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12 September, 14:39

A fast growing firm recently paid a dividend of $0.80 per share. The dividend is expected to increase at a rate of 30% rate for the next 4 years. Afterwards, a more stable 7% growth rate can be assumed. If a 10% discount rate is appropriate for this stock, what is its value?

A.$60.48

B. $60.18

C. $61.34

D. $73.86

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Answers (1)
  1. 12 September, 18:18
    0
    The value of the stock today is $60.48 and option A is the correct answer.

    Explanation:

    The two stage growth model of DDM will be used to calculate the value of this stock today. The two stage growth model is used when there are 2 different dividend growth rates. The 30% growth rate can be termed as g1 while the 7% growth rate which is assumed to remain constant forever can be termed as g2.

    The formula for price/value under this model is,

    Value or P0 = D1 / (1+r) + D2 / (1+r) ^2 + ... + Dn / (1+r) ^n +

    [Dn * (1+g2) / (r - g2) ] / (1+r) ^n

    Value today = 0.8 * (1+0.3) / (1+0.1) + 0.8 * (1+0.3) ^2 / (1+0.1) ^2 +

    0.8 * (1+0.3) ^3 / (1+0.1) ^3 + 0.8 * (1+0.3) ^4 / (1+0.1) ^4 +

    [ (0.8 * (1+0.3) ^4 * (1+0.07) / (0.1 - 0.07)) / (1+0.1) ^4 ]

    Value today = $60.60 which is closest to $60.48 and A is the answer.

    The difference of $0.12 in the answer is because of the rounding off as the immediate calculations were not rounded off in the calculation of $60.60
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