CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
A trust will pay 1,000 per year forever, with the first payment at the end of year 6. The discount rate is 5% per year. The value of the trust's payment stream today is closest to:
The value today is about 15,671. The perpetuity formula gives 20,000 one year before the first payment, which is at time 5. That amount must then be discounted five years at 5%. Discounting six years or not discounting at all gives the other values.
- A14,924
- B15,671Correct
- C20,000
Explanation
Valued one period before the first payment, the perpetuity is worth 1,000/0.05 = 20,000 at t = 5. Discounting 5 years to today gives 20,000 / 1.05^5 = 20,000 / 1.27628 = 15,671. Discounting 6 years gives 14,924, which wrongly uses the payment date instead of the date one period earlier. The 20,000 figure omits discounting.
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