Finding the dividend per share when we have constant dividend growth

Question

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?

juhist · Answer

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.

Finding the dividend per share when we have constant dividend growth

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