Question

Consider the following three stocks:a. Stock A is expected to provide a dividend of $10 per share forever.b. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth isexpected to be 4% per year forever.c. Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth isexpected to be 20% per year for 5 years and zero thereafter.If the market capitalization rate for each stock is 10%, which stock is the most valuable?

Answer 1

Answer:

Stock A is the best option.

Explanation:

We use gordon dividend model

$\frac{divends}{return-growth} = Intrinsic \: Value$

return for all stock = 10%

Stock A

dividend 10

grow = 0

10/.1 = 100

Stock B

dividend 5

grow 0.04

5/(0.10-0.04) = 83.33

Stock C

For this case, we will calculate the present value of the dividends, as there is a finite number

We get each dividen by multiply the previous one by the grow rate

Year 1:      5dividends x (1 + 20% grow)= 5 x 1.2 = 6

Year 2:     6 dividends x 1.2 = 8.64

And so on.

Then we calcualte the present value for each dividend:

$\frac{Dividen}{(1 + rate)^{time} } = PV$

$\frac{5}{(1 + 0.1)^{1} } = PV$

$\frac{6}{(1 + 0.1)^{2} } = PV$

$\frac{8.64}{(1 + 0.1)^{3} } = PV$

Then we add them together and get the value of stock C

$\left[\begin{array}{ccc}Year&Dividend&Present Value\\1&6&5.4545\\2&7.2&5.9504\\3&8.64&6.4914\\4&10.368&7.0815\\5&12.4416&7.7253\\Net&Value&32.7031\\\end{array}\right]$

stock C 32.7031

From the comparrison, Stock A is the best option.