Perpetuity
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In
Real estate and preferred stock are among some types of investments that affect the results of a perpetuity, and prices can be established using techniques for valuing a perpetuity.[1] Perpetuities are but one of the time value of money methods for valuing financial assets.
Perpetuities can be structured as a perpetual bond and are a form of ordinary annuities. The concept is closely linked to terminal value and terminal growth rate in valuation.
Detailed description
A perpetuity is an
The value of the perpetuity is finite because receipts that are anticipated far in the future have extremely low present value (present value of the future cash flows). Unlike a typical bond, because the principal is never repaid, there is no present value for the principal. Assuming that payments begin at the end of the current period, the price of a perpetuity is simply the coupon amount over the appropriate discount rate or yield; that is,
where PV = present value of the perpetuity, A = the amount of the periodic payment, and r = yield, discount rate or interest rate.[2]
To give a numerical example, a 3% UK government war loan will trade at 50 pence per pound in a yield environment of 6%, while at 3% yield it is trading at par. That is, if the face value of the loan is £100 and the annual payment £3, the value of the loan is £50 when market interest rates are 6%, and £100 when they are 3%.
The
This of course follows the fact that for bigger changes the new price must be calculated with the present-value formula given that for changes greater than a few basis-points the calculated duration is not reflective of the true-change in price.
Real-life examples
Valuing real estate with a
UK government perpetuities (called
The constant growth dividend discount model for the valuation of the common stock of a corporation is another example. This model assumes that the market price per share is equal to the discounted stream of all future dividends, which is assumed to be perpetual. If the discount rate for stocks (shares) with this level of systematic risk is 12.50%, then a constant perpetuity of dividend income per dollar is eight dollars. However, if the future dividends represent a perpetuity increasing at 5.00% per year, then the dividend discount model, in effect, subtracts 5.00% off the discount rate of 12.50% for 7.50% implying that the price per dollar of income is $13.33.
References
- ^ "Perpetuity". Investopedia. 24 November 2003. Retrieved 26 May 2016.
- ^ Luenberger, David (2009). Investment Science. New York City: Oxford University Press. p. 45.
- ^ "fixed income – Duration of perpetual bond". Quantitative Finance Stack Exchange. Retrieved 2021-05-13.