You can buy a perpetuity that pays $1,000 annually?

Question

and your required rate of return on this investment is 15%. You should be indifferent to buying or not buying the investment if it were offered at a price of what?

Answer 1

The present value of a perpetuity that offers 1000 at the end of each year at a rate of 15% is

PV=1000/0.15= 6666.67

EDIT: just in case you are a newb to annuities this is how you arrive at it:

The sum of the present value of each payment is the present value of the investment.  It is the geometric series  

PV=1000/1.15 + 1000/(1.15^2) + 1000/(1.15)^3 + ....

This geometric sum is

PV= lim n-> inf  (1000/1.15) [1 - (1/1.15)^n  ]/ (1- 1/1.15)

=(1000/1.15)/ (1-1/1.15)

=1000/0.15

While I only know the theory of this I doubt anyone would offer an annuity with a 15% annual return rate.  Seems pretty high to me.

Answer 2

no

Answer 3

You should be indifferent to buying/not buying the perpetuity if the price is $6,666.67.  Anything above that amount should not be purchased because you would need a rate of return higher than 15%.  Anything below is a go since it's a discounted perpetuity.

Ron, ChFC