Question

A7X Corp. just paid a dividend of $1.35 per share. The dividends are expected to grow at 30 percent for the next 7 years and then level off to a growth rate of 8 percent indefinitely. If the required return is 14 percent, what is the price of the stock today?

$77.47

$75.92

$60.94

$79.02

$.14

Answer 1

Answer: The correct option is $77.47

To determine the present value, we need to discount the future dividends.
After 7 years, the growth will become constant and will be equal to 8%
After 7 years, the value of the stock=(Dividend in year 7)*(1+Constant growth rate)/(Required return-Constant growth rate)
=(1.35*(1+30%)^7*(1+8%))/(14%-8%)
=152.4788963

Present value=(Dividend in year 1)/(1+discount rate)^1+(Dividend in year 2)/(1+discount rate)^2+....+(Dividend in year 7)/(1+discount rate)^7+(Value of stock after 7 years)/(1+discount rate)^7

Dividend in year 1=(Dividend just paid)*(1+Dividend growth rate)

=1.35*(1+30%)/(1+14%)^1+1.35*(1+30%)^2/(1+14%)^2+1.35*(1+30%)^3/(1+14%)^3+1.35*(1+30%)^4/(1+14%)^4+1.35*(1+30%)^5/(1+14%)^5+1.35*(1+30%)^6/(1+14%)^6+1.35*(1+30%)^7/(1+14%)^7 +152.4788963/(1+14%)^7

=1.539473684+1.755540166+2.001931768+2.282904648+2.603312318+2.968689486+3.385347659+60.93625786
=77.47345759 or $77.47 (Rounded to two decimal places)