Question

The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 20% a year for the next four years and then decreasing the growth rate to 5% per year. The company just paid its annual dividend in the amount of $1.00 per share. What is the current value of one share if the required rate of return is 9.25%?

Answer 1

Intrinsic Value = $38.0025

Step-by-step explanation:

`\left[\begin{array}{ccc}Year&Dividends&Present \: Value\\0&1&-\\1&1.2&1.0984\\2&1.44&1.2065\\3&1.728&1.3252\\4&2.0736&1.4556\\5&51.2301&32.9168\\Intrinsic&Value&38.0025\\\end{array}\right]`

Fist, we calcualte the increase of the dividends, by multipling by (1+growth) 1.20 until year 4.

At year 5 we multiply by 1.05

Because from here the company will have a fixed growth rate, we can apply the dividend growth model

`(divends)/(return-growth) = Intrinsic \: Value`

1.52838/ (0.0925-0.05) = 51.2301

Next we have to bring all these dividends, which are placed in futures date, to present value:

`(Principal)/((1 + rate)^(time) ) = PV`

for example

`(1.728)/((1 + 0.0925)^(3) ) = PV`

PV = 1.3252

Lastly, we add all the PV to get the intrinsic value of the share today.