Could I Industries just paid a dividend of $1.15 per share. The dividends are expected to grow at a rate of 18 percent for the next six years and then level off to a growth rate of 7 percent indefinitely. If the required return is 15 percent, what is the value of the stock today

$26.56

Explanation:

Present value of stock = Dividend in year 1 / (1 + required rate of return) + Dividend in year 2 / (1 + required rate of return)² + Dividend in year 3 / (1 + required rate of return)³ + Dividend in year 4 / (1 + required rate of return)⁴ + Dividend in year 5 / (1 + required rate of return)⁵ + Dividend in year 6 / (1 + required rate of return)⁶ + Terminal value /  (1 + required rate of return)⁶

Terminal value = ( Dividend in year 6 * (1 + growth rate) / ( required rate of return - growth rate)

= (1.15 * (1 + 18%)⁶ * (1 + 7%) ) / (15% - 7%)

= $41.5225

Present value of stock:

= (1.15 * 1.18) / (1 + 15%) + (1.15 * 1.18²) / (1 + 15%)² + (1.15 * 1.18³) / (1 + 15%)³ + (1.15 * 1.18⁴) / (1 + 15%)⁴ + (1.15 * 1.18⁵) / (1 + 15%)⁵ + (1.15 * 1.18⁶) / (1 + 15%)⁶ + (41.5225) / (1 + 15%)⁶

= $26.55585976

= $26.56

b

explanation:

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this