Question

just paid a dividend of $1.60 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on the company's stock is 17 percent, what will a share of stock sell for today

Answer 1

Answer:

The share will sell for $16.31

Explanation:

From the given information, the schedule of expected dividends is shown below:

Year     Growth  Dividend Calculation  

0                        1.6  

1            20%      1.6(1.2) = 1.92

2           15%       1.6(1.2)(1.15) = 2.208

3            10%      1.6(1.2)(1.15)(1.1) = 2.4288

4            5%       1.6(1.2)(1.15)(1.1)(1.05) = 2.55024

5            5%       1.6(1.2)(1.15)(1.1)(1.05)(1.05) = 2.677752

Price of the stock today = $\frac{D1}{(1+ke)^1}+\frac{D2}{(1+ke)^2}+\frac{D3}{(1+ke)^3}+\frac{D4}{(1+ke)^4}+\frac{P4}{(1+ke)^4}$.

where P4 = $\frac{D5}{ke-g}$

Price of the stock today = $\frac{1.92}{(1+0.17)^1}+\frac{2.208}{(1+0.17)^2}+\frac{2.4288}{(1+0.17)^3}+\frac{2.55024}{(1+0.17)^4}+\frac{2.677752}{(0.17-0.05)(1+0.17)^4}$= $16.31