Instructor: Jon Hooks Show bio

Jon has taught Economics and Finance for 32 years. He holds a Ph.D., in Economics from Michigan State University, and is a CFA charter holder.

Some investments are fully taxable, while other investments have specific tax advantages. In this lesson, we will compare pre-tax and after-tax return calculations, as well as taxable equivalent returns. Updated: 08/19/2021

Taxes and Returns

Kevin has $5,000 that he wants to invest. He has maxed out his 401(k) and IRA contributions and is worried about the effects of taxes on his return. Investments are taxed in two ways. First, you are taxed on any income from the investment unless it is tax exempt. Second, you are taxed on any realized gains. Realized gains occur when you sell the investment.

For example, if you buy a stock for $20 (referred to as Po) per share, receive a $2 dividend (or C1), and then sell the stock after one year for $24 (or P1), then you have a realized capital gain (long term since you held the stock at least one year) of $4 and dividend income of $2. Your one-year, pre-tax return on investment is given by:

  • Pre-tax return on investment = ((P1 - Po + C1) / Po
  • ($24 - $20 + $2) / $20 = 30%

Long-term capital gains are taxed at a reduced rate when realized. Short-term capital gains (those held less than one year) and dividends are always realized and taxed as ordinary income in the year they are paid. After-tax return on investment is the net return to the investor after ordinary income and capital gains taxes are subtracted. It is calculated as:

  • After-tax return on investment = ((P1 - Po) (1 - Tc) / Po) + C1(1 - To) / Po

Tc is the long-term capital gains tax rate and To is the income tax rate on ordinary income.

If Kevins ordinary income tax rate is 25% and his long-term capital gains tax rate is 20%, then his after-tax return on investment is:

  • (($24 - $20)(1 - 0.20)) / $20 + $2(1 - 0.25) / $20) = 23.5%

Capital gains are taxable on every investment, including stocks and bonds. However, bonds have an added tax complication. While stock dividends are always taxable, some bond interest is not. Therefore, before you can calculate your after-tax return you have to determine if your bond interest is taxable.

Taxable Equivalents

Lets return to Kevin. He wants to invest in a relatively safe place but is turned off by low bank interest rates and is afraid of stock market volatility. Bonds are taxed the same way as stocks. However, investors often buy bonds for the interest earned beyond any possible capital gains. Thus, it is important to understand before- and after-tax bond yields.

Kevin has never invested in bonds but decides he will in order to earn a higher interest rate. His friend tells him he should look at Treasury bonds or Michigan (the state in which he resides) municipal bonds. He looks online and sees that a 10-year Treasury bond has a rate of 4%, while a 10-year State of Michigan Bond (Muni) has a rate of 3.2%.

Another friend tells him he can get an even higher rate on a corporate bond. He sees that a bond issued by a local company that he respects has bonds yielding 4.25% and decides to invest in the corporate bond. What further tax issues should he have considered?

Since corporate bonds are fully taxable, the norm in finance is to calculate taxable equivalents of tax-exempt bonds (called grossing up) and compare them to the taxable yield.

Treasury Bonds

Treasury bonds are taxable at the federal level and tax exempt at the state and local level. We will focus on just state taxes here, as the principle is the same for local taxes and state bonds make up the bulk of muni investing, especially in the world of mutual funds. Finding the taxable equivalent yield of a Treasury bond is relatively simple for investors that do not itemize taxes:

  • Taxable equivalent yield = Treasury yield / (1 - Ts), where Ts = the state income tax rate

For example, if you are in the 20% federal income tax bracket and face a 6% state income tax rate and a Treasury bond was yielding 4%, then assuming you do not itemize tax deductions your taxable equivalent rate would be:

  • Taxable equivalent yield = 0.04 / (1 - 0.06) = 4.26%

This means that, ignoring risk and maturity, you would be indifferent between a corporate bond offering 4.26% and a 4% Treasury bond. However, you would choose the Treasury bond in this case since it offers lower risk.

If you itemize, the calculation becomes:

  • Taxable equivalent yield = Treasury yield / (1 - Ts(1 - Tf)), where Tf = the federal income tax rate and Ts = the state income tax rate

In our example above the calculation is:

  • Taxable equivalent yield = 0.04 / (1 - 0.06(1 - 0.2)) = 4.20%

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