Question

RedTick Incorporation is a start-up company. It plans to pay no dividends over the next five years because it must reinvest all earnings in the company to finance growth. The company plans to begin dividends of RM3 per share starting in year 6, then the dividend is expected to grow at 10 per cent per year for the next three years, and 6 per cent per year in perpetuity beyond that. If the required return on RedTick’s stock is 15 percent, what should be today’s stock price?

Answer 1

Calculation of today's stock price:

In the given case, first dividend is paid in 6th year. Further, growth rate of dividend is constant after year 9. Since growth rate is constant after year 9, hence terminal year is year 9. Accordingly, we should first calculate the value of stock at the end of year 9, also known as terminal value.

 

D6(Dividend for year 6) = RM3

D7(Dividend for year 7) = D6(1+growth rate in year 7)

                                           = RM3(1+0.10)

                                           = RM3.3

 

D8 = D7(1+grwoth rate)

      = RM3.3(1+0.10)

      = RM3.63

 

D9 = D8(1+growth rate in year 9)

      = RM3.63(1+0.10)

      = RM3.993

 

Terminal value = D9(1+terminal growth rate)/(Required return-Terminal growth rate)

                           = RM3.993(1+0.06)/(0.15-0.06)

                           = RM4.23258/0.09

                           = RM47.03

 

Now, calculate the value of stock at the end of 5th year(P5), since the firm dividend is paid in 6th year.

 

P6 = Present value of dividends + Present value of terminal value

      = D6/(1+Required return)^1+D7/(1+Required return)^2+D8/(1+Required return)^3+[(D9+Terminal Value)/(1+Required return)^4]

      = RM3/(1+0.15)^1+RM3.3/(1+0.15)^2+RM3.63/(1+0.15)^3+[(RM3.993+RM47.03)/(1+0.15)^4]

      = RM2.61+RM2.50+RM2.39+RM29.17

      = RM36.66

 

Now, Today's value of stock is:

 = Present value of value of stock at the end of year 5

 = Value of stock at the end of year 5/(1+Required return)^no. of years

 = RM36.66/(1+0.15)^5

 = RM18.23

 

Now, Today's value of stock is = RM18.23