How inflation affects returns and dividends

How inflation is linked to returns AND dividends? We know that adj returns are (1+return)/(1+inflation) -1

But how do we account for dividends?

Suppose: 10% annual return 3% inflation 4% dividend yield

Suppose we have 100.000\$ invested in year 0. At the end of year 0 we have earned 6.80% ((1+10%)/(1+3%)-1) + 0.97% of dividends reinvested (1+4%)/(1+3%)-1 and so on?

Or do we account dividend yield as it is (4%) without adjusting for inflation, since we have already adjusted the return and then it would be like double counting? (the dividend yield is a function of the price - in this case a function of the asset value - which is already adjusted for inflation)

Thanks all Note: edits to the question are quickly adding details and changing the validity of my answer here.

Presumably, the dividend is part of the 10% return for the year, no needing to account for it separately. To adjust for “real” return, I’d multiply that \$110,000 by .97 and that results in an inflation-adjusted return.

If, in fact, you meant to say that at year end you have an investment valued at \$110,000 and \$4000 in cash from the dividend, I’d have to change my answer.

Given the comment below, both figures get adjusted, you multiply both the \$110,000 in year-end value of the investment and the \$4000 in cash by the 3% reduction for inflation. And a 4% dividend is really 3.88% after inflation.

• The second part is what I mean. No need to discuss the generous assumptions here, we all know that 10% yearly and 4% dividends is almost impossible to achieve consistently. I am here to discuss with you guys how and if would you adjust the div yield for inflation, since the return is already adjusted May 10 '19 at 15:01
• I updated my answer per your comment. No debate, just math May 10 '19 at 15:04
• Since dividend yield is a function of price, wouldn't it be true that since inflation is already reflected in the price, you'd be double-counting it by applying it to the dividend yield also? May 10 '19 at 15:32
• Joe, what's confusing is combining an inflation adjusted quarterly dividend with an annual return. The original question and subsequent comments are misleading and confusing and therefore, accurate answers are hard to formulate. May 11 '19 at 16:44
• Joe - Apart from the errant info in the question, the dividend is a distraction which sent the OP off on a wild goose chase. It might add 10-20 basis points of compounding, depending on share price when received and reinvested. That's the only variable in the comparison of a hypothetical non dividend stock yielding 10% EOY to a 4% dividend paying stock yielding 10% EOY (other than dividend taxation if non sheltered). I mentioned in my answer that it would be double counting as did D Stanley about 10 comments back. That's the end of it unless the OP wants to clarify and explain his assumptions. May 11 '19 at 21:45

I think that you are double counting. A dividend is a return of your investment. It does not provide Total Return because the stock exchanges reduce share price by the amount of the dividend on the ex-div date (as Joe alluded to).

IOW, if you have a 100 shares of a \$100 stock worth \$10,000 that pays a 4% annual dividend, on the ex-date you will have 100 shares of a \$99 stock worth \$9,900 and you are due \$100 on the Payable Date. It's the same \$10,000 either way, ignoring taxation if non sheltered. You can't have inflation ravage the \$10k as well as the \$100 or in the case of your example, ravage the \$110k end of year one Total Return Value and the \$1,000 dividend. It's already included

Where this gets complicated is that with dividend reinvesting, the prices at quarterly reinvestment will vary. OK, you assume constant share price growth and you make that linear to simplify. In addition, you have another complication with the compounding from dividend reinvestment.

The end result is that TR = Dividend + Return from compounding + Position appreciation and the total is 10%.

I'm not versed in the formulas for this so I'll not offer any solution. But FWIW, the following two web sites agree that \$100k with a 4% dividend rate and 3% inflation would turn \$100k into \$106,796 after one year. The first one (Zacks) is the first part of the calculation that you used. The second gives a 10 year calculation of \$192,999 which is less than your numbers:

https://finance.zacks.com/calculate-returns-investments-inflation-1850.html

https://www.americanfunds.com/individual/planning/tools/taxes-and-inflation-calculator/results.htm

• I read the question, and thought OP agreed, He starts year with \$100K invested, and ends with \$110K in stock plus \$4000 cash from dividends. Then he edited an image and updated text to move to annual return of 6.8%, plus a .97% dividend (How did 4%/yr turn into .97?). I am at the point (post edit) where I don't know what the question is, and am likely to delete my own answer in favor of yours. +1 May 10 '19 at 17:02
• Joe, From the phrasing, I too wasn't sure about the whole thing so I went with the assumption that 10% was the Total Return which would include the dividend. May 10 '19 at 17:17
• "you have an investment valued at \$110,000 and \$4000 in cash from the dividend" "The second part is what I mean." OP then warned me away from questioning such a high assumption. A total 10% wouldn't require any warning. It's lower than history. 14%? That's why he just wanted math. Then div dropped to 1%? May 10 '19 at 17:22
• @joetaxpayer the 6.8% comes from 1.1/1.03-1 and 0.97% comes from 1.04/1.03-1 May 11 '19 at 9:03
• @Saverio - (1) If there was no inflation, how much would \$100k be worth after one year? (2) In your displayed image, why are you combining an inflation adjusted quarterly dividend of 1% in a line with a 6.80% annual return? Line 0 --> 0 100,000 6.80% .97% 971 107,767 . Regardless of the calculations, that will confuse the reader. May 11 '19 at 16:40