To calculate the yield to maturity (YTM) of a STRIPS (Separate Trading of Registered Interest and Principal Securities), we can use the formula for the present value of a single sum:
\[ PV = \frac{F}{(1 + r)^n} \]
Where:
- \(PV\) is the present value (market price of the STRIPS)
- \(F\) is the face value (amount paid at maturity, typically $1,000 for STRIPS)
- \(r\) is the yield to maturity (YTM) expressed as a decimal
- \(n\) is the number of years to maturity
Given:
- \(PV = 301.00\)
- \(F = 1000\) (assuming the typical face value for STRIPS)
- \(n = 10\)
Substituting into the formula, we have:
\[ 301 = \frac{1000}{(1 + r)^{10}} \]
Now, we need to solve for \(r\).
First, multiply both sides by \((1 + r)^{10}\):
\[ 301(1 + r)^{10} = 1000 \]
Next, divide both sides by 301:
\[ (1 + r)^{10} = \frac{1000}{301} \]
Calculating the right side:
\[ \frac{1000}{301} \approx 3.32 \]
Now take the tenth root of both sides:
\[ 1 + r = (3.32)^{\frac{1}{10}} \]
Calculating \( (3.32)^{\frac{1}{10}} \):
Approximately,
\[ (3.32)^{\frac{1}{10}} \approx 1.1285 \]
Subtracting 1 gives us:
\[ r \approx 1.1285 - 1 = 0.1285 \]
This means that the yield to maturity (YTM) is approximately \(0.1285\) or \(12.85%\).
Therefore, the yield to maturity is approximately 12.85%.