Why tax on the inflation part of the coupon takes most of a bond's real income, line by line from a Treasury bill to a high-yield bond.
Take the tax off first, then the inflation: real after-tax yield = (1 + yield × (1 − tax rate)) / (1 + inflation) − 1. For an illustrative US investor at a 37 per cent combined marginal rate with inflation at 2.80 per cent, a 5.15 per cent BBB bond earns 0.43 per cent real after tax, and a 4.00 per cent Treasury bill, exempt from state tax, earns minus 0.08 per cent. Tax takes 81.1 per cent of the bond's real income, because it is levied on the part of the coupon that only replaces inflation.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A bond coupon does two jobs. Part of it compensates for the fall in the value of money; the rest is the real return. The tax authority does not distinguish them: it taxes the whole nominal coupon. Subtracting inflation first and then applying tax to what is left therefore taxes only the real part, and overstates the result. The correct order follows the money: the coupon arrives, tax is paid on all of it, and what remains is deflated.
| Input | Value |
|---|---|
| Federal marginal rate on interest | 32% |
| State marginal rate, not deducted federally | 5% |
| Expected inflation | 2.80% |
| Treasury bill yield, exempt from state tax | 4.00% |
| BBB corporate bond yield | 5.15% |
| B high-yield bond yield, displayed | 8.75% |
| Same bond after expected default losses | 6.95% |
After-tax nominal yield = y × (1 − t)
Real after-tax yield = (1 + y × (1 − t)) / (1 + π) − 1
Excel: =(1+B2*(1-B3))/(1+B4)-1
Step 1, the tax. On the BBB bond, 37 per cent of 5.15 is 1.9055 per cent, leaving 3.2445 per cent after tax.
Step 2, the inflation. 1.032445 / 1.028 = 1.004324, a real after-tax yield of 0.43 per cent. On $100,000 that is $432 of purchasing power a year, from $5,150 of coupon.
Step 3, the effective tax on real income. The real pre-tax yield is 5.15 less 2.80, 2.35 per cent. The tax paid, 1.9055, is 81.1 per cent of it. On the Treasury bill the tax is 106.7 per cent of the real income: the investor pays more tax than the bill earns in real terms.
| Holding | Yield | Tax rate | After tax | Real after tax |
|---|---|---|---|---|
| Treasury bill | 4.00% | 32% | 2.72% | −0.08% |
| BBB corporate bond | 5.15% | 37% | 3.24% | 0.43% |
| B high-yield bond, displayed | 8.75% | 37% | 5.51% | 2.64% |
| B high-yield bond, after expected losses | 6.95% | 37% | 4.38% | 1.54% |
The high-yield line shows how the adjustments stack. 8.75 per cent on the screen becomes 6.95 per cent after an illustrative 1.80 per cent a year of expected default losses, 4.38 per cent after tax and 1.54 per cent after inflation: less than a fifth of the displayed number. The last two lines assume that default losses reduce taxable income one for one. In practice a default produces a capital loss, which may only offset capital gains, so the true after-tax figure can be lower still. How the expected loss is computed is in yield after expected default losses.
The break-even pre-tax yield for a zero real after-tax return is inflation divided by one minus the tax rate: 4.44 per cent for a fully taxable bond and 4.12 per cent for a Treasury bill at these rates. Anything yielding less loses purchasing power after tax.
| Inflation | Treasury bill | BBB bond | B bond, displayed |
|---|---|---|---|
| 2.0% | 0.71% | 1.22% | 3.44% |
| 2.8% | −0.08% | 0.43% | 2.64% |
| 4.0% | −1.23% | −0.73% | 1.45% |
| 5.0% | −2.17% | −1.67% | 0.49% |
Each point of inflation costs roughly a full point of real after-tax yield, because the tax on the nominal coupon does not fall when inflation rises. The bracket matters almost as much: at a 12 per cent federal rate (17 per cent combined) the BBB bond earns 1.43 per cent real after tax, at 22 per cent 0.93, and at 37 per cent only 0.18. A bond that is a sensible holding in a low bracket, or in a tax-deferred account, can be a losing one in a high bracket.
Subtracting inflation before tax. (5.15 − 2.80) × (1 − 0.37) gives 1.48 per cent, 1.05 points more than the correct 0.43. Almost all of the difference is the tax on the inflation part of the coupon: 2.80 per cent times 37 per cent, 1.04 per cent of principal a year, which the investor pays and the shortcut forgets; the small remainder comes from subtracting inflation instead of dividing by it. Quoting the real pre-tax yield, 2.35 per cent, is worse still. For a municipal bond, where the comparison runs the other way, see how to calculate tax-equivalent yield.
The Credit Investor follows one $500,000 portfolio from its displayed yield to what it earned, with a tax illustration for the vehicles, and the free workbook for this case reproduces every line.
After. Tax is levied on the whole nominal coupon, including the part that only replaces inflation. On a 5.15 per cent bond at a 37 per cent tax rate with 2.80 per cent inflation, the correct real after-tax yield is 0.43 per cent; subtracting inflation first gives 1.48 per cent, overstating it by 1.05 points, almost all of it the 1.04 per cent of principal paid in tax on the inflation component.
Yes, whenever its after-tax yield is below inflation. A 4.00 per cent bill taxed at an illustrative 32 per cent federal rate, with no state tax, yields 2.72 per cent after tax, which is minus 0.08 per cent real at 2.80 per cent inflation. The break-even bill yield at these rates is 4.12 per cent.
More than the headline rate suggests. On a 5.15 per cent bond with 2.80 per cent inflation, the real pre-tax yield is 2.35 per cent but the tax at 37 per cent is 1.9055 per cent of principal, 81.1 per cent of the real income. The lower the real yield, the higher this effective rate.
This article is one calculation from The Credit Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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