Tax-equivalent Yield Calculator

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What is tax-equivalent yield?

The coupon payments of tax-exempt municipal bonds are exempt from Federal income tax. We use the tax-equivalent yield to explain the yield that would be needed on a taxable bond (corporate, treasury, MBS) to match the yield of the tax-exempt muni that benefits from the tax-exemption. Jump to the tax-equivalent yield calculator.

WARNING: This post contains bond math and is not for the faint of heart.

Example:

You can buy a tax-exempt municipal bond that yields 2.5% or a corporate bond that yields 3%. Your marginal tax rate is 35%. Which bond will provide a better yield?

To solve this problem, we need to calculate the tax-equivalent yield of the municipal bond. This provides an “apples-to-apples” comparison of the tax-exempt bond and the taxable bond.

The formula is simple. The yield of the tax-exempt bond is divided by 1 minus the tax rate in decimal form.

Tax-equivalent Yield Formula

 

 

For the problem above, the formula looks like this:

Tax-equivalent Yield Problem

 

for a tax-equivalent yield of 3.846%

In this case, the tax-exempt municipal bond would provide .846% more yield per year than the corporate bond on a tax-equivalent basis. This means buying the municipal bond would be a better purchase from a yield perspective and not factoring in other  risks.

Examining the tax-equivalent yield through cash flow

Another way to look at tax-equivalent yield is through comparing the cash flow of a tax-exempt bond and a taxable bond.

In the example above, the municipal bond yields 2.5% per year.

Let’s assume the municipal bond was purchased at par for $1,000. Over 1 year, the bond will pay 2 coupon payments of $12.50 ($1,000 x (2.5%/2)). This income is not taxable so the investor receives the full amount of the coupon payment.

The corporate bond that yields 3% is taxable. For the $1,000 invested in the corporate bond, the investor will receive 2 coupon payments of $15 ($1,000 x (3.0%/2))  over 1 year. The marginal tax rate of 35% means that $5.25 of the corporate bond coupon payments will be paid in income tax.

For the municipal bond, the investor receives the full $25 coupon payment per year. After taxes, the corporate bond provides $19.5 in income.

Connecting Tax-equivalent yield with cash flows

To check the tax-equivalent yield solved in the problem above, we can work out the cash flows of a 3.846% yield. Remember, the tax-equivalent yield tells us the yield needed on a taxable bond to be equal to the tax-exempt bond.

Tax-exempt bond cash flows ($1,000 investment at 2.5%, 35% tax rate)

Coupon payment 1: $12.5

Coupon payment 2: $12.5

Total Taxes: 0

Total income: $25

Yield: $25 / $1,000 = 2.5%

Taxable bond cash flows ($1,000 investment at 3.846%, 35% tax rate)

Coupon payment 1: $19.23

Taxes: $6.73

Coupon payment 2: $19.23

Taxes: $6.73

Pre-tax income ($19.23 – $19.23): $38.46

Total taxes ($6.73 + $6.73) : $13.46

Total after-tax income ($38.46 – $13.46)  : $25

Yield: $25 / $1,000 = 2.5%


As you can see, the math works out and the taxable bond yielding 3.846% provides the same amount of after-tax income as the tax-exempt bond yielding 3%, assuming a 35% tax rate.

The tax-equivalent yield calculator will make the simple calculation for you. You can play around with it and see how taxes affects yield. It also shows how the tax benefit of municipal bonds can make taxable bonds less attractive as your tax rate increases. Likewise, municipal bonds are less beneficial at a lower tax rate.

Play around with it and my hope this post will benefit you on your hunt for yield.

Please provide any feedback or questions in the comment section below.

Tax-equivalent Yield Calculator

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