Question

You are considering two perpetuities which are identical in every way, except that perpetuity A will begin making annual payments of $P to you two years from today while the first $P payment for perpetuity B will occur one year from today. It must be true that the present value of perpetuity: A) A is greater than that of B by $P. B) B is greater than that of A by $P. C) B is equal to that of perpetuity A. D) A exceeds that of B by the PV of $P for one year. E) B exceeds that of A by the PV of $P for one year.

Answer 1

Answer:

E) B exceeds that of A by the PV of $P for one year.

Explanation:

A begins in 2 years in the future, while B starts one year into the future:

B:

$\frac{perpetuity}{(1 + rate)^{1}}$

A:

$\frac{perpetuity}{(1 + rate)^{2}} =$

The difference is this one year difference which, makes the return on A lower than B today. After the two years, past and both perpetuities begin, their value will be the same.