Time Value of Money Notes

Time Value of Money

  • Concept: Money available today is worth more than the same amount in the future.

    • Example: Would you prefer P 10,000 today or in 5 years?

Key Reasoning for Time Value of Money

  • Opportunity to invest can generate returns if the money is available now.

  • Future money is subject to uncertainty and inflation, reducing purchasing power over time.

Importance of Purchasing Power

  • Inflation diminishes the value and purchasing power of money.

  • Consider rate of return alongside inflation when investing.

Applications of Time Value of Money (TVM)

  • Investment Options Comparison

    • Evaluating different investments by considering potential returns.

  • Wage Fixation and Investment Proposals

    • Assessing the present value of future wages or investment returns.

  • Determining Interest Rates

Present Value (PV)

  • Definition: Determines the worth of future money in today’s terms.

  • Calculation: Use the formula PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n} where:

    • PV: Present Value

    • FV: Future Value

    • r: Rate of return (discount rate)

    • n: Number of periods

  • Discounting transforms future amounts to present value.

Future Value (FV)

  • Definition: Value of a current asset at a future date based on an assumed growth rate.

  • Calculation: Use the formula FV=PV(1+r)nFV = PV(1 + r)^n where:

    • FV: Future Value

    • PV: Present Value

    • r:Interest rate

    • n: Number of periods

  • Compounding reinvests interest to increase total value over time.

Interest Types

  • Simple Interest (SI)

    • Interest calculated only on the principal amount.
      Example: P 200 at 3% for 2 years:

    • Year 1: P 6, Year 2: P 6, Total Interest: P 12

  • Compound Interest (CI)

    • Interest calculated on the principal and previously earned interest.
      Example: P 200 at 3% for 2 years:

    • Year 1: P 6, Year 2: P 6.18, Total Interest: P 12.18

Example Interest Calculations (₱10,000 at 5% for 3 years)

  • Simple Interest:

    • SI = P(r)(t) = 10,000(0.05)(3) = P 1,500

    • Total Amount: P 11,500

  • Compound Interest:

    • A = P(1 + r)^n = 10,000(1 + 0.05)^3 = 11,576.25$

    • Interest Earned: P 1,576.25

Future Value Example with Interest Rate of 6% for 2 years

  • Year 1:

    • Fv1 = 100(1 + 0.06)^1 = 106

  • Year 2:

    • Fv2 = 100(1 + 0.06)^2 = 112.36

    • Difference of P 0.36 due to compounding.

Present Value Example: Vacation Planning

  • Future Cost: P 20,000 in 5 years with a 5% interest rate.

  • Calculation:
    PV=20,000(1+0.05)5≈15,664PV = \frac{20,000}{(1 + 0.05)^5} \approx 15,664

Conclusion

  • Present Value (PV) assesses future cash value in today's terms; Future Value (FV) predicts future worth based on present amounts.

  • Both are crucial for financial planning, allowing comparisons of present and future financial opportunities.