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

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