To calculate the yield to maturity (YTM) of a STRIPS (Separate Trading of Registered Interest and Principal of Securities), we can use the following formula for YTM with zero-coupon bonds:
\[ YTM = \left( \frac{F}{P} \right)^{\frac{1}{n}} - 1 \]
where:
- \( F \) = face value of the bond (which is typically $1,000 unless specified otherwise),
- \( P \) = current market price of the bond,
- \( n \) = number of years to maturity.
Given the values:
- \( F = 1000 \) (assuming standard face value),
- \( P = 371.00 \),
- \( n = 15.00 \).
Substituting the values into the formula gives:
\[ YTM = \left( \frac{1000}{371} \right)^{\frac{1}{15}} - 1 \]
Now, calculate \( \frac{1000}{371} \):
\[ \frac{1000}{371} \approx 2.694 \]
Next, take the 15th root of 2.694:
\[ YTM \approx \left( 2.694 \right)^{\frac{1}{15}} - 1 \]
Calculating the 15th root of 2.694 (which can be done using a scientific calculator or software):
\[ YTM \approx 1.0756 - 1 \]
Finally:
\[ YTM \approx 0.0756 \]
Multiplying by 100 to express this as a percentage:
\[ YTM \approx 7.56% \]
Thus, the yield to maturity (YTM) of the 15.00-year STRIPS is approximately 7.56%.