Your neighbor owns a perpetuity of $100 per year that has a discount rate of 6% per year.He offers to sell to you all but the next 20 cash flows (the first to be received one year from today)for $500.In other words,he keeps the first 20 cash flows of his perpetuity and you get all of the rest.Is this a good price for you if the appropriate discount rate is 6%?
A)No,because the entire perpetuity is worth only $1,666.67 and your neighbor is taking the best cash flows worth more than $1,200 in present value terms
B)Yes,because the present value of the remaining cash flows is $519.68 and you are buying them for only $500.
C)No,because the cash flows you receive are only worth $482.16 and that is less than the $500 your neighbor is asking for the cash flows.
D)This question cannot be answered.

Question

Quizplus · Accepted Answer

The present value of a perpetuity is calculated using the formula PV = C / r, where C is the cash flow per period and r is the discount rate. The entire perpetuity is worth $100 / 0.06 = $1,666.67. The present value of the first 20 cash flows can be calculated using the formula for the present value of an annuity: PV = C * [1 - (1 + r)^-n] / r, where n is the number of periods. For the first 20 cash flows, this is $100 * [1 - (1 + 0.06)^-20] / 0.06 = $1,147.01. The value of the remaining cash flows is the difference between the total perpetuity and the first 20 cash flows: $1,666.67 - $1,147.01 = $519.66. Since you are buying them for $500, it's a good price.

Your Neighbor Owns a Perpetuity of $100 Per Year That