Question

The dividend for Should I, Inc., is currently $1.70 per share. It is expected to grow at 12 percent next year and then decline linearly to a perpetual rate of 3 percent beginning in four years. If you required a return of 16 percent on the stock, what is the most you would pay per share?

Answer 1

Explanation:
Given that the company is expected to grow at 12% in the next year. Then the growth rate will decline linearly (like 12%, 9%,and 6%) to a perpetual growth rate of 3% beginning in four years.

So, the growth rates will be 12%, 9%, and 6% in 1-3 years, then it will grow at a stable growth rate of 3% forever (or perpetuity).
The dividend for the company is currently $1.70 per share.
Dividend in the coming (or next) year that is D1=$1.7*(1+12%)=$1.7*(1.12)=$1.904
Similarly, in coming years, dividends will be:

D2=$1.904*(1+9%)=$2.07536
D3=$2.07536*(1+6%)=$2.1998816
D4=$2.1998816*(1+3%)=$2.265878048
The growth becomes stable (equal to 3%) beginning in four years. So, we need to calculate the terminal value.

Price at year 3 (or P3)=D3*(1+ stable or perpetual growth rate)/(Required rate of return-Perpetual growth rate)
Given that, the required rate of return is 16%.

Price at year 3 (or P3)=$2.1998816*(1+3%)/(16%-3%)=$2.265878048/(16%-3%)=$17.42983114
Now, we need to discount the values D1, D2, D3 and P3 to present value using the discount rate of 16% (which is the required rate of return here) to get the price today that we would pay.
So, Price=$1.904/(1+16%)^1+$2.07536/(1+16%)^2+$2.1998816/(1+16%)^3+$17.42983114/(1+16%)^3
=$1.904/(1.16)^1+$2.07536/(1.16)^2+$2.1998816/(1.16)^3+$17.42983114/(1.16)^3
=$1.904/(1.16)+$2.07536/1.3456+$2.1998816/1.560896+$17.42983114/1.560896

=$1.6413793+$1.542330559+$1.409371028+$11.16655507
=$15.7596 or $15.76 (rounded upto two decimal places)
So, we would pay $15.76 per share.