Video: Time Value Of Money

Video transcript

This edited accessibility transcript was prepared from the tutorial’s teaching outline because the source video has no caption file. It follows the lesson sequence and formulas while removing repetition.

The time value of money begins with a simple principle: a dollar available today is normally worth more than the same dollar received in the future. Money received today can be invested and may earn a return. Inflation can also reduce what a future dollar will buy, and future payments carry uncertainty. For those reasons, investors compare cash flows only after placing them at the same point in time.

There are two main directions in a time-value calculation. Compounding moves a present amount forward to a future value. Discounting brings a future amount back to a present value. The future-value formula is FV equals PV multiplied by one plus the periodic rate, raised to the number of periods. In symbols, FV = PV × (1 + r)ⁿ. Present value reverses the calculation: PV = FV ÷ (1 + r)ⁿ.

Suppose you invest $1,000 at 5% a year. After one year, the balance is $1,050. In the second year, the 5% return applies to both the original $1,000 and the first year’s $50 return. After five years, annual compounding produces approximately $1,276. After ten years it produces approximately $1,629, and after twenty years approximately $2,653. This accelerating effect is compound growth.

The interest rate and number of periods must use the same frequency. If a rate is quoted annually and the calculation uses monthly periods, convert the annual rate to an appropriate monthly rate and count the total number of months. Also confirm whether interest compounds annually, monthly, daily or continuously. Different conventions produce different results.

Present value asks the opposite question. If an investment promises $1,000 five years from now and the appropriate required return is 5%, divide the future payment by 1.05 raised to the fifth power. The present value is about $784. That does not mean the future payment is reduced. It means that approximately $784 invested today at 5% would grow to $1,000 in five years.

The discount rate represents the return required for waiting and accepting risk. A higher discount rate produces a lower present value because investors demand more compensation. A longer delay also generally reduces present value. Selecting the rate is therefore an assumption, not a purely mechanical step. Inflation, uncertainty, opportunity cost and the risk of the cash flow should all be considered.

Many decisions involve a series of payments rather than one lump sum. An annuity is a sequence of equal payments made at regular intervals. An ordinary annuity pays at the end of each period, while an annuity due pays at the beginning. Loans, savings plans, pensions and some investment cash flows can be analysed with annuity calculations. Unequal cash flows should normally be discounted one by one and then added together.

Spreadsheet programs can perform these calculations with functions such as FV for future value, PV for present value, PMT for a regular loan or savings payment, RATE for the periodic rate and NPER for the number of periods. Check the sign convention: money paid out and money received are usually entered with opposite signs. A sign error can make a correct formula appear to return an unexpected negative result.

For a loan, the repayment calculation combines the amount borrowed, periodic interest rate, number of repayments and any remaining balance. An amortisation schedule then separates each payment into interest and principal. Early payments often contain more interest because the outstanding balance is larger. As the balance falls, more of each payment reduces principal.

Time-value methods are also used to compare investments. Future value can estimate how savings may grow. Present value can compare expected dividends, bond payments or other future cash flows. Net present value subtracts the initial cost from the present value of expected cash inflows. A positive result means the discounted inflows exceed the stated cost under the chosen assumptions, but it does not remove investment risk.

Always test the assumptions. Recalculate using lower and higher rates, shorter and longer time periods, and different cash-flow estimates. Small changes can have a large effect over long horizons. Inflation-adjusted, or real, rates should be distinguished from nominal rates that include inflation. Taxes, fees and irregular timing may also change the result.

The practical takeaway is to place competing cash flows on the same date before comparing them. Identify whether you are moving money forward through compounding or backward through discounting, match the rate to the period, state the assumptions and test more than one scenario. Time value of money is a framework for clearer comparison, not a guarantee of future returns.