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CFA Level I · CFA Level I Exam · Fixed-Income Bond Valuation: Prices and Yields

A two-year, 5% annual-coupon bond with a par value of 100 is valued using spot rates of 3% for one year and 4% for two years. The bond's arbitrage-free price is closest to:

The price is about 101.93. Discount the first-year coupon of 5 at the 3% one-year spot rate, giving 4.85, and the final payment of 105 at the 4% two-year spot rate squared, giving 97.08. Adding the two present values gives 101.93.

  1. A101.93Correct
  2. B103.83
  3. C105.82

Explanation

Discount each cash flow at its own spot rate: 5/1.03 = 4.854 and 105/1.04^2 = 105/1.0816 = 97.078. The sum is about 101.93. Discounting both flows at 3% gives 103.83, which uses the wrong rate for the final cash flow. Dividing by 1.04 instead of squaring it gives 105.82.

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