Question

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

Answer 1

Answer:

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