An insurance company offers an investor a perpetual stream of annual cash flows, which starts in a year and will pay $300 annually thereafter. The investor considers that the interest rate for discounting should be an EAR of 8%. The insurance asks $6,000 today to buy the perpetuity. Then, the investor should buy the perpetuity.

Question

BlackTom AI · Accepted Answer

To start, restate what the problem is asking: determine whether, given a perpetuity that pays 300 annually starting in year 1 and a required discount rate of 8% EAR, the investor should buy the perpetuity if the price is 6,000 today.
Option A: True. This would claim that buying the perpetuity is the correct action. However, using the perpetuity present value formula for payments starting in year 1, the value today is PV = 300 / 0.08 = 3,750. This is the amount an investor should be willing to pay to receive 300 every year forever starting in year 1 at an 8% discount rate. Since the asked price is 6,000, which is significantly higher than 3,750, paying 6,000 would yield a negative net present value. Therefore, the statement that the investor should buy the perpetuity is incorrect.
Option B: False. This option states that the investor should not buy the perpetuity at a price of 6,000. The calculation above shows the fair value (NPV at purchase) is 3,750, so a purchase price of 6,000 implies a negative NPV of 6,000 - 3,750 = 2,250. The investor would experience a loss relative to the required 8% return.
Explaining why the other related considerations are not changing the outcome: the payment begins in year 1, so there is no need for a one-year delay in the cash flows beyond the standard perpetuity model; the 8% EAR is an annual rate appropriate for this cash flow stream, so the PV formula 300 / 0.08 applies directly; there is no compounding or varying rate to complicate the calculation in this simplified setup.
In summary, the perpetuity’s fair value at an 8% discount rate is 3,750, which is well below the offered price of 6,000, so the correct stance is that the investor should not buy the perpetuity. The true/false statement should thus be evaluated as False.

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