# Finding the dividend per share when we have constant dividend growth

For the following question, what is the dividend per share?

My answer was 2.585 by saying that 5.5% return must come from the dividend yield and the other 5.5% coming from the capital gains rate. We know P0 is 47 and so D1 must be 2.585. My friend disagrees and says we are after D0 and that we must divide D1 by the Dividend Yield to get D0, which i do not understand. Could someone explain this please?

• Ironically, dividends do not provide total return. Only share price appreciation does that. Apr 4, 2020 at 12:26
• @BobBaerker Share price appreciation is not a component of total return for the entire mass of investors. If one investor sells a share, another investor buys the share. Every sale has a buyer and seller in equal amounts. Both of these think they are doing a beneficial transaction. Only dividends and dividend-equivalents (like company purchasing back shares) are part of total return. Apr 4, 2020 at 12:43
• @juhist - Apart from the Captain Obvious statement that "Every sale has a buyer and seller in equal amounts" (I have no clue what relevance that has to total return), your understanding of total return is lacking. I suggest that you read this: investopedia.com/terms/t/totalreturn.asp . If you understand that content then you'll understand that without share price appreciation, there is no total return. Apr 4, 2020 at 13:10
• Share price is just a number of paper. It is irrelevant. (Edit: or actually, it has relevance because it affects the dividend yield. If the share price goes down, your yield goes up.) Apr 4, 2020 at 13:18
• @juhist Not at all, sorry. The dividend means nothing. If you get \$X of dividend, the share price goes down by \$X on the ex-dividend date. So share price difference is even the most relevant part of the total return, while dividend payments reduce this price difference and thus must be taken into account. Sep 2, 2020 at 7:22

This depends on when the next dividend will be paid.

Basically, if the dividend yield is 5.5% then the dividend paid 1 year from now must be 2.585.

But, Gordon's formula makes certain assumptions about when the next dividend will be paid. If they do not hold, the dividend could be slightly different.

For example, type into GNU Octave: `2.585*sum(1./(1.055).^[1:10000])` and you will get `47.000`

Type into GNU Octave: `2.585*sum(1./(1.055).^[0:10000])` and you will get `49.585`.

So, in principle, if the next dividend is paid tomorrow, the Gordon's formula needs slight adjustments.

• What does it mean current dividend then?For this question I assume gordons assumptions hold. Do I need to discount my dividend by 1.055? If so why that figure? Is that because g = 1.055?? Apr 4, 2020 at 12:30
• @InvestingScientist If the dividend is paid tomorrow, you do have to divide it by 1.055. If the dividend is paid 1 year from now, you do not have to divide it by 1.055 and your answer of 2.585 is correct. The figure 1.055 comes from the dividend growth rate (5.5%, half of the 11% total yield). Apr 4, 2020 at 12:40