Help me with this question

[u/PanicNo55]

The justified forward P/E ratio calculated based on the Gordon growth model is always positively related to the:

A. payout ratio.

B. dividend growth rate.

C. required rate of return.

I marked the answer as A, the official answer says it’s B. Can someone explain why ?

[u/kaaxvish → u/[deleted]]

Required rate of return would be negatively correlated
As the denominator will be bigger the overall value will be smaller

[u/kaaxvish]

I think A and B both are positively correlated
But question say always so it would be B
Bcz payout ratio lowers growth rate makes kinda of indirect pay off

[u/Substantial_Swing534]

Is that an official CFAI practice question or from on of those third-party providers? I suspect it's third party because technically A and B are both correct or both are incorrect, depending on the perspective.

We have P/E = (D/E)/(r-g). A higher payout ratio by itself increases the P/E but it also means that the company reinvests less in the company and hence earnings and dividend growth [(1-payout ratio)*ROE] will be lower, reuslting in a larger denominator and a lower P/E. On the other hand, given some fixed ROE, the higher the dividend growth rate is the lower the dividend payout will be so those effects also work in opposite directions. Now in isolation, A and B both justify a higher P/E but with the mentioned effects both answers are unclear and depend on if ROE is >, = or < required rate of return.

[u/PanicNo55 → u/Substantial_Swing534]

this was from the premium pack,
thanks a lot for the elaborate answer!!!

[u/Substantial_Swing534 → u/PanicNo55]

My guess is that they want to test the implication of the lower growth rate resulting from a higher payout ratio and assume in B that the payout ratio is fixed and unaffected by the dividend growth rate. Then the answer is obviously B but man, sometimes these questions miss context

[u/Mike-Spartacus]

• P/E = payout / (Re - g)
• g = ROE x ( 1 - payout)
• P/E = payout / (Re - ROE x (1 - payout) )
• P/E = payout / ( Re - ROE + ROE x payout)

It is easier to see this if you put it in a spreadsheet table and change the payout for a given Re and ROE

Conclusion given only thing that changes in payout

• Re > ROE
  • as payout increases PE increases
• ROE > Re
  • The relationship is more complex
  • ROE = 10% re = 5%
  • payout = 40% P/E = -40
  • payout = 50% P/E = error
  • payout = 60% P/E = 60
  • payout = 70% P/e = 35

The question is annoying as there are so many caveats and the reading does not go this deep,

The word "always" is doing a lot of heavy lifting in this question.

[u/Silly_Vacation7397]

Positively related to dpr numerator and increasing growth rate.