1/(1+r)) + CF₂*(1/(1+r)²) + ...

  • Example Calculation:

    • CF₀ = $10, CF₁ = $10, CF₂ = $10

    • If r = 10%, then PV = $27.36 (approx.).

Valuing Simple Cash Flow Streams

  • Cash flows that are consistent over time can be valued using the Present Value formula.

Perpetuities and Annuities

Constant Perpetuities

  • Formula: PV = CF / r

    • Example: A $1 perpetuity at r = 10% has a PV = $10.

Growing Perpetuities

  • Formula: PV = CF / (r - g)

    • Important: The condition r > g must hold.

  • Example: Dividend growth model for stocks.

Valuing Annuities

  • An annuity can be viewed as the difference between a perpetuity that starts now and one that starts later.

  • Formula: PV of Annuity = C × (1 - (1 + r)⁻ᵀ) / r

    • Example: For a constant cash flow received for T years.

Summary of Key Financial Concepts

  • Time Value of Money: Fundamental in investment planning and decision-making.

  • Present Value & Future Value: Tools for evaluating investments and cash flow.

  • Rules of Thumb: Simplifies financial calculations, such as the Rule of 72 for estimating investment doubling time.

Final Thoughts

  • Always consider the implications of inflation and interest rates when planning financial investments.

  • Practical applications of these concepts are critical for personal finance planning, including retirement and education funding.