Which of the following statements regarding growing perpetuities is FALSE?

Question

BlackTom AI · Accepted Answer

Question focus: growing perpetuities and their properties. Analyzing each option helps pinpoint which statement is false. Option a: 'we can find the present value of a growing perpetuity but not its future value.' In standard finance, we can compute the present value (PV) of a growing perpetuity using PV0 = CF1 / (r - g) given r > g. The concept of a future value (FV) at time t can also be discussed or computed (e.g., FVt = CF1 × [(1+g)^(t-1)] × (1+r)^(t-1) depending on definitions), but for an infinite horizon the perpetual series does not have a finite FV at infinity. The statement as written can be misleading or false depending on interpretation, but the common teaching emphasizes the PV formula and notes the perpetuity grows forever; a precise reading may render this option suspect. Option b: 'We assume that r < g for a growing perpetuity.' This is the clear false statement. The standard growing perpetuity formula PV0 = CF1 / (r - g) requires r > g to produce a finite present value. If r ≤ g, the PV either diverges to infinity (r = g) or does not converge (r < g). Therefore the assumption r < g is not correct for a growing perpetuity with finite value. Option c: 'A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.' This is a correct description: payments occur periodically and grow at a constant rate indefinitely. It matches the textbook definition. Option d: 'PV of a growing perpetuity at time 0 equals CF1/(r-g).' This is the standard formula for the present value at time 0 when r > g, so this statement is true provided the usual condition holds. It aligns with the core formula for growing perpetuities. In summary, option b is the statement that conflicts with the fundamental requirement r > g for a finite PV of a growing perpetuity, making it the false choice among the options presented.

Which of the following statements regarding growing perpetuities is FALSE?单项选择题

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