CFA Level 1: Perpetuity vs. Annuity - Financial Calculation and Comparison

Perpetuity vs. Annuity: Finding the Equivalent Annual Payment

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Question

A perpetuity pays $1,000 a year. You have a discount rate of 10% per year. If you are indifferent between buying this perpetuity and a 7-year annuity, how much does the annuity pay per year?

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A. B. C. D.

Explanation

The value of the perpetuity is 1,000/0.1 = $10,000. If the annuity pays $C per year, then its value is C/0.1*[1 - 1/(1.1)^7] = 4.868C. For you to be indifferent between these two, the two values must be equal, giving C = 10,000/4.868 = $2,054.

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