CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
An analyst compares two alternatives: receiving 12,000 in 3 years, or receiving a lump sum today. With a discount rate of 5% per year compounded annually, the lump sum today that makes the investor indifferent is closest to:
The equivalent lump sum today is about 10,366. Discount 12,000 over three years at 5%: 12,000 divided by 1.05 cubed. Discounting for only one year would give 11,429, which understates the time needed.
- A10,366Correct
- B10,800
- C11,429
Explanation
PV = 12,000/1.05^3 = 12,000/1.157625 = 10,366. The 10,800 figure is 12,000/1.111 (using simple interest 12,000/1.15 is 10,435; 10,800 is a 10% haircut with no basis). The 11,429 figure discounts only one year (12,000/1.05), a wrong-period error.
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