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.
Answer: B
Explanation: B) Value of perpetuity = PMT/r = $100/.06 = $1,666.67.
PV of a 20-year annuity = PMT × = $100 × = $1,146.99.
The difference, or the value of the remaining cash flows = $1,666.67 - $1,146.99 = $519.68.
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