Question

Miller Juice, Inc. is not paying a dividend right now, but is expected to pay a $4.56 dividend three years from now. Investors expect that dividend to grow by 4% every year forever. If the required return on the stock investment is 14%, what should be the price of Miller Juice stock today?

Group of answer choices

$36.49

$53.69

$43.84

$47.42

Answer 1

This is a question of constant growth Dividend Discount Model (DDM), where we find the price of the share using the DDM formula and discount it to the appropriate time of valuation.

In this sum, the DDM price will be calculated at the end of 3rd year, hence, if we are valuing the stock today, we need to discount the value 3 years back to get the price today.

So, the formula for the constant growth DDM is D1/(Re-g), where D1 is the dividend next year Re is the required rate and g is the growth rate.

So, as on the end of year 3, the D1 that we will receive is $4.56 grown by 4% i.e. $4.742

Re is 14% and g is 4%. Substituting the values in the formula, we get, 4.742/(0.14-0.04)

= $47.42.

But, this value of $47.42 is standing at the end of Year 3, so we again discount it 3 years back to get the PV today.

So, 47.42/(1.14)^3

= $32.01

Note: But, since this answer is not in the choices given, we can assume that the value of $47.42 is standing at the end of Year 2 and the dividends are received at the beginning of 3rd year. Then we need to discount the value of 47.42 by only 2 years. Then we get the value today as $36.49.