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Thirsty Cactus Corp. just paid a dividend of $1.50 per share. The dividends are expected to grow at 25 percent for the next 9 years and then level off to a 5 percent growth rate indefinitely. If the required return is 13 percent, what is the price of the stock today?

Sagot :

Answer:

$143.40

Explanation:

The dividend for the next year = [tex]\text{ current year dividend} \times (1 + \text{growth})[/tex]  

                                                   = $ 1.50 x (1 + 0.13)

                                                   = 1.50 x 1.30

                                                   = $ 1.95

The dividend in the second year = 1.95 x 1.30

                                                       = $ 2.54

Similarly, the dividend for the year 9 is = [tex]$1.50 \times (1.30)^9$[/tex]

                                                                = $ 15.91

The value of the stock at the end of year 9,

[tex]$=\frac{\text{Dividend of year 10}}{\text{(Required rate of return - Growth rate)}}$[/tex]

[tex]$=\frac{15.91\times1.05}{0.13-0.05}$[/tex]

= $ 208.81

The present value factor [tex]$=\frac{1}{(1+r)^n}$[/tex]

where, r = rate of interest = 13% = 0.13

            n = years (1 to 9)

So, the present value factor for the 2nd year is [tex]$=\frac{1}{(1+0.13)^2}$[/tex]

                                                                              [tex]$=\frac{1}{(1.13)^2}$[/tex]

                                                                              [tex]$=\frac{1}{1.2769}$[/tex]

                                                                              = 0.783147

Therefore, the price of the stock today is calculated as to be $ 143.40

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