Sunday, October 23, 2005

Calculating Tax Equivalent Yields

Pepper and I had a good long discussion at the pool hall about various options for a low-risk income producing investment of $20,000 (LaLa and the gear girl were otherwise engaged in a friendly game of darts...they do not understand our nebbishy ways). We were primarily wondering if I-bonds were suddenly a playa given the recent high CPI-U and the extra bonus of not being taxed by the state on interest. Or was a state municipal bond fund better? Or a taxable socially responsible bond fund?

I was obsessed with doing the math but it was a struggle since I'm still learning. If I've made some mistakes, please let me know!

Tax Equivalent Yield Formula

tax equivalent yield = yield / ( 1 - applicable tax rates)

Operation Parameters
  • Federal Marginal Tax Rate: 25%
  • MA State Tax Rate: 5.3%
  • Amount invested: $20,000

Option 1: I-Bond (5.29%)
Federal tax is deferred on an I-Bond, but it is exempt from MA tax. Since we can't predict the future fixed rates or the CPI-U, I assumed a buy in late October and selling in 14 months. This would count as 15 months and the 3 months of as yet unknown interest would be forfeit. Jonathan has already done all the hard work to figure out the blended rate in this case as 5.02%. Since only state tax can be factored in here, the taxable equivalent yield is 5.29%. The yield is paid out as interest (cash).

Option 2: MA Sales Tax Bond (5.52%)
Digging around the Fidelity site, I found a single municipal bond with a relatively high yield to compare. The current price is $108.511 per $100 so $20,000 would buy 184 bonds ( I think I have that right). The coupon pays 5% so the yield is currently calculated at 3.85%. Because this bond is federal and state tax free, the taxable equivalent yield is just over 5.52%

Option 3: FDMMX (approx 5.82%)
The Fidelity Massachusetts Municipal Income Fund is federal and state tax free. This fund requires an initial investment of $10,000. The current price per share is $12.03 so $20k would by roughly 1662 shares. The dividend is currently $0.04 per share. Given that dividends are re-invested (They *are* reinvested, right? if so, approx 5-6 shares a month added), I ended up estimating a yield of 4.06 which is a taxable equivalent yield of 5.82%

So if my calculations are right I-Bonds don't look that sexy compared to the munis (I-Bonds are sexy for other reasons though including low barrier to entry for such a nice rate) and a taxable bond fund would have to yield at least 5.52% after all expenses and loads were accounted for in order to really compete with municipal bonds...

Or am I all wrong?

[Update: Of course, Dinkytown has a helpful calculator for figuring out TEY on a Municipal Bond]


  1. You are not taking into account duration risk. The i-bond has unusual characteristics in that you can't redeem it for a year, then you can redeem with a small penalty until year 5, then you can redeem penalty-free until year 30. Additionally it is inflation adjusted.

    The muni bond is, if like most muni bonds, not redeemable until maturity. In addition, it is likely callable, which means the issuer can redeem it if that is advantageous to him (i.e. if interest rates go down).

    The muni bond mutual fund is basically just a portfolio of muni bonds so you get some diversification but have to pay fees. Remember that muni bonds are usually not inflation adjusted as well.

    Lots of very high paid financial experts try to figure out the value of callability, inflation protection, and other features of bonds. It is NOT appropriate to value dissimilar instruments simply according to yield.

  2. Thanks for the additional information and clarity hedged.

    My purpose was specifically to try out some TEY calculations, to get a view on comparitive TEYs.

    What isn't clear in the post is that the original question was I-Bonds vs. Calvert Income Fund and I was curious about some of the other comparisons myself so hence the TEY

    And you are also right that I did not include Fidelity's 0.42 expense ratio etc but I'd love to know how to do that math to do that


    And I'm certainly no financial expert nor do I claim expertise. I'm just a layperson struggling with all this info, so the post was just as much about getting further information as it was about sharing a small piece of my process.

  3. I believe the NAV value of the Fidelity Tax-Free MA Muni Bond fund already is "net" (net asset value) of the expense ratio, so the .04 cent per share yield you indicate already accounts for expenses


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