Jia's Fashions recently paid a $2 annual dividend. The company is projecting that its dividends will grow by 20 percent next year, 12 percent annually for the two years after that, and then at 6 percent annually thereafter. Based on this information, how much should Jia's Fashions common stock sell for today if her required return is 10.5%?

Question

Quizplus · Accepted Answer

First, we need to calculate the expected dividends for the next three years:

- Next year: $2 x 1.2 = $2.40
- Year 2: $2.40 x 1.12 = $2.688
- Year 3: $2.688 x 1.12 = $3.006

After that, we can use the constant growth formula to calculate the present value of the stock:
PV = D1 / (r - g)
Where:
- PV: present value
- D1: dividend expected in the next period
- r: required return
- g: constant growth rate

So, for year 4 and beyond, we have:
- g = 6%
- D4 = $3.006 x 1.06 = $3.1858

And, applying the formula:
PV = $2.40 / (0.105 - 0.20) + $2.688 / (0.105 - 0.12)^2 + $3.006 / (0.105 - 0.12)^3 + $3.1858 / (0.105 - 0.06) x (1 / (1 + 0.105)^4) = $59.16

Therefore, the stock should sell for $59.16 today. The answer is C.

Jia's Fashions Recently Paid a $2 Annual Dividend