CDB against LCI and LCA: which one nets more after tax
Your data
The benchmark rate is a field and not a number written into the page, because it moves. Put in the one you are actually being offered today.
Which products your bank offers you, and at what rate, is another question, and this page does not answer it. It only takes the two rates you were quoted and works out what is left after tax.
Results
What the tax-free one has to pay to tie with the taxed one, as a percent of the benchmark
—
| What the taxed one earns before anything is taken out | — |
| Income tax rate that applies to that holding period, in percent | — |
| What the tax takes from the taxed one | — |
| What the taxed one is left with | — |
| What the tax-free one is left with, with nothing taken out | — |
| Difference between them, and which one wins | — |
The same comparison at four holding periods
| Days held | Tax rate | Rate needed to tie | Winner at your rates |
|---|
Each line is worked out for that exact day rather than for a range, because the rate needed to tie keeps drifting up inside a single tax bracket as well: it is not a flat step. The big moves happen when the holding period crosses a bracket.
This is the whole point of the page. The rate the tax-free one needs is not one number, so a note whose rate never changes can win at one horizon and lose at another. Take a tax-free note paying eighty-two against a taxed one paying the full benchmark: it wins up to three hundred and sixty days, and from three hundred and sixty-one it loses.
That is a single day changing the answer, and it is worth seeing why. On day three hundred and sixty the tax rate is twenty in a hundred and the tie is at about eighty; on day three hundred and sixty-one it drops to seventeen and a half, and the tie jumps to about eighty-two and a half. Less tax on the taxed one makes it harder to beat, so waiting one more day to take the money out can flip which product was the better buy.
Is an LCI always better than a CDB because it is tax free?
No, and the gap is smaller than the words tax free suggest. Being exempt is worth exactly the tax the other one pays, so a tax-free note only has to beat what is left of the taxed one after tax, not the taxed one's headline rate.
With a CDB paying 100% of the benchmark, the tax-free note ties at about 77% for a six-month holding, about 80% at one year and about 86% at three years. Below those numbers the taxed CDB wins even after paying its tax.
What rate does a tax-free note need to match a CDB?
Take the rate of the CDB and remove the income tax that applies to your holding period. The tax falls on the yield only, never on the amount you put in.
The subtraction is not quite a subtraction, because yield compounds. Working it out properly instead of just multiplying by the tax rate moves the answer by up to 1.2 percentage points over three years, which is the same order of magnitude as the difference between the two offers you are comparing.
| Days held | Income tax on the yield |
|---|---|
| 1 - 180 | 22.5% |
| 181 - 360 | 20% |
| 361 - 720 | 17.5% |
| 721 or more | 15% |
Does the day I take the money out change which one is better?
Yes, and by more than most people expect. A tax-free note paying 82% of the benchmark beats a CDB paying 100% up to day 360, and loses from day 361, without its own rate changing at all.
The reason is that the tax on the CDB drops from 20% to 17.5% at that point. Less tax on the taxed one makes it harder to beat, so the rate the tax-free one needs jumps from about 80% to about 82.5% overnight. One more day of waiting can flip which product was the better buy.
What happens if I take the money out in the first thirty days?
A separate tax applies on top of the income tax, and it is severe: it takes 96% of the yield on day one and still 3% on day twenty-nine, reaching zero only on day thirty.
In that window it is that tax, and not the choice of product, deciding your result. Tax-free notes of this kind usually cannot be cashed in before ninety days anyway, so comparing products on a horizon that short is answering the wrong question.
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