Constant Growth Dividend Discount...

[priehl]

Can someone help me out with the relations in a Constant Dividend Discount Question?

Which of the following statements about the application of the constant growth dividend discount model to the valuation of an equity security is least likely correct?

a)Price is positively related to the growth rate and negatively related to the dividend
b)required rate of return is negatively related to the price and positively related to the growth rate
c)growth rate is positively related to the return on equity and negatively related to the dividend payout ratio
d)price is positively related to the roe and negatively related to the investor's required ror

The answer is a.

I'm in agreement with the price being positively related to the growth rate, but it seems like an increase in dividend will decrease the retention rate which will decrease the growth rate, and my assumption has always been that a decrease in the growth rate would always decrease the value of the stock more than the increase in the dividend payment.

Can someone set me straight w/ a general rule of thumb in this situation?

Thanks much.

 

[cpk123]

d0 * (1+g) / (r-g)

when g increases - numerator increases, denominator decreases. both of which causes P to increase.
so price is positively related to g.

when dividend increases, g decreases as you have stated, so r-g increases and thus the price decreases.

CP

 

[bpdulog]

Just look at the formula: P0=DIV1/r-g

If the numerator is higher price will be higher. I think the question assumes all other factors remaining equal. A firm can have higher earnings, which will increase the dollar amount of it's dividend while keeping g constant.

Hope that helps!

 

[bchadwick]

priehl, you make an interesting point, but you are overthinking the question.

The price of a stock basically reflects 1) expected payment (for a DDM, in form of dividends), AND 2) expected growth of that payment. The larger the payment, the more the stock is worth. The faster the expected growth, the more the stock is worth. Sudden collapses in stock prices are typically more about sudden changes in the growth expectation than about sudden cuts of dividend payments (although this can happen too).

If you look at the DDM, you have Dividends in the numerator, so as dividends increase, so does the price. The growth is in both the numerator and the denominator, but each of them makes the ratio get larger as G gets bigger (at long as G < cost of equity).

Your point is probably worth modeling in real life, since if ROE > Rce, your shareholders will be getting more if you don't pay dividends at all, and paying higher dividends will reduce the growth rate. However, that's a second-order effect in the DDM, and they're probably asking about what happens if D goes up "holding everything else constant." And in any case, if you're not paying any dividends at all, like many growing companies, the constant growth DDM doesn't really apply, since the the result of 0 dividends is that the stock should be 0.

 

[priehl]

Yes, you all were right, the question assumes all other constant. Thanks much for the clarification. Between the gotcha questions, and those that I over think I'm killing myself on these practice tests.