Taxable Equivalent Yield Calculator

1. What is the Taxable Equivalent Yield Calculator?

Definition: This calculator computes the taxable equivalent yield (\( TEY \)), which adjusts a tax-exempt bond’s yield to reflect its equivalent yield if it were taxable, based on the investor’s marginal tax rate.

Purpose: Helps investors compare tax-exempt bonds (e.g., municipal bonds) with taxable investments, aiding in investment decision-making.

2. How Does the Calculator Work?

The calculator uses the following formula to compute the TEY:

Formula:

\( TEY = \frac{BY}{1 - MTR} \)

Where:

\( TEY \): Taxable Equivalent Yield (decimal)
\( BY \): Bond Yield (decimal)
\( MTR \): Marginal Tax Rate (decimal)

Steps:

Step 1: Determine bond yield. Input the yield of the tax-exempt bond (\( BY \)).
Step 2: Determine marginal tax rate. Input the investor’s marginal tax rate (\( MTR \)).
Step 3: Calculate TEY. Compute \( TEY = \frac{BY}{1 - MTR} \).

3. Importance of Taxable Equivalent Yield Calculation

Calculating TEY is crucial for:

Investment Comparison: Allows comparison of tax-exempt bonds with taxable bonds or other investments.
Tax Planning: Helps investors in high tax brackets assess the true value of tax-exempt yields.
Portfolio Optimization: Assists in balancing tax-efficient and taxable income sources.

4. Using the Calculator

Example (Bond A): \( BY = 6\% \), \( MTR = 30\% \):

Step 1: \( BY = 0.06 \).
Step 2: \( MTR = 0.30 \).
Step 3: \( TEY = \frac{0.06}{1 - 0.30} = \frac{0.06}{0.70} \approx 0.08571 \) (8.571%).
Results: \( BY = 6.000\% \), \( TEY = 8.571\% \).

A TEY of 8.571% indicates the tax-exempt 6% yield is equivalent to a 8.571% taxable yield for a 30% tax bracket investor.

Example 2: \( BY = 4\% \), \( MTR = 25\% \):

Step 1: \( BY = 0.04 \).
Step 2: \( MTR = 0.25 \).
Step 3: \( TEY = \frac{0.04}{1 - 0.25} = \frac{0.04}{0.75} \approx 0.05333 \) (5.333%).
Results: \( BY = 4.000\% \), \( TEY = 5.333\% \).

A TEY of 5.333% shows the 4% tax-exempt yield equals a 5.333% taxable yield for a 25% tax bracket.

Example 3: \( BY = 3.5\% \), \( MTR = 40\% \):

Step 1: \( BY = 0.035 \).
Step 2: \( MTR = 0.40 \).
Step 3: \( TEY = \frac{0.035}{1 - 0.40} = \frac{0.035}{0.60} \approx 0.05833 \) (5.833%).
Results: \( BY = 3.500\% \), \( TEY = 5.833\% \).

A TEY of 5.833% reflects the 3.5% tax-exempt yield’s taxable equivalent for a 40% tax bracket.

5. Frequently Asked Questions (FAQ)

Q: What is taxable equivalent yield?
A: TEY adjusts a tax-exempt bond’s yield to its taxable equivalent, considering the investor’s tax rate.

Q: Why use marginal tax rate?
A: The marginal tax rate reflects the highest tax bracket, determining the tax savings from tax-exempt income.

Q: Can TEY be negative?
A: No, as \( BY \) and \( 1 - MTR \) are positive, TEY remains positive.