CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
An investor is offered a perpetuity that pays 50 at the end of every year, with the first payment one year from today. The appropriate discount rate is 8% per year. The value of the perpetuity today is closest to:
The perpetuity is worth about 625. An ordinary perpetuity is valued by dividing the periodic payment by the discount rate, so 50 divided by 0.08 gives 625. Multiplying by the rate, or adding an extra period of growth, gives wrong values.
- A4
- B625Correct
- C675
Explanation
The present value of an ordinary perpetuity is PV = payment / r = 50 / 0.08 = 625. The 4.00 result comes from multiplying the payment by the rate instead of dividing. The 675 result wrongly treats the perpetuity as starting immediately by multiplying by (1 + r).
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