KEY TAKEAWAYS

  • The idea of the time value of money is fundamental to financial decisions.
  • The present value of the series of cash flows is equal to the sum of the present value of each cash flow.
  • A series of cash flows is an annuity when there are regular payments at regular intervals and each payment is the same amount.

  • To calculate the present value of an annuity, you need to know

    • the amount of the identical cash flows (\(CF\)),
    • the frequency of the cash flows,
    • the number of cash flows (\(t\)),
    • the discount rate (\(r\)) or the rate at which time affects value.

  • The calculation for the present value of an annuity yields valuable insights.

    • The more time (\(t\)), the more periods and the more periodic payments, that is, the more cash flows, and so the more liquidity and the more value.
    • The greater the cash flows, the more liquidity and the more value.
    • The greater the rate at which time affects value (\(r\)) or the greater the opportunity cost and risk or the greater the rate of discounting, the more time affects value.

  • The calculation for the future value of an annuity yields valuable insights.

    • The more time (\(t\)), the more periods and the more periodic payments, that is, the more cash flows, and so the more liquidity and the more value.
    • The greater the cash flows, the more liquidity and the more value.
    • The greater the rate at which time affects value (\(r\)) or the greater the rate of compounding, the more time affects value.

  • A perpetuity is an infinite annuity.