Question

1.    Stock X and Stock Y sell for the same price in today’s market.  Stock X has a required return of 12 percent.  Stock Y has a required return of 10 percent.  Stock X’s dividend is expected to grow at a constant rate of 6 percent a year, while Stock Y’s dividend is expected to grow at a constant rate of 4 percent.  Assume that the market is in equilibrium and expected returns equal required returns.  Which of the following statements is most correct?

                                                                  

1.   Stock X has a higher dividend yield than Stock Y.
2.   Stock Y has a higher dividend yield than Stock X.
3.   One year from now, Stock X’s price is expected to be higher than Stock Y’s price.
4.   Statements A and C are correct.
5.   Statements B and C are correct.

I don't get why A is not correct and C is correct instead?   

Answer 1

Option A is incorrect, and it can be seen if there is an actual calculation

DY= Dividend per share/ price per share

Dividend yield is calculated on the basis of Dividend and price but s=as the price of both stocks are same, here we will look into dividends. and if the dividend of Stock X is more than the dividend of stock Y, then it can be said that Dividend yield of X will be more than that of Y. but it is not the case here.

As the market price of both the stocks is same, but the growth rate of dividend of X is more than that of Y shows that the actual value of dividend of X is actually less than Y

It can understood by the following:

Value of stock = Dividend next year (Cost Required - Growth) for X = Dix (140.06) = T0.12 -0.06) 1.06 Di 0.06 for yo rou De D x 10.10 (1 +0.04) to,ou) 0.06 As Given P = py 1.06DI = loude 0.06 0.06 D = 0.98 De DK D₂

So the Dividend Yield of X will be less than Dividend yield of Y.

So A is incorrect,

Now as for statement C:

Value of stock = D₁ / (k - g)

where:
D1 = next year's expected annual dividend per share
k = the investor's discount rate or required rate of return,

g = the expected dividend growth rate

as the difference between the (k-g) is same for both stock=, i.e, 0.06 or 6%

and we already know that the dividend growth of stock X is more than that of Y. dividend will grow at rate of 2% more for stock X than Y .

so without even calculating we can say that the price of stock X will be more than of stock Y.

so the answer C is more correct.