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# perpetuity

last edited by 11 years, 10 months ago

# Perpetuity

constant stream of cash flows without end.

examples: some British Bonds are perpetuities

## Value of Perpetuity

PV = C/r,

where C = yearly Cash payment, and r= rate of return interest

example: perpetuity paying \$500 a year, with relevant interest rate of 12%, the value of the perpetuity is

= \$ 500 / 0.12

= \$4,166.67

Note: if the interest rate had been LOWER 10%, then the value (of the perpetuity) would be HIGHER

= \$500 / .10

= \$5000.00

So, the value increases with decreases in interest rates, and vice-versa

## Assume perpetual dividend

If you assume a perpetuity, then the valuation is very simple.  The formula is just PV = C / r,  where C = the cash flow into perpetuity, and the r = the discount rate.   So, if you know that a firm is going to pay out a constant dividend for ever, that is your cash flow as an investor.  The value of the firm is calculate by dividing that dividend (cash flow) by the appropriate discount rate.

But, most companies grow over time..... not problem, then just assume a perpetual dividend payment with growth.  The formula is still simple, its just  PV = C / r-g,  where g = the growth.  So, if you know that a company will always pay out a dividend and that the dividend will grow by x% per year,then just subtract the r-g to find the (lower) new discount rate, and divide.  The result is the PV of that expected future cash flow.

But, be careful when assuming a growing perpetuity, and dont assume that it will eventually grow so big that it is unrealistic.