## After-Tax Yield Equivalency

It must be fall! The time when an old man’s fancy lightly turns to thoughts of tax planning! I received my first indication of the change in season today …

My correspondent sent me the following calculation and wondered why the after-tax yield on a dividend that he was investigating was lower than the pre-tax yield … he attached a calculation:

 Tax Effect on Dividends A Preferred Shares Purchase Price \$100.00 B Dividend Rate of Return 4.25% C Yearly Amount of Dividends (A*B) \$4.25 D Gross-Up Percentage 45% E Taxable (i.e. Grossed-Up) Amount of Dividends = (1+D)*C \$6.16 F Tax Rate 30% G Tax on Grossed-up Amount of Dividends (F*E) \$1.85 H Tax Credit Percentage 19% I Tax Credit (H * G) \$0.35 J Net Tax (G-I) \$1.50 K After Tax Return (C-J) \$2.75 L After Tax Rate of Return (K/A) 2.75%

My correspondent’s problem was that he had been told that “L” should be more than “B”.

Well, he was quite right to be suspicious! An after tax rate of return higher than the pre-tax rate implies a negative taxation rate; and while such things may sometimes happen to a very small extent in some corners of the tax world, given very particular (and relatively small!) numbers, it’s just not there for most of us! It will doubtless be a promise in the next Federal election campaign, however.

I suspect that my correspondent was told a garbled version of something that really is a general rule: that dividend income is better than interest income and that a dividend of \$1 will always leave more in your pocket than an interest receipt of \$1. Always? Well, there might be some exceptions! I will stress that I am not a tax expert and that anything I say about taxes should be checked!

What we need to illustrate this is a few more lines in the calculation:

 Additional Lines for Interest Equivalency Factor M Rate of tax on interest income (from tables) 43.4% N Percentage of Interest Income kept (1-M) 56.6% O Interest Required to produce after-tax amount (= K / N) \$4.86 P Equivalency Factor (= O / C) 1.14

So what we conclude from this particular equivalency factor is that:

• a dividend yield of 4.25% will produce the same amount of after-tax income as an interest yield of 4.86%
• For any given dividend yield, we can multiply by 1.14 to get the interest rate to which it is equivalent
• For any given interest rate, we can divide by 1.14 to get the dividend yield to which it is equivalent

Note that this 1.14 figure is very low and is probably an error due to the fact that I simply put in a “generic” tax rate for income rather than looking one up that was actually consistent with the other data.

Another problem is that my correspondent’s figure of \$1.50 tax on \$4.25 dividend is an all-in rate of 35%, which looks pretty high to me. I suspect that the tax factors [(D), (F) and (H)] are incorrect; but more details and sources are required to check this. Most equivalency factors are in the neighborhood of 1.30 – 1.40.

Tax rates for different types of income can be obtained from Ernst & Young’s Tax Calculator. I’ve also written an article in which equivalency factors were vital and calculated for a wide variety of provinces and income levels.

### 4 Responses to “After-Tax Yield Equivalency”

1. J says:

Hi!
I’m the one who asked the question and you are quite right… a more correct recap of what I was told is that “a preferred share that pays x% is equivalent to getting plain old interest income of y%”. And the number quoted for y is always greater than x. Good “catch”. Thanks for the response.

2. like_to_retire says:

The bond equivalency factor can really jump around when your taxable income is near the ~\$72K tax bracket limits too.

I’ve played with Quick Tax using net incomes around the \$70K mark, and if you test \$1000 of bond income versus \$5000 of bond income on top of that income level, the equivalency factor can jump from 1.5 up to over 2.1.

ltr

3. […] Month-end scheduling is still a problem! I’m not going to be reporting much today, but those desperate for reading material can look at my commentary on the Blinder Op-Ed, Changes in the HIMIPref™ Indices, MAPF Performance, an updated commentary on the new issues or a note on After-tax Yield Equivalency, all of which are new since last time. […]

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