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The Highfield Company is going through a five-year of fast growth at 20% initially, and then it will grow at a perpetual rate of 4%. The required rate of return is 10% and it just paid a dividend of $2. What is the stock price today?
a) 43.88
b) 86.26
c) 66.64
d) 31.5

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Shahzaibfaraz

Answer:

P0 = $66.6429 rounded off to $66.64

Option c is the correct answer

Explanation:

Using the two stage growth model of dividend discount model, we can calculate the price of the stock today. The DDM values a stock based on the present value of the expected future dividends from the stock. The formula to calculate the price of the stock today is,

P0 = D0 * (1+g1) / (1+r)  +  D0 * (1+g1)^2 / (1+r)^2  +  ...  +  D0 * (1+g1)^n / (1+r)^n  +  [(D0 * (1+g1)^n * (1+g2) / (r - g2)) / (1+r)^n]

Where,

  • g1 is the initial growth rate
  • g2 is the constant growth rate
  • r is the required rate of return

P0 = 2* (1+0.2) / (1+0.1)  +  2 * (1+0.2)^2 / (1+0.1)^2  +  2 * (1+0.2)^3 / (1+0.1)^3  

+  2 * (1+0.2)^4 / (1+0.1)^4  +  2 * (1+0.2)^5 / (1+0.1)^5  +

[(2 * (1+0.2)^5 * (1+0.04)  /  (0.1 - 0.04)) / (1+0.1)^5]

P0 = $66.6429 rounded off to $66.64

The stock price today is option C. $66.64.

Calculation of the stock price:

For determining the stock price, following calculations need to be made

D0 = $2

D1 = D0 * (1 + g1) = $2 * (1 + 0.20) = $2.40

D2 = D1 * (1 + g1) = $2.40 * (1 + 0.20) = $2.88

D3 = D2 * (1 + g1) = $2.88 * (1 + 0.20) = $3.46

D4 = D3 * (1 + g1) = $3.46 * (1 + 0.20) = $4.15

D5 = D4 * (1 + g1) = $4.15 * (1 + 0.20) = $4.98

D6 = D5 * (1 + gC) = $4.98 * (1 + 0.04) = $5.18

Now

P5 = D6/(r - gC) = $5.18/(0.10-0.04) = $5.18/0.06 = $86.26

Now the price of the stock today is

= [D1/(1+r)] + [D2/(1+r)2] + [D3/(1+r)3] + [D4/(1+r)4] + [(D5+P5)/(1+r)5]

= [$2.40/(1+0.10)] + [$2.88/(1+0.10)2] + [$3.46/(1+0.10)3] + [$4.15/(1+0.10)4] + [($4.98+$86.26)/(1+0.10)5]

= $2.18 + $2.38 + $2.60 + $2.83 + $56.65

= $66.64

hence, The stock price today is option C. $66.64.

Learn more about the stock here; https://brainly.com/question/24330980

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