perpetuity

Examples of perpetuity in the following topics:

• Calculating Perpetuities

  • Perpetuities are a special type of annuity; a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever.
  • There aren't many actual perpetuities, but the United Kingdom has issued them in the past.
  • To find the FV of a perpetuity would require setting a number of periods which would mean that the perpetuity up to that point can be treated as an ordinary annuity.
  • There is, however, a PV formula for perpetuities .
  • The PV of a growing perpetuity is represented as $PVGP \ = \ {A \over ( i - g )}$ .

• Expected Dividends and Constant Growth

  • The PEG ratio is a special case in the Sum of Perpetuities Method (SPM) equation.
  • Derived from the compound interest formula using the present value of a perpetuity equation, SPM is an alternative to the Gordon Growth Model.

• Calculating Annuities

  • An annuity is essentially a loan, a multi-period investment that is paid back over a fixed (or perpetual, in the case of a perpetuity)  period of time.
  • Generally speaking, annuities and perpetuities will have consistent payments over time.

• Pros and Cons of a Corporation

  • The corporate structure is less simple to found and maintain but has the advantages of limited liability and perpetual life.

• Discounted Dividend vs. Corporate Valuation

  • g is the constant growth rate in perpetuity expected for the dividends.
  • a) The presumption of a steady and perpetual growth rate less than the cost of capital may not be reasonable.

• The Valuation of Stocks

  • . , subsequently, the market price becomes a perpetuity, where we simplify a stock's value to Equation 16.
  • Many investors want their dividends to grow over time, and Equation 16 can include a dividend growth rate.If the dividend grows at g percent per year, then we update the present value formula to include a dividend growth rate in Equation 18.Consequently, we can simplify this infinite sequence into something similar to a perpetuity.
  • Steady state – the corporation begins paying dividends over time that increase at a constant rate.This occurs after the corporation becomes mature.Consequently, we calculate the cash flows as a perpetuity.
  • Third year becomes the perpetuity because the corporation begins increasing the dividend at a constant rate.For this example, we must observe the time subscripts.Remember, we calculate the stock price, P, one period before the dividend payment, D, in Equation 24.
  • Second, we set the dividend to $10, for the fourth time period, or D4 = $10.Next, we calculate the perpetuity that begins in Period 3 in Equation 26.

• Annuities

  • Perpetuities: Payments continue forever.

• Other Types of Bonds

  • Perpetual bonds are also often called perpetuities or "perps. " They have no maturity date.

• Floating-Rate Bonds

  • Perpetual FRBs are another form of FRBs that are also called irredeemable or unrated FRBs and are akin to a form of capital.

• The Nature of Bonds

  • An exception is an irredeemable bond, such as Consols, which is a perpetuity, that is, a bond with no maturity.