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CFA Level I · CFA Level I Exam · The Time Value of Money in Finance

An analyst compares a perpetuity with a 20-year ordinary annuity, both paying the same fixed amount each year at the same discount rate. If the discount rate rises, which instrument's present value will most likely fall by the larger percentage?

The perpetuity will most likely fall by the larger percentage. Its cash flows extend indefinitely, so more of its value comes from distant payments that are discounted more heavily when rates rise. The 20-year annuity has a limited horizon and is therefore less sensitive.

  1. AThe perpetuityCorrect
  2. BThe 20-year annuity
  3. CBoth fall by the same percentage

Explanation

The perpetuity's value depends on all distant cash flows, which are most heavily affected by a higher discount rate. The annuity stops after 20 years, so it has less value in far-off payments and a shorter effective duration. Therefore the perpetuity's present value is more sensitive to the rate change.

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