Question

What is the value of a company stock if it grows at a supernormal rate of 18% for the first four years, and then slows down to a constant growth rate of 10%. The company just paid annual dividend of $2.00/share, and the rate of return on common stock (rcs) is 13%.

Possible Solution:

Supernormal Growth:

D0 = $2.00
D1 = 2.00(1+0.18) = $2.36
D2 = 2.36(1+0.18) = $2.78
D3 = 2.78(1+0.18) = $3.28
D4 = 3.28(1+0.18) = $3.87


Constant Growth:

D5 = [3.87(1+0.10)] / [0.13 – 0.10] = 4.257 / 0.03 = $141.90


NPV = 141.90 / [(1+0.13)^4] = 141.90 / 1.630 = $87.03?

Answer 1

The supernormal rate and the constant growth rate require us to calculate the annulised rate. If we assume the stock will be kept for 10 years, then the 6 years at 10% will reduce the annulised (kind of average over 10 years) rate to be 13.14%. Do your own calculations to confirm this.
However, at the end of the question, the round number 13% is already given as the rate of return, so we don't really have to go through annulization.

Dividends are usually paid each quarter, so that the projected annual dividend is $2*4=$8, at a rate of return of 13%. Assuming the stock is not over- or under-valued, and the dividend is not reinvested, the stock is valued at $8/0.13=$61.54.