Question

Consider an infinitely lived asset that pays risk-free dividend dt = 1 at every date t. Suppose that one-period risk-free rate of return is r = 0.1 at every date t. Show that asset price pt = 10 for every t satisfies the NPV relation with no bubble. Give an example of price sequence {pt} such that there is a strictly positive bubble.

Answer 1

Divident = 1

R=0.1

Asset price = 10

PV of the asset = D/R (Perpetuity formula)

=1/0.1 = 10

So as per this formula T is not necessary, because this is infinitely lived asset which is going to pay dividend forever. This is practically not possible, but we assume it is going to pay forever because of the fact that this is assumed as an infinitely lived asset.

So for any dividend paying asset which pays a risk free dividend, the price of an asset will be positive. This is like a bond which repays fixed interest at fixed intervals of time.