Which of the following is true about perpetuities?

Question

BlackTom AI · Accepted Answer

We start by restating the question: Which of the following is true about perpetuities? The options are as follows:
Option a: 'All of the above are true statements.'
Option b: 'All else equal, the value of a perpetuity is higher when the periodic cash flow is higher.'
Option c: 'If two perpetuities have the same present value and the same interest rate, they must have the same cash flows.'
Option d: 'All else equal, the value of a perpetuity is higher when the interest rate is lower.'

Now, evaluate each option.

Option b analysis: For a perpetuity, the present value formula is PV = CF / r, where CF is the periodic cash flow and r is the interest rate per period. If r is held constant and CF increases, PV increases linearly. Therefore, all else equal, a higher cash flow yields a higher value. This statement is true.

Option c analysis: If two perpetuities share the same PV and the same r, then their cash flows must satisfy CF = PV × r for each perpetuity. Since PV and r are identical for both, their CF must also be identical. Hence, they must have the same cash flows. This statement is true.

Option d analysis: Again using PV = CF / r, if CF is held constant and r decreases, PV increases. Therefore, all else equal, a lower interest rate leads to a higher value. This statement is true.

Option a analysis: Since options b, c, and d are all true, option a claims that all the above statements are true. Given the conclusions for b, c, and d, this is also a true statement. However, we treat this as part of analysis rather than declaring the final answer directly, per the question’s structure.

Overall, each of the statements b, c, and d is individually true, and the compound option a correctly encompasses them as all being true.

MCD2170 - T2 - 2025 Key Concept 4 Video Quiz

Which of the following is true about perpetuities?

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