CFA Level 1: Determine Yield to Maturity of a 15-Year Zero-Coupon Bond

Yield to Maturity Calculation for a 15-Year Zero-Coupon Bond

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Question

Jack Hare, CFA, is a fixed income analyst. Hare is evaluating a 15-year zero-coupon bond, which is priced at $30.83. Determine the issue's approximate yield to maturity.

Answers

Explanations

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A. B. C.

C

To determine the approximate yield to maturity (YTM) of the 15-year zero-coupon bond, we can use the formula for calculating YTM:

YTM=(FaceValuePrice)1n1YTM = \left( \frac{Face Value}{Price} \right)^{\frac{1}{n}} - 1

Where:

  • Face Value is the future value of the bond at maturity.
  • Price is the current market price of the bond.
  • n is the number of years to maturity.

In this case, we are given that the bond is priced at $30.83, and it has a maturity of 15 years. However, the face value of the bond is not provided in the question.

To solve for the YTM, we need to know the face value of the bond. Without that information, we cannot calculate the exact YTM. Therefore, it seems that there may be some missing information in the question.

However, if we assume that the face value of the bond is $100 (a common assumption for zero-coupon bonds), we can calculate the approximate YTM as follows:

YTM=(FaceValuePrice)1n1YTM = \left( \frac{Face Value}{Price} \right)^{\frac{1}{n}} - 1

YTM=(10030.83)1151YTM = \left( \frac{100}{30.83} \right)^{\frac{1}{15}} - 1

Using a calculator, we find:

YTM0.0683YTM \approx 0.0683

Multiplying by 100 to convert to a percentage, the approximate YTM is approximately 6.83%.

Given that the available answer choices are 6%, 7%, and 8%, the closest answer would be A. 6%.

However, it is important to note that the exact YTM calculation depends on the face value of the bond, which is not provided in the question. Therefore, this is an approximation based on the assumption of a face value of $100.