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TIME VALUE OF MONEY

TIME VALUE OF MONEY

TIME VALUE OF MONEY (Part 1)

  • Definition: The time value of money refers to the idea that the value of money does not remain the same at all points in time. The money available at the present time is worth more than the same amount in the future since it has the potential to earn returns (or interest).
  • Key Concepts:
    • Time Value of Money (TVM): The value associated with the same sum of money received at various points on the timeline.
    • Annuity: A series of fixed cash flows at regular intervals.
    • Perpetuity: A series of fixed cash flows that continues indefinitely.
  • Importance of Time Value of Money:
    • Helps in comparing cash flows received in different time periods.
    • Enables investors to make informed decisions about investments.
    • Takes into account the risk-free rate of return, inflation, and other factors that affect the value of money over time.
  • Parameters in Time Value of Money:
    • Cash Inflows or Outflows: Can be in the form of single period cash flow or a stream of uneven or even cash flows.
    • Rate of Interest: Also known as compounding rate or discount rate.
    • Time Period: Can be annual or any other fraction thereof like monthly, quarterly, etc.
    • Frequency of Cash Flows: Can be fixed or variable.
  • Calculating Present Value (PV) and Future Value (FV):
    • Present Value (PV): The amount that you would pay today for a cash flow that comes in the future.
    • Future Value (FV): The value of an investment at some point in the future.
    • Formula for PV: PV = FV / (1 + r)^n, where FV is the future value, r is the rate of return, and n is the number of periods.
    • Formula for FV: FV = PV x (1 + r)^n, where PV is the present value, r is the rate of return, and n is the number of periods.
  • Calculating Rate of Return:
    • Rate of Return: The percentage rate that is earned on a particular investment.
    • Compounded Annual Growth Rate (CAGR): The underlying compound interest rate that equates the end value of the investment with its beginning value.
    • Formula for CAGR: CAGR = ((End Value / Beginning Value) ^ (1/n)) - 1, where End Value is the future value, Beginning Value is the present value, and n is the number of years.

TIME VALUE OF MONEY (Part 2)

  • CAGR (Compound Annual Growth Rate): The accepted standard measure of return on investment in financial markets, except in case of returns that involve periods of less than one year. It can be calculated using the formula: CAGR = ((FV/PV) ^ (1/n)) - 1, where FV is the future value, PV is the present value, and n is the number of years.
  • CAGR Calculation: Can be done using the RATE formula in Excel: CAGR = RATE(n,,-PV,FV), where n is the number of years, PV is the present value, and FV is the future value.
  • Example of CAGR Calculation: If an investment of Rs. 10.50 grows to Rs. 12.25 in 3 years, the CAGR can be calculated as: CAGR = ((12.25/10.5) ^ (1/3)) - 1 = 5.27%.

Periodic Investments or Pay-outs

  • Equated Monthly Instalment (EMI): A regular payment made to a lender, which can be calculated using the PMT formula in Excel: PMT = (r/n, n*12, -PV), where r is the rate of interest, n is the number of years, and PV is the present value.
  • Example of EMI Calculation: If a loan of Rs 30 lakh is taken for 20 years at an interest rate of 6.5% per annum, the EMI can be calculated as: PMT = (0.065/12, 240, -3000000) = Rs 22,367.

Period of the Loan (NPER)

  • NPER Formula: Can be used to calculate the time period required to pay off a loan, given the rate of interest, EMI, and present value. The formula is: NPER = (r/n, -PMT, PV), where r is the rate of interest, n is the number of times interest is compounded per year, PMT is the EMI, and PV is the present value.
  • Example of NPER Calculation: If a loan of Rs 5 lakh is taken at an interest rate of 8% per annum, with an EMI of Rs 12,000, the time period required to pay off the loan can be calculated as: NPER = (0.08/12, -12000, 500000) = 48.97 months.

Annuity

  • Definition: A sum of money paid at regular periods, such as monthly, quarterly, or annually. Annuities can be of two types: fixed annuity and flexible annuity.
  • Fixed Annuity: Provides fixed returns at regular periods, such as a fixed deposit with a bank.
  • Flexible Annuity: Provides returns that are benchmarked to inflation or index returns, and can change over time.
  • Ordinary Annuity: An annuity where the payment is made at the end of the relevant time period.
  • Annuity Due: An annuity where the payment is made at the start of the period, instead of at the end.

Calculation of Annuity

  • Present Value Formula: Can be used to calculate the present value of an annuity, using the formula: PV = PV(r, n, -PMT), where r is the rate of interest, n is the number of years, and PMT is the annuity payment.
  • Example of Annuity Calculation: If an annuity of Rs 5,000 is paid out each year for 4 years at a rate of return of 10%, the present value can be calculated as: PV = PV(0.1, 4, -5000) = Rs 15,849.

Perpetuity

  • Definition: A cash flow from an investment that goes on forever, with no finite period.
  • Present Value Formula: Can be used to calculate the present value of a perpetuity, using the formula: PV = C/r, where C is the cash flow and r is the discount rate.
  • Example of Perpetuity Calculation: If a bond pays out Rs 10,000 as interest on an annual basis, and the discount rate is 8%, the present value of the perpetuity can be calculated as: PV = 10,000/0.08 = Rs 125,000.
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