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Dividend Discount Model - use of growth factor

How to use growth (g) model in such ques. I am not able to understand this concept.

This one is from CFAI mock.

w/o g, answer is = 3/(15%-17.5%*40%)=37.5

with g, answer is = 3*(1+17.5%*40%)/(15%-17.5%*40%)=40.13

Q. An investor gathers the following information about a company:

Current earnings per share

Current dividend per share

Required rate of return

Return on equity (ROE)

Using the dividend discount model, the value of the company’s stock is closest to:

  1. $40.13.
  2. $73.67.
  3. $37.50.
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The Gordon Growth Model is:

V0 = D1 / (rg) = D0(1 + g) / (rg)

You have to have the growth factor in the numerator to get to D1.

Simplify the complicated side; don't complify the simplicated side.

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Thanks Sir.

I am confused because there are questions where answer is based on D/(r-g) and by not taking dividend growth. Esp in multi stage growth questions.

If not specified in ques, whats the way to gauge that this growth is starting (to continue) in current period or it was always there (from the beginning)

So whats the answer here? 40.13?

If the answer is $40.13 then this is how I got the answer.

Sustainable growth rate formula = (1 - dividend payout ratio) * ROE

(1 - 0.6) * 17.5 = 7%

Then it’s just the DDM model

3(1.07) / (0.15 - 0.07) = $40.13