![]() ![]() The above equation is the basis of the Gordon Growth Model. ![]() The present value of a growing perpetuity can be calculated as follows: PV of Growing Perpetuity = There might be a situation in which the payments comprising the perpetuity might grow at a rate g. Rearranging the above equation, we get the formula to find present value of a perpetuity: PV of Perpetuity = This can be expressed mathematically as follows: If we want the endowment to finance scholarships each year perpetually, the interest earned on PV in one year must equal PMT. Let the endowment value be PV, the annual scholarship withdrawals be PMT and i being the periodic interest rate. Let’s follow the endowment example above. A real estate investment can be treated as a perpetuity of rentals. The dividend discount model values a share of common stock by treating it as a perpetuity of constant dividend payments. The present value formula PV FV/ (1+i)n states that present value is equal to the future value divided by the sum of 1 plus interest rate per period raised to the number of time. Some models treat different investments and liabilities are perpetuities. i interest rate per period in decimal form. one year and there are infinite number of payments. ![]() This constitutes a perpetuity because the payment is fixed, there is equal duration between each payment, i.e. Let’s say a government wants to set up an endowment that will off $1 million each year in scholarship for ever. Present value of a perpetuity equals the periodic cash flow divided by the interest rate. Perpetuity is a perpetual annuity, it is a series of equal infinite cash flows that occur at the end of each period and there is equal interval of time between the cash flows. ![]()
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