Question

Perpetuities are also called annuities with an extended or unlimited life. Based on your understanding of perpetuities, answer the following questions. Which of the following are characteristics of a perpetuity? Check all that apply. The value of a perpetuity cannot be determined. The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant (in the future) cash flows.

Answer 1

Answer:

The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant (in the future) cash flows.

Explanation:

The perpetuities can becalculate as follow

C/rate = Perpetuities

the reasoning behind this formula:

$C * \frac{1-(1+r)^{-time} }{rate} = PV$

If we calculate limit whe ntime is infite,

because at more time 1 + r gets closer and closer to 0

we get on the dividend

1 - 0

So we have C x 1/i = C/i

Next part would be why the first cash flow is more relevant than the subsequent cash flow:

$\frac{Principal}{(1 + rate)^{time} } = PV$

Here if time increases, then the divisor get closer to ∞ so we have

P ( a constant) /∞ = 0

So the first cashflow is more relevant than the more distant cash flow